Finite Group Databasebeta

← #61814

Subgroups — #61814

Order 256.

844 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547C211yesmaximal, characteristic, complemented
2#3512C211yesmaximal, characteristic, complemented
3#3352C211yesmaximal, characteristic, complemented
4#3351C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3347C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3344C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3336C211yesmaximal, characteristic, complemented
11#3327C211yesmaximal, characteristic, complemented
12#3326C211yesmaximal, characteristic, complemented
13#3320C211yesmaximal, characteristic, complemented
14#3315C211yesmaximal, characteristic, complemented
15#3312C211yesmaximal, characteristic, complemented
16#3307C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3300C211yesmaximal, characteristic, complemented
19#3236C211yesmaximal, characteristic, complemented
20#3232C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3201C211yesmaximal, characteristic, complemented
25#3111C211yesmaximal, characteristic, complemented
26#3107C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3097C211yesmaximal, characteristic, complemented
30#3097C211yesmaximal, characteristic, complemented
31#2981C211yesmaximal, characteristic, complemented
32#562—21no—
33#562—21no—
34#555—21no—
35#555C2211yescharacteristic
36#554C2211yescharacteristic
37#553—21no—
38#553—21no—
39#553—21no—
40#553—21no—
41#553—21no—
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic
50#552C2211yescharacteristic
51#552C2211yescharacteristic
52D4×Q8C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic
55#547C2211yescharacteristic
56#544—21no—
57#542—21no—
58#542—21no—
59#541—21no—
60#540—21no—
61#540—21no—
62#537C2211yescharacteristic
63#537C2211yescharacteristic
64#537C2211yescharacteristic
65#537C2211yescharacteristic
66#536C2211yescharacteristic
67#536C2211yescharacteristic
68#533C2211yescharacteristic
69#532C2211yescharacteristic
70#529—21no—
71#529—21no—
72#529C2211yescharacteristic
73C2×#125C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#499C2211yescharacteristic
80#499C2211yescharacteristic
81#491C2211yescharacteristic
82#491C2211yescharacteristic
83#488C2211yescharacteristic
84#488C2211yescharacteristic
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#484C2211yescharacteristic
97#484C2211yescharacteristic
98#484C2211yescharacteristic
99#484C2211yescharacteristic
100#484C2211yescharacteristic
101#484C2211yescharacteristic
102#484C2211yescharacteristic
103#483C2211yescharacteristic
104#483C2211yescharacteristic
105#483C2211yescharacteristic
106#483C2211yescharacteristic
107#483C2211yescharacteristic
108#483C2211yescharacteristic
109#483C2211yescharacteristic
110#482C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic
114#482C2211yescharacteristic
115#481C2211yescharacteristic
116#481C2211yescharacteristic
117#481C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic
120#480C2211yescharacteristic
121#479C2211yescharacteristic
122#479C2211yescharacteristic
123#479C2211yescharacteristic
124#479C2211yescharacteristic
125#479C2211yescharacteristic
126#479C2211yescharacteristic
127#479C2211yescharacteristic
128#478C2211yescharacteristic
129#478C2211yescharacteristic
130#478C2211yescharacteristic
131#475C2211yescharacteristic
132#474C2211yescharacteristic
133#470C2211yescharacteristic
134#470C2211yescharacteristic
135#470C2211yescharacteristic
136#469C2211yescharacteristic
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic
144#466C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic
149#464C2211yescharacteristic
150#463C2211yescharacteristic
151#462C2211yescharacteristic
152#461C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#451C2211yescharacteristic
159#451C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic
164#448C2211yescharacteristic
165#442C2211yescharacteristic
166#441C2211yescharacteristic
167#440C2211yescharacteristic
168#440C2211yescharacteristic
169C4×Q16C2211yescharacteristic
170C4×Q16C2211yescharacteristic
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173#436C2211yescharacteristic
174#436C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic
178#435C2211yescharacteristic
179C8×D4C2211yescharacteristic
180C8×D4C2211yescharacteristic
181#432C2211yescharacteristic
182#431C2211yescharacteristic
183#428C2211yescharacteristic
184#428C2211yescharacteristic
185#428C2211yescharacteristic
186#428C2211yescharacteristic
187#427C2211yescharacteristic
188#427C2211yescharacteristic
189C2×#107C2211yescharacteristic
190C2×#106C2211yescharacteristic
191#419C2211yescharacteristic
192#419C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197C2×#103C2211yescharacteristic
198C2×#103C2211yescharacteristic
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic
202#408C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D411yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232#127D411yescharacteristic
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#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124D411yescharacteristic
266#124D411yescharacteristic
267#124C2311yescharacteristic
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121D411yescharacteristic
330#121D411yescharacteristic
331#121D411yescharacteristic
332#121D411yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#121C2311yescharacteristic
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372#117—21no—
373#117—21no—
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#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C4⋊C4C2311yescharacteristic
400C2×C42—21no—
401C2×C42C2311yescharacteristic
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
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
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#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8C2×D411yescharacteristic
496C2×Q8C2×D411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×D411yescharacteristic
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546Q16—41no—
547Q16—41no—
548Q16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16—41no—
553D8—41no—
554M16—41no—
555M16—41no—
556M16—41no—
557M16—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8C2411yescharacteristic
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
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⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
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⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23C22×D411yescharacteristic
682C23C22×D411yescharacteristic
683C23C22×D411yescharacteristic
684C23C22×D411yescharacteristic
685C23C22×D411yescharacteristic
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—81no—
697Q8—81no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—42no—
714D4—81no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C2511yescharacteristic
775C8—21no—
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22C23×D411yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4#58511yescharacteristic
829C4#58511yescharacteristic
830C2—41no—
831C2—41no—
832C2—41no—
833C2—41no—
834C2—41no—
835C2—81no—
836C2—81no—
837C2#348511yescharacteristic
838C2#358411yescharacteristic
839C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3547C2semidirect
2. #3512C2semidirect
3. #3352C2semidirect
4. #3351C2semidirect
5. #3348C2semidirect
6. #3347C2semidirect
7. #3346C2semidirect
8. #3344C2semidirect
9. #3337C2semidirect
10. #3336C2semidirect
11. #3327C2semidirect
12. #3326C2semidirect
13. #3320C2semidirect
14. #3315C2semidirect
15. #3312C2semidirect
16. #3307C2semidirect
17. #3301C2semidirect
18. #3300C2semidirect
19. #3236C2semidirect
20. #3232C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3201C2semidirect
24. #3201C2semidirect
25. #3111C2semidirect
26. #3107C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3097C2semidirect
30. #3097C2semidirect
31. #2981C2semidirect

Maximal subgroups

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

subgroupindex
#35472
#35122
#33522
#33512
#33482
#33472
#33462
#33442
#33372
#33362
#33272
#33262
#33202
#33152
#33122
#33072
#33012
#33002
#32362
#32322
#32042
#32032
#32012
#31112
#31072
#30992
#30982
#30972
#29812