Finite Group Databasebeta

← #61799

Subgroups — #61799

Order 256.

867 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic, complemented
2#3511C211yesmaximal, characteristic, complemented
3#3350C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3347C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3344C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3321C211yesmaximal, characteristic, complemented
12#3319C211yesmaximal, characteristic, complemented
13#3316C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3311C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3306C211yesmaximal, characteristic, complemented
19#3239C211yesmaximal, characteristic, complemented
20#3238C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3111C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3097C211yesmaximal, characteristic, complemented
30#3096C211yesmaximal, characteristic, complemented
31#2980C211yesmaximal, characteristic, complemented
32#563—21no—
33#560—21no—
34#556C2211yescharacteristic
35#556C2211yescharacteristic, complemented
36#555—21no—
37#555C2211yescharacteristic
38#555C2211yescharacteristic, complemented
39#554C2211yescharacteristic
40#554C2211yescharacteristic, complemented
41#553—21no—
42#553—21no—
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#551—21no—
48#548—21no—
49#548—21no—
50#548C2211yescharacteristic
51#548C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#542—21no—
57#542—21no—
58#540—21no—
59#540—21no—
60#538—21no—
61#538—21no—
62#537C2211yescharacteristic
63#537C2211yescharacteristic
64#537C2211yescharacteristic
65#537C2211yescharacteristic, complemented
66#536C2211yescharacteristic
67#535C2211yescharacteristic
68#533—21no—
69#532—21no—
70#532C2211yescharacteristic
71C2×C4⋊Q8C2211yescharacteristic, complemented
72#529C2211yescharacteristic
73#529C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76C4×#41C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#489C2211yescharacteristic
82#489C2211yescharacteristic
83#489C2211yescharacteristic
84#489C2211yescharacteristic
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic
99#483C2211yescharacteristic, complemented
100#483C2211yescharacteristic, complemented
101#483C2211yescharacteristic, complemented
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic
110#482C2211yescharacteristic, complemented
111#481C2211yescharacteristic
112#481C2211yescharacteristic
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#480C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#477C2211yescharacteristic, complemented
127#476C2211yescharacteristic
128#476C2211yescharacteristic
129#475C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic
132#474C2211yescharacteristic
133#470C2211yescharacteristic
134#470C2211yescharacteristic, complemented
135#469C2211yescharacteristic
136#469C2211yescharacteristic
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic
142#467C2211yescharacteristic, complemented
143#466C2211yescharacteristic
144#466C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic
165#442C2211yescharacteristic
166#442C2211yescharacteristic
167#441C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#440C2211yescharacteristic
170#440C2211yescharacteristic
171#440C2211yescharacteristic, complemented
172#440C2211yescharacteristic, complemented
173#435C2211yescharacteristic
174#435C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179#435C2211yescharacteristic, complemented
180#435C2211yescharacteristic, complemented
181#432C2211yescharacteristic, complemented
182#432C2211yescharacteristic, complemented
183#428C2211yescharacteristic
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202#408C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8—21no—
211C22×Q8C2311yescharacteristic
212C22×D4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D411yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237#127—21no—
238#127D411yescharacteristic
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#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
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#124C2311yescharacteristic
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—
283C22⋊Q8—21no—
284C22⋊Q8—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⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
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#121D411yescharacteristic
326#121D411yescharacteristic
327#121D411yescharacteristic
328#121D411yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#120—21no—
340#120—21no—
341#120—21no—
342#120—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
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×D4—21no—
366C4×D4—21no—
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
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⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
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#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
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
476#97C2311yescharacteristic
477#97C2311yescharacteristic
478C24—21no—
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—
488#41—41no—
489#41—82no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—82no—
499C2×Q8C2×D411yescharacteristic
500C2×Q8C2×D411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×Q8C2411yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4C2×D411yescharacteristic
550C22×C4C2×D411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556Q16—41no—
557Q16—41no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561SD16—41no—
562D8—41no—
563D8—41no—
564M16—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
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⋊C4—21no—
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
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⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42C2×D411yescharacteristic
679C42C2×D411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23C22×D411yescharacteristic
689C23C22×D411yescharacteristic
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692C23C22×D411yescharacteristic
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—41no—
700Q8—41no—
701Q8—42no—
702Q8—42no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—42no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
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—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C2511yescharacteristic
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—162no—
820C22C23×D411yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4#58511yescharacteristic
844C4#58511yescharacteristic
845C2—41no—
846C2—41no—
847C2—41no—
848C2—41no—
849C2—41no—
850C2—81no—
851C2—81no—
852C2—81no—
853C2#348511yescharacteristic
854C2#358511yescharacteristic
855C2#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. #3551C2semidirect
2. #3511C2semidirect
3. #3350C2semidirect
4. #3349C2semidirect
5. #3348C2semidirect
6. #3347C2semidirect
7. #3346C2semidirect
8. #3345C2semidirect
9. #3344C2semidirect
10. #3343C2semidirect
11. #3321C2semidirect
12. #3319C2semidirect
13. #3316C2semidirect
14. #3314C2semidirect
15. #3313C2semidirect
16. #3311C2semidirect
17. #3308C2semidirect
18. #3306C2semidirect
19. #3239C2semidirect
20. #3238C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3201C2semidirect
24. #3198C2semidirect
25. #3111C2semidirect
26. #3111C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3097C2semidirect
30. #3096C2semidirect
31. #2980C2semidirect
35. #556C22semidirect
38. #555C22semidirect
40. #554C22semidirect
53. #547C22semidirect
65. #537C22semidirect
71. C2×C4⋊Q8C22semidirect
75. #520C22semidirect
76. C4×#41C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #484C22semidirect
97. #484C22semidirect
99. #483C22semidirect
100. #483C22semidirect
101. #483C22semidirect
102. #483C22semidirect
110. #482C22semidirect
115. #481C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #477C22semidirect
129. #475C22semidirect
130. #475C22semidirect
134. #470C22semidirect
140. #468C22semidirect
142. #467C22semidirect
148. #465C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
163. #448C22semidirect
167. #441C22semidirect
168. #441C22semidirect
171. #440C22semidirect
172. #440C22semidirect
177. #435C22semidirect
178. #435C22semidirect
179. #435C22semidirect
180. #435C22semidirect
181. #432C22semidirect
182. #432C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #419C22semidirect
197. C2×#103C22semidirect
201. #408C22semidirect
202. #408C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#35112
#33502
#33492
#33482
#33472
#33462
#33452
#33442
#33432
#33212
#33192
#33162
#33142
#33132
#33112
#33082
#33062
#32392
#32382
#32042
#32032
#32012
#31982
#31112
#30992
#30982
#30972
#30962
#29802