Finite Group Databasebeta

← #61782

Subgroups — #61782

Order 256.

869 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3494C211yesmaximal, characteristic, complemented
3#3357C211yesmaximal, characteristic, complemented
4#3355C211yesmaximal, characteristic, complemented
5#3353C211yesmaximal, characteristic, complemented
6#3351C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3347C211yesmaximal, characteristic, complemented
9#3346C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3330C211yesmaximal, characteristic, complemented
12#3329C211yesmaximal, characteristic, complemented
13#3326C211yesmaximal, characteristic, complemented
14#3326C211yesmaximal, characteristic, complemented
15#3321C211yesmaximal, characteristic, complemented
16#3320C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3307C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3242C211yesmaximal, characteristic, complemented
21#3200C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3194C211yesmaximal, characteristic, complemented
24#3193C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3098C211yesmaximal, characteristic, complemented
28#3097C211yesmaximal, characteristic, complemented
29#3095C211yesmaximal, characteristic, complemented
30#3093C211yesmaximal, characteristic, complemented
31#2978C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#556C2211yescharacteristic, complemented
35#555C2211yescharacteristic
36#555C2211yescharacteristic
37#554—21no—
38#554C2211yescharacteristic, complemented
39#553—21no—
40#553C2211yescharacteristic
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552C2211yescharacteristic, complemented
46#551—21no—
47#551—21no—
48D4×Q8C2211yescharacteristic, complemented
49#548C2211yescharacteristic, complemented
50#548C2211yescharacteristic, complemented
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546—21no—
55#546—21no—
56#544C2211yescharacteristic
57#542—21no—
58#542—21no—
59#542C2211yescharacteristic
60#541C2211yescharacteristic
61#540—21no—
62#539—21no—
63#538—21no—
64#538—21no—
65#537C2211yescharacteristic
66#536C2211yescharacteristic
67#535C2211yescharacteristic
68#532—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72C2×C22⋊Q8C2211yescharacteristic
73C2×#121C2211yescharacteristic
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#491C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#487C2211yescharacteristic, complemented
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic
97#484C2211yescharacteristic
98#484C2211yescharacteristic, complemented
99#484C2211yescharacteristic, complemented
100#484C2211yescharacteristic, complemented
101#484C2211yescharacteristic, complemented
102#483C2211yescharacteristic
103#483C2211yescharacteristic, complemented
104#483C2211yescharacteristic, complemented
105#483C2211yescharacteristic, complemented
106#482C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#480C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#477C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#469C2211yescharacteristic
134#469C2211yescharacteristic
135#469C2211yescharacteristic, complemented
136#468C2211yescharacteristic
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic, complemented
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#466C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#463C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#461C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#450C2211yescharacteristic
154#450C2211yescharacteristic
155#450C2211yescharacteristic
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic, complemented
159#449C2211yescharacteristic, complemented
160#448C2211yescharacteristic
161#448C2211yescharacteristic
162#448C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic
165#442C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×SD16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic, complemented
174#436C2211yescharacteristic, complemented
175#436C2211yescharacteristic, complemented
176#436C2211yescharacteristic, complemented
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179#435C2211yescharacteristic, complemented
180#435C2211yescharacteristic, complemented
181#433C2211yescharacteristic
182#433C2211yescharacteristic
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190C2×#107C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#419C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#417C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic
202#407C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4—21no—
211C22×D4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127—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#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
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#124C2311yescharacteristic
267#123—21no—
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#123D411yescharacteristic
284#123D411yescharacteristic
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⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8D411yescharacteristic
300C22⋊Q8D411yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
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#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#120—21no—
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8—21no—
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×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
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#107C2311yescharacteristic
415#107C2311yescharacteristic
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#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—82no—
487#41—82no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8C2×D411yescharacteristic
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×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—82no—
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2411yescharacteristic
526C2×D4C2411yescharacteristic
527C2×D4C2411yescharacteristic
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×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2×D411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559SD16—41no—
560D8—41no—
561D8—41no—
562M16—41no—
563M16—41no—
564M16—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
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
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—81no—
690C23—81no—
691C23C22×D411yescharacteristic
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—41no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
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—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
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×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—82no—
820C22—162no—
821C22C23×D411yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
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—41no—
844C4#58511yescharacteristic
845C4#58511yescharacteristic
846C2—41no—
847C2—41no—
848C2—41no—
849C2—41no—
850C2—41no—
851C2—81no—
852C2—81no—
853C2—81no—
854C2#348511yescharacteristic
855C2#358511yescharacteristic
856C2#358611yescharacteristic
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. #3541C2semidirect
2. #3494C2semidirect
3. #3357C2semidirect
4. #3355C2semidirect
5. #3353C2semidirect
6. #3351C2semidirect
7. #3350C2semidirect
8. #3347C2semidirect
9. #3346C2semidirect
10. #3343C2semidirect
11. #3330C2semidirect
12. #3329C2semidirect
13. #3326C2semidirect
14. #3326C2semidirect
15. #3321C2semidirect
16. #3320C2semidirect
17. #3308C2semidirect
18. #3307C2semidirect
19. #3243C2semidirect
20. #3242C2semidirect
21. #3200C2semidirect
22. #3198C2semidirect
23. #3194C2semidirect
24. #3193C2semidirect
25. #3123C2semidirect
26. #3118C2semidirect
27. #3098C2semidirect
28. #3097C2semidirect
29. #3095C2semidirect
30. #3093C2semidirect
31. #2978C2semidirect
34. #556C22semidirect
38. #554C22semidirect
44. #553C22semidirect
45. #552C22semidirect
48. D4×Q8C22semidirect
49. #548C22semidirect
50. #548C22semidirect
53. #547C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #491C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #487C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
98. #484C22semidirect
99. #484C22semidirect
100. #484C22semidirect
101. #484C22semidirect
103. #483C22semidirect
104. #483C22semidirect
105. #483C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #482C22semidirect
114. #482C22semidirect
115. #481C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #477C22semidirect
129. #476C22semidirect
130. #475C22semidirect
131. #474C22semidirect
132. #474C22semidirect
135. #469C22semidirect
142. #468C22semidirect
143. #468C22semidirect
144. #468C22semidirect
145. #466C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #461C22semidirect
152. #461C22semidirect
158. #449C22semidirect
159. #449C22semidirect
162. #448C22semidirect
163. #448C22semidirect
165. #442C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×SD16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
173. #436C22semidirect
174. #436C22semidirect
175. #436C22semidirect
176. #436C22semidirect
177. #435C22semidirect
178. #435C22semidirect
179. #435C22semidirect
180. #435C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. #427C22semidirect
190. C2×#107C22semidirect
191. #419C22semidirect
192. #419C22semidirect
193. #419C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #417C22semidirect
197. #416C22semidirect
198. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#34942
#33572
#33552
#33532
#33512
#33502
#33472
#33462
#33432
#33302
#33292
#33262
#33212
#33202
#33082
#33072
#32432
#32422
#32002
#31982
#31942
#31932
#31232
#31182
#30982
#30972
#30952
#30932
#29782