Finite Group Databasebeta

← #62390

Subgroups — #62390

Order 256.

828 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3555C211yesmaximal, characteristic, complemented
2#3554C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3401C211yesmaximal, characteristic, complemented
5#3400C211yesmaximal, characteristic, complemented
6#3397C211yesmaximal, characteristic, complemented
7#3390C211yesmaximal, characteristic, complemented
8#3389C211yesmaximal, characteristic, complemented
9#3386C211yesmaximal, characteristic, complemented
10#3385C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3376C211yesmaximal, characteristic, complemented
13#3375C211yesmaximal, characteristic, complemented
14#3372C211yesmaximal, characteristic, complemented
15#3371C211yesmaximal, characteristic, complemented
16#3370C211yesmaximal, characteristic, complemented
17#3368C211yesmaximal, characteristic, complemented
18#3367C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3260C211yesmaximal, characteristic, complemented
21#3258C211yesmaximal, characteristic, complemented
22#3257C211yesmaximal, characteristic, complemented
23#3256C211yesmaximal, characteristic, complemented
24#3254C211yesmaximal, characteristic, complemented
25#3181C211yesmaximal, characteristic, complemented
26#3180C211yesmaximal, characteristic, complemented
27#3179C211yesmaximal, characteristic, complemented
28#3178C211yesmaximal, characteristic, complemented
29#3175C211yesmaximal, characteristic, complemented
30#3174C211yesmaximal, characteristic, complemented
31#2961C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#562—21no—
35#562—21no—
36#559C2211yescharacteristic
37#559C2211yescharacteristic
38#559C2211yescharacteristic
39Q82C2211yescharacteristic
40#557C2211yescharacteristic
41#557C2211yescharacteristic
42#557C2211yescharacteristic
43#557C2211yescharacteristic
44#556—21no—
45#556C2211yescharacteristic
46#556C2211yescharacteristic
47#556C2211yescharacteristic
48#554C2211yescharacteristic
49#554C2211yescharacteristic
50#554C2211yescharacteristic
51#552—21no—
52#550C2211yescharacteristic
53D4×Q8C2211yescharacteristic
54#548—21no—
55#547—21no—
56#544—21no—
57#542—21no—
58#542C2211yescharacteristic
59#542C2211yescharacteristic
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#541—21no—
63#541—21no—
64#541—21no—
65#541C2211yescharacteristic
66#541C2211yescharacteristic
67#540C2211yescharacteristic
68#540C2211yescharacteristic
69#539—21no—
70#539—21no—
71#536—21no—
72#533C2211yescharacteristic
73#533C2211yescharacteristic
74#532C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#500C2211yescharacteristic
82#499C2211yescharacteristic
83#497C2211yescharacteristic
84#497C2211yescharacteristic
85#496C2211yescharacteristic
86#496C2211yescharacteristic
87#495C2211yescharacteristic
88#492C2211yescharacteristic
89#491C2211yescharacteristic
90#491C2211yescharacteristic
91#490C2211yescharacteristic
92#490C2211yescharacteristic
93#489C2211yescharacteristic
94#489C2211yescharacteristic
95#489C2211yescharacteristic
96#489C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#487C2211yescharacteristic
100#486C2211yescharacteristic
101#479C2211yescharacteristic
102#479C2211yescharacteristic
103#479C2211yescharacteristic
104#479C2211yescharacteristic
105#479C2211yescharacteristic
106#479C2211yescharacteristic
107#478C2211yescharacteristic
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#477C2211yescharacteristic
114#477C2211yescharacteristic
115#477C2211yescharacteristic
116#477C2211yescharacteristic
117#477C2211yescharacteristic
118#476C2211yescharacteristic
119#475C2211yescharacteristic
120#474C2211yescharacteristic
121#474C2211yescharacteristic
122#474C2211yescharacteristic
123#474C2211yescharacteristic
124#474C2211yescharacteristic
125#470C2211yescharacteristic
126#469C2211yescharacteristic
127#468C2211yescharacteristic
128#468C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic
131#468C2211yescharacteristic
132#468C2211yescharacteristic
133#467C2211yescharacteristic
134#467C2211yescharacteristic
135#466C2211yescharacteristic
136#466C2211yescharacteristic
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic
144#464C2211yescharacteristic
145#464C2211yescharacteristic
146#464C2211yescharacteristic
147#463C2211yescharacteristic
148#463C2211yescharacteristic
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#462C2211yescharacteristic
154#461C2211yescharacteristic
155#461C2211yescharacteristic
156#461C2211yescharacteristic
157#461C2211yescharacteristic
158#461C2211yescharacteristic
159#460C2211yescharacteristic
160#460C2211yescharacteristic
161#460C2211yescharacteristic
162#460C2211yescharacteristic
163#460C2211yescharacteristic
164#459C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#446C2211yescharacteristic
168#446C2211yescharacteristic
169#446C2211yescharacteristic
170#446C2211yescharacteristic
171#446C2211yescharacteristic
172#446C2211yescharacteristic
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic
176#441C2211yescharacteristic
177#441C2211yescharacteristic
178#441C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic
182#440C2211yescharacteristic
183#440C2211yescharacteristic
184#440C2211yescharacteristic
185#440C2211yescharacteristic
186#440C2211yescharacteristic
187#440C2211yescharacteristic
188#440C2211yescharacteristic
189C4×Q16C2211yescharacteristic
190C4×Q16C2211yescharacteristic
191C4×SD16C2211yescharacteristic
192C4×SD16C2211yescharacteristic
193C4×SD16C2211yescharacteristic
194C4×SD16C2211yescharacteristic
195C4×D8C2211yescharacteristic
196C4×D8C2211yescharacteristic
197#424C2211yescharacteristic
198#424C2211yescharacteristic
199#423C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic
202C2×#97C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C22×Q8—21no—
206C2×Q16C2311yescharacteristic
207C2×Q16C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D411yescharacteristic
233C4⋊Q8D411yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243#127C2311yescharacteristic
244#127C2311yescharacteristic
245#127C2311yescharacteristic
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#126—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#125—21no—
274#125—21no—
275#125—21no—
276#125D411yescharacteristic
277#125D411yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#125C2311yescharacteristic
282#125C2311yescharacteristic
283#125C2311yescharacteristic
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124—21no—
290#124—21no—
291#124—21no—
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
297#124C2311yescharacteristic
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—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⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8D411yescharacteristic
335C22⋊Q8D411yescharacteristic
336C22⋊Q8D411yescharacteristic
337C22⋊Q8D411yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121C2311yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117C2311yescharacteristic
401#117C2311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C42C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
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#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#97C2311yescharacteristic
467#97C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—82no—
479#41—82no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—82no—
487C2×Q8C2×D411yescharacteristic
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2×D411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4C2411yescharacteristic
506C2×D4C2411yescharacteristic
507C2×D4C2411yescharacteristic
508C2×D4C2411yescharacteristic
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C2×D411yescharacteristic
522C22×C4C2×D411yescharacteristic
523C22×C4C2411yescharacteristic
524Q16—22no—
525Q16—41no—
526Q16—41no—
527SD16—22no—
528SD16—22no—
529SD16—41no—
530SD16—41no—
531SD16—41no—
532SD16—41no—
533SD16—41no—
534SD16—41no—
535SD16—41no—
536SD16—41no—
537D8—22no—
538D8—41no—
539D8—41no—
540M16—41no—
541M16—41no—
542C2×C8—22no—
543C2×C8—41no—
544C2×C8C2411yescharacteristic
545C2×C8C2411yescharacteristic
546C2×C8C2411yescharacteristic
547C2×C8C2411yescharacteristic
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
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⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
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⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42C2×D411yescharacteristic
665C42C2×D411yescharacteristic
666C42C2411yescharacteristic
667C42C2411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23C22×D411yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—42no—
690Q8—81no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694Q8—81no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—42no—
704D4—81no—
705D4—81no—
706D4—81no—
707D4—81no—
708D4—81no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4C22×D411yescharacteristic
742C2×C4C22×D411yescharacteristic
743C2×C4C22×D411yescharacteristic
744C2×C4C22×D411yescharacteristic
745C2×C4C22×D411yescharacteristic
746C2×C4C22×D411yescharacteristic
747C2×C4C22×D411yescharacteristic
748C2×C4C22×D411yescharacteristic
749C2×C4C22×D411yescharacteristic
750C2×C4C22×D411yescharacteristic
751C2×C4C22×D411yescharacteristic
752C2×C4C22×D411yescharacteristic
753C2×C4C22×D411yescharacteristic
754C2×C4C2511yescharacteristic
755C8—21no—
756C8—21no—
757C8—21no—
758C8—21no—
759C8—21no—
760C8—21no—
761C8—21no—
762C82−1+412yes—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22C23×D411yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4C2×2−1+411yescharacteristic
805C4#58511yescharacteristic
806C2—41no—
807C2—81no—
808C2—81no—
809C2—81no—
810C2—81no—
811C2#349711yescharacteristic
812C2#358511yescharacteristic
813C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3555C2semidirect
2. #3554C2semidirect
3. #3401C2semidirect
4. #3401C2semidirect
5. #3400C2semidirect
6. #3397C2semidirect
7. #3390C2semidirect
8. #3389C2semidirect
9. #3386C2semidirect
10. #3385C2semidirect
11. #3377C2semidirect
12. #3376C2semidirect
13. #3375C2semidirect
14. #3372C2semidirect
15. #3371C2semidirect
16. #3370C2semidirect
17. #3368C2semidirect
18. #3367C2semidirect
19. #3262C2semidirect
20. #3260C2semidirect
21. #3258C2semidirect
22. #3257C2semidirect
23. #3256C2semidirect
24. #3254C2semidirect
25. #3181C2semidirect
26. #3180C2semidirect
27. #3179C2semidirect
28. #3178C2semidirect
29. #3175C2semidirect
30. #3174C2semidirect
31. #2961C2semidirect

Maximal subgroups

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

subgroupindex
#35552
#35542
#34012
#34002
#33972
#33902
#33892
#33862
#33852
#33772
#33762
#33752
#33722
#33712
#33702
#33682
#33672
#32622
#32602
#32582
#32572
#32562
#32542
#31812
#31802
#31792
#31782
#31752
#31742
#29612