Finite Group Databasebeta

← D17×#3344 #17912863

Subgroups — D17×#3344 #17912863

Order 4352.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×#554C211yesmaximal, characteristic
2D17×#552C211yesmaximal, characteristic
3#14541246C211yesmaximal, characteristic, complemented
4#14541245C211yesmaximal, characteristic, complemented
5#14541244C211yesmaximal, characteristic, complemented
6#14541243C211yesmaximal, characteristic, complemented
7#14541242C211yesmaximal, characteristic, complemented
8#14541241C211yesmaximal, characteristic, complemented
9#14541240C211yesmaximal, characteristic, complemented
10#14541239C211yesmaximal, characteristic, complemented
11#14541238C211yesmaximal, characteristic, complemented
12#14541237C211yesmaximal, characteristic, complemented
13#14541236C211yesmaximal, characteristic, complemented
14#14541235C211yesmaximal, characteristic, complemented
15#14541234C211yesmaximal, characteristic, complemented
16#14541233C211yesmaximal, characteristic, complemented
17#14541232C211yesmaximal, characteristic, complemented
18D17×#501C211yesmaximal, characteristic, complemented
19D17×#484C211yesmaximal, characteristic, complemented
20D17×#485C211yesmaximal, characteristic, complemented
21D17×#483C211yesmaximal, characteristic, complemented
22D17×#483C211yesmaximal, characteristic, complemented
23D17×#479C211yesmaximal, characteristic, complemented
24D17×#475C211yesmaximal, characteristic, complemented
25D17×#470C211yesmaximal, characteristic, complemented
26D17×#467C211yesmaximal, characteristic, complemented
27D17×#441C211yesmaximal, characteristic, complemented
28D17×#435C211yesmaximal, characteristic
29D17×#428C211yesmaximal, characteristic, complemented
30C2×#106×D17C211yesmaximal, characteristic, complemented
31C17×#3344C211yesmaximal, characteristic, complemented
32C2×Q16×D17C2211yescharacteristic
33C2×M16×D17C2211yescharacteristic
34C22×C8×D17C2211yescharacteristic
35#11763520C2211yescharacteristic
36#11763519C2211yescharacteristic
37#11763518—21no—
38#11763517C2211yescharacteristic
39#11763517C2211yescharacteristic
40#11763516C2211yescharacteristic
41#11763515—21no—
42#11763514C2211yescharacteristic
43#11763514C2211yescharacteristic
44#11763513—21no—
45#11763513—21no—
46#11763501C2211yescharacteristic
47#11763500C2211yescharacteristic
48#11763499C2211yescharacteristic
49#11763498C2211yescharacteristic
50#11763497C2211yescharacteristic
51#11763496—21no—
52#11763495—21no—
53#11763494C2211yescharacteristic
54#11763493C2211yescharacteristic
55#11763492—21no—
56#11763491—21no—
57C4⋊Q8×D17C2211yescharacteristic
58#126×D17—21no—
59#125×D17—21no—
60#125×D17—21no—
61#125×D17C2211yescharacteristic
62#123×D17—21no—
63C22⋊Q8×D17—21no—
64C22⋊Q8×D17—21no—
65C22⋊Q8×D17C2211yescharacteristic
66C22⋊Q8×D17C2211yescharacteristic
67C22⋊Q8×D17C2211yescharacteristic
68C22⋊Q8×D17C2211yescharacteristic
69C4×Q8×D17C2211yescharacteristic
70C4×Q8×D17C2211yescharacteristic
71C4×D4×D17—21no—
72C4×D4×D17C2211yescharacteristic
73#117×D17—21no—
74#117×D17C2211yescharacteristic
75C2×C4⋊C4×D17C2211yescharacteristic
76C2×C4⋊C4×D17C2211yescharacteristic
77C2×C4⋊C4×D17C2211yescharacteristic
78#11763219C2211yescharacteristic, complemented
79#11763218C2211yescharacteristic, complemented
80#11763217C2211yescharacteristic, complemented
81#11763217C2211yescharacteristic, complemented
82#11763216C2211yescharacteristic, complemented
83#11763216C2211yescharacteristic, complemented
84#11763215C2211yescharacteristic, complemented
85#11763153C2211yescharacteristic, complemented
86#11763152C2211yescharacteristic, complemented
87#11763151C2211yescharacteristic, complemented
88#11763150C2211yescharacteristic, complemented
89#11763149C2211yescharacteristic, complemented
90#11763148C2211yescharacteristic, complemented
91#11763147C2211yescharacteristic, complemented
92#11763146C2211yescharacteristic, complemented
93#11763146C2211yescharacteristic, complemented
94#11763145C2211yescharacteristic, complemented
95#11763144C2211yescharacteristic, complemented
96#11763143C2211yescharacteristic, complemented
97#11763143C2211yescharacteristic, complemented
98#11763142C2211yescharacteristic, complemented
99#11763141C2211yescharacteristic, complemented
100#11763141C2211yescharacteristic, complemented
101#11763141C2211yescharacteristic, complemented
102#11763141C2211yescharacteristic, complemented
103#11763140C2211yescharacteristic, complemented
104#11763140C2211yescharacteristic, complemented
105#11763139C2211yescharacteristic, complemented
106#11763139C2211yescharacteristic, complemented
107#11763138C2211yescharacteristic, complemented
108#11763138C2211yescharacteristic, complemented
109#11763138C2211yescharacteristic, complemented
110#11763138C2211yescharacteristic, complemented
111#11763137C2211yescharacteristic, complemented
112#11763137C2211yescharacteristic, complemented
113#11763119C2211yescharacteristic, complemented
114#11763118C2211yescharacteristic, complemented
115#11763117C2211yescharacteristic, complemented
116#11763116C2211yescharacteristic, complemented
117#11763115C2211yescharacteristic, complemented
118#11763114C2211yescharacteristic, complemented
119#11763113C2211yescharacteristic, complemented
120#11763095C2211yescharacteristic, complemented
121#11763094C2211yescharacteristic, complemented
122#11763093C2211yescharacteristic, complemented
123#11763093C2211yescharacteristic, complemented
124#11763092C2211yescharacteristic, complemented
125#11763092C2211yescharacteristic, complemented
126#11763091C2211yescharacteristic, complemented
127#11763068C2211yescharacteristic, complemented
128#11763067C2211yescharacteristic, complemented
129#11763066C2211yescharacteristic, complemented
130#11763066C2211yescharacteristic, complemented
131#11763065C2211yescharacteristic, complemented
132#11763065C2211yescharacteristic, complemented
133#11763064C2211yescharacteristic, complemented
134#11763051C2211yescharacteristic, complemented
135#11763050C2211yescharacteristic, complemented
136#11763049C2211yescharacteristic, complemented
137#11763049C2211yescharacteristic, complemented
138#11763048C2211yescharacteristic, complemented
139#11763048C2211yescharacteristic, complemented
140#11763047C2211yescharacteristic, complemented
141#11762917C2211yescharacteristic, complemented
142#11762916C2211yescharacteristic, complemented
143#11762915C2211yescharacteristic, complemented
144#11762914C2211yescharacteristic, complemented
145#11762914C2211yescharacteristic, complemented
146#11762913C2211yescharacteristic, complemented
147#11762913C2211yescharacteristic, complemented
148#11762883C2211yescharacteristic
149#11762882C2211yescharacteristic
150#11762881C2211yescharacteristic
151#11762880C2211yescharacteristic
152#11762879C2211yescharacteristic
153#11762878C2211yescharacteristic
154#11762877C2211yescharacteristic
155#11762852C2211yescharacteristic, complemented
156#11762851C2211yescharacteristic, complemented
157#11762850C2211yescharacteristic, complemented
158#11762850C2211yescharacteristic, complemented
159#11762849C2211yescharacteristic, complemented
160#11762848C2211yescharacteristic, complemented
161#11762848C2211yescharacteristic, complemented
162#107×D17C2211yescharacteristic
163#107×D17C2211yescharacteristic
164#107×D17C2211yescharacteristic
165C2×#10587488C2211yescharacteristic, complemented
166C2×#10587479C2211yescharacteristic, complemented
167C2×#10587479C2211yescharacteristic, complemented
168#106×D17C2211yescharacteristic
169#106×D17C2211yescharacteristic
170#106×D17C2211yescharacteristic
171#106×D17C2211yescharacteristic
172#106×D17C2211yescharacteristic
173#106×D17C2211yescharacteristic
174#106×D17C2211yescharacteristic, complemented
175#106×D17C2211yescharacteristic, complemented
176#106×D17C2211yescharacteristic, complemented
177#106×D17C2211yescharacteristic, complemented
178C4⋊C8×D17C2211yescharacteristic
179#103×D17C2211yescharacteristic
180#103×D17C2211yescharacteristic
181#103×D17C2211yescharacteristic
182#103×D17C2211yescharacteristic
183#103×D17C2211yescharacteristic
184#103×D17C2211yescharacteristic
185C22⋊C8×D17C2211yescharacteristic
186C22⋊C8×D17C2211yescharacteristic
187#97×D17C2211yescharacteristic
188C17×#554C2211yescharacteristic
189C17×#552C2211yescharacteristic
190C17×#501C2211yescharacteristic, complemented
191C17×#485C2211yescharacteristic, complemented
192C17×#484C2211yescharacteristic, complemented
193C17×#483C2211yescharacteristic, complemented
194C17×#483C2211yescharacteristic, complemented
195C17×#479C2211yescharacteristic, complemented
196C17×#475C2211yescharacteristic, complemented
197C17×#470C2211yescharacteristic, complemented
198C17×#467C2211yescharacteristic, complemented
199C17×#441C2211yescharacteristic, complemented
200C17×#435C2211yescharacteristic
201C17×#428C2211yescharacteristic, complemented
202C2×C17×#106C2211yescharacteristic, complemented
203C2×Q8×D17—21no—
204C2×Q8×D17C2311yescharacteristic
205C2×Q8×D17C2311yescharacteristic
206C2×D4×D17D411yescharacteristic
207C22×C4×D17—21no—
208C22×C4×D17—21no—
209C22×C4×D17—21no—
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C2×Q16×C17C2311yescharacteristic
213C2×M16×C17C2311yescharacteristic
214C22×C8×C17C2311yescharacteristic
215C17×C4⋊Q8C2311yescharacteristic
216C17×#126—21no—
217C17×#125—21no—
218C17×#125—21no—
219C17×#125C2311yescharacteristic
220C17×#123—21no—
221C17×C22⋊Q8—21no—
222C17×C22⋊Q8—21no—
223C17×C22⋊Q8C2311yescharacteristic
224C17×C22⋊Q8C2311yescharacteristic
225C17×C22⋊Q8C2311yescharacteristic
226C17×C22⋊Q8C2311yescharacteristic
227C4×Q8×C17C2311yescharacteristic
228C4×Q8×C17C2311yescharacteristic
229C4×D4×C17—21no—
230C4×D4×C17C2311yescharacteristic
231C17×#117—21no—
232C17×#117C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236#10587632—21no—
237#10587632—21no—
238#10587632C2311yescharacteristic
239#10587632C2311yescharacteristic
240#10587632C2311yescharacteristic
241#10587632C2311yescharacteristic
242Q8×Dic17C2311yescharacteristic
243Q8×Dic17C2311yescharacteristic
244#10587630—21no—
245C2×#63231C2311yescharacteristic
246C2×#63231C2311yescharacteristic
247#10587621—21no—
248D4×Dic17—21no—
249D4×Dic17D411yescharacteristic
250#10587615—21no—
251C4×C22⋊D17—21no—
252C4×C22⋊D17—21no—
253C4×C22⋊D17C2311yescharacteristic
254C4×C22⋊D17C2311yescharacteristic
255#10587612—21no—
256#10587612C2311yescharacteristic
257C2×C4⋊Dic17C2311yescharacteristic
258C2×C4⋊Dic17C2311yescharacteristic
259C2×C4⋊Dic17C2311yescharacteristic
260#10587610—21no—
261#10587610—21no—
262#10587610C2311yescharacteristic
263#10587610C2311yescharacteristic
264#10587610C2311yescharacteristic
265#10587610C2311yescharacteristic
266C2×#63225—21no—
267C2×#63225—21no—
268C2×#63225—21no—
269C2×#63223C2311yescharacteristic
270C22×#3622C2311yescharacteristic
271Q16×D17—24no—
272M16×D17—24no—
273C2×Dic68C2311yescharacteristic
274C2×#63218C2311yescharacteristic
275C2×#63218C2311yescharacteristic
276C2×C8×D17—24no—
277C2×C8×D17C2311yescharacteristic
278C2×C8×D17C2311yescharacteristic
279C2×C8×D17C2311yescharacteristic
280C2×C8×D17C2311yescharacteristic
281C2×C8×D17C2311yescharacteristic
282C2×C8×D17C2311yescharacteristic
283#10587584—21no—
284#10587584—21no—
285#10587584—21no—
286#10587583—21no—
287#10587583—21no—
288#10587583C2311yescharacteristic
289#10587583C2311yescharacteristic
290#10587583C2311yescharacteristic
291#10587583C2311yescharacteristic
292#10587582—21no—
293#10587582—21no—
294#10587582—21no—
295#10587582—21no—
296#10587582—21no—
297#10587582—21no—
298#10587582—21no—
299#10587582—21no—
300#10587580—21no—
301#10587580—21no—
302#10587579—21no—
303#10587579D411yescharacteristic
304#10587578—21no—
305#10587578—21no—
306#10587578C2311yescharacteristic
307#10587578C2311yescharacteristic
308C4⋊C4×D17—21no—
309C4⋊C4×D17—21no—
310C4⋊C4×D17—21no—
311C4⋊C4×D17—21no—
312C4⋊C4×D17—21no—
313C4⋊C4×D17—21no—
314C4⋊C4×D17—21no—
315C4⋊C4×D17—21no—
316C4⋊C4×D17—21no—
317C4⋊C4×D17—21no—
318C4⋊C4×D17—21no—
319C4⋊C4×D17—21no—
320C4⋊C4×D17—21no—
321C4⋊C4×D17—21no—
322C4⋊C4×D17—21no—
323C4⋊C4×D17D411yescharacteristic
324C4⋊C4×D17C2311yescharacteristic
325C4⋊C4×D17C2311yescharacteristic
326C4⋊C4×D17C2311yescharacteristic
327C4⋊C4×D17C2311yescharacteristic
328C4⋊C4×D17C2311yescharacteristic
329C4⋊C4×D17C2311yescharacteristic
330C4⋊C4×D17C2311yescharacteristic
331C4⋊C4×D17C2311yescharacteristic
332C4⋊C4×D17C2311yescharacteristic
333C4⋊C4×D17C2311yescharacteristic
334C4⋊C4×D17C2311yescharacteristic
335C4⋊C4×D17C2311yescharacteristic
336#10587576—21no—
337#10587576—21no—
338#10587576—21no—
339#10587576—21no—
340#10587576C2311yescharacteristic
341#10587576C2311yescharacteristic
342#10587575—21no—
343#10587575—21no—
344#10587575—21no—
345#10587575—21no—
346#10587575—21no—
347#10587575—21no—
348#10587575—21no—
349#10587575—21no—
350#10587575—21no—
351#10587575—21no—
352#10587574—21no—
353#10587574C2311yescharacteristic
354#10587574C2311yescharacteristic
355#10587573—21no—
356#10587573—21no—
357#10587573C2311yescharacteristic
358#10587573C2311yescharacteristic
359#10587572—21no—
360#10587569—21no—
361#10587569—21no—
362#10587567—21no—
363#10587567—21no—
364#10587567D411yescharacteristic
365#10587567D411yescharacteristic
366C22⋊C4×D17—21no—
367C22⋊C4×D17—21no—
368C22⋊C4×D17—21no—
369C22⋊C4×D17—21no—
370C22⋊C4×D17—21no—
371C22⋊C4×D17D411yescharacteristic
372C22⋊C4×D17D411yescharacteristic
373#10587565—21no—
374#10587565—21no—
375#10587565—21no—
376#10587564—21no—
377#10587564—21no—
378#10587564—21no—
379#10587564—21no—
380#10587564—21no—
381#10587564—21no—
382#10587564—21no—
383#10587564—21no—
384#10587563—21no—
385#10587563—21no—
386#10587563—21no—
387#10587562—21no—
388C4×D68—21no—
389C4×D68C2311yescharacteristic
390#10587558—21no—
391#10587558—21no—
392#10587558—21no—
393C42×D17—21no—
394C42×D17—21no—
395C42×D17—21no—
396C42×D17C2311yescharacteristic
397#10587556—21no—
398#10587556—21no—
399#10587556C2311yescharacteristic
400#10587555C2311yescharacteristic
401C4×Dic34—21no—
402C4×Dic34—21no—
403C4×Dic34C2311yescharacteristic
404C4×Dic34C2311yescharacteristic
405C17×#107C2311yescharacteristic
406C17×#107C2311yescharacteristic
407C17×#107C2311yescharacteristic
408C17×#106C2311yescharacteristic
409C17×#106C2311yescharacteristic
410C17×#106C2311yescharacteristic
411C17×#106C2311yescharacteristic
412C17×#106C2311yescharacteristic
413C17×#106C2311yescharacteristic
414C17×C4⋊C8C2311yescharacteristic
415C17×#103C2311yescharacteristic
416C17×#103C2311yescharacteristic
417C17×#103C2311yescharacteristic
418C17×#103C2311yescharacteristic
419C17×#103C2311yescharacteristic
420C17×#103C2311yescharacteristic
421C17×C22⋊C8C2311yescharacteristic
422C17×C22⋊C8C2311yescharacteristic
423C17×#97C2311yescharacteristic
424#10587506C2311yescharacteristic
425#10587506C2311yescharacteristic
426#10587506C2311yescharacteristic
427#10587506C2311yescharacteristic
428#10587506C2311yescharacteristic
429#10587506C2311yescharacteristic
430C22⋊#3622C2311yescharacteristic
431C22⋊#3622C2311yescharacteristic
432#10587491C2311yescharacteristic
433#10587491C2311yescharacteristic
434#10587491C2311yescharacteristic
435#10587491C2311yescharacteristic
436#10587489C2311yescharacteristic
437#10587489C2311yescharacteristic
438#10587489C2311yescharacteristic
439#10587488C2311yescharacteristic
440#10587488C2311yescharacteristic
441#10587488C2311yescharacteristic
442#10587488C2311yescharacteristic
443#10587488C2311yescharacteristic
444#10587488C2311yescharacteristic
445#10587487C2311yescharacteristic
446#10587487C2311yescharacteristic
447#10587487C2311yescharacteristic
448#10587487C2311yescharacteristic
449#10587487C2311yescharacteristic
450#10587487C2311yescharacteristic
451#10587486C2311yescharacteristic
452#10587486C2311yescharacteristic
453#10587485C2311yescharacteristic
454#10587485C2311yescharacteristic
455#10587481C2311yescharacteristic
456#10587481C2311yescharacteristic
457#10587481C2311yescharacteristic
458#10587481C2311yescharacteristic
459#10587481C2311yescharacteristic
460#10587481C2311yescharacteristic
461#10587479C2311yescharacteristic
462#10587479C2311yescharacteristic
463#10587479C2311yescharacteristic
464#10587479C2311yescharacteristic
465#10587479C2311yescharacteristic
466#10587479C2311yescharacteristic
467#10587479C2311yescharacteristic
468#10587479C2311yescharacteristic
469#10587479C2311yescharacteristic
470#10587479C2311yescharacteristic
471#10587479C2311yescharacteristic
472#10587479C2311yescharacteristic
473#10587478C2311yescharacteristic
474#10587478C2311yescharacteristic
475#10587478C2311yescharacteristic
476#10587478C2311yescharacteristic
477#10587478C2311yescharacteristic
478#10587478C2311yescharacteristic
479C4⋊#3622C2311yescharacteristic
480#10587474C2311yescharacteristic
481C23×D17C2×D411yescharacteristic
482C23×D17C2×D411yescharacteristic
483C2×Q8×C17—21no—
484C2×Q8×C17C2411yescharacteristic
485C2×Q8×C17C2411yescharacteristic
486C2×D4×C17C2×D411yescharacteristic
487C22×C4×C17—21no—
488C22×C4×C17—21no—
489C22×C4×C17—21no—
490C22×C4×C17C2411yescharacteristic
491C22×C4×C17C2411yescharacteristic
492C2×C22⋊D17C2×D411yescharacteristic
493C2×C22⋊D17C2×D411yescharacteristic
494C22×Dic17—21no—
495C22×Dic17—21no—
496C22×Dic17—21no—
497C22×Dic17C2×D411yescharacteristic
498C22×Dic17C2×D411yescharacteristic
499Q8×D17—22no—
500Q8×D17—22no—
501Q8×D17—22no—
502Q8×D17—22no—
503Q8×D17—82no—
504D4×D17—24no—
505C2×D68C2×D411yescharacteristic
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—21no—
511C2×C4×D17—21no—
512C2×C4×D17—21no—
513C2×C4×D17—21no—
514C2×C4×D17—21no—
515C2×C4×D17—21no—
516C2×C4×D17—21no—
517C2×C4×D17—21no—
518C2×C4×D17—21no—
519C2×C4×D17—21no—
520C2×C4×D17—21no—
521C2×C4×D17—21no—
522C2×C4×D17—21no—
523C2×C4×D17—21no—
524C2×C4×D17—44no—
525C2×C4×D17—82no—
526C2×C4×D17—82no—
527C2×C4×D17C2×D411yescharacteristic
528C2×C4×D17C2×D411yescharacteristic
529C2×C4×D17C2×D411yescharacteristic
530C2×C4×D17C2×D411yescharacteristic
531C2×C4×D17C2×D411yescharacteristic
532C2×C4×D17C2×D411yescharacteristic
533C2×C4×D17C2411yescharacteristic
534C2×C4×D17C2411yescharacteristic
535C2×C4×D17C2411yescharacteristic
536C2×Dic34—21no—
537C2×Dic34—21no—
538C2×Dic34—21no—
539C2×Dic34—21no—
540C2×Dic34—21no—
541C2×Dic34C2411yescharacteristic
542C2×Dic34C2411yescharacteristic
543Q16×C17—22no—
544M16×C17—22no—
545C2×C8×C17—22no—
546C2×C8×C17C2411yescharacteristic
547C2×C8×C17C2411yescharacteristic
548C2×C8×C17C2411yescharacteristic
549C2×C8×C17C2411yescharacteristic
550C4⋊C4×C17—21no—
551C4⋊C4×C17—21no—
552C4⋊C4×C17—21no—
553C4⋊C4×C17—21no—
554C4⋊C4×C17—21no—
555C4⋊C4×C17—21no—
556C4⋊C4×C17—21no—
557C4⋊C4×C17—21no—
558C4⋊C4×C17—21no—
559C4⋊C4×C17—21no—
560C4⋊C4×C17—21no—
561C4⋊C4×C17—21no—
562C4⋊C4×C17C2×D411yescharacteristic
563C4⋊C4×C17C2411yescharacteristic
564C4⋊C4×C17C2411yescharacteristic
565C4⋊C4×C17C2411yescharacteristic
566C4⋊C4×C17C2411yescharacteristic
567C4⋊C4×C17C2411yescharacteristic
568C4⋊C4×C17C2411yescharacteristic
569C22⋊C4×C17—21no—
570C22⋊C4×C17—21no—
571C22⋊C4×C17—21no—
572C22⋊C4×C17—21no—
573C22⋊C4×C17—21no—
574C22⋊C4×C17C2×D411yescharacteristic
575C22⋊C4×C17C2×D411yescharacteristic
576C42×C17—21no—
577C42×C17—21no—
578C42×C17—21no—
579C42×C17C2411yescharacteristic
580C22⋊Dic17—21no—
581C22⋊Dic17—21no—
582C22⋊Dic17—21no—
583C22⋊Dic17—21no—
584C22⋊Dic17—21no—
585C22⋊Dic17C2×D411yescharacteristic
586C22⋊Dic17C2×D411yescharacteristic
587#63231—22no—
588#63231—22no—
589#63227—21no—
590#63227—21no—
591#63227—21no—
592#63227—21no—
593#63227—21no—
594#63227—21no—
595#63227—21no—
596#63227—21no—
597#63227—21no—
598#63227—21no—
599#63227C2×D411yescharacteristic
600#63227C2×D411yescharacteristic
601#63227C2×D411yescharacteristic
602#63227C2×D411yescharacteristic
603C4⋊Dic17—21no—
604C4⋊Dic17—21no—
605C4⋊Dic17—21no—
606C4⋊Dic17—21no—
607C4⋊Dic17—21no—
608C4⋊Dic17—21no—
609C4⋊Dic17—21no—
610C4⋊Dic17—21no—
611C4⋊Dic17—21no—
612C4⋊Dic17—21no—
613C4⋊Dic17—21no—
614C4⋊Dic17—21no—
615C4⋊Dic17C2×D411yescharacteristic
616C4⋊Dic17C2411yescharacteristic
617C4⋊Dic17C2411yescharacteristic
618C4⋊Dic17C2411yescharacteristic
619C4⋊Dic17C2411yescharacteristic
620C4⋊Dic17C2411yescharacteristic
621C4⋊Dic17C2411yescharacteristic
622#63225—21no—
623#63225—21no—
624#63225—21no—
625#63225—21no—
626#63225—21no—
627#63225—21no—
628#63225—21no—
629#63225—21no—
630#63225—21no—
631#63225—21no—
632#63225—21no—
633#63225—21no—
634#63225—21no—
635#63225—21no—
636#63225—21no—
637#63225—21no—
638#63225—21no—
639#63225—21no—
640#63225—21no—
641#63225—21no—
642#63225—21no—
643#63225—21no—
644#63225—21no—
645#63225—21no—
646#63225—21no—
647#63225—21no—
648#63225—21no—
649#63225—21no—
650#63225—21no—
651#63225—21no—
652#63225C2×D411yescharacteristic
653#63225C2×D411yescharacteristic
654C4×Dic17—21no—
655C4×Dic17—21no—
656C4×Dic17—21no—
657C4×Dic17—21no—
658C4×Dic17—21no—
659C4×Dic17—21no—
660C4×Dic17—21no—
661C4×Dic17—21no—
662C4×Dic17—21no—
663C4×Dic17C2×D411yescharacteristic
664C4×Dic17C2×D411yescharacteristic
665C4×Dic17C2411yescharacteristic
666#63223—22no—
667C2×#3622—22no—
668C2×#3622C2411yescharacteristic
669C2×#3622C2411yescharacteristic
670C2×#3622C2411yescharacteristic
671C2×#3622C2411yescharacteristic
672Dic68—22no—
673#63218—22no—
674#63218—22no—
675C8×D17—22no—
676C8×D17—22no—
677C8×D17—22no—
678C8×D17—22no—
679C8×D17—22no—
680C8×D17#4114yes—
681C2×#3344—171nomaximal, Sylow
682C23×C17C22×D411yescharacteristic
683C23×C17C22×D411yescharacteristic
684C22×D17—22no—
685C22×D17—22no—
686C22×D17—22no—
687C22×D17—22no—
688C22×D17—22no—
689C22×D17#13714yes—
690C22×D17C22×D411yescharacteristic
691C22×D17C22×D411yescharacteristic
692C22×D17C22×D411yescharacteristic
693Q8×C17—21no—
694Q8×C17—21no—
695Q8×C17—21no—
696Q8×C17—21no—
697Q8×C17—81no—
698D4×C17—22no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—21no—
705C2×C4×C17—21no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—42no—
712C2×C4×C17—81no—
713C2×C4×C17—81no—
714C2×C4×C17C22×D411yescharacteristic
715C2×C4×C17C22×D411yescharacteristic
716C2×C4×C17C22×D411yescharacteristic
717C2×C4×C17C22×D411yescharacteristic
718C2×C4×C17C2511yescharacteristic
719C22⋊D17—22no—
720C22⋊D17—22no—
721C2×Dic17—22no—
722C2×Dic17—22no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—42no—
732C2×Dic17—81no—
733C2×Dic17—81no—
734C2×Dic17C22×D411yescharacteristic
735C2×Dic17C22×D411yescharacteristic
736C2×Dic17C22×D411yescharacteristic
737C2×Dic17C22×D411yescharacteristic
738C2×Dic17C22×D411yescharacteristic
739D68—22no—
740C4×D17—22no—
741C4×D17—22no—
742C4×D17—22no—
743C4×D17—22no—
744C4×D17—21no—
745C4×D17—21no—
746C4×D17—21no—
747C4×D17—21no—
748C4×D17—22no—
749C4×D17—22no—
750C4×D17—42no—
751C4×D17—42no—
752C4×D17—42no—
753C4×D17—42no—
754C4×D17—42no—
755C4×D17—42no—
756C4×D17—42no—
757C4×D17—42no—
758C4×D17—42no—
759C4×D17—42no—
760C4×D17—81no—
761C4×D17—81no—
762C4×D17—81no—
763C4×D17—81no—
764C4×D17C2×#4112yes—
765C4×D172−1+412yes—
766Dic34—21no—
767Dic34—21no—
768Dic34—21no—
769Dic34—21no—
770Dic34—42no—
771Dic34—42no—
772Dic34—81no—
773Dic34—81no—
774Dic34—81no—
775C8×C17—21no—
776C8×C17—21no—
777C8×C17—21no—
778C8×C17C2×#4112yes—
779#3622—21no—
780#3622—21no—
781#3622—21no—
782#3622C2×#4112yes—
783C2×#554—171no—
784C2×#552—171no—
785#3344—171no—
786#3344—171no—
787#3344—171no—
788#3344—171no—
789#3344—171no—
790#3344—171no—
791#3344—171no—
792#3344—171no—
793#3344—171no—
794#3344—171no—
795#3344—171no—
796#3344—171no—
797#3344—171no—
798#3344—171no—
799#3344—171no—
800#3344D1711yescharacteristic, direct product factor
801C2×#501—171no—
802C2×#484—171no—
803C2×#485—171no—
804C2×#483—171no—
805C2×#483—171no—
806C2×#479—171no—
807C2×#475—171no—
808C2×#470—171no—
809C2×#467—171no—
810C2×#441—171no—
811C2×#435—171no—
812C2×#428—171no—
813C22×#106—171no—
814C22×C17—21no—
815C22×C17—21no—
816C22×C17—21no—
817C22×C17—21no—
818C22×C17—21no—
819C22×C17C2×#13712yes—
820C22×C17C23×D411yescharacteristic
821C2×D17—21no—
822C2×D17—21no—
823C2×D17—28no—
824C2×D17—21no—
825C2×D17—21no—
826C2×D17—21no—
827C2×D17—44no—
828C2×D17#54712yes—
829C2×D17C2×#13712yes—
830C2×D17C2×#13712yes—
831C2×D17#57712yes—
832C4×C17—21no—
833C4×C17—21no—
834C4×C17—21no—
835C4×C17—21no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17C22×#4111yescharacteristic
845C4×C17C2×2−1+411yescharacteristic
846Dic17—21no—
847Dic17—21no—
848Dic17—21no—
849Dic17—21no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856Dic17—41no—
857Dic17—41no—
858Dic17#54712yes—
859C22×Q16—171no—
860C22×M16—171no—
861C23×C8—171no—
862#554—171no—
863#554—171no—
864#554—171no—
865#554—171no—
866#554—171no—
867#554—171no—
868#554—171no—
869#554—341no—
870#554—341no—
871#554—341no—
872#554—341no—
873#554C2×D1711yescharacteristic
874#552—171no—
875#552—171no—
876#552—171no—
877#552—171no—
878#552—171no—
879#552—171no—
880#552—171no—
881#552—341no—
882#552—341no—
883#552—341no—
884#552—341no—
885#552C2×D1711yescharacteristic
886C2×C4⋊Q8—171no—
887C2×#126—341no—
888C2×#125—171no—
889C2×#125—341no—
890C2×#125—341no—
891C2×#123—341no—
892C2×C22⋊Q8—171no—
893C2×C22⋊Q8—171no—
894C2×C22⋊Q8—171no—
895C2×C22⋊Q8—171no—
896C2×C22⋊Q8—341no—
897C2×C22⋊Q8—341no—
898C2×C4×Q8—171no—
899C2×C4×Q8—171no—
900C2×C4×D4—171no—
901C2×C4×D4—341no—
902C2×#117—171no—
903C2×#117—341no—
904C22×C4⋊C4—171no—
905C22×C4⋊C4—171no—
906C22×C4⋊C4—171no—
907#501—171no—
908#501—171no—
909#501—171no—
910#501—171no—
911#501—171no—
912#501—171no—
913#501—171no—
914#501C2×D1711yescharacteristic, complemented
915#485—171no—
916#485—171no—
917#485—171no—
918#485—171no—
919#485—171no—
920#485—171no—
921#485—171no—
922#485C2×D1711yescharacteristic, complemented
923#484—171no—
924#484—171no—
925#484—171no—
926#484—171no—
927#484—171no—
928#484—171no—
929#484—171no—
930#484C2×D1711yescharacteristic, complemented
931#483—171no—
932#483—171no—
933#483—171no—
934#483—171no—
935#483—171no—
936#483—171no—
937#483—171no—
938#483—171no—
939#483—171no—
940#483—171no—
941#483—171no—
942#483—171no—
943#483—171no—
944#483—171no—
945#483C2×D1711yescharacteristic, complemented
946#483C2×D1711yescharacteristic, complemented
947#479—171no—
948#479—171no—
949#479—171no—
950#479—171no—
951#479—171no—
952#479—171no—
953#479—171no—
954#479C2×D1711yescharacteristic, complemented
955#475—171no—
956#475—171no—
957#475—171no—
958#475—171no—
959#475—171no—
960#475—171no—
961#475—171no—
962#475C2×D1711yescharacteristic, complemented
963#470—171no—
964#470—171no—
965#470—171no—
966#470—171no—
967#470—171no—
968#470—171no—
969#470—171no—
970#470C2×D1711yescharacteristic, complemented
971#467—171no—
972#467—171no—
973#467—171no—
974#467—171no—
975#467—171no—
976#467—171no—
977#467—171no—
978#467C2×D1711yescharacteristic, complemented
979#441—171no—
980#441—171no—
981#441—171no—
982#441—171no—
983#441—171no—
984#441—171no—
985#441—171no—
986#441C2×D1711yescharacteristic, complemented
987#435—171no—
988#435—171no—
989#435—171no—
990#435—171no—
991#435—171no—
992#435—171no—
993#435—171no—
994#435C2×D1711yescharacteristic
995#428—171no—
996#428—171no—
997#428—171no—
998#428—171no—
999#428—171no—
1000#428—171no—
1001#428—171no—
1002#428C2×D1711yescharacteristic, complemented
1003C2×#107—171no—
1004C2×#107—171no—
1005C2×#107—171no—
1006C2×#106—171no—
1007C2×#106—171no—
1008C2×#106—171no—
1009C2×#106—171no—
1010C2×#106—171no—
1011C2×#106—171no—
1012C2×#106—171no—
1013C2×#106—171no—
1014C2×#106—171no—
1015C2×#106—171no—
1016C2×#106—171no—
1017C2×#106—171no—
1018C2×#106—171no—
1019C2×#106C2×D1711yescharacteristic, complemented
1020C2×C4⋊C8—171no—
1021C2×#103—171no—
1022C2×#103—171no—
1023C2×#103—171no—
1024C2×#103—171no—
1025C2×#103—171no—
1026C2×#103—171no—
1027C2×C22⋊C8—171no—
1028C2×C22⋊C8—171no—
1029C2×#97—171no—
1030C2×C17—22no—
1031C2×C17—41no—
1032C2×C17C2×#54711yescharacteristic
1033C2×C17C22×#13711yescharacteristic
1034C2×C17C2×#57711yescharacteristic
1035D17—22no—
1036D17—41no—
1037D17#334414yesdirect product factor
1038C22×Q8—171no—
1039C22×Q8—171no—
1040C22×Q8—341no—
1041C22×D4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—341no—
1045C23×C4—341no—
1046C23×C4—341no—
1047C2×Q16—171no—
1048C2×Q16—171no—
1049C2×Q16—171no—
1050C2×Q16—344no—
1051C2×Q16C22×D1711yescharacteristic
1052C2×M16—171no—
1053C2×M16—171no—
1054C2×M16—171no—
1055C2×M16—344no—
1056C2×M16C22×D1711yescharacteristic
1057C22×C8—171no—
1058C22×C8—171no—
1059C22×C8—171no—
1060C22×C8—171no—
1061C22×C8—171no—
1062C22×C8—171no—
1063C22×C8—171no—
1064C22×C8—344no—
1065C22×C8C22×D1711yescharacteristic
1066C4⋊Q8—171no—
1067C4⋊Q8—171no—
1068C4⋊Q8—171no—
1069C4⋊Q8—341no—
1070C4⋊Q8—341no—
1071C4⋊Q8C22×D1711yescharacteristic
1072#126—21no—
1073#126—341no—
1074#126—341no—
1075#126—341no—
1076#126—341no—
1077#126—341no—
1078#126—341no—
1079#126—341no—
1080#125—21no—
1081#125—21no—
1082#125—171no—
1083#125—171no—
1084#125—171no—
1085#125—341no—
1086#125—341no—
1087#125—341no—
1088#125—341no—
1089#125—341no—
1090#125—341no—
1091#125—341no—
1092#125—341no—
1093#125—341no—
1094#125—341no—
1095#125—341no—
1096#125—341no—
1097#125—341no—
1098#125—341no—
1099#125—341no—
1100#125—341no—
1101#125C22×D1711yescharacteristic
1102#123—21no—
1103#123—341no—
1104#123—341no—
1105#123—341no—
1106#123—341no—
1107#123—341no—
1108#123—341no—
1109#123—341no—
1110C22⋊Q8—21no—
1111C22⋊Q8—21no—
1112C22⋊Q8—171no—
1113C22⋊Q8—171no—
1114C22⋊Q8—171no—
1115C22⋊Q8—171no—
1116C22⋊Q8—171no—
1117C22⋊Q8—171no—
1118C22⋊Q8—171no—
1119C22⋊Q8—171no—
1120C22⋊Q8—171no—
1121C22⋊Q8—171no—
1122C22⋊Q8—171no—
1123C22⋊Q8—171no—
1124C22⋊Q8—341no—
1125C22⋊Q8—341no—
1126C22⋊Q8—341no—
1127C22⋊Q8—341no—
1128C22⋊Q8—341no—
1129C22⋊Q8—341no—
1130C22⋊Q8—341no—
1131C22⋊Q8—341no—
1132C22⋊Q8—341no—
1133C22⋊Q8—341no—
1134C22⋊Q8—341no—
1135C22⋊Q8—341no—
1136C22⋊Q8—341no—
1137C22⋊Q8—341no—
1138C22⋊Q8—341no—
1139C22⋊Q8—341no—
1140C22⋊Q8—341no—
1141C22⋊Q8—341no—
1142C22⋊Q8—341no—
1143C22⋊Q8—341no—
1144C22⋊Q8—341no—
1145C22⋊Q8—341no—
1146C22⋊Q8C22×D1711yescharacteristic
1147C22⋊Q8C22×D1711yescharacteristic
1148C22⋊Q8C22×D1711yescharacteristic
1149C22⋊Q8C22×D1711yescharacteristic
1150C4×Q8—171no—
1151C4×Q8—171no—
1152C4×Q8—171no—
1153C4×Q8—171no—
1154C4×Q8—171no—
1155C4×Q8—171no—
1156C4×Q8—341no—
1157C4×Q8—341no—
1158C4×Q8—341no—
1159C4×Q8—341no—
1160C4×Q8C22×D1711yescharacteristic
1161C4×Q8C22×D1711yescharacteristic
1162C4×D4—21no—
1163C4×D4—171no—
1164C4×D4—171no—
1165C4×D4—171no—
1166C4×D4—171no—
1167C4×D4—171no—
1168C4×D4—171no—
1169C4×D4—171no—
1170C4×D4—341no—
1171C4×D4—341no—
1172C4×D4—341no—
1173C4×D4—341no—
1174C4×D4—341no—
1175C4×D4—341no—
1176C4×D4—341no—
1177C4×D4C22×D1711yescharacteristic
1178#117—21no—
1179#117—171no—
1180#117—171no—
1181#117—171no—
1182#117—341no—
1183#117—341no—
1184#117—341no—
1185#117—341no—
1186#117—341no—
1187#117—341no—
1188#117—341no—
1189#117—341no—
1190#117—341no—
1191#117C22×D1711yescharacteristic
1192C2×C4⋊C4—171no—
1193C2×C4⋊C4—171no—
1194C2×C4⋊C4—171no—
1195C2×C4⋊C4—171no—
1196C2×C4⋊C4—171no—
1197C2×C4⋊C4—171no—
1198C2×C4⋊C4—171no—
1199C2×C4⋊C4—171no—
1200C2×C4⋊C4—171no—
1201C2×C4⋊C4—171no—
1202C2×C4⋊C4—171no—
1203C2×C4⋊C4—171no—
1204C2×C4⋊C4—171no—
1205C2×C4⋊C4—171no—
1206C2×C4⋊C4—171no—
1207C2×C4⋊C4—171no—
1208C2×C4⋊C4—341no—
1209C2×C4⋊C4—341no—
1210C2×C4⋊C4—341no—
1211C2×C4⋊C4—341no—
1212C2×C4⋊C4—341no—
1213C2×C4⋊C4—341no—
1214C2×C4⋊C4—341no—
1215C2×C4⋊C4—341no—
1216C2×C4⋊C4—341no—
1217C2×C4⋊C4—341no—
1218C2×C4⋊C4—341no—
1219C2×C4⋊C4—341no—
1220C2×C4⋊C4—341no—
1221C2×C4⋊C4—341no—
1222C2×C4⋊C4—341no—
1223C2×C4⋊C4—341no—
1224C2×C4⋊C4—341no—
1225C2×C4⋊C4—341no—
1226C2×C4⋊C4C22×D1711yescharacteristic
1227C2×C4⋊C4C22×D1711yescharacteristic
1228C2×C4⋊C4C22×D1711yescharacteristic
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—341no—
1232C2×C22⋊C4—341no—
1233C2×C22⋊C4—341no—
1234C2×C22⋊C4—341no—
1235C2×C22⋊C4—341no—
1236C2×C42—171no—
1237C2×C42—341no—
1238C2×C42—341no—
1239C2×C42—341no—
1240#107—171no—
1241#107—171no—
1242#107—171no—
1243#107—171no—
1244#107—171no—
1245#107—171no—
1246#107—171no—
1247#107—171no—
1248#107—171no—
1249#107C22×D1711yescharacteristic
1250#107C22×D1711yescharacteristic
1251#107C22×D1711yescharacteristic
1252#106—171no—
1253#106—171no—
1254#106—171no—
1255#106—171no—
1256#106—171no—
1257#106—171no—
1258#106—171no—
1259#106—171no—
1260#106—171no—
1261#106—171no—
1262#106—171no—
1263#106—171no—
1264#106—171no—
1265#106—171no—
1266#106—171no—
1267#106—171no—
1268#106—171no—
1269#106—171no—
1270#106C22×D1711yescharacteristic
1271#106C22×D1711yescharacteristic
1272#106C22×D1711yescharacteristic
1273#106C22×D1711yescharacteristic
1274#106C22×D1711yescharacteristic
1275#106C22×D1711yescharacteristic
1276C4⋊C8—171no—
1277C4⋊C8—171no—
1278C4⋊C8—171no—
1279C4⋊C8C22×D1711yescharacteristic
1280#103—171no—
1281#103—171no—
1282#103—171no—
1283#103—171no—
1284#103—171no—
1285#103—171no—
1286#103—171no—
1287#103—171no—
1288#103—171no—
1289#103—171no—
1290#103—171no—
1291#103—171no—
1292#103—171no—
1293#103—171no—
1294#103—171no—
1295#103—171no—
1296#103—171no—
1297#103—171no—
1298#103C22×D1711yescharacteristic
1299#103C22×D1711yescharacteristic
1300#103C22×D1711yescharacteristic
1301#103C22×D1711yescharacteristic
1302#103C22×D1711yescharacteristic
1303#103C22×D1711yescharacteristic
1304C22⋊C8—171no—
1305C22⋊C8—171no—
1306C22⋊C8—171no—
1307C22⋊C8—171no—
1308C22⋊C8—171no—
1309C22⋊C8—171no—
1310C22⋊C8C22×D1711yescharacteristic
1311C22⋊C8C22×D1711yescharacteristic
1312#97—171no—
1313#97—171no—
1314#97—171no—
1315#97C22×D1711yescharacteristic
1316C17C2×#334411yescharacteristic, complemented, Sylow
1317C24—171no—
1318C24—171no—
1319C2×Q8—21no—
1320C2×Q8—171no—
1321C2×Q8—171no—
1322C2×Q8—341no—
1323C2×Q8—341no—
1324C2×Q8—341no—
1325C2×Q8—341no—
1326C2×Q8—342no—
1327C2×Q8—342no—
1328C2×Q8—342no—
1329C2×Q8—342no—
1330C2×Q8—341no—
1331C2×Q8—1362no—
1332C2×Q8C23×D1711yescharacteristic
1333C2×Q8C23×D1711yescharacteristic
1334C2×D4—171no—
1335C2×D4—171no—
1336C2×D4—171no—
1337C2×D4—344no—
1338C2×D4D4×D1711yescharacteristic
1339C22×C4—21no—
1340C22×C4—21no—
1341C22×C4—21no—
1342C22×C4—171no—
1343C22×C4—171no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—171no—
1349C22×C4—171no—
1350C22×C4—171no—
1351C22×C4—171no—
1352C22×C4—171no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—341no—
1358C22×C4—341no—
1359C22×C4—341no—
1360C22×C4—341no—
1361C22×C4—341no—
1362C22×C4—341no—
1363C22×C4—341no—
1364C22×C4—341no—
1365C22×C4—341no—
1366C22×C4—341no—
1367C22×C4—341no—
1368C22×C4—341no—
1369C22×C4—341no—
1370C22×C4—341no—
1371C22×C4—341no—
1372C22×C4—341no—
1373C22×C4—341no—
1374C22×C4—684no—
1375C22×C4—1362no—
1376C22×C4—1362no—
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379Q16—22no—
1380Q16—342no—
1381Q16—342no—
1382Q16—342no—
1383M16—22no—
1384M16—342no—
1385M16—342no—
1386M16—342no—
1387C2×C8—22no—
1388C2×C8—171no—
1389C2×C8—174no—
1390C2×C8—171no—
1391C2×C8—171no—
1392C2×C8—171no—
1393C2×C8—342no—
1394C2×C8—342no—
1395C2×C8—342no—
1396C2×C8—342no—
1397C2×C8—342no—
1398C2×C8—342no—
1399C2×C8C23×D1711yescharacteristic
1400C2×C8C23×D1711yescharacteristic
1401C2×C8C23×D1711yescharacteristic
1402C2×C8C23×D1711yescharacteristic
1403C4⋊C4—21no—
1404C4⋊C4—21no—
1405C4⋊C4—21no—
1406C4⋊C4—21no—
1407C4⋊C4—21no—
1408C4⋊C4—21no—
1409C4⋊C4—21no—
1410C4⋊C4—21no—
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—171no—
1416C4⋊C4—171no—
1417C4⋊C4—171no—
1418C4⋊C4—171no—
1419C4⋊C4—171no—
1420C4⋊C4—171no—
1421C4⋊C4—171no—
1422C4⋊C4—171no—
1423C4⋊C4—171no—
1424C4⋊C4—341no—
1425C4⋊C4—341no—
1426C4⋊C4—341no—
1427C4⋊C4—341no—
1428C4⋊C4—341no—
1429C4⋊C4—341no—
1430C4⋊C4—341no—
1431C4⋊C4—341no—
1432C4⋊C4—341no—
1433C4⋊C4—341no—
1434C4⋊C4—341no—
1435C4⋊C4—341no—
1436C4⋊C4—341no—
1437C4⋊C4—341no—
1438C4⋊C4—341no—
1439C4⋊C4—341no—
1440C4⋊C4—341no—
1441C4⋊C4—341no—
1442C4⋊C4—341no—
1443C4⋊C4—341no—
1444C4⋊C4—341no—
1445C4⋊C4—341no—
1446C4⋊C4—341no—
1447C4⋊C4—341no—
1448C4⋊C4—341no—
1449C4⋊C4—341no—
1450C4⋊C4—341no—
1451C4⋊C4—341no—
1452C4⋊C4—341no—
1453C4⋊C4—341no—
1454C4⋊C4—341no—
1455C4⋊C4—341no—
1456C4⋊C4—341no—
1457C4⋊C4—341no—
1458C4⋊C4—341no—
1459C4⋊C4—341no—
1460C4⋊C4—341no—
1461C4⋊C4—341no—
1462C4⋊C4—341no—
1463C4⋊C4—341no—
1464C4⋊C4—341no—
1465C4⋊C4—341no—
1466C4⋊C4D4×D1711yescharacteristic
1467C4⋊C4C23×D1711yescharacteristic
1468C4⋊C4C23×D1711yescharacteristic
1469C4⋊C4C23×D1711yescharacteristic
1470C4⋊C4C23×D1711yescharacteristic
1471C4⋊C4C23×D1711yescharacteristic
1472C4⋊C4C23×D1711yescharacteristic
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—171no—
1479C22⋊C4—171no—
1480C22⋊C4—171no—
1481C22⋊C4—171no—
1482C22⋊C4—171no—
1483C22⋊C4—171no—
1484C22⋊C4—341no—
1485C22⋊C4—341no—
1486C22⋊C4—341no—
1487C22⋊C4—341no—
1488C22⋊C4—341no—
1489C22⋊C4—341no—
1490C22⋊C4—341no—
1491C22⋊C4—341no—
1492C22⋊C4—341no—
1493C22⋊C4—341no—
1494C22⋊C4—341no—
1495C22⋊C4—341no—
1496C22⋊C4—341no—
1497C22⋊C4—341no—
1498C22⋊C4—341no—
1499C22⋊C4D4×D1711yescharacteristic
1500C22⋊C4D4×D1711yescharacteristic
1501C42—21no—
1502C42—21no—
1503C42—21no—
1504C42—171no—
1505C42—171no—
1506C42—171no—
1507C42—341no—
1508C42—341no—
1509C42—341no—
1510C42—341no—
1511C42—341no—
1512C42—341no—
1513C42—341no—
1514C42—341no—
1515C42—341no—
1516C42C23×D1711yescharacteristic
1517C23—171no—
1518C23—174no—
1519C23—171no—
1520C23—171no—
1521C23—342no—
1522C23—342no—
1523C23—342no—
1524C23—342no—
1525C23—342no—
1526C23C2×D4×D1711yescharacteristic
1527C23C2×D4×D1711yescharacteristic
1528Q8—21no—
1529Q8—21no—
1530Q8—21no—
1531Q8—21no—
1532Q8—81no—
1533Q8—341no—
1534Q8—341no—
1535Q8—341no—
1536Q8—341no—
1537Q8—682no—
1538Q8—682no—
1539Q8—1361no—
1540Q8—1361no—
1541Q8—1361no—
1542D4—22no—
1543D4—342no—
1544D4—342no—
1545D4—342no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—42no—
1559C2×C4—81no—
1560C2×C4—81no—
1561C2×C4—171no—
1562C2×C4—172no—
1563C2×C4—172no—
1564C2×C4—171no—
1565C2×C4—171no—
1566C2×C4—171no—
1567C2×C4—171no—
1568C2×C4—342no—
1569C2×C4—342no—
1570C2×C4—342no—
1571C2×C4—342no—
1572C2×C4—342no—
1573C2×C4—342no—
1574C2×C4—342no—
1575C2×C4—342no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—682no—
1589C2×C4—682no—
1590C2×C4—682no—
1591C2×C4—682no—
1592C2×C4—682no—
1593C2×C4—682no—
1594C2×C4—682no—
1595C2×C4—682no—
1596C2×C4—682no—
1597C2×C4—682no—
1598C2×C4—682no—
1599C2×C4—1361no—
1600C2×C4—1361no—
1601C2×C4—1361no—
1602C2×C4—1361no—
1603C2×C4—1361no—
1604C2×C4—1361no—
1605C2×C4C2×D4×D1711yescharacteristic
1606C2×C4C2×D4×D1711yescharacteristic
1607C2×C4C2×D4×D1711yescharacteristic
1608C2×C4C2×D4×D1711yescharacteristic
1609C2×C4C24×D1711yescharacteristic
1610C8—21no—
1611C8—21no—
1612C8—21no—
1613C8—172no—
1614C8—341no—
1615C8—341no—
1616C8—341no—
1617C8#41×D1712yes—
1618C22—21no—
1619C22—21no—
1620C22—21no—
1621C22—21no—
1622C22—21no—
1623C22—172no—
1624C22—172no—
1625C22—172no—
1626C22—172no—
1627C22—348no—
1628C22—341no—
1629C22—341no—
1630C22—341no—
1631C22—341no—
1632C22—341no—
1633C22—684no—
1634C22#137×D1712yes—
1635C22C22×D4×D1711yescharacteristic
1636C4—21no—
1637C4—21no—
1638C4—21no—
1639C4—21no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—172no—
1649C4—341no—
1650C4—341no—
1651C4—341no—
1652C4—341no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4C2×#41×D1711yescharacteristic
1662C42−1+4×D1711yescharacteristic
1663C2—22no—
1664C2—41no—
1665C2—174no—
1666C2—342no—
1667C2—681no—
1668C2D17×#54711yescharacteristic
1669C2C2×#137×D1711yescharacteristic
1670C2D17×#57711yescharacteristic
subgroupG/H
centerC22C22×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#3344C2
socleC22×C17C23×D4
prime radicalC2×D4×D17D4
hypercenter#3344D17
hypocenterC17C2×#3344
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3344

Complements

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

NH ≅ G/Ntype
3. #14541246C2semidirect
4. #14541245C2semidirect
5. #14541244C2semidirect
6. #14541243C2semidirect
7. #14541242C2semidirect
8. #14541241C2semidirect
9. #14541240C2semidirect
10. #14541239C2semidirect
11. #14541238C2semidirect
12. #14541237C2semidirect
13. #14541236C2semidirect
14. #14541235C2semidirect
15. #14541234C2semidirect
16. #14541233C2semidirect
17. #14541232C2semidirect
18. D17×#501C2semidirect
19. D17×#484C2semidirect
20. D17×#485C2semidirect
21. D17×#483C2semidirect
22. D17×#483C2semidirect
23. D17×#479C2semidirect
24. D17×#475C2semidirect
25. D17×#470C2semidirect
26. D17×#467C2semidirect
27. D17×#441C2semidirect
29. D17×#428C2semidirect
30. C2×#106×D17C2semidirect
31. C17×#3344C2semidirect
78. #11763219C22semidirect
79. #11763218C22semidirect
80. #11763217C22semidirect
81. #11763217C22semidirect
82. #11763216C22semidirect
83. #11763216C22semidirect
84. #11763215C22semidirect
85. #11763153C22semidirect
86. #11763152C22semidirect
87. #11763151C22semidirect
88. #11763150C22semidirect
89. #11763149C22semidirect
90. #11763148C22semidirect
91. #11763147C22semidirect
92. #11763146C22semidirect
93. #11763146C22semidirect
94. #11763145C22semidirect
95. #11763144C22semidirect
96. #11763143C22semidirect
97. #11763143C22semidirect
98. #11763142C22semidirect
99. #11763141C22semidirect
100. #11763141C22semidirect
101. #11763141C22semidirect
102. #11763141C22semidirect
103. #11763140C22semidirect
104. #11763140C22semidirect
105. #11763139C22semidirect
106. #11763139C22semidirect
107. #11763138C22semidirect
108. #11763138C22semidirect
109. #11763138C22semidirect
110. #11763138C22semidirect
111. #11763137C22semidirect
112. #11763137C22semidirect
113. #11763119C22semidirect
114. #11763118C22semidirect
115. #11763117C22semidirect
116. #11763116C22semidirect
117. #11763115C22semidirect
118. #11763114C22semidirect
119. #11763113C22semidirect
120. #11763095C22semidirect
121. #11763094C22semidirect
122. #11763093C22semidirect
123. #11763093C22semidirect
124. #11763092C22semidirect
125. #11763092C22semidirect
126. #11763091C22semidirect
127. #11763068C22semidirect
128. #11763067C22semidirect
129. #11763066C22semidirect
130. #11763066C22semidirect
131. #11763065C22semidirect
132. #11763065C22semidirect
133. #11763064C22semidirect
134. #11763051C22semidirect
135. #11763050C22semidirect
136. #11763049C22semidirect
137. #11763049C22semidirect
138. #11763048C22semidirect
139. #11763048C22semidirect
140. #11763047C22semidirect
141. #11762917C22semidirect
142. #11762916C22semidirect
143. #11762915C22semidirect
144. #11762914C22semidirect
145. #11762914C22semidirect
146. #11762913C22semidirect
147. #11762913C22semidirect
155. #11762852C22semidirect
156. #11762851C22semidirect
157. #11762850C22semidirect
158. #11762850C22semidirect
159. #11762849C22semidirect
160. #11762848C22semidirect
161. #11762848C22semidirect
165. C2×#10587488C22semidirect
166. C2×#10587479C22semidirect
167. C2×#10587479C22semidirect
174. #106×D17C22semidirect
175. #106×D17C22semidirect
176. #106×D17C22semidirect
177. #106×D17C22semidirect
190. C17×#501C22semidirect
191. C17×#485C22semidirect
192. C17×#484C22semidirect
193. C17×#483C22semidirect
194. C17×#483C22semidirect
195. C17×#479C22semidirect
196. C17×#475C22semidirect
197. C17×#470C22semidirect
198. C17×#467C22semidirect
199. C17×#441C22semidirect
201. C17×#428C22semidirect
202. C2×C17×#106C22semidirect
800. #3344D17direct (N × H)
914. #501C2×D17semidirect
922. #485C2×D17semidirect
930. #484C2×D17semidirect
945. #483C2×D17semidirect
946. #483C2×D17semidirect
954. #479C2×D17semidirect
962. #475C2×D17semidirect
970. #470C2×D17semidirect
978. #467C2×D17semidirect
986. #441C2×D17semidirect
1002. #428C2×D17semidirect
1019. C2×#106C2×D17semidirect
1037. D17#3344direct (N × H)
1316. C17C2×#3344semidirect

Maximal subgroups

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

subgroupindex
D17×#5542
D17×#5522
#145412462
#145412452
#145412442
#145412432
#145412422
#145412412
#145412402
#145412392
#145412382
#145412372
#145412362
#145412352
#145412342
#145412332
#145412322
D17×#5012
D17×#4842
D17×#4852
D17×#4832
D17×#4792
D17×#4752
D17×#4702
D17×#4672
D17×#4412
D17×#4352
D17×#4282
C2×#106×D172
C17×#33442
C2×#334417