Finite Group Databasebeta

← #7660447

Subgroups — #7660447

Order 512.

4600 conjugacy classes of subgroups.

The subgroup lattice has 1253 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52289C213yesmaximal, complemented
2#42499C213yesmaximal, complemented
3#42497C213yesmaximal, complemented
4#42496C213yesmaximal, complemented
5#42494C213yesmaximal, complemented
6#42492C213yesmaximal, complemented
7#42488C213yesmaximal, complemented
8#39977C213yesmaximal, complemented
9#39972C213yesmaximal, complemented
10#39623C213yesmaximal, complemented
11#39497C213yesmaximal, complemented
12#38964C213yesmaximal, complemented
13#38963C213yesmaximal, complemented
14#37314C213yesmaximal, complemented
15#37312C213yesmaximal, complemented
16#37311C213yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36474C211yesmaximal, characteristic, complemented
21#36456C211yesmaximal, characteristic
22#36431C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35971C211yesmaximal, characteristic, complemented
25#35957C211yesmaximal, characteristic, complemented
26#35937C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic
28#35748C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic
30#34263C211yesmaximal, characteristic
31#34250C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2868C2213yes—
40#2864C2213yes—
41#2862C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2841C2216yes—
46#2841C2216yes—
47#2807C2213yes—
48#2806C2216yes—
49#2802C2213yes—
50#2802C2213yes—
51#2792C2216yes—
52#2792C2213yes—
53#2792C2213yes—
54#2791C2216yes—
55#2790C2213yes—
56#2790C2216yes—
57#2790C2213yes—
58#2788C2216yes—
59#2788C2216yes—
60#2774C2216yes—
61#2768C2216yes—
62#2763C2216yes—
63#2763C2213yes—
64#2755C2213yes—
65#2755C2213yes—
66#2755C2216yes—
67#2742C2213yes—
68#2734C2216yes—
69#2729C2216yes—
70#2729C2216yes—
71#2729C2216yes—
72#2720C2216yes—
73#2720C2216yes—
74#2713C2211yescharacteristic
75#2713C2213yes—
76#2713C2216yes—
77#2704C2216yes—
78#2704C2213yes—
79#2704C2213yes—
80#2677C2216yes—
81#2677C2213yes—
82#2667C2216yes—
83#2665C2216yes—
84#2660C2213yes—
85#2660C2213yes—
86#2659C2216yes—
87#2647C2213yes—
88#2647C2213yes—
89#2629C2216yes—
90#2629C2213yes—
91#2628C2216yes—
92#2628C2213yes—
93#2627C2216yes—
94#2584C2213yes—
95#2584C2213yes—
96#2580C2213yes—
97#2580C2213yes—
98#2571C2213yes—
99#2571C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2570C2213yes—
103#2570C2213yes—
104#2567C2213yes—
105#2567C2213yes—
106#2567C2213yes—
107#2567C2213yes—
108#2566C2213yes—
109#2566C2213yes—
110#2563C2213yes—
111#2552C2213yes—
112#2552C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2551C2213yes—
116#2551C2213yes—
117#2551C2213yes—
118#2551C2213yes—
119#2551C2213yes—
120#2551C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2550C2213yes—
124#2550C2213yes—
125#2550C2213yes—
126#2550C2213yes—
127#2550C2213yes—
128#2550C2213yes—
129#2546C2213yes—
130#2546C2213yes—
131#2542C2213yes—
132#2538C2213yes—
133#2538C2213yes—
134#2509C2213yes—
135#2509C2213yes—
136#2509C2213yes—
137#2508C2213yes—
138#2508C2213yes—
139#2508C2213yes—
140#2508C2213yes—
141#2508C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2507C2213yes—
146#2507C2213yes—
147#2507C2213yes—
148#2507C2213yes—
149#2506C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2452C2213yes—
155#2452C2213yes—
156#2452C2213yes—
157#2452C2213yes—
158#2442C2213yes—
159#2441C2213yes—
160#2440C2216yes—
161#2440C2216yes—
162#2440C2213yes—
163#2440C2213yes—
164#2440C2213yes—
165#2439C2216yes—
166#2439C2216yes—
167#2439C2213yes—
168#2439C2213yes—
169#2439C2213yes—
170#2438C2216yes—
171#2438C2216yes—
172#2402C2213yes—
173#2402C2213yes—
174#2399C2213yes—
175#2399C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2357C2213yes—
179#2357C2213yes—
180#2354C2213yes—
181#2354C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2349C2213yes—
203#2349C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206#2345C2213yes—
207#2345C2213yes—
208#2344C2213yes—
209#2344C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2329C2216yes—
215#2319C2213yes—
216#2319C2213yes—
217#2317C2216yes—
218#2317C2213yes—
219#2316C2213yes—
220#2314C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2298C2213yes—
229#2298C2213yes—
230#2296C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233C2×#389C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239Q82—44no—
240Q82—44no—
241#557—44no—
242#557—44no—
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2316yes—
254C2×C4⋊Q8C2316yes—
255C2×C4⋊Q8C2316yes—
256C2×#125C2311yescharacteristic
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2316yes—
269#520—44no—
270#520Q8116yescomplemented
271C4×#41—44no—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2316yes—
299C2×#117C2316yes—
300C2×#117C2313yes—
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2316yes—
303C22×C4⋊C4C2313yes—
304C22×C42C2313yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2316yes—
314#400C2313yes—
315#400C2316yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2311yescharacteristic
320#400C2311yescharacteristic
321#399C2316yes—
322#399C2316yes—
323#399C2313yes—
324#399C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2313yes—
348#398C2311yescharacteristic
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#396C2313yes—
360#396C2316yes—
361#396C2316yes—
362#396C2316yes—
363#396C2313yes—
364#396C2316yes—
365#396C2316yes—
366#396C2313yes—
367#396C2316yes—
368#396C2313yes—
369#395C2313yes—
370#395C2316yes—
371#395C2316yes—
372#395C2316yes—
373#395C2316yes—
374#395C2316yes—
375#395C2316yes—
376#395C2316yes—
377#395C2313yes—
378#395C2316yes—
379#395C2316yes—
380#395C2311yescharacteristic
381#395C2313yes—
382#395C2311yescharacteristic
383#395C2313yes—
384#395C2313yes—
385#395C2313yes—
386#395C2313yes—
387#395C2313yes—
388#395C2316yes—
389#393C2316yes—
390#393C2316yes—
391#393C2313yes—
392#393C2316yes—
393#393C2316yes—
394#393C2313yes—
395#391C2311yescharacteristic
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2316yes—
400#391C2316yes—
401#391C2316yes—
402#391C2316yes—
403#391C2316yes—
404#391C2316yes—
405#391C2313yes—
406#391C2311yescharacteristic
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2313yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2316yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2311yescharacteristic
481#389C2313yes—
482#388C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#387C2311yescharacteristic
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2313yes—
520#387C2313yes—
521#387C2311yescharacteristic
522#387C2311yescharacteristic
523#387C2311yescharacteristic
524#385C2313yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
528#385C2313yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2313yes—
536#385C2313yes—
537#385C2313yes—
538#385C2313yes—
539#385C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2316yes—
545#384C2316yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2316yes—
567#382C2316yes—
568#381C2316yes—
569#381C2316yes—
570#380C2313yes—
571#380C2316yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2316yes—
578#380C2316yes—
579#380C2316yes—
580#380C2316yes—
581#380C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620#376C2313yes—
621#376C2313yes—
622C2×#95C2316yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41C2×Q818yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2411yescharacteristic
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2416yes—
633C22×Q8C2416yes—
634C22×Q8C2411yescharacteristic
635C22×D4C2413yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2416yes—
639C23×C4C2413yes—
640C23×C4C2416yes—
641C4⋊Q8—24no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—46no—
650C4⋊Q8—46no—
651C4⋊Q8—86no—
652C4⋊Q8—86no—
653C4⋊Q8—86no—
654#125—24no—
655#125—46no—
656#125—46no—
657#125—46no—
658#125—46no—
659#125—46no—
660#125—86no—
661C22⋊Q8—212no—
662C22⋊Q8—46no—
663C22⋊Q8—86no—
664C22⋊Q8—86no—
665C22⋊Q8—86no—
666C22⋊Q8—86no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—46no—
680C4×Q8—46no—
681C4×Q8—46no—
682C4×Q8—46no—
683C4×Q8C2×Q818yes—
684C4×Q8C2×Q818yes—
685C4×D4—46no—
686C4×D4—46no—
687C4×D4—46no—
688C4×D4—46no—
689C4×D4C2×Q8124yes—
690C4×D4C2×Q8124yes—
691#117—46no—
692#117—412no—
693#117—46no—
694#117—86no—
695#117C2×Q8124yes—
696C2×C4⋊C4—46no—
697C2×C4⋊C4—86no—
698C2×C4⋊C4C2×Q8124yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C42—46no—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2416yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2411yescharacteristic
823C2×C42C2413yes—
824C2×C42C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2416yes—
828#95C2416yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2416yes—
849#95C2411yescharacteristic
850#95C2416yes—
851#95C2416yes—
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893C24C2513yes—
894#41—232no—
895C2×Q8—22no—
896C2×Q8—22no—
897C2×Q8—26no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—41no—
901C2×Q8—41no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—43no—
905C2×Q8—43no—
906C2×Q8—43no—
907C2×Q8—46no—
908C2×Q8—46no—
909C2×Q8—46no—
910C2×Q8—46no—
911C2×Q8—46no—
912C2×Q8—46no—
913C2×Q8C22×Q814yes—
914C2×Q8H(5,𝔽2)14yes—
915C2×Q82−1+414yes—
916C2×D4—26no—
917C2×D4—26no—
918C2×D4C22×Q8112yes—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—46no—
923C22×C4—46no—
924C22×C4—43no—
925C22×C4—43no—
926C22×C4—43no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—46no—
930C22×C4—46no—
931C22×C4—46no—
932C22×C4C22×Q8112yes—
933C22×C4C22×Q8124yes—
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2513yes—
937C22×C4C2513yes—
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—46no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—41no—
996C4⋊C4—43no—
997C4⋊C4—46no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4C22×Q8112yes—
1042C4⋊C4C22×Q8112yes—
1043C4⋊C4C22×Q8112yes—
1044C4⋊C4C22×Q814yes—
1045C4⋊C42−1+414yes—
1046C22⋊C4—26no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—46no—
1053C22⋊C4—43no—
1054C22⋊C4—46no—
1055C22⋊C4—43no—
1056C22⋊C4—46no—
1057C22⋊C4—46no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—43no—
1061C22⋊C4C22×Q8112yes—
1062C22⋊C4C22×Q8112yes—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—26no—
1075C42—22no—
1076C42—22no—
1077C42—26no—
1078C42—41no—
1079C42—43no—
1080C42—46no—
1081C42—43no—
1082C42—46no—
1083C42—43no—
1084C42—43no—
1085C42—43no—
1086C42—43no—
1087C42C22×Q8112yes—
1088C42C22×Q8112yes—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23C23×Q816yes—
1096C23C2611yescharacteristic
1097Q8—44no—
1098Q8—44no—
1099Q8—86no—
1100Q8—86no—
1101Q8—166no—
1102Q8—166no—
1103Q8#544116yes—
1104D4—224no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—224no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—424no—
1185C2×C4—86no—
1186C2×C4—86no—
1187C2×C4—166no—
1188C2×C4C23×Q812yes—
1189C2×C4C23×Q812yes—
1190C2×C4C23×Q816yes—
1191C2×C4C23×Q816yes—
1192C2×C4C23×Q812yes—
1193C2×C4C23×Q816yes—
1194C2×C4C2×H(5,𝔽2)16yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+412yes—
1197C2×C4C2×2−1+412yes—
1198C2×C4C2×2−1+416yes—
1199C2×C4#58512yes—
1200C22—26no—
1201C22—26no—
1202C22—26no—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22C24×Q811yescharacteristic
1208C22C22×H(5,𝔽2)11yescharacteristic
1209C22C22×2−1+411yescharacteristic
1210C22C22×2−1+411yescharacteristic
1211C22C2×#58511yescharacteristic
1212C22H(7,𝔽2)11yescharacteristic
1213C22H(7,𝔽2)11yescharacteristic
1214C4—26no—
1215C4—26no—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—41no—
1224C4—43no—
1225C4—41no—
1226C4—41no—
1227C4—43no—
1228C4—41no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—41no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—41no—
1237C4—41no—
1238C4—43no—
1239C4—41no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4C2×#544112yes—
1244C2—46no—
1245C2C22×#54411yescharacteristic
1246C2#6294311yescharacteristic
1247C2#6295211yescharacteristic
1248C2#6298911yescharacteristic
1249C2Q8×2−1+411yescharacteristic
1250C2#6301511yescharacteristic
1251C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52289C2semidirect
2. #42499C2semidirect
3. #42497C2semidirect
4. #42496C2semidirect
5. #42494C2semidirect
6. #42492C2semidirect
7. #42488C2semidirect
8. #39977C2semidirect
9. #39972C2semidirect
10. #39623C2semidirect
11. #39497C2semidirect
12. #38964C2semidirect
13. #38963C2semidirect
14. #37314C2semidirect
15. #37312C2semidirect
16. #37311C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×#125C2semidirect
19. #36475C2semidirect
20. #36474C2semidirect
23. #35971C2semidirect
24. #35971C2semidirect
25. #35957C2semidirect
26. #35937C2semidirect
270. #520Q8semidirect

Maximal subgroups

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

subgroupindex
#522892
#424992
#424972
#424962
#424942
#424922
#424882
#399772
#399722
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