Finite Group Databasebeta

← #17919908

Subgroups — #17919908

Order 4352.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543077C211yesmaximal, characteristic, complemented
2#14542417C211yesmaximal, characteristic, complemented
3#14541016C211yesmaximal, characteristic, complemented
4#14541002C211yesmaximal, characteristic, complemented
5#14540927C211yesmaximal, characteristic, complemented
6#14540867C211yesmaximal, characteristic, complemented
7#14540822C211yesmaximal, characteristic, complemented
8#14540807C211yesmaximal, characteristic, complemented
9#14540636C211yesmaximal, characteristic, complemented
10#14540609C211yesmaximal, characteristic, complemented
11#14540496C211yesmaximal, characteristic, complemented
12D4×#63219C211yesmaximal, characteristic, complemented
13#14540420C211yesmaximal, characteristic, complemented
14#14540386C211yesmaximal, characteristic, complemented
15#14540314C211yesmaximal, characteristic, complemented
16#14540299C211yesmaximal, characteristic, complemented
17#14540284C211yesmaximal, characteristic, complemented
18#14540284C211yesmaximal, characteristic, complemented
19#14539880C211yesmaximal, characteristic, complemented
20#14539858C211yesmaximal, characteristic, complemented
21#14539657C211yesmaximal, characteristic, complemented
22#14539638C211yesmaximal, characteristic, complemented
23#14539616C211yesmaximal, characteristic, complemented
24#14539577C211yesmaximal, characteristic, complemented
25#14539037C211yesmaximal, characteristic, complemented
26#14538970C211yesmaximal, characteristic, complemented
27#14538091C211yesmaximal, characteristic, complemented
28#14538063C211yesmaximal, characteristic, complemented
29#14538014C211yesmaximal, characteristic, complemented
30C2×#11762962C211yesmaximal, characteristic, complemented
31C17×#2976C211yesmaximal, characteristic, complemented
32C2×#10587696C2211yescharacteristic
33C23×D68C2211yescharacteristic
34C2×#10587595C2211yescharacteristic, complemented
35C2×#10587594C2211yescharacteristic, complemented
36C2×#10587594C2211yescharacteristic, complemented
37C2×#10587594C2211yescharacteristic, complemented
38C2×#10587590C2211yescharacteristic, complemented
39C22×#63219C2211yescharacteristic, complemented
40C22×#63219C2211yescharacteristic, complemented
41C22×#63219C2211yescharacteristic, complemented
42#11763560—21no—
43#11763554—21no—
44#11763529C2211yescharacteristic, complemented
45#11763516C2211yescharacteristic, complemented
46#11763513—21no—
47#11763505C2211yescharacteristic, complemented
48#11763502—21no—
49#11763499C2211yescharacteristic, complemented
50D4×Dic34C2211yescharacteristic, complemented
51#11763468C2211yescharacteristic, complemented
52#11763468C2211yescharacteristic, complemented
53#11763464C2211yescharacteristic, complemented
54#11763455C2211yescharacteristic
55#11763455C2211yescharacteristic
56#11763455C2211yescharacteristic
57#11763455C2211yescharacteristic
58#11763450—21no—
59#11763450—21no—
60D4×D68C2211yescharacteristic
61D4×D68C2211yescharacteristic
62D4×D68C2211yescharacteristic
63D4×D68C2211yescharacteristic
64#11763443—21no—
65#11763443—21no—
66#11763430C2211yescharacteristic, complemented
67#11763427—21no—
68#11763421C2211yescharacteristic, complemented
69#11763402—21no—
70#11763394—21no—
71#11763394—21no—
72#11763387C2211yescharacteristic, complemented
73#11763380C2211yescharacteristic, complemented
74#11763378C2211yescharacteristic
75#11763373C2211yescharacteristic
76#11763370—21no—
77#11763370—21no—
78#11763320C2211yescharacteristic
79#11763320C2211yescharacteristic, complemented
80C2×#10587610C2211yescharacteristic, complemented
81#120×D17—21no—
82#120×D17—21no—
83#11763283C2211yescharacteristic
84#11763203C2211yescharacteristic, complemented
85#11763198C2211yescharacteristic, complemented
86#11763193C2211yescharacteristic, complemented
87#11763182C2211yescharacteristic, complemented
88#11763174C2211yescharacteristic, complemented
89#11763169C2211yescharacteristic, complemented
90#11763164C2211yescharacteristic, complemented
91#11763156C2211yescharacteristic, complemented
92#11763151C2211yescharacteristic, complemented
93#11763151C2211yescharacteristic, complemented
94#11763151C2211yescharacteristic, complemented
95#11763151C2211yescharacteristic, complemented
96#11763145C2211yescharacteristic, complemented
97#11763134C2211yescharacteristic, complemented
98#11763134C2211yescharacteristic, complemented
99#11763134C2211yescharacteristic, complemented
100#11763134C2211yescharacteristic, complemented
101#11763128C2211yescharacteristic, complemented
102#11763128C2211yescharacteristic, complemented
103#11763123C2211yescharacteristic, complemented
104#11763110C2211yescharacteristic, complemented
105#11763110C2211yescharacteristic, complemented
106#11763100C2211yescharacteristic, complemented
107#11763090C2211yescharacteristic, complemented
108#11763067C2211yescharacteristic, complemented
109#11763067C2211yescharacteristic, complemented
110#11763062C2211yescharacteristic, complemented
111#11763055C2211yescharacteristic, complemented
112#11763055C2211yescharacteristic, complemented
113#11763055C2211yescharacteristic, complemented
114#11763055C2211yescharacteristic, complemented
115#11763055C2211yescharacteristic, complemented
116#11763050C2211yescharacteristic, complemented
117#11763045C2211yescharacteristic, complemented
118#11763045C2211yescharacteristic, complemented
119#11763038C2211yescharacteristic, complemented
120#11763038C2211yescharacteristic, complemented
121#11763038C2211yescharacteristic, complemented
122#11763038C2211yescharacteristic, complemented
123#11763038C2211yescharacteristic, complemented
124#11763032C2211yescharacteristic, complemented
125#11763032C2211yescharacteristic, complemented
126#11763032C2211yescharacteristic, complemented
127#11763025C2211yescharacteristic, complemented
128#11763025C2211yescharacteristic, complemented
129#11763025C2211yescharacteristic, complemented
130#11763015C2211yescharacteristic, complemented
131#11763015C2211yescharacteristic, complemented
132#11763010C2211yescharacteristic, complemented
133#11763010C2211yescharacteristic, complemented
134#11763010C2211yescharacteristic, complemented
135#11763005C2211yescharacteristic, complemented
136#11762973C2211yescharacteristic, complemented
137#11762973C2211yescharacteristic, complemented
138#11762973C2211yescharacteristic, complemented
139#11762973C2211yescharacteristic, complemented
140#11762973C2211yescharacteristic, complemented
141#11762973C2211yescharacteristic, complemented
142#11762973C2211yescharacteristic, complemented
143#11762967C2211yescharacteristic, complemented
144#11762962C2211yescharacteristic
145#11762962C2211yescharacteristic
146#11762962C2211yescharacteristic
147#11762962C2211yescharacteristic, complemented
148#11762962C2211yescharacteristic, complemented
149#11762962C2211yescharacteristic, complemented
150#11762962C2211yescharacteristic, complemented
151#11762962C2211yescharacteristic, complemented
152#11762962C2211yescharacteristic, complemented
153#11762962C2211yescharacteristic, complemented
154#11762962C2211yescharacteristic, complemented
155#11762962C2211yescharacteristic, complemented
156#11762962C2211yescharacteristic, complemented
157#11762962C2211yescharacteristic, complemented
158#11762962C2211yescharacteristic, complemented
159#11762956C2211yescharacteristic, complemented
160#11762956C2211yescharacteristic, complemented
161#11762956C2211yescharacteristic, complemented
162#11762956C2211yescharacteristic, complemented
163#11762956C2211yescharacteristic, complemented
164#11762950C2211yescharacteristic, complemented
165#11762950C2211yescharacteristic, complemented
166#11762950C2211yescharacteristic, complemented
167#11762945C2211yescharacteristic
168#11762945C2211yescharacteristic, complemented
169#11762945C2211yescharacteristic, complemented
170#11762945C2211yescharacteristic, complemented
171#11762945C2211yescharacteristic, complemented
172#11762922C2211yescharacteristic, complemented
173#11762911C2211yescharacteristic, complemented
174#11762911C2211yescharacteristic, complemented
175#11762911C2211yescharacteristic, complemented
176C4×#63219C2211yescharacteristic, complemented
177C4×#63219C2211yescharacteristic, complemented
178C4×#63219C2211yescharacteristic, complemented
179C4×D136C2211yescharacteristic, complemented
180#11762815C2211yescharacteristic, complemented
181#11762815C2211yescharacteristic, complemented
182#11762815C2211yescharacteristic, complemented
183#11762811C2211yescharacteristic, complemented
184#11762806C2211yescharacteristic, complemented
185C2×#10587492C2211yescharacteristic, complemented
186C2×#10587492C2211yescharacteristic, complemented
187C2×#10587492C2211yescharacteristic, complemented
188C17×#525C2211yescharacteristic
189C17×#436C2211yescharacteristic, complemented
190C17×#436C2211yescharacteristic, complemented
191C17×#435C2211yescharacteristic, complemented
192C17×#435C2211yescharacteristic, complemented
193C17×#435C2211yescharacteristic, complemented
194C17×#435C2211yescharacteristic, complemented
195C8×D4×C17C2211yescharacteristic, complemented
196C8×D4×C17C2211yescharacteristic, complemented
197C17×#433C2211yescharacteristic, complemented
198C17×#433C2211yescharacteristic, complemented
199C17×#408C2211yescharacteristic, complemented
200C17×#408C2211yescharacteristic, complemented
201C17×#407C2211yescharacteristic, complemented
202C2×C17×C22⋊C8C2211yescharacteristic, complemented
203C24×D17—21no—
204C2×#41×C17C2311yescharacteristic
205C23×C4×C17C2311yescharacteristic
206#10587696—42no—
207#10587696—42no—
208C2×#63256—21no—
209C2×D4×D17—21no—
210C2×D4×D17—21no—
211C2×D4×D17—21no—
212C2×D4×D17—21no—
213C2×D4×D17—21no—
214C2×D4×D17—21no—
215C2×D4×D17—21no—
216C2×#63252C2311yescharacteristic
217C2×#63252C2311yescharacteristic
218C2×#63252C2311yescharacteristic
219C2×#63252C2311yescharacteristic
220C2×#63252C2311yescharacteristic, complemented
221C22×D68—21no—
222C22×D68—21no—
223C22×D68—21no—
224C22×D68—42no—
225C22×D68—42no—
226C22×D68C2311yescharacteristic
227C22×D68C2311yescharacteristic
228C22×D68C2311yescharacteristic
229C22×D68C2311yescharacteristic
230C22×D68C2311yescharacteristic
231C22×D68C2311yescharacteristic
232C22×D68C2311yescharacteristic
233C22×D68C2311yescharacteristic
234C22×Dic34C2311yescharacteristic
235C22×Dic34C2311yescharacteristic, complemented
236C2×M16×C17C2311yescharacteristic
237C2×M16×C17C2311yescharacteristic
238C2×M16×C17C2311yescharacteristic, complemented
239C2×M16×C17C2311yescharacteristic, complemented
240C22×C8×C17C2311yescharacteristic
241C22×C8×C17C2311yescharacteristic
242C22×C8×C17C2311yescharacteristic, complemented
243C22×C8×C17C2311yescharacteristic, complemented
244C17×#123D411yescharacteristic
245C17×#123D411yescharacteristic
246C17×C22⋊Q8D411yescharacteristic
247C17×C22⋊Q8D411yescharacteristic
248C17×#121D411yescharacteristic
249C17×#121D411yescharacteristic
250C17×#120D411yescharacteristic
251C17×#120D411yescharacteristic
252C4×D4×C17C2311yescharacteristic
253C4×D4×C17C2311yescharacteristic
254C4×D4×C17C2311yescharacteristic
255C4×D4×C17C2311yescharacteristic
256C17×#117C2311yescharacteristic
257#10587639—21no—
258#10587639—21no—
259C2×C22⋊Dic17—21no—
260#10587633—21no—
261#10587632—21no—
262#10587630—21no—
263#10587626—21no—
264#10587625—21no—
265#10587625—21no—
266#10587625—21no—
267#10587625—21no—
268#10587625—21no—
269#10587624—21no—
270#10587624—21no—
271#10587623—21no—
272#10587623—21no—
273#10587623—21no—
274#10587623—21no—
275#10587623—21no—
276#10587623—21no—
277#10587622—21no—
278#10587622—21no—
279#10587621—21no—
280#10587621—21no—
281#10587621—21no—
282D4×Dic17—21no—
283D4×Dic17—21no—
284#10587616C2311yescharacteristic
285#10587616C2311yescharacteristic
286#10587616C2311yescharacteristic
287#10587616C2311yescharacteristic
288#10587616C2311yescharacteristic
289#10587616C2311yescharacteristic
290#10587616C2311yescharacteristic
291#10587616C2311yescharacteristic
292#10587616C2311yescharacteristic, complemented
293#10587615—21no—
294#10587615—21no—
295C4×C22⋊D17—21no—
296C4×C22⋊D17—21no—
297C4×C22⋊D17—21no—
298C4×C22⋊D17—21no—
299#10587612C2311yescharacteristic
300#10587612C2311yescharacteristic
301#10587612C2311yescharacteristic, complemented
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic, complemented
304#10587610—21no—
305#10587610—21no—
306#10587610C2311yescharacteristic
307#10587610C2311yescharacteristic
308#10587610C2311yescharacteristic
309#10587610C2311yescharacteristic
310#10587610C2311yescharacteristic
311#10587610C2311yescharacteristic
312#10587610C2311yescharacteristic
313#10587610C2311yescharacteristic
314#10587610C2311yescharacteristic, complemented
315#10587610C2311yescharacteristic, complemented
316#10587610C2311yescharacteristic, complemented
317C2×#63225—21no—
318#10587595—42no—
319#10587594—42no—
320#10587594—42no—
321#10587594—42no—
322C2×Dic68C2311yescharacteristic, complemented
323C2×Dic68C2311yescharacteristic, complemented
324C2×Dic68C2311yescharacteristic, complemented
325#10587590—42no—
326C2×D136C2311yescharacteristic
327C2×D136C2311yescharacteristic
328C2×D136C2311yescharacteristic
329C2×D136C2311yescharacteristic
330C2×D136C2311yescharacteristic, complemented
331C2×#63219—42no—
332C2×#63219—42no—
333C2×#63219—42no—
334C2×#63219C2311yescharacteristic
335C2×#63219C2311yescharacteristic
336C2×#63219C2311yescharacteristic
337C2×#63219C2311yescharacteristic
338C2×#63219C2311yescharacteristic
339C2×#63219C2311yescharacteristic
340C2×#63219C2311yescharacteristic
341C2×#63219C2311yescharacteristic
342C2×#63219C2311yescharacteristic
343C2×#63219C2311yescharacteristic
344C2×#63219C2311yescharacteristic
345C2×#63219C2311yescharacteristic
346C2×#63219C2311yescharacteristic, complemented
347C2×#63219C2311yescharacteristic, complemented
348C2×#63219C2311yescharacteristic, complemented
349C2×#63219C2311yescharacteristic, complemented
350#10587584—21no—
351#10587584—21no—
352#10587582—21no—
353#10587582—21no—
354#10587582—21no—
355#10587581—21no—
356#10587581—21no—
357#10587581—21no—
358#10587581—21no—
359#10587581—21no—
360#10587581—21no—
361#10587580—21no—
362#10587580—21no—
363#10587580—21no—
364#10587580—21no—
365#10587579—21no—
366#10587579—21no—
367C4⋊C4×D17—21no—
368#10587576—21no—
369#10587575—21no—
370#10587575—21no—
371#10587575—21no—
372#10587574—21no—
373#10587573—21no—
374#10587571—21no—
375#10587571—21no—
376#10587571—21no—
377#10587570—21no—
378#10587570—21no—
379#10587570—21no—
380#10587570—21no—
381#10587569—21no—
382#10587569—21no—
383#10587569—21no—
384#10587569—21no—
385#10587568—21no—
386#10587568—21no—
387#10587568—21no—
388#10587568—21no—
389#10587568—21no—
390#10587568—21no—
391#10587568—21no—
392#10587568—21no—
393#10587568—21no—
394#10587568—21no—
395#10587567—21no—
396#10587567—21no—
397#10587567—21no—
398C22⋊C4×D17—21no—
399C22⋊C4×D17—21no—
400C22⋊C4×D17—21no—
401C22⋊C4×D17—21no—
402C22⋊C4×D17—21no—
403C22⋊C4×D17—21no—
404#10587565—21no—
405#10587565—21no—
406#10587565—21no—
407#10587565—21no—
408#10587565—21no—
409#10587564—21no—
410#10587564—21no—
411#10587564—21no—
412#10587564—21no—
413#10587563—21no—
414#10587561C2311yescharacteristic
415#10587561C2311yescharacteristic
416#10587561C2311yescharacteristic, complemented
417#10587560C2311yescharacteristic
418#10587560C2311yescharacteristic
419C4×D68C2311yescharacteristic
420C4×D68C2311yescharacteristic
421C4×D68C2311yescharacteristic
422C4×D68C2311yescharacteristic
423C4×D68C2311yescharacteristic, complemented
424#10587556C2311yescharacteristic, complemented
425#10587555C2311yescharacteristic, complemented
426#10587555C2311yescharacteristic, complemented
427C4×Dic34C2311yescharacteristic, complemented
428C4×Dic34C2311yescharacteristic, complemented
429C4×Dic34C2311yescharacteristic, complemented
430C17×C4⋊C8C2311yescharacteristic, complemented
431C17×C4⋊C8C2311yescharacteristic, complemented
432C17×C4⋊C8C2311yescharacteristic, complemented
433C17×C4⋊C8C2311yescharacteristic, complemented
434C17×C22⋊C8C2311yescharacteristic
435C17×C22⋊C8C2311yescharacteristic
436C17×C22⋊C8C2311yescharacteristic
437C17×C22⋊C8C2311yescharacteristic
438C17×C22⋊C8C2311yescharacteristic
439C17×C22⋊C8C2311yescharacteristic
440C17×C22⋊C8C2311yescharacteristic
441C17×C22⋊C8C2311yescharacteristic
442C17×C22⋊C8C2311yescharacteristic, complemented
443C17×C22⋊C8C2311yescharacteristic, complemented
444C17×C22⋊C8C2311yescharacteristic, complemented
445C17×C22⋊C8C2311yescharacteristic, complemented
446C17×#97C2311yescharacteristic, complemented
447C17×#97C2311yescharacteristic, complemented
448C4×C8×C17C2311yescharacteristic, complemented
449C4×C8×C17C2311yescharacteristic, complemented
450#10587492C2311yescharacteristic
451#10587492C2311yescharacteristic
452#10587492C2311yescharacteristic
453#10587492C2311yescharacteristic
454#10587492C2311yescharacteristic
455#10587492C2311yescharacteristic
456#10587492C2311yescharacteristic
457#10587492C2311yescharacteristic
458#10587492C2311yescharacteristic
459#10587492C2311yescharacteristic
460#10587492C2311yescharacteristic
461#10587492C2311yescharacteristic
462#10587492C2311yescharacteristic
463#10587492C2311yescharacteristic
464#10587492C2311yescharacteristic
465#10587492C2311yescharacteristic
466#10587492C2311yescharacteristic, complemented
467#10587492C2311yescharacteristic, complemented
468#10587492C2311yescharacteristic, complemented
469#10587492C2311yescharacteristic, complemented
470#10587492C2311yescharacteristic, complemented
471#10587492C2311yescharacteristic, complemented
472#10587489C2311yescharacteristic, complemented
473#10587489C2311yescharacteristic, complemented
474#10587489C2311yescharacteristic, complemented
475#10587489C2311yescharacteristic, complemented
476#10587488C2311yescharacteristic, complemented
477#10587488C2311yescharacteristic, complemented
478#10587488C2311yescharacteristic, complemented
479#10587488C2311yescharacteristic, complemented
480#10587487C2311yescharacteristic, complemented
481#10587487C2311yescharacteristic, complemented
482#10587487C2311yescharacteristic, complemented
483#10587487C2311yescharacteristic, complemented
484#10587487C2311yescharacteristic, complemented
485#10587487C2311yescharacteristic, complemented
486#10587487C2311yescharacteristic, complemented
487#10587487C2311yescharacteristic, complemented
488#10587487C2311yescharacteristic, complemented
489#10587487C2311yescharacteristic, complemented
490C24×C17C2×D411yescharacteristic
491C23×D17—21no—
492C23×D17—21no—
493C23×D17—21no—
494C23×D17—21no—
495C23×D17—21no—
496C23×D17—21no—
497C23×D17—21no—
498C23×D17—21no—
499C23×D17—44no—
500C23×D17—82no—
501C23×D17—82no—
502#41×C17—41no—
503#41×C17—41no—
504C2×Q8×C17C2×D411yescharacteristic
505C2×D4×C17C2×D411yescharacteristic
506C2×D4×C17C2×D411yescharacteristic
507C2×D4×C17C2×D411yescharacteristic
508C2×D4×C17C2×D411yescharacteristic
509C2×D4×C17C2×D411yescharacteristic
510C2×D4×C17C2×D411yescharacteristic
511C2×D4×C17C2×D411yescharacteristic
512C22×C4×C17—41no—
513C22×C4×C17—41no—
514C22×C4×C17C2×D411yescharacteristic
515C22×C4×C17C2×D411yescharacteristic
516C22×C4×C17C2×D411yescharacteristic
517C22×C4×C17C2411yescharacteristic
518C22×C4×C17C2411yescharacteristic
519C22×C4×C17C2411yescharacteristic
520C22×C4×C17C2411yescharacteristic
521C22×C4×C17C2411yescharacteristic
522C2×C22⋊D17—21no—
523C2×C22⋊D17—21no—
524C2×C22⋊D17—21no—
525C2×C22⋊D17—21no—
526C2×C22⋊D17—21no—
527C2×C22⋊D17—21no—
528C2×C22⋊D17—21no—
529C2×C22⋊D17—21no—
530C2×C22⋊D17—21no—
531C2×C22⋊D17—21no—
532C2×C22⋊D17—21no—
533C2×C22⋊D17—21no—
534C2×C22⋊D17—21no—
535C2×C22⋊D17—21no—
536C22×Dic17—21no—
537C22×Dic17—21no—
538C22×Dic17—21no—
539C22×Dic17—21no—
540#63256—44no—
541D4×D17—44no—
542D4×D17—44no—
543D4×D17—44no—
544D4×D17—82no—
545D4×D17—82no—
546D4×D17—82no—
547D4×D17—82no—
548#63252—22no—
549#63252—22no—
550#63252—41no—
551#63252—41no—
552#63252—41no—
553#63252—41no—
554#63252—41no—
555#63252—41no—
556#63252—41no—
557#63252—41no—
558C2×D68—21no—
559C2×D68—22no—
560C2×D68—22no—
561C2×D68—22no—
562C2×D68—22no—
563C2×D68—22no—
564C2×D68—22no—
565C2×D68—22no—
566C2×D68—22no—
567C2×D68—21no—
568C2×D68—21no—
569C2×D68—21no—
570C2×D68—21no—
571C2×D68—21no—
572C2×D68—21no—
573C2×D68—21no—
574C2×D68—21no—
575C2×D68—21no—
576C2×D68—21no—
577C2×D68—21no—
578C2×D68—41no—
579C2×D68—41no—
580C2×D68—41no—
581C2×D68—41no—
582C2×D68—41no—
583C2×D68—41no—
584C2×D68—41no—
585C2×D68—41no—
586C2×D68—44no—
587C2×D68—44no—
588C2×D68—44no—
589C2×D68C2411yescharacteristic
590C2×D68C2411yescharacteristic
591C2×D68C2411yescharacteristic
592C2×D68C2411yescharacteristic
593C2×D68C2411yescharacteristic
594C2×D68C2411yescharacteristic
595C2×C4×D17—21no—
596C2×C4×D17—21no—
597C2×C4×D17—21no—
598C2×C4×D17—21no—
599C2×C4×D17—21no—
600C2×C4×D17—21no—
601C2×C4×D17—21no—
602C2×C4×D17—21no—
603C2×C4×D17—21no—
604C2×C4×D17—21no—
605C2×Dic34—21no—
606C2×Dic34—21no—
607C2×Dic34—21no—
608C2×Dic34—41no—
609C2×Dic34—41no—
610C2×Dic34—41no—
611C2×Dic34—41no—
612C2×Dic34C2411yescharacteristic
613C2×Dic34C2411yescharacteristic
614C2×Dic34C2411yescharacteristic
615C2×Dic34C2411yescharacteristic
616M16×C17—41no—
617M16×C17—41no—
618M16×C17—41no—
619M16×C17—41no—
620C2×C8×C17—41no—
621C2×C8×C17—41no—
622C2×C8×C17—41no—
623C2×C8×C17—41no—
624C2×C8×C17C2411yescharacteristic
625C2×C8×C17C2411yescharacteristic
626C2×C8×C17C2411yescharacteristic
627C2×C8×C17C2411yescharacteristic
628C2×C8×C17C2411yescharacteristic
629C2×C8×C17C2411yescharacteristic
630C2×C8×C17C2411yescharacteristic
631C2×C8×C17C2411yescharacteristic
632C4⋊C4×C17C2×D411yescharacteristic
633C4⋊C4×C17C2×D411yescharacteristic
634C4⋊C4×C17C2×D411yescharacteristic
635C4⋊C4×C17C2×D411yescharacteristic
636C4⋊C4×C17C2×D411yescharacteristic
637C4⋊C4×C17C2×D411yescharacteristic
638C22⋊C4×C17C2×D411yescharacteristic
639C22⋊C4×C17C2×D411yescharacteristic
640C22⋊C4×C17C2×D411yescharacteristic
641C22⋊C4×C17C2×D411yescharacteristic
642C22⋊C4×C17C2×D411yescharacteristic
643C22⋊C4×C17C2×D411yescharacteristic
644C22⋊C4×C17C2×D411yescharacteristic
645C22⋊C4×C17C2×D411yescharacteristic
646C22⋊C4×C17C2×D411yescharacteristic
647C22⋊C4×C17C2×D411yescharacteristic
648C42×C17C2411yescharacteristic
649C42×C17C2411yescharacteristic
650C22⋊Dic17—21no—
651C22⋊Dic17—21no—
652C22⋊Dic17—21no—
653C22⋊Dic17—21no—
654C22⋊Dic17—21no—
655C22⋊Dic17—21no—
656C22⋊Dic17—21no—
657C22⋊Dic17—21no—
658C22⋊Dic17—21no—
659C22⋊Dic17—21no—
660C22⋊Dic17—21no—
661C22⋊Dic17—21no—
662C22⋊Dic17—21no—
663C22⋊Dic17—21no—
664#63227—21no—
665#63227—21no—
666#63227—21no—
667#63227—21no—
668#63227—21no—
669#63227—21no—
670#63227—21no—
671#63227—21no—
672#63227—21no—
673#63227—21no—
674#63227—21no—
675#63227—21no—
676#63227—21no—
677#63227—21no—
678#63227—21no—
679#63227—21no—
680#63227—21no—
681#63227—21no—
682#63227—21no—
683#63227—21no—
684C4⋊Dic17—21no—
685C4⋊Dic17—21no—
686C4⋊Dic17—21no—
687C4⋊Dic17—21no—
688C4⋊Dic17—21no—
689C4⋊Dic17C2411yescharacteristic
690C4⋊Dic17C2411yescharacteristic
691C4⋊Dic17C2411yescharacteristic
692C4⋊Dic17C2411yescharacteristic
693C4⋊Dic17C2411yescharacteristic
694C4⋊Dic17C2411yescharacteristic
695#63225—21no—
696#63225—21no—
697#63225—21no—
698#63225—21no—
699#63225—21no—
700#63225—21no—
701#63225—21no—
702#63225—21no—
703#63225—21no—
704#63225—21no—
705#63225—21no—
706#63225—21no—
707#63225—21no—
708#63225—21no—
709#63225—21no—
710#63225—21no—
711C4×Dic17—21no—
712C4×Dic17—21no—
713C4×Dic17—21no—
714C4×Dic17—21no—
715C4×Dic17—21no—
716C4×Dic17—21no—
717Dic68—41no—
718Dic68—41no—
719Dic68—41no—
720D136—22no—
721D136—22no—
722D136—41no—
723D136—41no—
724D136—41no—
725#63219—22no—
726#63219—22no—
727#63219—22no—
728#63219—22no—
729#63219—22no—
730#63219—22no—
731#63219—41no—
732#63219—41no—
733#63219—41no—
734#63219—41no—
735#63219—41no—
736#63219—41no—
737#63219—41no—
738#63219—41no—
739#63219—41no—
740#63219—41no—
741#61610—171nomaximal, Sylow
742C23×C17—22no—
743C23×C17—41no—
744C23×C17—41no—
745C23×C17C22×D411yescharacteristic
746C23×C17C22×D411yescharacteristic
747C23×C17C22×D411yescharacteristic
748C23×C17C22×D411yescharacteristic
749C23×C17C22×D411yescharacteristic
750C22×D17—21no—
751C22×D17—21no—
752C22×D17—24no—
753C22×D17—21no—
754C22×D17—21no—
755C22×D17—21no—
756C22×D17—21no—
757C22×D17—42no—
758C22×D17—42no—
759C22×D17—42no—
760C22×D17—42no—
761C22×D17—42no—
762C22×D17—42no—
763C22×D17—42no—
764C22×D17—42no—
765C22×D17—42no—
766C22×D17—42no—
767C22×D17—42no—
768C22×D17—81no—
769C22×D17—81no—
770C22×D17—81no—
771C22×D17—81no—
772C22×D17—81no—
773C22×D17—81no—
774C22×D17—81no—
775C22×D17—81no—
776C22×D17—81no—
777C22×D17—81no—
778C22×D17—81no—
779C22×D17—81no—
780C22×D17—816no—
781Q8×C17—41no—
782D4×C17—22no—
783D4×C17—22no—
784D4×C17—41no—
785D4×C17—41no—
786D4×C17—41no—
787D4×C17—41no—
788D4×C17—41no—
789C2×C4×C17—21no—
790C2×C4×C17—21no—
791C2×C4×C17—21no—
792C2×C4×C17—21no—
793C2×C4×C17—21no—
794C2×C4×C17—21no—
795C2×C4×C17—21no—
796C2×C4×C17—21no—
797C2×C4×C17—21no—
798C2×C4×C17—21no—
799C2×C4×C17—41no—
800C2×C4×C17—41no—
801C2×C4×C17—41no—
802C2×C4×C17C22×D411yescharacteristic
803C2×C4×C17C22×D411yescharacteristic
804C2×C4×C17C22×D411yescharacteristic
805C2×C4×C17C22×D411yescharacteristic
806C2×C4×C17C22×D411yescharacteristic
807C2×C4×C17C22×D411yescharacteristic
808C2×C4×C17C22×D411yescharacteristic
809C2×C4×C17C22×D411yescharacteristic
810C2×C4×C17C22×D411yescharacteristic
811C2×C4×C17C2511yescharacteristic
812C22⋊D17—42no—
813C22⋊D17—42no—
814C22⋊D17—42no—
815C22⋊D17—42no—
816C22⋊D17—42no—
817C22⋊D17—42no—
818C22⋊D17—81no—
819C22⋊D17—81no—
820C22⋊D17—81no—
821C22⋊D17—81no—
822C22⋊D17—81no—
823C22⋊D17—81no—
824C22⋊D17—81no—
825C22⋊D17—81no—
826C2×Dic17—21no—
827C2×Dic17—21no—
828C2×Dic17—21no—
829C2×Dic17—21no—
830C2×Dic17—21no—
831C2×Dic17—21no—
832C2×Dic17—21no—
833C2×Dic17—21no—
834C2×Dic17—21no—
835C2×Dic17—21no—
836C2×Dic17—81no—
837C2×Dic17—81no—
838C2×Dic17—81no—
839C2×Dic17—81no—
840D68—24no—
841D68—21no—
842D68—21no—
843D68—21no—
844D68—21no—
845D68—21no—
846D68—21no—
847D68—21no—
848D68—21no—
849D68—21no—
850D68—21no—
851D68—42no—
852D68—42no—
853D68—42no—
854D68—42no—
855D68—42no—
856D68—42no—
857D68—42no—
858D68—81no—
859D68—81no—
860D68—81no—
861D68—81no—
862D68H(5,𝔽2)12yes—
863D68H(5,𝔽2)12yes—
864C4×D17—42no—
865C4×D17—42no—
866C4×D17—42no—
867C4×D17—81no—
868C4×D17—81no—
869C4×D17—81no—
870C4×D17—81no—
871C4×D17—81no—
872C4×D17—81no—
873C4×D17—81no—
874Dic34—21no—
875Dic34—21no—
876Dic34—21no—
877Dic34—21no—
878Dic34—21no—
879Dic34—21no—
880Dic34—21no—
881Dic34—21no—
882Dic34—81no—
883Dic34—81no—
884Dic34—81no—
885C8×C17—21no—
886C8×C17—21no—
887C8×C17—21no—
888C8×C17—21no—
889C8×C17—21no—
890C8×C17—21no—
891C8×C17—21no—
892C8×C17—21no—
893#3541—171no—
894#3484—171no—
895#3324—171no—
896#3323—171no—
897#3318—171no—
898#3314—171no—
899#3311—171no—
900#3310—171no—
901#3297—171no—
902#3295—171no—
903#3282—171no—
904D4×SD16—171no—
905#3275—171no—
906#3272—171no—
907#3267—171no—
908#3266—171no—
909#3265—171no—
910#3265—171no—
911#3224—171no—
912#3222—171no—
913#3200—171no—
914#3198—171no—
915#3196—171no—
916#3191—171no—
917#3123—171no—
918#3118—171no—
919#3012—171no—
920#3009—171no—
921#3003—171no—
922C2×#450—171no—
923#2976D1711yescharacteristic, complemented
924C22×C17—21no—
925C22×C17—21no—
926C22×C17—21no—
927C22×C17—21no—
928C22×C17—21no—
929C22×C17—21no—
930C22×C17—21no—
931C22×C17—21no—
932C22×C17—21no—
933C22×C17—21no—
934C22×C17—21no—
935C22×C17—21no—
936C22×C17—21no—
937C22×C17—21no—
938C22×C17—44no—
939C22×C17#57712yes—
940C22×C17C23×D411yescharacteristic
941C2×D17—22no—
942C2×D17—22no—
943C2×D17—41no—
944C2×D17—41no—
945C2×D17—41no—
946C2×D17—41no—
947C2×D17—41no—
948C2×D17—41no—
949C2×D17—41no—
950C2×D17—41no—
951C2×D17—41no—
952C2×D17—41no—
953C2×D17—41no—
954C2×D17—41no—
955C2×D17—41no—
956C2×D17—41no—
957C2×D17—41no—
958C2×D17—41no—
959C2×D17—84no—
960C2×D17—84no—
961C2×D17—84no—
962C2×D17—84no—
963C2×D17—84no—
964C2×D17—84no—
965C2×D17—162no—
966C2×D17—162no—
967C4×C17—21no—
968C4×C17—21no—
969C4×C17—21no—
970C4×C17—21no—
971C4×C17—21no—
972C4×C17—21no—
973C4×C17—21no—
974C4×C17—21no—
975C4×C17—21no—
976C4×C17C2×H(5,𝔽2)11yescharacteristic
977C4×C17C2×H(5,𝔽2)11yescharacteristic
978Dic17—41no—
979Dic17—41no—
980Dic17—41no—
981Dic17—41no—
982Dic17—41no—
983Dic17—41no—
984Dic17—41no—
985Dic17—41no—
986Dic17—41no—
987Dic17—41no—
988C2×H(5,𝔽2)—171no—
989C23×D4—171no—
990C2×#137—171no—
991C2×AGL(1,ℤ/8)—171no—
992C2×AGL(1,ℤ/8)—171no—
993C2×AGL(1,ℤ/8)—171no—
994C2×#135—171no—
995C22×SD16—171no—
996C22×SD16—171no—
997C22×SD16—171no—
998#563—341no—
999#562—341no—
1000#556—171no—
1001#554—171no—
1002#554—341no—
1003#553—171no—
1004#553—341no—
1005#552—171no—
1006D4×Q8—171no—
1007#548—171no—
1008#548—171no—
1009#547—171no—
1010#546—171no—
1011#546—171no—
1012#546—171no—
1013#546—171no—
1014#546—341no—
1015#546—341no—
1016D42—171no—
1017D42—171no—
1018D42—171no—
1019D42—171no—
1020D42—341no—
1021D42—341no—
1022#542—171no—
1023#542—341no—
1024#541—171no—
1025#539—341no—
1026#538—341no—
1027#538—341no—
1028#537—171no—
1029#536—171no—
1030#535—171no—
1031#535—171no—
1032#534—341no—
1033#534—341no—
1034#525—171no—
1035#525—171no—
1036#525C2×D1711yescharacteristic
1037C2×C22⋊Q8—171no—
1038C2×#120—341no—
1039C2×#120—341no—
1040#518—171no—
1041#497—171no—
1042#496—171no—
1043#495—171no—
1044#492—171no—
1045#490—171no—
1046#489—171no—
1047#488—171no—
1048#486—171no—
1049#485—171no—
1050#485—171no—
1051#485—171no—
1052#485—171no—
1053#484—171no—
1054#482—171no—
1055#482—171no—
1056#482—171no—
1057#482—171no—
1058#481—171no—
1059#481—171no—
1060#480—171no—
1061#478—171no—
1062#478—171no—
1063#476—171no—
1064#474—171no—
1065#470—171no—
1066#470—171no—
1067#469—171no—
1068#468—171no—
1069#468—171no—
1070#468—171no—
1071#468—171no—
1072#468—171no—
1073#467—171no—
1074#466—171no—
1075#466—171no—
1076#465—171no—
1077#465—171no—
1078#465—171no—
1079#465—171no—
1080#465—171no—
1081#464—171no—
1082#464—171no—
1083#464—171no—
1084#463—171no—
1085#463—171no—
1086#463—171no—
1087#461—171no—
1088#461—171no—
1089#460—171no—
1090#460—171no—
1091#460—171no—
1092#459—171no—
1093#452—171no—
1094#452—171no—
1095#452—171no—
1096#452—171no—
1097#452—171no—
1098#452—171no—
1099#452—171no—
1100#451—171no—
1101#450—171no—
1102#450—171no—
1103#450—171no—
1104#450—171no—
1105#450—171no—
1106#450—171no—
1107#450—171no—
1108#450—171no—
1109#450—171no—
1110#450—171no—
1111#450—171no—
1112#450—171no—
1113#450—171no—
1114#450—171no—
1115#450—171no—
1116#449—171no—
1117#449—171no—
1118#449—171no—
1119#449—171no—
1120#449—171no—
1121#448—171no—
1122#448—171no—
1123#448—171no—
1124#447—171no—
1125#447—171no—
1126#447—171no—
1127#447—171no—
1128#447—171no—
1129#442—171no—
1130#440—171no—
1131#440—171no—
1132#440—171no—
1133C4×SD16—171no—
1134C4×SD16—171no—
1135C4×SD16—171no—
1136C4×D8—171no—
1137#436C2×D1711yescharacteristic, complemented
1138#436C2×D1711yescharacteristic, complemented
1139#435C2×D1711yescharacteristic, complemented
1140#435C2×D1711yescharacteristic, complemented
1141#435C2×D1711yescharacteristic, complemented
1142#435C2×D1711yescharacteristic, complemented
1143C8×D4C2×D1711yescharacteristic, complemented
1144C8×D4C2×D1711yescharacteristic, complemented
1145#433C2×D1711yescharacteristic, complemented
1146#433C2×D1711yescharacteristic, complemented
1147#418—171no—
1148#418—171no—
1149#418—171no—
1150#417—171no—
1151#416—171no—
1152C2×#102—171no—
1153C2×#102—171no—
1154C2×#102—171no—
1155#408C2×D1711yescharacteristic, complemented
1156#408C2×D1711yescharacteristic, complemented
1157#407C2×D1711yescharacteristic, complemented
1158C2×C22⋊C8C2×D1711yescharacteristic, complemented
1159C2×C17—22no—
1160C2×C17—41no—
1161C2×C17—41no—
1162C2×C17—41no—
1163C2×C17—41no—
1164C2×C17#348411yescharacteristic
1165C2×C17C2×#57711yescharacteristic
1166C2×C17#358511yescharacteristic
1167D17—42no—
1168D17—42no—
1169D17—81no—
1170D17—81no—
1171D17—81no—
1172D17—81no—
1173C25—341no—
1174H(5,𝔽2)—682no—
1175H(5,𝔽2)—682no—
1176C2×#41—171no—
1177C2×#41—171no—
1178C2×#41—171no—
1179C2×#41—171no—
1180C2×#41—171no—
1181C2×#41—341no—
1182C2×#41C22×D1711yescharacteristic
1183C22×Q8—171no—
1184C22×Q8—171no—
1185C22×D4—171no—
1186C22×D4—171no—
1187C22×D4—171no—
1188C22×D4—171no—
1189C22×D4—171no—
1190C22×D4—171no—
1191C22×D4—171no—
1192C22×D4—171no—
1193C22×D4—341no—
1194C22×D4—341no—
1195C22×D4—341no—
1196C22×D4—341no—
1197C22×D4—341no—
1198C22×D4—341no—
1199C22×D4—341no—
1200C22×D4—341no—
1201C22×D4—341no—
1202C22×D4—341no—
1203C22×D4—682no—
1204C22×D4—682no—
1205C23×C4C22×D1711yescharacteristic
1206#137—682no—
1207AGL(1,ℤ/8)—682no—
1208AGL(1,ℤ/8)—682no—
1209AGL(1,ℤ/8)—682no—
1210#135—682no—
1211C2×Q16—171no—
1212C2×Q16—171no—
1213C2×Q16—171no—
1214C2×SD16—171no—
1215C2×SD16—171no—
1216C2×SD16—171no—
1217C2×SD16—171no—
1218C2×SD16—171no—
1219C2×SD16—171no—
1220C2×SD16—171no—
1221C2×SD16—171no—
1222C2×SD16—171no—
1223C2×SD16—171no—
1224C2×SD16—171no—
1225C2×SD16—171no—
1226C2×SD16—171no—
1227C2×SD16—171no—
1228C2×SD16—171no—
1229C2×SD16—171no—
1230C2×SD16—682no—
1231C2×SD16—682no—
1232C2×SD16—682no—
1233C2×D8—171no—
1234C2×D8—171no—
1235C2×D8—171no—
1236C2×D8—171no—
1237C2×D8—171no—
1238C2×M16C22×D1711yescharacteristic
1239C2×M16C22×D1711yescharacteristic
1240C2×M16C22×D1711yescharacteristic, complemented
1241C2×M16C22×D1711yescharacteristic, complemented
1242C22×C8C22×D1711yescharacteristic
1243C22×C8C22×D1711yescharacteristic
1244C22×C8C22×D1711yescharacteristic, complemented
1245C22×C8C22×D1711yescharacteristic, complemented
1246C4⋊Q8—171no—
1247C4⋊Q8—171no—
1248C4⋊Q8—341no—
1249C4⋊Q8—341no—
1250#127—171no—
1251#127—171no—
1252#127—341no—
1253#126—341no—
1254#126—341no—
1255#126—341no—
1256#126—341no—
1257#126—341no—
1258#126—341no—
1259#126—341no—
1260#125—171no—
1261#125—341no—
1262#125—341no—
1263#125—341no—
1264#125—341no—
1265#124—171no—
1266#124—171no—
1267#124—171no—
1268#124—341no—
1269#124—341no—
1270#124—341no—
1271#124—341no—
1272#124—341no—
1273#124—341no—
1274#123—341no—
1275#123—341no—
1276#123—341no—
1277#123—341no—
1278#123—341no—
1279#123—341no—
1280#123—341no—
1281#123—341no—
1282#123—341no—
1283#123—341no—
1284#123—341no—
1285#123—341no—
1286#123—341no—
1287#123D6811yescharacteristic
1288#123D6811yescharacteristic
1289C22⋊Q8—171no—
1290C22⋊Q8—171no—
1291C22⋊Q8—171no—
1292C22⋊Q8—171no—
1293C22⋊Q8—171no—
1294C22⋊Q8—171no—
1295C22⋊Q8—171no—
1296C22⋊Q8—171no—
1297C22⋊Q8—171no—
1298C22⋊Q8—171no—
1299C22⋊Q8—171no—
1300C22⋊Q8—341no—
1301C22⋊Q8—341no—
1302C22⋊Q8—341no—
1303C22⋊Q8—341no—
1304C22⋊Q8—341no—
1305C22⋊Q8—341no—
1306C22⋊Q8—341no—
1307C22⋊Q8—341no—
1308C22⋊Q8—341no—
1309C22⋊Q8—341no—
1310C22⋊Q8D6811yescharacteristic
1311C22⋊Q8D6811yescharacteristic
1312#121—171no—
1313#121—171no—
1314#121—171no—
1315#121—171no—
1316#121—171no—
1317#121—171no—
1318#121—171no—
1319#121—171no—
1320#121—171no—
1321#121—341no—
1322#121—341no—
1323#121—341no—
1324#121—341no—
1325#121—341no—
1326#121—341no—
1327#121—341no—
1328#121—341no—
1329#121—341no—
1330#121—341no—
1331#121—341no—
1332#121—341no—
1333#121—341no—
1334#121—341no—
1335#121—341no—
1336#121—341no—
1337#121—341no—
1338#121D6811yescharacteristic
1339#121D6811yescharacteristic
1340#120—341no—
1341#120—341no—
1342#120—341no—
1343#120—341no—
1344#120—341no—
1345#120—341no—
1346#120—341no—
1347#120—341no—
1348#120—341no—
1349#120—341no—
1350#120—341no—
1351#120—341no—
1352#120—341no—
1353#120—341no—
1354#120—341no—
1355#120—341no—
1356#120—341no—
1357#120—341no—
1358#120D6811yescharacteristic
1359#120D6811yescharacteristic
1360C4×Q8—171no—
1361C4×Q8—171no—
1362C4×Q8—171no—
1363C4×Q8—341no—
1364C4×D4—171no—
1365C4×D4—171no—
1366C4×D4—171no—
1367C4×D4—171no—
1368C4×D4—171no—
1369C4×D4—341no—
1370C4×D4—341no—
1371C4×D4—341no—
1372C4×D4—341no—
1373C4×D4—341no—
1374C4×D4—341no—
1375C4×D4—341no—
1376C4×D4—341no—
1377C4×D4—341no—
1378C4×D4—341no—
1379C4×D4—341no—
1380C4×D4C22×D1711yescharacteristic
1381C4×D4C22×D1711yescharacteristic
1382C4×D4C22×D1711yescharacteristic
1383C4×D4C22×D1711yescharacteristic
1384#117—171no—
1385#117—171no—
1386#117—171no—
1387#117—341no—
1388#117C22×D1711yescharacteristic
1389C2×C4⋊C4—171no—
1390C2×C4⋊C4—171no—
1391C2×C4⋊C4—341no—
1392C2×C4⋊C4—341no—
1393C2×C22⋊C4—341no—
1394C2×C22⋊C4—341no—
1395C2×C22⋊C4—341no—
1396C2×C22⋊C4—341no—
1397C2×C22⋊C4—341no—
1398C2×C22⋊C4—341no—
1399C2×C22⋊C4—341no—
1400#107—171no—
1401#107—171no—
1402#107—171no—
1403#107—171no—
1404#106—171no—
1405#106—171no—
1406#106—171no—
1407#106—171no—
1408C4⋊C8C22×D1711yescharacteristic, complemented
1409C4⋊C8C22×D1711yescharacteristic, complemented
1410C4⋊C8C22×D1711yescharacteristic, complemented
1411C4⋊C8C22×D1711yescharacteristic, complemented
1412#103—171no—
1413#103—171no—
1414#103—171no—
1415#103—171no—
1416#103—171no—
1417#103—171no—
1418#103—171no—
1419#103—171no—
1420#103—171no—
1421#103—171no—
1422#102—171no—
1423#102—171no—
1424#102—171no—
1425#102—171no—
1426#102—171no—
1427#102—171no—
1428#102—171no—
1429#102—171no—
1430#102—171no—
1431#102—171no—
1432#102—171no—
1433#102—171no—
1434#102—171no—
1435#102—171no—
1436#102—171no—
1437#102—171no—
1438#102—171no—
1439#102—171no—
1440#102—171no—
1441#102—171no—
1442#102—171no—
1443#102—171no—
1444C22⋊C8C22×D1711yescharacteristic
1445C22⋊C8C22×D1711yescharacteristic
1446C22⋊C8C22×D1711yescharacteristic
1447C22⋊C8C22×D1711yescharacteristic
1448C22⋊C8C22×D1711yescharacteristic
1449C22⋊C8C22×D1711yescharacteristic
1450C22⋊C8C22×D1711yescharacteristic
1451C22⋊C8C22×D1711yescharacteristic
1452C22⋊C8C22×D1711yescharacteristic, complemented
1453C22⋊C8C22×D1711yescharacteristic, complemented
1454C22⋊C8C22×D1711yescharacteristic, complemented
1455C22⋊C8C22×D1711yescharacteristic, complemented
1456#97C22×D1711yescharacteristic, complemented
1457#97C22×D1711yescharacteristic, complemented
1458C4×C8C22×D1711yescharacteristic, complemented
1459C4×C8C22×D1711yescharacteristic, complemented
1460C17#6161011yescharacteristic, complemented, Sylow
1461C24—341no—
1462C24—341no—
1463C24—341no—
1464C24—341no—
1465C24—341no—
1466C24—341no—
1467C24—341no—
1468C24—341no—
1469C24—684no—
1470C24—1362no—
1471C24—1362no—
1472C24C2×D6811yescharacteristic
1473#41—41no—
1474#41—41no—
1475#41—342no—
1476#41—342no—
1477#41—681no—
1478#41—681no—
1479#41—681no—
1480#41—681no—
1481#41—681no—
1482#41—681no—
1483#41—681no—
1484#41—681no—
1485#41—684no—
1486C2×Q8—171no—
1487C2×Q8—171no—
1488C2×Q8—171no—
1489C2×Q8—171no—
1490C2×Q8—341no—
1491C2×Q8—341no—
1492C2×Q8—341no—
1493C2×Q8—681no—
1494C2×Q8—681no—
1495C2×Q8—681no—
1496C2×Q8—681no—
1497C2×Q8C2×D6811yescharacteristic
1498C2×D4—171no—
1499C2×D4—171no—
1500C2×D4—171no—
1501C2×D4—171no—
1502C2×D4—171no—
1503C2×D4—171no—
1504C2×D4—342no—
1505C2×D4—342no—
1506C2×D4—342no—
1507C2×D4—342no—
1508C2×D4—342no—
1509C2×D4—342no—
1510C2×D4—342no—
1511C2×D4—342no—
1512C2×D4—341no—
1513C2×D4—341no—
1514C2×D4—341no—
1515C2×D4—341no—
1516C2×D4—341no—
1517C2×D4—341no—
1518C2×D4—341no—
1519C2×D4—341no—
1520C2×D4—341no—
1521C2×D4—341no—
1522C2×D4—341no—
1523C2×D4—341no—
1524C2×D4—341no—
1525C2×D4—341no—
1526C2×D4—341no—
1527C2×D4—341no—
1528C2×D4—341no—
1529C2×D4—341no—
1530C2×D4—341no—
1531C2×D4—341no—
1532C2×D4—341no—
1533C2×D4—341no—
1534C2×D4—341no—
1535C2×D4—341no—
1536C2×D4—341no—
1537C2×D4—341no—
1538C2×D4—681no—
1539C2×D4—681no—
1540C2×D4—681no—
1541C2×D4—681no—
1542C2×D4—681no—
1543C2×D4—681no—
1544C2×D4—681no—
1545C2×D4—681no—
1546C2×D4—684no—
1547C2×D4—684no—
1548C2×D4—684no—
1549C2×D4—684no—
1550C2×D4—684no—
1551C2×D4—684no—
1552C2×D4—1362no—
1553C2×D4—1362no—
1554C2×D4—1362no—
1555C2×D4—1362no—
1556C2×D4C2×D6811yescharacteristic
1557C2×D4C2×D6811yescharacteristic
1558C2×D4C2×D6811yescharacteristic
1559C2×D4C2×D6811yescharacteristic
1560C2×D4C2×D6811yescharacteristic
1561C2×D4C2×D6811yescharacteristic
1562C2×D4C2×D6811yescharacteristic
1563C22×C4—41no—
1564C22×C4—41no—
1565C22×C4—341no—
1566C22×C4—341no—
1567C22×C4—341no—
1568C22×C4—341no—
1569C22×C4—341no—
1570C22×C4—341no—
1571C22×C4—341no—
1572C22×C4—341no—
1573C22×C4—341no—
1574C22×C4—341no—
1575C22×C4—341no—
1576C22×C4—341no—
1577C22×C4—341no—
1578C22×C4—341no—
1579C22×C4C2×D6811yescharacteristic
1580C22×C4C2×D6811yescharacteristic
1581C22×C4C2×D6811yescharacteristic
1582C22×C4C23×D1711yescharacteristic
1583C22×C4C23×D1711yescharacteristic
1584C22×C4C23×D1711yescharacteristic
1585C22×C4C23×D1711yescharacteristic
1586C22×C4C23×D1711yescharacteristic
1587Q16—681no—
1588Q16—681no—
1589Q16—681no—
1590SD16—342no—
1591SD16—342no—
1592SD16—342no—
1593SD16—342no—
1594SD16—342no—
1595SD16—342no—
1596SD16—681no—
1597SD16—681no—
1598SD16—681no—
1599SD16—681no—
1600SD16—681no—
1601SD16—681no—
1602SD16—681no—
1603SD16—681no—
1604SD16—681no—
1605SD16—681no—
1606D8—342no—
1607D8—342no—
1608D8—681no—
1609D8—681no—
1610D8—681no—
1611M16—41no—
1612M16—41no—
1613M16—41no—
1614M16—41no—
1615C2×C8—41no—
1616C2×C8—41no—
1617C2×C8—41no—
1618C2×C8—41no—
1619C2×C8C23×D1711yescharacteristic
1620C2×C8C23×D1711yescharacteristic
1621C2×C8C23×D1711yescharacteristic
1622C2×C8C23×D1711yescharacteristic
1623C2×C8C23×D1711yescharacteristic
1624C2×C8C23×D1711yescharacteristic
1625C2×C8C23×D1711yescharacteristic
1626C2×C8C23×D1711yescharacteristic
1627C4⋊C4—171no—
1628C4⋊C4—171no—
1629C4⋊C4—171no—
1630C4⋊C4—171no—
1631C4⋊C4—171no—
1632C4⋊C4—171no—
1633C4⋊C4—341no—
1634C4⋊C4—341no—
1635C4⋊C4—341no—
1636C4⋊C4—341no—
1637C4⋊C4—341no—
1638C4⋊C4—341no—
1639C4⋊C4—341no—
1640C4⋊C4—341no—
1641C4⋊C4—341no—
1642C4⋊C4—341no—
1643C4⋊C4—341no—
1644C4⋊C4—341no—
1645C4⋊C4—341no—
1646C4⋊C4—341no—
1647C4⋊C4—341no—
1648C4⋊C4—341no—
1649C4⋊C4—341no—
1650C4⋊C4—341no—
1651C4⋊C4—341no—
1652C4⋊C4—341no—
1653C4⋊C4—341no—
1654C4⋊C4C2×D6811yescharacteristic
1655C4⋊C4C2×D6811yescharacteristic
1656C4⋊C4C2×D6811yescharacteristic
1657C4⋊C4C2×D6811yescharacteristic
1658C4⋊C4C2×D6811yescharacteristic
1659C4⋊C4C2×D6811yescharacteristic
1660C22⋊C4—341no—
1661C22⋊C4—341no—
1662C22⋊C4—341no—
1663C22⋊C4—341no—
1664C22⋊C4—341no—
1665C22⋊C4—341no—
1666C22⋊C4—341no—
1667C22⋊C4—341no—
1668C22⋊C4—341no—
1669C22⋊C4—341no—
1670C22⋊C4—341no—
1671C22⋊C4—341no—
1672C22⋊C4—341no—
1673C22⋊C4—341no—
1674C22⋊C4—341no—
1675C22⋊C4—341no—
1676C22⋊C4—341no—
1677C22⋊C4—341no—
1678C22⋊C4—341no—
1679C22⋊C4—341no—
1680C22⋊C4—341no—
1681C22⋊C4—341no—
1682C22⋊C4—341no—
1683C22⋊C4—341no—
1684C22⋊C4—341no—
1685C22⋊C4—341no—
1686C22⋊C4—341no—
1687C22⋊C4—341no—
1688C22⋊C4—341no—
1689C22⋊C4—341no—
1690C22⋊C4—341no—
1691C22⋊C4—341no—
1692C22⋊C4—341no—
1693C22⋊C4—341no—
1694C22⋊C4C2×D6811yescharacteristic
1695C22⋊C4C2×D6811yescharacteristic
1696C22⋊C4C2×D6811yescharacteristic
1697C22⋊C4C2×D6811yescharacteristic
1698C22⋊C4C2×D6811yescharacteristic
1699C22⋊C4C2×D6811yescharacteristic
1700C22⋊C4C2×D6811yescharacteristic
1701C22⋊C4C2×D6811yescharacteristic
1702C22⋊C4C2×D6811yescharacteristic
1703C22⋊C4C2×D6811yescharacteristic
1704C42—341no—
1705C42—341no—
1706C42—341no—
1707C42—341no—
1708C42—341no—
1709C42—341no—
1710C42C23×D1711yescharacteristic
1711C42C23×D1711yescharacteristic
1712C23—22no—
1713C23—41no—
1714C23—41no—
1715C23—344no—
1716C23—341no—
1717C23—341no—
1718C23—341no—
1719C23—341no—
1720C23—341no—
1721C23—341no—
1722C23—682no—
1723C23—682no—
1724C23—682no—
1725C23—682no—
1726C23—682no—
1727C23—682no—
1728C23—682no—
1729C23—682no—
1730C23—682no—
1731C23—682no—
1732C23—682no—
1733C23—1361no—
1734C23—1361no—
1735C23—1361no—
1736C23—1361no—
1737C23—1361no—
1738C23—1361no—
1739C23—1361no—
1740C23—1361no—
1741C23—1361no—
1742C23—1361no—
1743C23—1361no—
1744C23—1361no—
1745C23—13616no—
1746C23C22×D6811yescharacteristic
1747C23C22×D6811yescharacteristic
1748C23C22×D6811yescharacteristic
1749C23C22×D6811yescharacteristic
1750C23C22×D6811yescharacteristic
1751Q8—41no—
1752Q8—341no—
1753Q8—341no—
1754Q8—341no—
1755Q8—341no—
1756Q8—341no—
1757Q8—341no—
1758Q8—341no—
1759Q8—341no—
1760Q8—1361no—
1761Q8—1361no—
1762Q8—1361no—
1763D4—22no—
1764D4—22no—
1765D4—41no—
1766D4—41no—
1767D4—41no—
1768D4—41no—
1769D4—41no—
1770D4—172no—
1771D4—172no—
1772D4—344no—
1773D4—341no—
1774D4—341no—
1775D4—341no—
1776D4—341no—
1777D4—341no—
1778D4—341no—
1779D4—341no—
1780D4—341no—
1781D4—341no—
1782D4—341no—
1783D4—682no—
1784D4—682no—
1785D4—682no—
1786D4—682no—
1787D4—682no—
1788D4—682no—
1789D4—682no—
1790D4—682no—
1791D4—682no—
1792D4—682no—
1793D4—682no—
1794D4—682no—
1795D4—682no—
1796D4—1361no—
1797D4—1361no—
1798D4—1361no—
1799D4—1361no—
1800D4—1361no—
1801D4—1361no—
1802D4—1361no—
1803D4—1361no—
1804D4—1361no—
1805D4—1361no—
1806D4—1361no—
1807D4—1361no—
1808C2×C4—21no—
1809C2×C4—21no—
1810C2×C4—21no—
1811C2×C4—21no—
1812C2×C4—21no—
1813C2×C4—21no—
1814C2×C4—21no—
1815C2×C4—21no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—41no—
1819C2×C4—41no—
1820C2×C4—41no—
1821C2×C4—341no—
1822C2×C4—341no—
1823C2×C4—341no—
1824C2×C4—341no—
1825C2×C4—341no—
1826C2×C4—341no—
1827C2×C4—341no—
1828C2×C4—341no—
1829C2×C4—341no—
1830C2×C4—341no—
1831C2×C4—682no—
1832C2×C4—682no—
1833C2×C4—682no—
1834C2×C4—1361no—
1835C2×C4—1361no—
1836C2×C4—1361no—
1837C2×C4—1361no—
1838C2×C4—1361no—
1839C2×C4—1361no—
1840C2×C4—1361no—
1841C2×C4—1361no—
1842C2×C4—1361no—
1843C2×C4—1361no—
1844C2×C4—1361no—
1845C2×C4C22×D6811yescharacteristic
1846C2×C4C22×D6811yescharacteristic
1847C2×C4C22×D6811yescharacteristic
1848C2×C4C22×D6811yescharacteristic
1849C2×C4C22×D6811yescharacteristic
1850C2×C4C22×D6811yescharacteristic
1851C2×C4C22×D6811yescharacteristic
1852C2×C4C22×D6811yescharacteristic
1853C2×C4C22×D6811yescharacteristic
1854C2×C4C24×D1711yescharacteristic
1855C8—21no—
1856C8—21no—
1857C8—21no—
1858C8—21no—
1859C8—21no—
1860C8—21no—
1861C8—21no—
1862C8—21no—
1863C22—21no—
1864C22—21no—
1865C22—21no—
1866C22—21no—
1867C22—21no—
1868C22—21no—
1869C22—21no—
1870C22—21no—
1871C22—21no—
1872C22—21no—
1873C22—21no—
1874C22—21no—
1875C22—21no—
1876C22—21no—
1877C22—44no—
1878C22—2722no—
1879C22—2722no—
1880C22—342no—
1881C22—342no—
1882C22—681no—
1883C22—681no—
1884C22—681no—
1885C22—681no—
1886C22—681no—
1887C22—681no—
1888C22—681no—
1889C22—681no—
1890C22—681no—
1891C22—681no—
1892C22—681no—
1893C22—681no—
1894C22—681no—
1895C22—681no—
1896C22—681no—
1897C22—681no—
1898C22—1364no—
1899C22—1364no—
1900C22—1364no—
1901C22—1364no—
1902C22—1364no—
1903C22—1364no—
1904C22#1176362112yes—
1905C22C23×D6811yescharacteristic
1906C4—21no—
1907C4—21no—
1908C4—21no—
1909C4—21no—
1910C4—21no—
1911C4—21no—
1912C4—21no—
1913C4—21no—
1914C4—21no—
1915C4—681no—
1916C4—681no—
1917C4—681no—
1918C4—681no—
1919C4—681no—
1920C4—681no—
1921C4—681no—
1922C4—681no—
1923C4—681no—
1924C4—681no—
1925C4H(5,𝔽2)×D1711yescharacteristic
1926C4H(5,𝔽2)×D1711yescharacteristic
1927C2—22no—
1928C2—41no—
1929C2—41no—
1930C2—41no—
1931C2—41no—
1932C2—682no—
1933C2—682no—
1934C2—1361no—
1935C2—1361no—
1936C2—1361no—
1937C2—1361no—
1938C2#1454242011yescharacteristic
1939C2C2×#1176362111yescharacteristic
1940C2#1454356511yescharacteristic
subgroupG/H
centerC22C23×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#2976C2
socleC22×C17C23×D4
hypercenter#2976D17
hypocenterC17#61610
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #525 ◁ #2976

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14543077C2semidirect
2. #14542417C2semidirect
3. #14541016C2semidirect
4. #14541002C2semidirect
5. #14540927C2semidirect
6. #14540867C2semidirect
7. #14540822C2semidirect
8. #14540807C2semidirect
9. #14540636C2semidirect
10. #14540609C2semidirect
11. #14540496C2semidirect
12. D4×#63219C2semidirect
13. #14540420C2semidirect
14. #14540386C2semidirect
15. #14540314C2semidirect
16. #14540299C2semidirect
17. #14540284C2semidirect
18. #14540284C2semidirect
19. #14539880C2semidirect
20. #14539858C2semidirect
21. #14539657C2semidirect
22. #14539638C2semidirect
23. #14539616C2semidirect
24. #14539577C2semidirect
25. #14539037C2semidirect
26. #14538970C2semidirect
27. #14538091C2semidirect
28. #14538063C2semidirect
29. #14538014C2semidirect
30. C2×#11762962C2semidirect
31. C17×#2976C2semidirect
34. C2×#10587595C22semidirect
35. C2×#10587594C22semidirect
36. C2×#10587594C22semidirect
37. C2×#10587594C22semidirect
38. C2×#10587590C22semidirect
39. C22×#63219C22semidirect
40. C22×#63219C22semidirect
41. C22×#63219C22semidirect
44. #11763529C22semidirect
45. #11763516C22semidirect
47. #11763505C22semidirect
49. #11763499C22semidirect
50. D4×Dic34C22semidirect
51. #11763468C22semidirect
52. #11763468C22semidirect
53. #11763464C22semidirect
66. #11763430C22semidirect
68. #11763421C22semidirect
72. #11763387C22semidirect
73. #11763380C22semidirect
79. #11763320C22semidirect
80. C2×#10587610C22semidirect
84. #11763203C22semidirect
85. #11763198C22semidirect
86. #11763193C22semidirect
87. #11763182C22semidirect
88. #11763174C22semidirect
89. #11763169C22semidirect
90. #11763164C22semidirect
91. #11763156C22semidirect
92. #11763151C22semidirect
93. #11763151C22semidirect
94. #11763151C22semidirect
95. #11763151C22semidirect
96. #11763145C22semidirect
97. #11763134C22semidirect
98. #11763134C22semidirect
99. #11763134C22semidirect
100. #11763134C22semidirect
101. #11763128C22semidirect
102. #11763128C22semidirect
103. #11763123C22semidirect
104. #11763110C22semidirect
105. #11763110C22semidirect
106. #11763100C22semidirect
107. #11763090C22semidirect
108. #11763067C22semidirect
109. #11763067C22semidirect
110. #11763062C22semidirect
111. #11763055C22semidirect
112. #11763055C22semidirect
113. #11763055C22semidirect
114. #11763055C22semidirect
115. #11763055C22semidirect
116. #11763050C22semidirect
117. #11763045C22semidirect
118. #11763045C22semidirect
119. #11763038C22semidirect
120. #11763038C22semidirect
121. #11763038C22semidirect
122. #11763038C22semidirect
123. #11763038C22semidirect
124. #11763032C22semidirect
125. #11763032C22semidirect
126. #11763032C22semidirect
127. #11763025C22semidirect
128. #11763025C22semidirect
129. #11763025C22semidirect
130. #11763015C22semidirect
131. #11763015C22semidirect
132. #11763010C22semidirect
133. #11763010C22semidirect
134. #11763010C22semidirect
135. #11763005C22semidirect
136. #11762973C22semidirect
137. #11762973C22semidirect
138. #11762973C22semidirect
139. #11762973C22semidirect
140. #11762973C22semidirect
141. #11762973C22semidirect
142. #11762973C22semidirect
143. #11762967C22semidirect
147. #11762962C22semidirect
148. #11762962C22semidirect
149. #11762962C22semidirect
150. #11762962C22semidirect
151. #11762962C22semidirect
152. #11762962C22semidirect
153. #11762962C22semidirect
154. #11762962C22semidirect
155. #11762962C22semidirect
156. #11762962C22semidirect
157. #11762962C22semidirect
158. #11762962C22semidirect
159. #11762956C22semidirect
160. #11762956C22semidirect
161. #11762956C22semidirect
162. #11762956C22semidirect
163. #11762956C22semidirect
164. #11762950C22semidirect
165. #11762950C22semidirect
166. #11762950C22semidirect
168. #11762945C22semidirect
169. #11762945C22semidirect
170. #11762945C22semidirect
171. #11762945C22semidirect
172. #11762922C22semidirect
173. #11762911C22semidirect
174. #11762911C22semidirect
175. #11762911C22semidirect
176. C4×#63219C22semidirect
177. C4×#63219C22semidirect
178. C4×#63219C22semidirect
179. C4×D136C22semidirect
180. #11762815C22semidirect
181. #11762815C22semidirect
182. #11762815C22semidirect
183. #11762811C22semidirect
184. #11762806C22semidirect
185. C2×#10587492C22semidirect
186. C2×#10587492C22semidirect
187. C2×#10587492C22semidirect
189. C17×#436C22semidirect
190. C17×#436C22semidirect
191. C17×#435C22semidirect
192. C17×#435C22semidirect
193. C17×#435C22semidirect
194. C17×#435C22semidirect
195. C8×D4×C17C22semidirect
196. C8×D4×C17C22semidirect
197. C17×#433C22semidirect
198. C17×#433C22semidirect
199. C17×#408C22semidirect
200. C17×#408C22semidirect
201. C17×#407C22semidirect
202. C2×C17×C22⋊C8C22semidirect
220. C2×#63252C23semidirect
235. C22×Dic34C23semidirect
238. C2×M16×C17C23semidirect
239. C2×M16×C17C23semidirect
242. C22×C8×C17C23semidirect
243. C22×C8×C17C23semidirect
292. #10587616C23semidirect
301. #10587612C23semidirect
303. C2×C4⋊Dic17C23semidirect
314. #10587610C23semidirect
315. #10587610C23semidirect
316. #10587610C23semidirect
322. C2×Dic68C23semidirect
323. C2×Dic68C23semidirect
324. C2×Dic68C23semidirect
330. C2×D136C23semidirect
346. C2×#63219C23semidirect
347. C2×#63219C23semidirect
348. C2×#63219C23semidirect
349. C2×#63219C23semidirect
416. #10587561C23semidirect
423. C4×D68C23semidirect
424. #10587556C23semidirect
425. #10587555C23semidirect
426. #10587555C23semidirect
427. C4×Dic34C23semidirect
428. C4×Dic34C23semidirect
429. C4×Dic34C23semidirect
430. C17×C4⋊C8C23semidirect
431. C17×C4⋊C8C23semidirect
432. C17×C4⋊C8C23semidirect
433. C17×C4⋊C8C23semidirect
442. C17×C22⋊C8C23semidirect
443. C17×C22⋊C8C23semidirect
444. C17×C22⋊C8C23semidirect
445. C17×C22⋊C8C23semidirect
446. C17×#97C23semidirect
447. C17×#97C23semidirect
448. C4×C8×C17C23semidirect
449. C4×C8×C17C23semidirect
466. #10587492C23semidirect
467. #10587492C23semidirect
468. #10587492C23semidirect
469. #10587492C23semidirect
470. #10587492C23semidirect
471. #10587492C23semidirect
472. #10587489C23semidirect
473. #10587489C23semidirect
474. #10587489C23semidirect
475. #10587489C23semidirect
476. #10587488C23semidirect
477. #10587488C23semidirect
478. #10587488C23semidirect
479. #10587488C23semidirect
480. #10587487C23semidirect
481. #10587487C23semidirect
482. #10587487C23semidirect
483. #10587487C23semidirect
484. #10587487C23semidirect
485. #10587487C23semidirect
486. #10587487C23semidirect
487. #10587487C23semidirect
488. #10587487C23semidirect
489. #10587487C23semidirect
923. #2976D17semidirect
1137. #436C2×D17semidirect
1138. #436C2×D17semidirect
1139. #435C2×D17semidirect
1140. #435C2×D17semidirect
1141. #435C2×D17semidirect
1142. #435C2×D17semidirect
1143. C8×D4C2×D17semidirect
1144. C8×D4C2×D17semidirect
1145. #433C2×D17semidirect
1146. #433C2×D17semidirect
1155. #408C2×D17semidirect
1156. #408C2×D17semidirect
1157. #407C2×D17semidirect
1158. C2×C22⋊C8C2×D17semidirect
1240. C2×M16C22×D17semidirect
1241. C2×M16C22×D17semidirect
1244. C22×C8C22×D17semidirect
1245. C22×C8C22×D17semidirect
1408. C4⋊C8C22×D17semidirect
1409. C4⋊C8C22×D17semidirect
1410. C4⋊C8C22×D17semidirect
1411. C4⋊C8C22×D17semidirect
1452. C22⋊C8C22×D17semidirect
1453. C22⋊C8C22×D17semidirect
1454. C22⋊C8C22×D17semidirect
1455. C22⋊C8C22×D17semidirect
1456. #97C22×D17semidirect
1457. #97C22×D17semidirect
1458. C4×C8C22×D17semidirect
1459. C4×C8C22×D17semidirect
1460. C17#61610semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145430772
#145424172
#145410162
#145410022
#145409272
#145408672
#145408222
#145408072
#145406362
#145406092
#145404962
D4×#632192
#145404202
#145403862
#145403142
#145402992
#145402842
#145398802
#145398582
#145396572
#145396382
#145396162
#145395772
#145390372
#145389702
#145380912
#145380632
#145380142
C2×#117629622
C17×#29762
#6161017