Finite Group Databasebeta

← #7657114

Subgroups — #7657114

Order 512.

4861 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42694C213yesmaximal, complemented
2#42662C213yesmaximal, complemented
3#42625C213yesmaximal, complemented
4#42624C213yesmaximal, complemented
5#42588C213yesmaximal, complemented
6#42583C213yesmaximal, complemented
7#42524C213yesmaximal, complemented
8#42472C213yesmaximal, complemented
9#40117C213yesmaximal, complemented
10#40102C213yesmaximal, complemented
11#39236C213yesmaximal, complemented
12#39221C213yesmaximal, complemented
13#37625C213yesmaximal, complemented
14#37591C213yesmaximal, complemented
15#36445C211yesmaximal, characteristic, complemented
16#36433C211yesmaximal, characteristic, complemented
17#36433C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36059C211yesmaximal, characteristic, complemented
20#36049C211yesmaximal, characteristic, complemented
21#36049C211yesmaximal, characteristic, complemented
22#36049C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic
24#35957C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#35816C211yesmaximal, characteristic, complemented
27#35107C213yesmaximal, complemented
28#34596C213yesmaximal, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2857C2213yes—
42#2854C2213yes—
43#2854C2213yes—
44#2851C2213yes—
45#2830C2216yes—
46#2829C2216yes—
47#2829C2216yes—
48#2829C2216yes—
49#2801C2216yes—
50#2796C2216yes—
51#2795C2216yes—
52#2793C2216yes—
53#2777C2216yes—
54#2741C2216yes—
55#2737C2216yes—
56#2730C2216yes—
57#2710C2216yes—
58#2702C2216yes—
59#2701C2216yes—
60#2700C2216yes—
61#2700C2216yes—
62#2691C2216yes—
63#2686C2216yes—
64#2672C2216yes—
65#2665C2213yes—
66#2665C2213yes—
67#2663C2213yes—
68#2663C2213yes—
69#2662C2216yes—
70#2660C2213yes—
71#2655C2211yescharacteristic
72#2655C2213yes—
73#2653C2213yes—
74#2653C2213yes—
75#2652C2213yes—
76#2652C2213yes—
77#2651C2216yes—
78#2650C2213yes—
79#2650C2213yes—
80#2644C2213yes—
81#2644C2213yes—
82#2641C2213yes—
83#2641C2213yes—
84#2641C2213yes—
85#2638C2213yes—
86#2638C2213yes—
87#2630C2213yes—
88#2630C2216yes—
89#2630C2213yes—
90#2629C2213yes—
91#2624C2216yes—
92#2620C2216yes—
93#2619C2213yes—
94#2584C2213yes—
95#2580C2213yes—
96#2567C2213yes—
97#2566C2213yes—
98#2566C2213yes—
99#2562C2213yes—
100#2562C2213yes—
101#2562C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2550C2213yes—
105#2550C2213yes—
106#2548C2213yes—
107#2548C2213yes—
108#2548C2213yes—
109#2542C2213yes—
110#2541C2213yes—
111#2538C2213yes—
112#2538C2213yes—
113#2535C2213yes—
114#2525C2216yes—
115#2513C2213yes—
116#2513C2213yes—
117#2513C2213yes—
118#2513C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2500C2213yes—
122#2500C2213yes—
123#2497C2213yes—
124#2496C2213yes—
125#2495C2213yes—
126#2495C2213yes—
127#2495C2213yes—
128#2494C2213yes—
129#2491C2213yes—
130#2491C2213yes—
131#2491C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2485C2213yes—
142#2485C2213yes—
143#2477C2216yes—
144#2470C2216yes—
145#2468C2216yes—
146#2461C2216yes—
147#2461C2216yes—
148#2454C2213yes—
149#2454C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2445C2213yes—
155#2445C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2442C2213yes—
159#2441C2213yes—
160#2441C2213yes—
161#2441C2213yes—
162#2440C2213yes—
163#2439C2213yes—
164#2428C2213yes—
165#2428C2213yes—
166#2427C2216yes—
167#2422C2213yes—
168#2422C2216yes—
169#2422C2213yes—
170#2420C2213yes—
171#2420C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2401C2213yes—
175#2401C2213yes—
176#2399C2213yes—
177#2398C2213yes—
178#2398C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2392C2213yes—
182#2370C2213yes—
183#2370C2213yes—
184#2369C2213yes—
185#2366C2213yes—
186#2363C2213yes—
187#2363C2213yes—
188#2357C2213yes—
189#2355C2213yes—
190#2354C2213yes—
191#2354C2213yes—
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2345C2213yes—
203#2344C2213yes—
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2337C2216yes—
217#2335C2216yes—
218#2331C2213yes—
219#2330C2213yes—
220#2319C2213yes—
221#2314C2213yes—
222C4×#127C2213yes—
223C4×#125C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241#557—28no—
242#557—44no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×#127C2313yes—
251C2×#127C2313yes—
252C2×#127C2313yes—
253C2×#126C2316yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2316yes—
261C2×#124C2316yes—
262C2×#124C2316yes—
263C2×#123C2316yes—
264C2×#123C2313yes—
265C2×#123C2313yes—
266C2×#123C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2316yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2316yes—
278C2×#121C2316yes—
279#520—28no—
280C4×#41—44no—
281C4×#41—44no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2316yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2316yes—
313C22×C4⋊C4C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#401C2311yescharacteristic
317#401C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2311yescharacteristic
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2311yescharacteristic
328#400C2311yescharacteristic
329#400C2311yescharacteristic
330#400C2313yes—
331#399C2316yes—
332#399C2316yes—
333#399C2316yes—
334#399C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2311yescharacteristic
342#398C2311yescharacteristic
343#398C2311yescharacteristic
344#398C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#396C2313yes—
366#396C2316yes—
367#396C2316yes—
368#396C2316yes—
369#396C2313yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#395C2313yes—
379#395C2316yes—
380#395C2313yes—
381#395C2313yes—
382#395C2313yes—
383#395C2313yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2313yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#393C2313yes—
410#393C2316yes—
411#393C2313yes—
412#393C2313yes—
413#393C2313yes—
414#393C2313yes—
415#393C2313yes—
416#393C2313yes—
417#392C2313yes—
418#392C2316yes—
419#392C2316yes—
420#391C2316yes—
421#391C2313yes—
422#391C2316yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#390C2316yes—
427#390C2316yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2316yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2313yes—
453#390C2316yes—
454#390C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2316yes—
470#389C2313yes—
471#389C2316yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2311yescharacteristic
482#389C2313yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2316yes—
495#388C2313yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2316yes—
506#388C2316yes—
507#388C2316yes—
508#387C2313yes—
509#387C2316yes—
510#387C2313yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2313yes—
521#387C2311yescharacteristic
522#387C2311yescharacteristic
523#387C2313yes—
524#387C2311yescharacteristic
525#387C2313yes—
526#387C2311yescharacteristic
527#387C2313yes—
528#387C2311yescharacteristic
529#387C2313yes—
530#386C2316yes—
531#386C2316yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2313yes—
537#386C2313yes—
538#385C2313yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2313yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2316yes—
552#384C2313yes—
553#384C2313yes—
554#383C2316yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#381C2316yes—
561#381C2313yes—
562#381C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2316yes—
574#380C2316yes—
575#380C2313yes—
576#380C2313yes—
577#380C2316yes—
578#380C2313yes—
579#380C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2316yes—
583C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2416yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C22×D4C2416yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C4⋊Q8—212no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660#127—212no—
661#127—46no—
662#127—46no—
663#126—86no—
664#125—212no—
665#125—212no—
666#125—46no—
667#125—46no—
668#125—46no—
669#125—46no—
670#124—412no—
671#124—86no—
672#124—86no—
673#123—412no—
674#123—46no—
675#123—46no—
676#123—86no—
677C22⋊Q8—46no—
678C22⋊Q8—46no—
679C22⋊Q8—86no—
680C22⋊Q8—86no—
681#121—212no—
682#121—212no—
683#121—46no—
684#121—46no—
685#121—46no—
686#121—46no—
687#121—86no—
688#121—86no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—212no—
701C4×Q8—46no—
702C4×Q8—46no—
703C4×Q8#4118yes—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—46no—
715C4×D4—86no—
716#117—212no—
717#117—46no—
718#117—46no—
719#117—86no—
720C2×C4⋊C4—212no—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C42—46no—
822C2×C42—46no—
823C2×C42C2413yes—
824C2×C42C2411yescharacteristic
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2416yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2416yes—
842C2×C42C2416yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845C2×C42C2413yes—
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
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#95C2416yes—
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2416yes—
889#95C2413yes—
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2416yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908C24C2513yes—
909C24C2513yes—
910C24C2513yes—
911#41—416no—
912#41—416no—
913#41—416no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8C2×#4114yes—
924C2×Q8H(5,𝔽2)14yes—
925C2×Q82−1+414yes—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—212no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—43no—
938C2×D4—43no—
939C2×D4—43no—
940C2×D4—43no—
941C2×D4—46no—
942C2×D4—43no—
943C2×D4—43no—
944C2×D4—46no—
945C2×D4—43no—
946C2×D4—43no—
947C2×D4—46no—
948C2×D4—46no—
949C2×D4—46no—
950C2×D4—46no—
951C2×D4—46no—
952C2×D4—46no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—212no—
963C22×C4—26no—
964C22×C4—26no—
965C22×C4—26no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—46no—
971C22×C4—43no—
972C22×C4—43no—
973C22×C4—43no—
974C22×C4—46no—
975C22×C4—43no—
976C22×C4—43no—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2513yes—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—212no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—26no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—43no—
1030C4⋊C4—46no—
1031C4⋊C4—43no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—46no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—46no—
1049C4⋊C4—46no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4C2×#41112yes—
1059C22⋊C4—26no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—46no—
1067C22⋊C4—46no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—46no—
1082C22⋊C4—46no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—46no—
1089C22⋊C4—46no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—46no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—26no—
1116C42—22no—
1117C42—41no—
1118C42—41no—
1119C42—43no—
1120C42—43no—
1121C42—43no—
1122C42—46no—
1123C42—43no—
1124C42—43no—
1125C42—46no—
1126C42—46no—
1127C42C2×#41112yes—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23—23no—
1145C23—23no—
1146C23—23no—
1147C23—23no—
1148C23—23no—
1149C23C2611yescharacteristic
1150Q8—86no—
1151Q8—86no—
1152Q8—86no—
1153Q8#542116yes—
1154D4—412no—
1155D4—412no—
1156D4—412no—
1157D4—412no—
1158D4—812no—
1159D4—86no—
1160D4—86no—
1161D4—166no—
1162D4—166no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—412no—
1241C2×C4—412no—
1242C2×C4—412no—
1243C2×C4—812no—
1244C2×C4—86no—
1245C2×C4—86no—
1246C2×C4—86no—
1247C2×C4—86no—
1248C2×C4C22×#4112yes—
1249C2×C4C22×#4116yes—
1250C2×C4C22×#4116yes—
1251C2×C4C2×H(5,𝔽2)16yes—
1252C2×C4C2×2−1+416yes—
1253C2×C4#58512yes—
1254C2×C4#58512yes—
1255C22—43no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22—43no—
1273C22—43no—
1274C22—43no—
1275C22—43no—
1276C22C23×#4111yescharacteristic
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22C2×#58511yescharacteristic
1281C22H(7,𝔽2)11yescharacteristic
1282C22H(7,𝔽2)11yescharacteristic
1283C4—22no—
1284C4—26no—
1285C4—22no—
1286C4—22no—
1287C4—41no—
1288C4—41no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—43no—
1294C4—43no—
1295C4—41no—
1296C4—43no—
1297C4—41no—
1298C4—41no—
1299C4—43no—
1300C4—43no—
1301C4—43no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—43no—
1309C4—43no—
1310C4C2×#542112yes—
1311C2—83no—
1312C2—83no—
1313C2—83no—
1314C2C22×#54211yescharacteristic
1315C2#6279311yescharacteristic
1316C2#6285811yescharacteristic
1317C2#6289911yescharacteristic
1318C2#6289911yescharacteristic
1319C2#6295211yescharacteristic
1320C2#6295211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36029C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42694C2semidirect
2. #42662C2semidirect
3. #42625C2semidirect
4. #42624C2semidirect
5. #42588C2semidirect
6. #42583C2semidirect
7. #42524C2semidirect
8. #42472C2semidirect
9. #40117C2semidirect
10. #40102C2semidirect
11. #39236C2semidirect
12. #39221C2semidirect
13. #37625C2semidirect
14. #37591C2semidirect
15. #36445C2semidirect
16. #36433C2semidirect
17. #36433C2semidirect
18. #36431C2semidirect
19. #36059C2semidirect
20. #36049C2semidirect
21. #36049C2semidirect
22. #36049C2semidirect
24. #35957C2semidirect
25. #35898C2semidirect
26. #35816C2semidirect
27. #35107C2semidirect
28. #34596C2semidirect
29. #34336C2semidirect
30. #34263C2semidirect
31. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#426942
#426622
#426252
#426242
#425882
#425832
#425242
#424722
#401172
#401022
#392362
#392212
#376252
#375912
#364452
#364332
#364312
#360592
#360492
#360292
#359572
#358982
#358162
#351072
#345962
#343362
#342632
C4×#5502