Finite Group Databasebeta

← #61769

Subgroups — #61769

Order 256.

855 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3540C211yesmaximal, characteristic, complemented
2#3493C211yesmaximal, characteristic, complemented
3#3350C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3347C211yesmaximal, characteristic, complemented
7#3342C211yesmaximal, characteristic, complemented
8#3341C211yesmaximal, characteristic, complemented
9#3340C211yesmaximal, characteristic, complemented
10#3340C211yesmaximal, characteristic, complemented
11#3321C211yesmaximal, characteristic, complemented
12#3319C211yesmaximal, characteristic, complemented
13#3313C211yesmaximal, characteristic, complemented
14#3311C211yesmaximal, characteristic, complemented
15#3301C211yesmaximal, characteristic, complemented
16#3300C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3201C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3191C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3124C211yesmaximal, characteristic, complemented
27#3097C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30#3091C211yesmaximal, characteristic, complemented
31#2977C211yesmaximal, characteristic, complemented
32H(3,𝔽4)—21no—
33#560—21no—
34#559—21no—
35#556—21no—
36#556C2211yescharacteristic
37#556C2211yescharacteristic
38#556C2211yescharacteristic
39#556C2211yescharacteristic, complemented
40#555—21no—
41#555C2211yescharacteristic
42#555C2211yescharacteristic
43#555C2211yescharacteristic
44#555C2211yescharacteristic, complemented
45#553—21no—
46#553C2211yescharacteristic
47#553C2211yescharacteristic, complemented
48#552—21no—
49#552C2211yescharacteristic
50#552C2211yescharacteristic, complemented
51#551—21no—
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#542—21no—
58#542—21no—
59#542C2211yescharacteristic
60#542C2211yescharacteristic
61#538—21no—
62#538—21no—
63#538—21no—
64#538—21no—
65#537C2211yescharacteristic
66#536C2211yescharacteristic
67#535C2211yescharacteristic
68#529—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic
73#525C2211yescharacteristic, complemented
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#489C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#488C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#484C2211yescharacteristic, complemented
100#483C2211yescharacteristic, complemented
101#483C2211yescharacteristic, complemented
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic
116#481C2211yescharacteristic
117#481C2211yescharacteristic, complemented
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, complemented
128#476C2211yescharacteristic, complemented
129#475C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#469C2211yescharacteristic, complemented
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic, complemented
138#467C2211yescharacteristic, complemented
139#467C2211yescharacteristic, complemented
140#466C2211yescharacteristic
141#466C2211yescharacteristic
142#466C2211yescharacteristic, complemented
143#465C2211yescharacteristic
144#465C2211yescharacteristic
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#435C2211yescharacteristic
174#435C2211yescharacteristic
175#435C2211yescharacteristic, complemented
176#435C2211yescharacteristic, complemented
177C8×D4C2211yescharacteristic
178C8×D4C2211yescharacteristic
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic, complemented
182#433C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#427C2211yescharacteristic, complemented
186#427C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188#427C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#416C2211yescharacteristic
194#416C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C22×C8C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232#127—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#125—21no—
248#125—21no—
249#125—21no—
250#125C2311yescharacteristic
251#125C2311yescharacteristic
252#124—21no—
253#124—21no—
254#124—21no—
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#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124C2311yescharacteristic
271#124C2311yescharacteristic
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—
285#123D411yescharacteristic
286#123D411yescharacteristic
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8D411yescharacteristic
295C22⋊Q8D411yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
320#121D411yescharacteristic
321#121C2311yescharacteristic
322#121C2311yescharacteristic
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#120—21no—
332#120—21no—
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337#120—21no—
338#120D411yescharacteristic
339#120D411yescharacteristic
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
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#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393C2×C4⋊C4—21no—
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
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
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24C2×D411yescharacteristic
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—21no—
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8C2×D411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
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×D4—21no—
512C2×D4—21no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2411yescharacteristic
523C2×D4C2411yescharacteristic
524C2×D4C2411yescharacteristic
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—41no—
538C22×C4—41no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546C22×C4C2411yescharacteristic
547Q16—41no—
548Q16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16—41no—
553D8—41no—
554D8—41no—
555M16—41no—
556M16—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
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—81no—
701Q8—81no—
702Q8—81no—
703Q8—81no—
704Q8—81no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—42no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
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—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C2511yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—82no—
813C22—162no—
814C22C23×D411yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4#58511yescharacteristic
838C4#58511yescharacteristic
839C2—41no—
840C2—41no—
841C2—41no—
842C2—41no—
843C2—41no—
844C2—81no—
845C2—81no—
846C2—81no—
847C2#348511yescharacteristic
848C2#358411yescharacteristic
849C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3540C2semidirect
2. #3493C2semidirect
3. #3350C2semidirect
4. #3349C2semidirect
5. #3348C2semidirect
6. #3347C2semidirect
7. #3342C2semidirect
8. #3341C2semidirect
9. #3340C2semidirect
10. #3340C2semidirect
11. #3321C2semidirect
12. #3319C2semidirect
13. #3313C2semidirect
14. #3311C2semidirect
15. #3301C2semidirect
16. #3300C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3201C2semidirect
22. #3198C2semidirect
23. #3191C2semidirect
24. #3191C2semidirect
25. #3125C2semidirect
26. #3124C2semidirect
27. #3097C2semidirect
28. #3096C2semidirect
29. #3091C2semidirect
30. #3091C2semidirect
31. #2977C2semidirect
39. #556C22semidirect
44. #555C22semidirect
47. #553C22semidirect
50. #552C22semidirect
56. #544C22semidirect
73. #525C22semidirect
75. #520C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #498C22semidirect
81. #489C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #488C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
98. #484C22semidirect
99. #484C22semidirect
100. #483C22semidirect
101. #483C22semidirect
102. #483C22semidirect
109. #482C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #482C22semidirect
114. #482C22semidirect
117. #481C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #477C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #475C22semidirect
130. #475C22semidirect
131. #474C22semidirect
132. #474C22semidirect
133. #470C22semidirect
134. #469C22semidirect
135. #468C22semidirect
136. #468C22semidirect
137. #467C22semidirect
138. #467C22semidirect
139. #467C22semidirect
142. #466C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
158. #450C22semidirect
163. #448C22semidirect
164. #447C22semidirect
165. #442C22semidirect
166. #441C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
175. #435C22semidirect
176. #435C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #427C22semidirect
186. #427C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. #427C22semidirect
190. #427C22semidirect
191. #419C22semidirect
192. #418C22semidirect
197. C2×#103C22semidirect
198. C2×#102C22semidirect
201. C2×C22⋊C8C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35402
#34932
#33502
#33492
#33482
#33472
#33422
#33412
#33402
#33212
#33192
#33132
#33112
#33012
#33002
#32972
#32962
#32442
#32432
#32012
#31982
#31912
#31252
#31242
#30972
#30962
#30912
#29772