Finite Group Databasebeta

← #17243102

Subgroups — #17243102

Order 4352.

1548 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537124C211yesmaximal, characteristic, complemented
2#14537097C211yesmaximal, characteristic, complemented
3#14536292C211yesmaximal, characteristic, complemented
4#14536286C211yesmaximal, characteristic, complemented
5#14536259C211yesmaximal, characteristic, complemented
6#14536209C211yesmaximal, characteristic, complemented
7#14536185C211yesmaximal, characteristic, complemented
8#14536142C211yesmaximal, characteristic, complemented
9#14536016C211yesmaximal, characteristic, complemented
10#14536009C211yesmaximal, characteristic
11#14535988C211yesmaximal, characteristic, complemented
12#14535925C211yesmaximal, characteristic, complemented
13#14535903C211yesmaximal, characteristic, complemented
14#14535755C211yesmaximal, characteristic, complemented
15#14535417C211yesmaximal, characteristic, complemented
16#14535281C211yesmaximal, characteristic, complemented
17#14535233C211yesmaximal, characteristic, complemented
18#14534884C211yesmaximal, characteristic, complemented
19#14534859C211yesmaximal, characteristic, complemented
20#14534365C211yesmaximal, characteristic
21#14534306C211yesmaximal, characteristic, complemented
22#14534203C211yesmaximal, characteristic, complemented
23#14533968C211yesmaximal, characteristic, complemented
24#14533656C211yesmaximal, characteristic, complemented
25#14533650C211yesmaximal, characteristic, complemented
26#14532458C211yesmaximal, characteristic, complemented
27#14532206C211yesmaximal, characteristic, complemented
28#14531534C211yesmaximal, characteristic, complemented
29#14531410C211yesmaximal, characteristic, complemented
30#14531224C211yesmaximal, characteristic, complemented
31C17×#2778C211yesmaximal, characteristic
32C2×#10587565C2211yescharacteristic
33C2×#10587610C2211yescharacteristic
34C2×#10587564C2211yescharacteristic
35C2×#10587564C2211yescharacteristic
36C2×#10587564C2211yescharacteristic
37C2×D4×Dic17C2211yescharacteristic
38C2×D4×Dic17C2211yescharacteristic
39C2×#10587563C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41#11762751C2211yescharacteristic
42#11762751C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762751C2211yescharacteristic
46#11762751C2211yescharacteristic
47#11762750C2211yescharacteristic
48#11762750C2211yescharacteristic
49#11762749C2211yescharacteristic
50#11762749C2211yescharacteristic
51#11762749C2211yescharacteristic
52#11762748C2211yescharacteristic
53#11762747C2211yescharacteristic
54#11762747C2211yescharacteristic
55#11762745C2211yescharacteristic
56#11762745C2211yescharacteristic
57#11762743C2211yescharacteristic
58#11762743C2211yescharacteristic
59#11762743C2211yescharacteristic
60#11762743C2211yescharacteristic
61#11762743C2211yescharacteristic
62#11762742C2211yescharacteristic
63#11762742C2211yescharacteristic
64#11762739C2211yescharacteristic
65#11762739C2211yescharacteristic
66#11762737C2211yescharacteristic
67#11762737C2211yescharacteristic
68#11762737C2211yescharacteristic
69#11762734C2211yescharacteristic
70#11762734C2211yescharacteristic
71#11762734C2211yescharacteristic
72#11762734C2211yescharacteristic
73#11762732C2211yescharacteristic
74#11762732C2211yescharacteristic
75#11762732C2211yescharacteristic
76#11762730C2211yescharacteristic
77#11762730C2211yescharacteristic
78#11762723C2211yescharacteristic
79#11762723C2211yescharacteristic
80#11762723C2211yescharacteristic
81#11762721C2211yescharacteristic
82#11762721C2211yescharacteristic
83#11762715C2211yescharacteristic
84#11762714C2211yescharacteristic
85#11762714C2211yescharacteristic
86#11762713C2211yescharacteristic
87#11762713C2211yescharacteristic
88#11762713C2211yescharacteristic
89#11762712C2211yescharacteristic
90#11762708C2211yescharacteristic
91#11762708C2211yescharacteristic
92#11762708C2211yescharacteristic
93#11762707C2211yescharacteristic
94#11762706C2211yescharacteristic
95#11762704C2211yescharacteristic
96#11762704C2211yescharacteristic
97#11762703C2211yescharacteristic
98#11762703C2211yescharacteristic
99#11762703C2211yescharacteristic
100#11762703C2211yescharacteristic
101#11762702C2211yescharacteristic
102#11762702C2211yescharacteristic
103#11762702C2211yescharacteristic
104#11762702C2211yescharacteristic
105#11762702C2211yescharacteristic
106#11762697C2211yescharacteristic
107#11762697C2211yescharacteristic
108#11762697C2211yescharacteristic
109#11762697C2211yescharacteristic
110#11762697C2211yescharacteristic
111#11762697C2211yescharacteristic
112#11762697C2211yescharacteristic
113#11762696C2211yescharacteristic
114#11762696C2211yescharacteristic
115#11762696C2211yescharacteristic
116#11762696C2211yescharacteristic
117#11762696C2211yescharacteristic
118#11762696C2211yescharacteristic
119#11762694C2211yescharacteristic
120#11762694C2211yescharacteristic
121#11762694C2211yescharacteristic
122#11762694C2211yescharacteristic
123#11762694C2211yescharacteristic
124#11762694C2211yescharacteristic
125#11762694C2211yescharacteristic
126#11762692C2211yescharacteristic
127#11762692C2211yescharacteristic
128#11762692C2211yescharacteristic
129#11762692C2211yescharacteristic
130#11762692C2211yescharacteristic
131#11762691C2211yescharacteristic
132#11762691C2211yescharacteristic
133#11762690C2211yescharacteristic
134#11762689C2211yescharacteristic
135#11762689C2211yescharacteristic
136#11762689C2211yescharacteristic
137#11762689C2211yescharacteristic
138#11762689C2211yescharacteristic
139#11762689C2211yescharacteristic
140#11762684C2211yescharacteristic
141#11762684C2211yescharacteristic
142#11762684C2211yescharacteristic
143#11762684C2211yescharacteristic
144#11762684C2211yescharacteristic
145#11762682C2211yescharacteristic
146#11762682C2211yescharacteristic
147#11762682C2211yescharacteristic
148#11762681C2211yescharacteristic
149#11762681C2211yescharacteristic
150#11762681C2211yescharacteristic
151#11762677C2211yescharacteristic
152#11762676C2211yescharacteristic
153#11762676C2211yescharacteristic
154#11762676C2211yescharacteristic
155#11762673C2211yescharacteristic
156#11762670C2211yescharacteristic
157#11762670C2211yescharacteristic
158#11762670C2211yescharacteristic
159#11762670C2211yescharacteristic
160#11762669C2211yescharacteristic
161#11762669C2211yescharacteristic
162#11762667C2211yescharacteristic
163#11762667C2211yescharacteristic
164#11762667C2211yescharacteristic
165C4⋊C4×Dic17C2211yescharacteristic
166C4×#63225C2211yescharacteristic
167#11762660C2211yescharacteristic
168C22⋊C4×Dic17C2211yescharacteristic
169C22⋊C4×Dic17C2211yescharacteristic
170#11762654C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C17×#401C2211yescharacteristic
173C17×#400C2211yescharacteristic
174C17×#397C2211yescharacteristic
175C17×#394C2211yescharacteristic
176C17×#394C2211yescharacteristic
177C17×#392C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C17×#380C2211yescharacteristic
187C22×D4×C17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×Dic17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C23×Dic17C2311yescharacteristic
196C23×Dic17C2311yescharacteristic
197C22×Dic34C2311yescharacteristic
198C22×Dic34C2311yescharacteristic
199C2×C4⋊C4×C17C2311yescharacteristic
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C22⋊C4×C17C2311yescharacteristic
204C2×C22⋊C4×C17C2311yescharacteristic
205C2×C22⋊C4×C17C2311yescharacteristic
206C2×C22⋊C4×C17C2311yescharacteristic
207C2×C22⋊C4×C17C2311yescharacteristic
208C2×C22⋊C4×C17C2311yescharacteristic
209C2×C22⋊C4×C17C2311yescharacteristic
210C2×C22⋊C4×C17C2311yescharacteristic
211C2×C22⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C42×C17C2311yescharacteristic
217C2×C22⋊Dic17C2311yescharacteristic
218C2×C22⋊Dic17C2311yescharacteristic
219C2×C22⋊Dic17C2311yescharacteristic
220C2×C22⋊Dic17C2311yescharacteristic
221C2×C22⋊Dic17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224C2×C22⋊Dic17C2311yescharacteristic
225C2×C22⋊Dic17C2311yescharacteristic
226C2×C22⋊Dic17C2311yescharacteristic
227C2×C22⋊Dic17C2311yescharacteristic
228C2×C22⋊Dic17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236D4×Dic17—24no—
237D4×Dic17—24no—
238C2×C4⋊Dic17C2311yescharacteristic
239C2×C4⋊Dic17C2311yescharacteristic
240C2×C4⋊Dic17C2311yescharacteristic
241C2×C4⋊Dic17C2311yescharacteristic
242C2×C4⋊Dic17C2311yescharacteristic
243C2×C4⋊Dic17C2311yescharacteristic
244C2×C4⋊Dic17C2311yescharacteristic
245C2×C4⋊Dic17C2311yescharacteristic
246C2×C4⋊Dic17C2311yescharacteristic
247C2×C4⋊Dic17C2311yescharacteristic
248C2×C4⋊Dic17C2311yescharacteristic
249C2×C4⋊Dic17C2311yescharacteristic
250C2×C4⋊Dic17C2311yescharacteristic
251#10587610—42no—
252C2×#63225C2311yescharacteristic
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×#63225C2311yescharacteristic
257C2×#63225C2311yescharacteristic
258C2×#63225C2311yescharacteristic
259C2×#63225C2311yescharacteristic
260C2×#63225C2311yescharacteristic
261C2×#63225C2311yescharacteristic
262C2×#63225C2311yescharacteristic
263C2×#63225C2311yescharacteristic
264C2×#63225C2311yescharacteristic
265C2×#63225C2311yescharacteristic
266C2×#63225C2311yescharacteristic
267C2×#63225C2311yescharacteristic
268C2×#63225C2311yescharacteristic
269C2×#63225C2311yescharacteristic
270C2×#63225C2311yescharacteristic
271C2×#63225C2311yescharacteristic
272C2×C4×Dic17—42no—
273C2×C4×Dic17C2311yescharacteristic
274C2×C4×Dic17C2311yescharacteristic
275C2×C4×Dic17C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282C2×C4×Dic17C2311yescharacteristic
283C2×C4×Dic17C2311yescharacteristic
284#10587565—42no—
285#10587564—24no—
286#10587564—42no—
287#10587564—42no—
288#10587563—42no—
289C17×#95C2311yescharacteristic
290C17×#95C2311yescharacteristic
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301#10587502C2311yescharacteristic
302#10587502C2311yescharacteristic
303#10587502C2311yescharacteristic
304#10587502C2311yescharacteristic
305#10587502C2311yescharacteristic
306#10587502C2311yescharacteristic
307#10587502C2311yescharacteristic
308#10587502C2311yescharacteristic
309#10587502C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351C24×C17C2411yescharacteristic
352C24×C17C2411yescharacteristic
353C24×C17C2411yescharacteristic
354C2×D4×C17—22no—
355C2×D4×C17—22no—
356C2×D4×C17—22no—
357C2×D4×C17—22no—
358C2×D4×C17—41no—
359C2×D4×C17—41no—
360C2×D4×C17—41no—
361C2×D4×C17—41no—
362C2×D4×C17—41no—
363C22×C4×C17—22no—
364C22×C4×C17—41no—
365C22×C4×C17—41no—
366C22×C4×C17—41no—
367C22×C4×C17—41no—
368C22×C4×C17—41no—
369C22×C4×C17C2411yescharacteristic
370C22×C4×C17C2411yescharacteristic
371C22×C4×C17C2411yescharacteristic
372C22×C4×C17C2411yescharacteristic
373C22×C4×C17C2411yescharacteristic
374C22×C4×C17C2411yescharacteristic
375C22×C4×C17C2411yescharacteristic
376C22×C4×C17C2411yescharacteristic
377C22×C4×C17C2411yescharacteristic
378C22×C4×C17C2411yescharacteristic
379C22×C4×C17C2411yescharacteristic
380C22×C4×C17C2411yescharacteristic
381C22×Dic17—22no—
382C22×Dic17—22no—
383C22×Dic17—22no—
384C22×Dic17—41no—
385C22×Dic17—41no—
386C22×Dic17—41no—
387C22×Dic17—41no—
388C22×Dic17—41no—
389C22×Dic17—41no—
390C22×Dic17—41no—
391C22×Dic17—41no—
392C22×Dic17—41no—
393C22×Dic17—41no—
394C22×Dic17—41no—
395C22×Dic17#4114yes—
396C22×Dic17C2411yescharacteristic
397C22×Dic17C2411yescharacteristic
398C22×Dic17C2411yescharacteristic
399C22×Dic17C2411yescharacteristic
400C22×Dic17C2411yescharacteristic
401C22×Dic17C2411yescharacteristic
402C22×Dic17C2411yescharacteristic
403C22×Dic17C2411yescharacteristic
404C22×Dic17C2411yescharacteristic
405C22×Dic17C2411yescharacteristic
406C22×Dic17C2411yescharacteristic
407C22×Dic17C2411yescharacteristic
408C22×Dic17C2411yescharacteristic
409C22×Dic17C2411yescharacteristic
410C22×Dic17C2411yescharacteristic
411C22×Dic17C2411yescharacteristic
412C2×Dic34—22no—
413C2×Dic34—22no—
414C2×Dic34—41no—
415C2×Dic34—41no—
416C2×Dic34—41no—
417C2×Dic34—41no—
418C4⋊C4×C17—41no—
419C4⋊C4×C17—41no—
420C4⋊C4×C17—41no—
421C4⋊C4×C17—41no—
422C22⋊C4×C17—22no—
423C22⋊C4×C17—22no—
424C22⋊C4×C17—22no—
425C22⋊C4×C17—22no—
426C22⋊C4×C17—41no—
427C22⋊C4×C17—41no—
428C22⋊C4×C17—41no—
429C22⋊C4×C17—41no—
430C22⋊C4×C17—41no—
431C22⋊C4×C17—41no—
432C22⋊C4×C17—41no—
433C22⋊C4×C17—41no—
434C22⋊C4×C17—41no—
435C42×C17—41no—
436C22⋊Dic17—22no—
437C22⋊Dic17—22no—
438C22⋊Dic17—22no—
439C22⋊Dic17—22no—
440C22⋊Dic17—22no—
441C22⋊Dic17—22no—
442C22⋊Dic17—41no—
443C22⋊Dic17—41no—
444C22⋊Dic17—41no—
445C22⋊Dic17—41no—
446C22⋊Dic17—41no—
447C22⋊Dic17—41no—
448C22⋊Dic17—41no—
449C22⋊Dic17—41no—
450C22⋊Dic17—41no—
451C22⋊Dic17—41no—
452C22⋊Dic17—41no—
453C22⋊Dic17—41no—
454C22⋊Dic17—41no—
455C4⋊Dic17—22no—
456C4⋊Dic17—22no—
457C4⋊Dic17—22no—
458C4⋊Dic17—22no—
459C4⋊Dic17—41no—
460C4⋊Dic17—41no—
461C4⋊Dic17—41no—
462C4⋊Dic17—41no—
463C4⋊Dic17—41no—
464C4⋊Dic17—41no—
465C4⋊Dic17—41no—
466C4⋊Dic17—41no—
467C4⋊Dic17—41no—
468#63225—22no—
469#63225—22no—
470#63225—22no—
471#63225—22no—
472#63225—41no—
473#63225—41no—
474#63225—41no—
475#63225—41no—
476#63225—41no—
477#63225—41no—
478#63225—41no—
479#63225—41no—
480#63225—41no—
481#63225—41no—
482#63225—41no—
483#63225—41no—
484#63225—41no—
485#63225—41no—
486#63225—41no—
487#63225—41no—
488C4×Dic17—22no—
489C4×Dic17—22no—
490C4×Dic17—22no—
491C4×Dic17—22no—
492C4×Dic17—41no—
493C4×Dic17—41no—
494C4×Dic17—41no—
495C4×Dic17—41no—
496C4×Dic17—41no—
497C4×Dic17—41no—
498C4×Dic17—41no—
499#36790—171nomaximal, Sylow
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17—21no—
505C23×C17—21no—
506C23×C17—21no—
507C23×C17—21no—
508C23×C17—21no—
509C23×C17—21no—
510C23×C17—21no—
511C23×C17—21no—
512C23×C17—21no—
513C23×C17—21no—
514C23×C17—21no—
515C23×C17—21no—
516C23×C17—21no—
517C23×C17—21no—
518C23×C17—21no—
519C23×C17C2×#4112yes—
520C23×C172−1+412yes—
521C23×C17C2511yescharacteristic
522D4×C17—44no—
523D4×C17—44no—
524D4×C17—82no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17—21no—
539C2×C4×C17—21no—
540C2×C4×C17—21no—
541C2×C4×C17—21no—
542C2×C4×C17—21no—
543C2×C4×C17—21no—
544C2×C4×C17—21no—
545C2×C4×C17—21no—
546C2×C4×C17—21no—
547C2×C4×C17—21no—
548C2×C4×C17—21no—
549C2×C4×C17—21no—
550C2×C4×C17—21no—
551C2×C4×C17—21no—
552C2×C4×C17—21no—
553C2×C4×C17—21no—
554C2×C4×C17—21no—
555C2×C4×C17—21no—
556C2×C4×C17—21no—
557C2×C4×C17—21no—
558C2×C4×C17—21no—
559C2×C4×C17—21no—
560C2×C4×C17—44no—
561C2×C4×C17—82no—
562C2×C4×C17H(5,𝔽2)12yes—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—21no—
569C2×Dic17—21no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17—21no—
574C2×Dic17—21no—
575C2×Dic17—21no—
576C2×Dic17—21no—
577C2×Dic17—21no—
578C2×Dic17—21no—
579C2×Dic17—21no—
580C2×Dic17—21no—
581C2×Dic17—21no—
582C2×Dic17—21no—
583C2×Dic17—21no—
584C2×Dic17—21no—
585C2×Dic17—21no—
586C2×Dic17—21no—
587C2×Dic17—21no—
588C2×Dic17—21no—
589C2×Dic17—21no—
590C2×Dic17—21no—
591C2×Dic17—21no—
592C2×Dic17—21no—
593C2×Dic17—21no—
594C2×Dic17—21no—
595C2×Dic17—21no—
596C2×Dic17—21no—
597C2×Dic17—21no—
598C2×Dic17—21no—
599C2×Dic17—21no—
600C2×Dic17—21no—
601C2×Dic17—21no—
602C2×Dic17—21no—
603C2×Dic17—21no—
604C2×Dic17—21no—
605C2×Dic17—21no—
606C2×Dic17—21no—
607C2×Dic17—21no—
608C2×Dic17—21no—
609C2×Dic17—44no—
610C2×Dic17—44no—
611C2×Dic17—44no—
612C2×Dic17—82no—
613C2×Dic17—82no—
614C2×Dic17C2×#4112yes—
615C2×Dic17C2×#4112yes—
616Dic34—82no—
617Dic34—82no—
618#2855—171no—
619#2852—171no—
620#2778D1711yescharacteristic
621#2770—171no—
622#2770—171no—
623#2768—171no—
624#2764—171no—
625#2762—171no—
626#2758—171no—
627#2750—171no—
628#2749—171no—
629#2747—171no—
630#2743—171no—
631#2741—171no—
632#2728—171no—
633#2702—171no—
634#2692—171no—
635#2689—171no—
636#2655—171no—
637#2654—171no—
638#2600—171no—
639#2595—171no—
640#2587—171no—
641#2564—171no—
642#2533—171no—
643#2532—171no—
644#2438—171no—
645#2415—171no—
646#2332—171no—
647#2318—171no—
648#2290—171no—
649C22×C17—22no—
650C22×C17—22no—
651C22×C17—22no—
652C22×C17—22no—
653C22×C17—22no—
654C22×C17—22no—
655C22×C17—41no—
656C22×C17—41no—
657C22×C17—41no—
658C22×C17—41no—
659C22×C17—41no—
660C22×C17—41no—
661C22×C17—41no—
662C22×C17—41no—
663C22×C17—41no—
664C22×C17—41no—
665C22×C17—41no—
666C22×C17—41no—
667C22×C17—41no—
668C22×C17—41no—
669C22×C17—41no—
670C22×C17C22×#4111yescharacteristic
671C22×C17C2×H(5,𝔽2)11yescharacteristic
672C22×C17C2×2−1+411yescharacteristic
673C22×C17#58511yescharacteristic
674C22×C17#58511yescharacteristic
675C22×C17#58511yescharacteristic
676C22×C17#58511yescharacteristic
677C4×C17—22no—
678C4×C17—41no—
679C4×C17—41no—
680C4×C17—41no—
681C4×C17—41no—
682C4×C17—41no—
683C4×C17—41no—
684C4×C17—41no—
685C4×C17—41no—
686C4×C17—41no—
687C4×C17—41no—
688C4×C17—41no—
689Dic17—22no—
690Dic17—22no—
691Dic17—41no—
692Dic17—41no—
693Dic17—41no—
694Dic17—41no—
695Dic17—41no—
696Dic17—41no—
697Dic17—41no—
698Dic17—41no—
699Dic17—41no—
700Dic17—41no—
701Dic17—41no—
702Dic17—41no—
703Dic17—41no—
704Dic17—41no—
705C2×#126—171no—
706C2×C22⋊Q8—171no—
707C2×C22⋊Q8—171no—
708C2×C22⋊Q8—171no—
709C2×C22⋊Q8—171no—
710C2×C4×D4—171no—
711C2×C4×D4—171no—
712C2×#117—171no—
713C22×C42—171no—
714#401C2×D1711yescharacteristic
715#400—171no—
716#400—171no—
717#400—171no—
718#400—171no—
719#400—171no—
720#400—171no—
721#400—171no—
722#400—171no—
723#400—171no—
724#400—171no—
725#400—171no—
726#400—171no—
727#400—171no—
728#400—171no—
729#400C2×D1711yescharacteristic
730#399—171no—
731#399—171no—
732#398—171no—
733#398—171no—
734#398—171no—
735#398—171no—
736#398—171no—
737#398—171no—
738#398—171no—
739#398—171no—
740#398—171no—
741#397—171no—
742#397—171no—
743#397—171no—
744#397—171no—
745#397—171no—
746#397—171no—
747#397—171no—
748#397C2×D1711yescharacteristic
749#396—171no—
750#396—171no—
751#396—171no—
752#395—171no—
753#395—171no—
754#394—171no—
755#394—171no—
756#394—171no—
757#394C2×D1711yescharacteristic
758#394C2×D1711yescharacteristic
759#393—171no—
760#393—171no—
761#392C2×D1711yescharacteristic
762#391—171no—
763#391—171no—
764#391—171no—
765#391—171no—
766#391—171no—
767#391—171no—
768#390—171no—
769#389—171no—
770#389—171no—
771#389—171no—
772#389—171no—
773#389—171no—
774#389—171no—
775#389—171no—
776#388—171no—
777#388—171no—
778#388—171no—
779#388—171no—
780#388—171no—
781#388—171no—
782#388—171no—
783#388—171no—
784#388—171no—
785#388—171no—
786#388—171no—
787#388—171no—
788#388—171no—
789#388—171no—
790#388—171no—
791#388—171no—
792#388C2×D1711yescharacteristic
793#388C2×D1711yescharacteristic
794#388C2×D1711yescharacteristic
795#387—171no—
796#387—171no—
797#387—171no—
798#387—171no—
799#387—171no—
800#387—171no—
801#387—171no—
802#387—171no—
803#387—171no—
804#387—171no—
805#387—171no—
806#387—171no—
807#387—171no—
808#387—171no—
809#387—171no—
810#387—171no—
811#387—171no—
812#387—171no—
813#387—171no—
814#387—171no—
815#387—171no—
816#386—171no—
817#386—171no—
818#386—171no—
819#386—171no—
820#386—171no—
821#386—171no—
822#386C2×D1711yescharacteristic
823#386C2×D1711yescharacteristic
824#386C2×D1711yescharacteristic
825#386C2×D1711yescharacteristic
826#385—171no—
827#385—171no—
828#385—171no—
829#385—171no—
830#385—171no—
831#385—171no—
832#385—171no—
833#385—171no—
834#385—171no—
835#385—171no—
836#385—171no—
837#385C2×D1711yescharacteristic
838#383—171no—
839#383—171no—
840#383—171no—
841#383—171no—
842#382—171no—
843#381—171no—
844#381—171no—
845#381—171no—
846#381—171no—
847#380—171no—
848#380—171no—
849#380—171no—
850#380—171no—
851#380—171no—
852#380C2×D1711yescharacteristic
853C4×C4⋊C4—171no—
854C4×C4⋊C4—171no—
855C4×C4⋊C4—171no—
856C4×C22⋊C4—171no—
857C4×C22⋊C4—171no—
858#376—171no—
859C2×#95—171no—
860C2×C17—42no—
861C2×C17—42no—
862C2×C17—81no—
863C2×C17#345511yescharacteristic
864C2×C17#349511yescharacteristic
865C2×C17#350511yescharacteristic
866C2×C17#353311yescharacteristic
867C2×C17#354111yescharacteristic
868C2×C17#356411yescharacteristic
869C2×C17#356611yescharacteristic
870C22×Q8—171no—
871C22×Q8—171no—
872C22×D4C22×D1711yescharacteristic
873C22×D4C22×D1711yescharacteristic
874C22×D4C22×D1711yescharacteristic
875C23×C4—171no—
876C23×C4—171no—
877C23×C4—171no—
878C23×C4—171no—
879C23×C4—171no—
880C23×C4C22×D1711yescharacteristic
881C23×C4C22×D1711yescharacteristic
882#126—682no—
883C22⋊Q8—344no—
884C22⋊Q8—682no—
885C22⋊Q8—682no—
886C22⋊Q8—682no—
887C4×D4—344no—
888C4×D4—344no—
889#117—682no—
890C2×C4⋊C4—171no—
891C2×C4⋊C4—171no—
892C2×C4⋊C4—171no—
893C2×C4⋊C4—171no—
894C2×C4⋊C4—171no—
895C2×C4⋊C4—171no—
896C2×C4⋊C4—171no—
897C2×C4⋊C4—171no—
898C2×C4⋊C4—171no—
899C2×C4⋊C4—171no—
900C2×C4⋊C4—171no—
901C2×C4⋊C4—171no—
902C2×C4⋊C4—171no—
903C2×C4⋊C4—171no—
904C2×C4⋊C4—171no—
905C2×C4⋊C4—171no—
906C2×C4⋊C4—171no—
907C2×C4⋊C4—171no—
908C2×C4⋊C4—171no—
909C2×C4⋊C4—171no—
910C2×C4⋊C4—171no—
911C2×C4⋊C4—171no—
912C2×C4⋊C4—171no—
913C2×C4⋊C4—171no—
914C2×C4⋊C4—171no—
915C2×C4⋊C4—171no—
916C2×C4⋊C4—171no—
917C2×C4⋊C4—171no—
918C2×C4⋊C4—171no—
919C2×C4⋊C4—171no—
920C2×C4⋊C4—171no—
921C2×C4⋊C4—171no—
922C2×C4⋊C4—171no—
923C2×C4⋊C4C22×D1711yescharacteristic
924C2×C4⋊C4C22×D1711yescharacteristic
925C2×C4⋊C4C22×D1711yescharacteristic
926C2×C4⋊C4C22×D1711yescharacteristic
927C2×C22⋊C4—171no—
928C2×C22⋊C4—171no—
929C2×C22⋊C4—171no—
930C2×C22⋊C4—171no—
931C2×C22⋊C4—171no—
932C2×C22⋊C4—171no—
933C2×C22⋊C4—171no—
934C2×C22⋊C4—171no—
935C2×C22⋊C4—171no—
936C2×C22⋊C4—171no—
937C2×C22⋊C4—171no—
938C2×C22⋊C4—171no—
939C2×C22⋊C4—171no—
940C2×C22⋊C4—171no—
941C2×C22⋊C4—171no—
942C2×C22⋊C4—171no—
943C2×C22⋊C4—171no—
944C2×C22⋊C4—171no—
945C2×C22⋊C4—171no—
946C2×C22⋊C4C22×D1711yescharacteristic
947C2×C22⋊C4C22×D1711yescharacteristic
948C2×C22⋊C4C22×D1711yescharacteristic
949C2×C22⋊C4C22×D1711yescharacteristic
950C2×C22⋊C4C22×D1711yescharacteristic
951C2×C22⋊C4C22×D1711yescharacteristic
952C2×C22⋊C4C22×D1711yescharacteristic
953C2×C22⋊C4C22×D1711yescharacteristic
954C2×C22⋊C4C22×D1711yescharacteristic
955C2×C22⋊C4C22×D1711yescharacteristic
956C2×C22⋊C4C22×D1711yescharacteristic
957C2×C22⋊C4C22×D1711yescharacteristic
958C2×C22⋊C4C22×D1711yescharacteristic
959C2×C42—171no—
960C2×C42—171no—
961C2×C42—171no—
962C2×C42—171no—
963C2×C42—171no—
964C2×C42—171no—
965C2×C42—171no—
966C2×C42—171no—
967C2×C42—171no—
968C2×C42—171no—
969C2×C42—171no—
970C2×C42—682no—
971C2×C42C22×D1711yescharacteristic
972#95—171no—
973#95—171no—
974#95—171no—
975#95—171no—
976#95—171no—
977#95—171no—
978#95—171no—
979#95—171no—
980#95—171no—
981#95—171no—
982#95—171no—
983#95—171no—
984#95—171no—
985#95—171no—
986#95—171no—
987#95—171no—
988#95—171no—
989#95—171no—
990#95—171no—
991#95—171no—
992#95—171no—
993#95—171no—
994#95—171no—
995#95—171no—
996#95—171no—
997#95—171no—
998#95—171no—
999#95—171no—
1000#95—171no—
1001#95—171no—
1002#95—171no—
1003#95—171no—
1004#95—171no—
1005#95—171no—
1006#95—171no—
1007#95—171no—
1008#95—171no—
1009#95—171no—
1010#95—171no—
1011#95—171no—
1012#95—171no—
1013#95—171no—
1014#95—171no—
1015#95—171no—
1016#95—171no—
1017#95—171no—
1018#95—171no—
1019#95—171no—
1020#95—171no—
1021#95—171no—
1022#95C22×D1711yescharacteristic
1023#95C22×D1711yescharacteristic
1024#95C22×D1711yescharacteristic
1025#95C22×D1711yescharacteristic
1026#95C22×D1711yescharacteristic
1027#95C22×D1711yescharacteristic
1028#95C22×D1711yescharacteristic
1029#95C22×D1711yescharacteristic
1030#95C22×D1711yescharacteristic
1031#95C22×D1711yescharacteristic
1032#95C22×D1711yescharacteristic
1033#95C22×D1711yescharacteristic
1034C17#3679011yescharacteristic, complemented, Sylow
1035C24C23×D1711yescharacteristic
1036C24C23×D1711yescharacteristic
1037C24C23×D1711yescharacteristic
1038C2×Q8—342no—
1039C2×Q8—342no—
1040C2×Q8—681no—
1041C2×Q8—681no—
1042C2×Q8—681no—
1043C2×Q8—681no—
1044C2×D4—22no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C22×C4—22no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—171no—
1060C22×C4—171no—
1061C22×C4—174no—
1062C22×C4—171no—
1063C22×C4—171no—
1064C22×C4—171no—
1065C22×C4—171no—
1066C22×C4—171no—
1067C22×C4—171no—
1068C22×C4—171no—
1069C22×C4—171no—
1070C22×C4—171no—
1071C22×C4—171no—
1072C22×C4—171no—
1073C22×C4—171no—
1074C22×C4—171no—
1075C22×C4—171no—
1076C22×C4—342no—
1077C22×C4—342no—
1078C22×C4—342no—
1079C22×C4—681no—
1080C22×C4—681no—
1081C22×C4—681no—
1082C22×C4—681no—
1083C22×C4—681no—
1084C22×C4—681no—
1085C22×C4—681no—
1086C22×C4—681no—
1087C22×C4—681no—
1088C22×C4—681no—
1089C22×C4—681no—
1090C22×C4C23×D1711yescharacteristic
1091C22×C4C23×D1711yescharacteristic
1092C22×C4C23×D1711yescharacteristic
1093C22×C4C23×D1711yescharacteristic
1094C22×C4C23×D1711yescharacteristic
1095C22×C4C23×D1711yescharacteristic
1096C22×C4C23×D1711yescharacteristic
1097C22×C4C23×D1711yescharacteristic
1098C22×C4C23×D1711yescharacteristic
1099C22×C4C23×D1711yescharacteristic
1100C22×C4C23×D1711yescharacteristic
1101C22×C4C23×D1711yescharacteristic
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—342no—
1107C4⋊C4—342no—
1108C4⋊C4—342no—
1109C4⋊C4—342no—
1110C4⋊C4—342no—
1111C4⋊C4—342no—
1112C4⋊C4—342no—
1113C4⋊C4—342no—
1114C4⋊C4—681no—
1115C4⋊C4—681no—
1116C4⋊C4—681no—
1117C4⋊C4—681no—
1118C4⋊C4—681no—
1119C4⋊C4—681no—
1120C4⋊C4—681no—
1121C4⋊C4—681no—
1122C4⋊C4—681no—
1123C4⋊C4—681no—
1124C4⋊C4—681no—
1125C4⋊C4—681no—
1126C4⋊C4—681no—
1127C4⋊C4—681no—
1128C4⋊C4—681no—
1129C4⋊C4—681no—
1130C4⋊C4—681no—
1131C4⋊C4—681no—
1132C4⋊C4—681no—
1133C4⋊C4—681no—
1134C4⋊C4—681no—
1135C4⋊C4—681no—
1136C4⋊C4—681no—
1137C4⋊C4—681no—
1138C4⋊C4—681no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—22no—
1143C22⋊C4—41no—
1144C22⋊C4—41no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—342no—
1153C22⋊C4—342no—
1154C22⋊C4—342no—
1155C22⋊C4—342no—
1156C22⋊C4—342no—
1157C22⋊C4—342no—
1158C22⋊C4—681no—
1159C22⋊C4—681no—
1160C22⋊C4—681no—
1161C22⋊C4—681no—
1162C22⋊C4—681no—
1163C22⋊C4—681no—
1164C22⋊C4—681no—
1165C22⋊C4—681no—
1166C22⋊C4—681no—
1167C22⋊C4—681no—
1168C22⋊C4—681no—
1169C22⋊C4—681no—
1170C22⋊C4—681no—
1171C42—41no—
1172C42—342no—
1173C42—342no—
1174C42—342no—
1175C42—342no—
1176C42—681no—
1177C42—681no—
1178C42—681no—
1179C42—681no—
1180C42—681no—
1181C42—681no—
1182C42—681no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23#41×D1712yes—
1203C23#1058769712yes—
1204C23C24×D1711yescharacteristic
1205Q8—1362no—
1206Q8—1362no—
1207D4—44no—
1208D4—44no—
1209D4—82no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—44no—
1246C2×C4—82no—
1247C2×C4—172no—
1248C2×C4—172no—
1249C2×C4—341no—
1250C2×C4—341no—
1251C2×C4—341no—
1252C2×C4—341no—
1253C2×C4—341no—
1254C2×C4—341no—
1255C2×C4—341no—
1256C2×C4—341no—
1257C2×C4—341no—
1258C2×C4—341no—
1259C2×C4—341no—
1260C2×C4—341no—
1261C2×C4—341no—
1262C2×C4—341no—
1263C2×C4—341no—
1264C2×C4—341no—
1265C2×C4—341no—
1266C2×C4—341no—
1267C2×C4—341no—
1268C2×C4—341no—
1269C2×C4—341no—
1270C2×C4—341no—
1271C2×C4—341no—
1272C2×C4—341no—
1273C2×C4—341no—
1274C2×C4—341no—
1275C2×C4—341no—
1276C2×C4—341no—
1277C2×C4—341no—
1278C2×C4—341no—
1279C2×C4—341no—
1280C2×C4—341no—
1281C2×C4—341no—
1282C2×C4—341no—
1283C2×C4—341no—
1284C2×C4—341no—
1285C2×C4—341no—
1286C2×C4—341no—
1287C2×C4—341no—
1288C2×C4—341no—
1289C2×C4—341no—
1290C2×C4—341no—
1291C2×C4—341no—
1292C2×C4—341no—
1293C2×C4—341no—
1294C2×C4—341no—
1295C2×C4—684no—
1296C2×C4—684no—
1297C2×C4—684no—
1298C2×C4—1362no—
1299C2×C4—1362no—
1300C2×C4#1058769612yes—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22C2×#41×D1711yescharacteristic
1323C22C2×#1058769611yescharacteristic
1324C22C2×#1058769711yescharacteristic
1325C22#1176364411yescharacteristic
1326C22#1176364411yescharacteristic
1327C22#1176364411yescharacteristic
1328C22#1176364411yescharacteristic
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—342no—
1342C4—342no—
1343C4—681no—
1344C4—681no—
1345C4—681no—
1346C4—681no—
1347C4—681no—
1348C4—681no—
1349C4—681no—
1350C4—681no—
1351C4—681no—
1352C4—681no—
1353C4—681no—
1354C4—681no—
1355C4—681no—
1356C4—681no—
1357C2—42no—
1358C2—42no—
1359C2—81no—
1360C2#1454216611yescharacteristic
1361C2#1454252311yescharacteristic
1362C2#1454261311yescharacteristic
1363C2#1454295211yescharacteristic
1364C2#1454307111yescharacteristic
1365C2#1454341011yescharacteristic
1366C2#1454344111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2778C2
prime radicalC17×#392C22
hypercenter#2778D17
hypocenterC17#36790
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2778

Complements

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

NH ≅ G/Ntype
1. #14537124C2semidirect
2. #14537097C2semidirect
3. #14536292C2semidirect
4. #14536286C2semidirect
5. #14536259C2semidirect
6. #14536209C2semidirect
7. #14536185C2semidirect
8. #14536142C2semidirect
9. #14536016C2semidirect
11. #14535988C2semidirect
12. #14535925C2semidirect
13. #14535903C2semidirect
14. #14535755C2semidirect
15. #14535417C2semidirect
16. #14535281C2semidirect
17. #14535233C2semidirect
18. #14534884C2semidirect
19. #14534859C2semidirect
21. #14534306C2semidirect
22. #14534203C2semidirect
23. #14533968C2semidirect
24. #14533656C2semidirect
25. #14533650C2semidirect
26. #14532458C2semidirect
27. #14532206C2semidirect
28. #14531534C2semidirect
29. #14531410C2semidirect
30. #14531224C2semidirect
1034. C17#36790semidirect

Maximal subgroups

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

subgroupindex
#145371242
#145370972
#145362922
#145362862
#145362592
#145362092
#145361852
#145361422
#145360162
#145360092
#145359882
#145359252
#145359032
#145357552
#145354172
#145352812
#145352332
#145348842
#145348592
#145343652
#145343062
#145342032
#145339682
#145336562
#145336502
#145324582
#145322062
#145315342
#145314102
#145312242
C17×#27782
#3679017