Finite Group Databasebeta

← #62517

Subgroups — #62517

Order 256.

799 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic
2#3555C211yesmaximal, characteristic, complemented
3#3390C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3387C211yesmaximal, characteristic, complemented
6#3385C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3350C211yesmaximal, characteristic, complemented
9#3349C211yesmaximal, characteristic, complemented
10#3349C211yesmaximal, characteristic, complemented
11#3349C211yesmaximal, characteristic, complemented
12#3348C211yesmaximal, characteristic, complemented
13#3346C211yesmaximal, characteristic, complemented
14#3344C211yesmaximal, characteristic, complemented
15#3342C211yesmaximal, characteristic, complemented
16#3340C211yesmaximal, characteristic, complemented
17#3337C211yesmaximal, characteristic, complemented
18#3336C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3242C211yesmaximal, characteristic, complemented
22#3242C211yesmaximal, characteristic, complemented
23#3233C211yesmaximal, characteristic, complemented
24#3231C211yesmaximal, characteristic, complemented
25#3181C211yesmaximal, characteristic, complemented
26#3178C211yesmaximal, characteristic, complemented
27#3178C211yesmaximal, characteristic, complemented
28#3164C211yesmaximal, characteristic, complemented
29#3163C211yesmaximal, characteristic, complemented
30#3162C211yesmaximal, characteristic, complemented
31#2968C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#563—21no—
35#562—21no—
36Q82C2211yescharacteristic
37#557—21no—
38#557C2211yescharacteristic
39#557C2211yescharacteristic
40#556—21no—
41#556—21no—
42#556C2211yescharacteristic
43#556C2211yescharacteristic
44#556C2211yescharacteristic
45#556C2211yescharacteristic
46#555C2211yescharacteristic
47#554C2211yescharacteristic
48#554C2211yescharacteristic
49#553C2211yescharacteristic
50#553C2211yescharacteristic
51#552—21no—
52#552C2211yescharacteristic
53#552C2211yescharacteristic
54#552C2211yescharacteristic
55#552C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#544C2211yescharacteristic
59#544C2211yescharacteristic
60#542—21no—
61#542—21no—
62#542—21no—
63#542C2211yescharacteristic
64#542C2211yescharacteristic
65#541—21no—
66#541—21no—
67#541—21no—
68#541—21no—
69#541C2211yescharacteristic
70#541C2211yescharacteristic
71#539—21no—
72#533C2211yescharacteristic
73#533C2211yescharacteristic
74#533C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#501C2211yescharacteristic
82#501C2211yescharacteristic
83#501C2211yescharacteristic
84#501C2211yescharacteristic
85#501C2211yescharacteristic
86#501C2211yescharacteristic
87#501C2211yescharacteristic
88#501C2211yescharacteristic
89#501C2211yescharacteristic
90#500C2211yescharacteristic
91#500C2211yescharacteristic
92#499C2211yescharacteristic
93#499C2211yescharacteristic
94#499C2211yescharacteristic
95#499C2211yescharacteristic
96#498C2211yescharacteristic
97#498C2211yescharacteristic
98#497C2211yescharacteristic
99#491C2211yescharacteristic
100#489C2211yescharacteristic
101#488C2211yescharacteristic
102#488C2211yescharacteristic
103#487C2211yescharacteristic
104#487C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#485C2211yescharacteristic
108#485C2211yescharacteristic
109#485C2211yescharacteristic
110#485C2211yescharacteristic
111#485C2211yescharacteristic
112#485C2211yescharacteristic
113#485C2211yescharacteristic
114#485C2211yescharacteristic
115#485C2211yescharacteristic
116#485C2211yescharacteristic
117#484C2211yescharacteristic
118#484C2211yescharacteristic
119#484C2211yescharacteristic
120#483C2211yescharacteristic
121#483C2211yescharacteristic
122#483C2211yescharacteristic
123#482C2211yescharacteristic
124#482C2211yescharacteristic
125#482C2211yescharacteristic
126#482C2211yescharacteristic
127#481C2211yescharacteristic
128#480C2211yescharacteristic
129#479C2211yescharacteristic
130#479C2211yescharacteristic
131#479C2211yescharacteristic
132#479C2211yescharacteristic
133#479C2211yescharacteristic
134#479C2211yescharacteristic
135#479C2211yescharacteristic
136#479C2211yescharacteristic
137#479C2211yescharacteristic
138#479C2211yescharacteristic
139#478C2211yescharacteristic
140#478C2211yescharacteristic
141#477C2211yescharacteristic
142#477C2211yescharacteristic
143#477C2211yescharacteristic
144#477C2211yescharacteristic
145#476C2211yescharacteristic
146#476C2211yescharacteristic
147#475C2211yescharacteristic
148#475C2211yescharacteristic
149#475C2211yescharacteristic
150#475C2211yescharacteristic
151#474C2211yescharacteristic
152#474C2211yescharacteristic
153#470C2211yescharacteristic
154#470C2211yescharacteristic
155#468C2211yescharacteristic
156#468C2211yescharacteristic
157#467C2211yescharacteristic
158#467C2211yescharacteristic
159#467C2211yescharacteristic
160#467C2211yescharacteristic
161#465C2211yescharacteristic
162#465C2211yescharacteristic
163#465C2211yescharacteristic
164#465C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#441C2211yescharacteristic
168#441C2211yescharacteristic
169#441C2211yescharacteristic
170#441C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic
175C4×Q16C2211yescharacteristic
176C4×Q16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×SD16C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic
187#431C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#428C2211yescharacteristic
191#428C2211yescharacteristic
192#427C2211yescharacteristic
193#427C2211yescharacteristic
194#427C2211yescharacteristic
195#427C2211yescharacteristic
196#427C2211yescharacteristic
197#427C2211yescharacteristic
198C2×#107C2211yescharacteristic
199C2×#106C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic
202C2×#97C2211yescharacteristic
203C2×Q16C2311yescharacteristic
204C2×Q16C2311yescharacteristic
205C2×SD16C2311yescharacteristic
206C2×SD16C2311yescharacteristic
207C2×M16C2311yescharacteristic
208C2×M16C2311yescharacteristic
209C22×C8C2311yescharacteristic
210C22×C8C2311yescharacteristic
211C22×C8C2311yescharacteristic
212C22×C8C2311yescharacteristic
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C2311yescharacteristic
223C4⋊Q8C2311yescharacteristic
224C4⋊Q8C2311yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126D411yescharacteristic
254#126D411yescharacteristic
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125D411yescharacteristic
274#125C2311yescharacteristic
275#125C2311yescharacteristic
276#125C2311yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#125C2311yescharacteristic
282#125C2311yescharacteristic
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124—21no—
290#124—21no—
291#124D411yescharacteristic
292#124C2311yescharacteristic
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123D411yescharacteristic
303#123D411yescharacteristic
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8D411yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334#121—21no—
335#121—21no—
336#121—21no—
337#121D411yescharacteristic
338#121C2311yescharacteristic
339#121C2311yescharacteristic
340#121C2311yescharacteristic
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C42C2311yescharacteristic
396#107C2311yescharacteristic
397#107C2311yescharacteristic
398#107C2311yescharacteristic
399#107C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430#106C2311yescharacteristic
431#106C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8C2×D411yescharacteristic
488C2×Q8C2411yescharacteristic
489C2×Q8C2411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D411yescharacteristic
495C2×D4C2×D411yescharacteristic
496C2×D4C2×D411yescharacteristic
497C2×D4C2411yescharacteristic
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4C2×D411yescharacteristic
506C22×C4C2×D411yescharacteristic
507C22×C4C2411yescharacteristic
508C22×C4C2411yescharacteristic
509C22×C4C2411yescharacteristic
510Q16—22no—
511Q16—22no—
512SD16—22no—
513SD16—22no—
514M16—22no—
515M16—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8C2411yescharacteristic
521C2×C8C2411yescharacteristic
522C2×C8C2411yescharacteristic
523C2×C8C2411yescharacteristic
524C2×C8C2411yescharacteristic
525C2×C8C2411yescharacteristic
526C2×C8C2411yescharacteristic
527C2×C8C2411yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4C2×D411yescharacteristic
580C4⋊C4C2×D411yescharacteristic
581C4⋊C4C2×D411yescharacteristic
582C4⋊C4C2×D411yescharacteristic
583C4⋊C4C2×D411yescharacteristic
584C4⋊C4C2×D411yescharacteristic
585C4⋊C4C2×D411yescharacteristic
586C4⋊C4C2×D411yescharacteristic
587C4⋊C4C2×D411yescharacteristic
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2411yescharacteristic
590C4⋊C4C2411yescharacteristic
591C4⋊C4C2411yescharacteristic
592C4⋊C4C2411yescharacteristic
593C4⋊C4C2411yescharacteristic
594C4⋊C4C2411yescharacteristic
595C4⋊C4C2411yescharacteristic
596C4⋊C4C2411yescharacteristic
597C4⋊C4C2411yescharacteristic
598C4⋊C4C2411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4C2×D411yescharacteristic
627C22⋊C4C2×D411yescharacteristic
628C22⋊C4C2×D411yescharacteristic
629C22⋊C4C2×D411yescharacteristic
630C22⋊C4C2×D411yescharacteristic
631C22⋊C4C2×D411yescharacteristic
632C22⋊C4C2×D411yescharacteristic
633C22⋊C4C2×D411yescharacteristic
634C22⋊C4C2×D411yescharacteristic
635C22⋊C4C2×D411yescharacteristic
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42C2×D411yescharacteristic
654C42C2×D411yescharacteristic
655C42C2411yescharacteristic
656C42C2411yescharacteristic
657C42C2411yescharacteristic
658C42C2411yescharacteristic
659C23—21no—
660C23C22×D411yescharacteristic
661C23C22×D411yescharacteristic
662C23C22×D411yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—41no—
670Q8—42no—
671Q8—81no—
672Q8—81no—
673Q8—81no—
674Q8—81no—
675Q8—81no—
676Q8—81no—
677Q8—81no—
678Q8—81no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—81no—
685D4—81no—
686D4—81no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4C22×D411yescharacteristic
718C2×C4C22×D411yescharacteristic
719C2×C4C22×D411yescharacteristic
720C2×C4C22×D411yescharacteristic
721C2×C4C22×D411yescharacteristic
722C2×C4C22×D411yescharacteristic
723C2×C4C22×D411yescharacteristic
724C2×C4C22×D411yescharacteristic
725C2×C4C22×D411yescharacteristic
726C2×C4C22×D411yescharacteristic
727C2×C4C22×D411yescharacteristic
728C2×C4C2511yescharacteristic
729C8—21no—
730C8—21no—
731C8—21no—
732C8—21no—
733C8—21no—
734C8—21no—
735C82−1+412yes—
736C82−1+412yes—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22C23×D411yescharacteristic
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4C2×2−1+411yescharacteristic
777C4C2×2−1+411yescharacteristic
778C2—41no—
779C2—41no—
780C2—41no—
781C2—81no—
782C2#349911yescharacteristic
783C2#358411yescharacteristic
784C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3565C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #3555C2semidirect
3. #3390C2semidirect
4. #3388C2semidirect
5. #3387C2semidirect
6. #3385C2semidirect
7. #3350C2semidirect
8. #3350C2semidirect
9. #3349C2semidirect
10. #3349C2semidirect
11. #3349C2semidirect
12. #3348C2semidirect
13. #3346C2semidirect
14. #3344C2semidirect
15. #3342C2semidirect
16. #3340C2semidirect
17. #3337C2semidirect
18. #3336C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3242C2semidirect
22. #3242C2semidirect
23. #3233C2semidirect
24. #3231C2semidirect
25. #3181C2semidirect
26. #3178C2semidirect
27. #3178C2semidirect
28. #3164C2semidirect
29. #3163C2semidirect
30. #3162C2semidirect
31. #2968C2semidirect

Maximal subgroups

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

subgroupindex
#35652
#35552
#33902
#33882
#33872
#33852
#33502
#33492
#33482
#33462
#33442
#33422
#33402
#33372
#33362
#32442
#32432
#32422
#32332
#32312
#31812
#31782
#31642
#31632
#31622
#29682