Finite Group Databasebeta

← #62161

Subgroups — #62161

Order 256.

823 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3518C211yesmaximal, characteristic, complemented
3#3387C211yesmaximal, characteristic, complemented
4#3385C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3376C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3349C211yesmaximal, characteristic, complemented
9#3348C211yesmaximal, characteristic, complemented
10#3347C211yesmaximal, characteristic, complemented
11#3342C211yesmaximal, characteristic, complemented
12#3340C211yesmaximal, characteristic, complemented
13#3321C211yesmaximal, characteristic, complemented
14#3320C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3312C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3300C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3262C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3243C211yesmaximal, characteristic, complemented
24#3237C211yesmaximal, characteristic, complemented
25#3121C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3082C211yesmaximal, characteristic, complemented
29#3082C211yesmaximal, characteristic, complemented
30#3076C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34Q82C2211yescharacteristic
35#557C2211yescharacteristic
36#556—21no—
37#556—21no—
38#556—21no—
39#556—21no—
40#556C2211yescharacteristic
41#556C2211yescharacteristic
42#556C2211yescharacteristic
43#556C2211yescharacteristic
44#555—21no—
45#555C2211yescharacteristic
46#555C2211yescharacteristic
47#554C2211yescharacteristic
48#553C2211yescharacteristic
49#553C2211yescharacteristic
50#552—21no—
51#552C2211yescharacteristic
52#552C2211yescharacteristic
53D4×Q8C2211yescharacteristic
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#542—21no—
59#542—21no—
60#542—21no—
61#542—21no—
62#542C2211yescharacteristic
63#542C2211yescharacteristic
64#542C2211yescharacteristic
65#542C2211yescharacteristic
66#541—21no—
67#539—21no—
68#533—21no—
69#533C2211yescharacteristic
70#533C2211yescharacteristic
71#529—21no—
72#529C2211yescharacteristic
73#529C2211yescharacteristic
74#519C2211yescharacteristic
75#519C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#500C2211yescharacteristic
82#498C2211yescharacteristic
83#491C2211yescharacteristic
84#491C2211yescharacteristic
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#488C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic
98#484C2211yescharacteristic
99#483C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#481C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic
108#479C2211yescharacteristic
109#479C2211yescharacteristic
110#479C2211yescharacteristic
111#479C2211yescharacteristic
112#479C2211yescharacteristic
113#479C2211yescharacteristic
114#479C2211yescharacteristic
115#479C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#477C2211yescharacteristic
120#477C2211yescharacteristic
121#477C2211yescharacteristic
122#477C2211yescharacteristic
123#477C2211yescharacteristic
124#477C2211yescharacteristic
125#476C2211yescharacteristic
126#476C2211yescharacteristic
127#475C2211yescharacteristic
128#475C2211yescharacteristic
129#475C2211yescharacteristic
130#475C2211yescharacteristic
131#475C2211yescharacteristic
132#475C2211yescharacteristic
133#475C2211yescharacteristic
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic
137#470C2211yescharacteristic
138#469C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic
144#466C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#464C2211yescharacteristic
153#464C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#462C2211yescharacteristic
158#461C2211yescharacteristic
159#452C2211yescharacteristic
160#451C2211yescharacteristic
161#451C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic
164#448C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#442C2211yescharacteristic
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#432C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#427C2211yescharacteristic
191#427C2211yescharacteristic
192#427C2211yescharacteristic
193#427C2211yescharacteristic
194#424C2211yescharacteristic
195#424C2211yescharacteristic
196C2×C4⋊C8C2211yescharacteristic
197#419C2211yescharacteristic
198#419C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic
201C2×#103C2211yescharacteristic
202C2×#103C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C22×Q8C2311yescharacteristic
205C22×Q8C2311yescharacteristic
206C2×Q16C2311yescharacteristic
207C2×Q16C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×D8C2311yescharacteristic
214C2×M16C2311yescharacteristic
215C2×M16C2311yescharacteristic
216C22×C8C2311yescharacteristic
217C22×C8C2311yescharacteristic
218C22×C8C2311yescharacteristic
219C22×C8C2311yescharacteristic
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
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#126D411yescharacteristic
253#126D411yescharacteristic
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125D411yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124D411yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123D411yescharacteristic
294#123D411yescharacteristic
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
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⋊Q8D411yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121D411yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C42—21no—
399C2×C42C2311yescharacteristic
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#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
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#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—22no—
479#41—41no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D411yescharacteristic
505C2×D4C2×D411yescharacteristic
506C2×D4C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
520C22×C4C2×D411yescharacteristic
521C22×C4C2411yescharacteristic
522C22×C4C2411yescharacteristic
523C22×C4C2411yescharacteristic
524Q16—22no—
525Q16—41no—
526Q16—41no—
527SD16—22no—
528SD16—41no—
529SD16—41no—
530SD16—41no—
531D8—41no—
532M16—41no—
533M16—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
540C2×C8C2411yescharacteristic
541C2×C8C2411yescharacteristic
542C2×C8C2411yescharacteristic
543C2×C8C2411yescharacteristic
544C2×C8C2411yescharacteristic
545C2×C8C2411yescharacteristic
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⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4C2×D411yescharacteristic
586C4⋊C4C2×D411yescharacteristic
587C4⋊C4C2×D411yescharacteristic
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2411yescharacteristic
596C4⋊C4C2411yescharacteristic
597C4⋊C4C2411yescharacteristic
598C4⋊C4C2411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
636C22⋊C4C2×D411yescharacteristic
637C22⋊C4C2×D411yescharacteristic
638C22⋊C4C2×D411yescharacteristic
639C22⋊C4C2×D411yescharacteristic
640C22⋊C4C2×D411yescharacteristic
641C22⋊C4C2×D411yescharacteristic
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42C2×D411yescharacteristic
664C42C2×D411yescharacteristic
665C42C2411yescharacteristic
666C42C2411yescharacteristic
667C42C2411yescharacteristic
668C42C2411yescharacteristic
669C23—21no—
670C23—21no—
671C23C22×D411yescharacteristic
672C23C22×D411yescharacteristic
673C23C22×D411yescharacteristic
674Q8—21no—
675Q8—21no—
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—41no—
682Q8—42no—
683Q8—42no—
684Q8—81no—
685Q8—81no—
686Q8—81no—
687Q8—81no—
688Q8—81no—
689Q8—81no—
690Q8—81no—
691Q82−1+412yes—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—42no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
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×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C22×D411yescharacteristic
741C2×C4C22×D411yescharacteristic
742C2×C4C22×D411yescharacteristic
743C2×C4C22×D411yescharacteristic
744C2×C4C22×D411yescharacteristic
745C2×C4C22×D411yescharacteristic
746C2×C4C22×D411yescharacteristic
747C2×C4C22×D411yescharacteristic
748C2×C4C2511yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—21no—
754C8—21no—
755C8—21no—
756C8—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22C23×D411yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4C2×2−1+411yescharacteristic
799C4#58511yescharacteristic
800C2—41no—
801C2—41no—
802C2—41no—
803C2—81no—
804C2—81no—
805C2#348911yescharacteristic
806C2#358411yescharacteristic
807C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
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
1. #3565C2semidirect
2. #3518C2semidirect
3. #3387C2semidirect
4. #3385C2semidirect
5. #3377C2semidirect
6. #3376C2semidirect
7. #3350C2semidirect
8. #3349C2semidirect
9. #3348C2semidirect
10. #3347C2semidirect
11. #3342C2semidirect
12. #3340C2semidirect
13. #3321C2semidirect
14. #3320C2semidirect
15. #3313C2semidirect
16. #3312C2semidirect
17. #3301C2semidirect
18. #3300C2semidirect
19. #3263C2semidirect
20. #3262C2semidirect
21. #3248C2semidirect
22. #3244C2semidirect
23. #3243C2semidirect
24. #3237C2semidirect
25. #3121C2semidirect
26. #3121C2semidirect
27. #3111C2semidirect
28. #3082C2semidirect
29. #3082C2semidirect
30. #3076C2semidirect
31. #2992C2semidirect

Maximal subgroups

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

subgroupindex
#35652
#35182
#33872
#33852
#33772
#33762
#33502
#33492
#33482
#33472
#33422
#33402
#33212
#33202
#33132
#33122
#33012
#33002
#32632
#32622
#32482
#32442
#32432
#32372
#31212
#31112
#30822
#30762
#29922