Finite Group Databasebeta

← #7697156

Subgroups — #7697156

Order 512.

4722 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59962C213yesmaximal, complemented
2#59507C213yesmaximal, complemented
3#59332C213yesmaximal, complemented
4#52240C213yesmaximal, complemented
5#45253C213yesmaximal, complemented
6#45211C213yesmaximal, complemented
7#45191C213yesmaximal, complemented
8#45118C213yesmaximal, complemented
9#45050C213yesmaximal, complemented
10#45007C213yesmaximal, complemented
11#39479C213yesmaximal, complemented
12#39080C213yesmaximal, complemented
13#38272C213yesmaximal, complemented
14#38260C213yesmaximal, complemented
15#38228C213yesmaximal, complemented
16#37884C213yesmaximal, complemented
17#36584C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36445C211yesmaximal, characteristic, complemented
20#36076C211yesmaximal, characteristic
21#36040C211yesmaximal, characteristic, complemented
22#36005C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34295C211yesmaximal, characteristic
28#34263C211yesmaximal, characteristic, complemented
29#34263C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31#34184C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2860C2213yes—
39#2859C2213yes—
40#2857C2213yes—
41#2794C2213yes—
42#2793C2213yes—
43#2791C2213yes—
44#2787C2213yes—
45#2781C2213yes—
46#2779C2213yes—
47#2773C2213yes—
48#2773C2216yes—
49#2771C2216yes—
50#2770C2213yes—
51#2767C2211yescharacteristic
52#2767C2216yes—
53#2762C2213yes—
54#2754C2213yes—
55#2754C2216yes—
56#2750C2216yes—
57#2747C2213yes—
58#2743C2216yes—
59#2743C2216yes—
60#2741C2213yes—
61#2739C2216yes—
62#2721C2213yes—
63#2707C2216yes—
64#2702C2213yes—
65#2702C2216yes—
66#2702C2216yes—
67#2695C2216yes—
68#2694C2216yes—
69#2690C2213yes—
70#2647C2213yes—
71#2647C2213yes—
72#2644C2213yes—
73#2628C2213yes—
74#2624C2213yes—
75#2624C2213yes—
76#2609C2216yes—
77#2601C2216yes—
78#2580C2213yes—
79#2575C2216yes—
80#2575C2216yes—
81#2571C2213yes—
82#2571C2213yes—
83#2571C2213yes—
84#2570C2213yes—
85#2570C2213yes—
86#2563C2213yes—
87#2562C2216yes—
88#2553C2216yes—
89#2553C2216yes—
90#2552C2213yes—
91#2542C2213yes—
92#2538C2213yes—
93#2517C2216yes—
94#2513C2213yes—
95#2513C2213yes—
96#2512C2213yes—
97#2512C2213yes—
98#2512C2213yes—
99#2512C2213yes—
100#2509C2213yes—
101#2509C2213yes—
102#2509C2213yes—
103#2509C2213yes—
104#2509C2213yes—
105#2509C2213yes—
106#2508C2213yes—
107#2508C2213yes—
108#2507C2213yes—
109#2507C2213yes—
110#2506C2213yes—
111#2506C2213yes—
112#2504C2213yes—
113#2501C2213yes—
114#2498C2216yes—
115#2498C2216yes—
116#2497C2213yes—
117#2497C2213yes—
118#2496C2216yes—
119#2496C2213yes—
120#2496C2213yes—
121#2495C2213yes—
122#2494C2213yes—
123#2493C2216yes—
124#2488C2216yes—
125#2488C2216yes—
126#2487C2213yes—
127#2486C2213yes—
128#2485C2216yes—
129#2479C2216yes—
130#2475C2216yes—
131#2470C2216yes—
132#2454C2213yes—
133#2454C2213yes—
134#2454C2213yes—
135#2454C2213yes—
136#2445C2213yes—
137#2445C2213yes—
138#2445C2213yes—
139#2445C2213yes—
140#2442C2213yes—
141#2442C2213yes—
142#2441C2216yes—
143#2441C2213yes—
144#2441C2213yes—
145#2438C2216yes—
146#2422C2213yes—
147#2422C2213yes—
148#2420C2213yes—
149#2420C2213yes—
150#2419C2216yes—
151#2402C2213yes—
152#2402C2213yes—
153#2401C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2395C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2369C2213yes—
160#2366C2213yes—
161#2363C2213yes—
162#2361C2213yes—
163#2359C2216yes—
164#2357C2213yes—
165#2357C2213yes—
166#2357C2213yes—
167#2355C2213yes—
168#2354C2213yes—
169#2354C2213yes—
170#2354C2213yes—
171#2352C2213yes—
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188#2349C2213yes—
189#2349C2213yes—
190#2349C2213yes—
191#2349C2213yes—
192#2345C2213yes—
193#2345C2213yes—
194#2345C2213yes—
195#2344C2213yes—
196#2344C2213yes—
197#2344C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2331C2213yes—
207#2330C2213yes—
208#2328C2213yes—
209#2324C2213yes—
210#2319C2213yes—
211#2319C2213yes—
212#2319C2213yes—
213#2317C2213yes—
214#2317C2213yes—
215#2314C2213yes—
216#2314C2213yes—
217#2314C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#126C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×#121C2213yes—
223#2298C2213yes—
224#2298C2213yes—
225#2298C2213yes—
226#2295C2213yes—
227#2293C2213yes—
228#2293C2213yes—
229#2293C2213yes—
230#2290C2213yes—
231#2285C2213yes—
232C2×#382C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#550—28no—
242C2×C4⋊Q8C2313yes—
243C2×#127C2313yes—
244C2×#126C2313yes—
245C2×#126C2316yes—
246C2×#126C2316yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#123C2316yes—
252C2×#123C2316yes—
253C2×#123C2316yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2316yes—
256C2×#121C2313yes—
257C2×#121C2313yes—
258#520—28no—
259#520—28no—
260#520—28no—
261C4×#41—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2316yes—
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2316yes—
291C2×#117C2316yes—
292C2×#117C2316yes—
293C22×C4⋊C4C2313yes—
294C22×C4⋊C4C2313yes—
295C22×C4⋊C4C2313yes—
296C22×C42C2313yes—
297#401C2313yes—
298#400C2313yes—
299#400C2316yes—
300#400C2313yes—
301#400C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2313yes—
309#400C2316yes—
310#400C2311yescharacteristic
311#400C2313yes—
312#400C2311yescharacteristic
313#400C2311yescharacteristic
314#400C2313yes—
315#400C2313yes—
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2316yes—
321#399C2316yes—
322#399C2316yes—
323#399C2313yes—
324#399C2313yes—
325#399C2316yes—
326#399C2313yes—
327#399C2316yes—
328#398C2313yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2311yescharacteristic
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2316yes—
347#397C2313yes—
348#397C2316yes—
349#397C2316yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2316yes—
356#397C2316yes—
357#396C2313yes—
358#396C2316yes—
359#396C2316yes—
360#396C2313yes—
361#396C2313yes—
362#396C2316yes—
363#396C2316yes—
364#395C2313yes—
365#394C2316yes—
366#394C2316yes—
367#394C2316yes—
368#394C2313yes—
369#394C2316yes—
370#394C2313yes—
371#394C2313yes—
372#394C2313yes—
373#393C2313yes—
374#393C2316yes—
375#391C2313yes—
376#391C2316yes—
377#391C2313yes—
378#391C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2316yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2316yes—
429#389C2316yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2311yescharacteristic
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2316yes—
449#388C2313yes—
450#388C2313yes—
451#388C2313yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2313yes—
456#388C2316yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#387C2311yescharacteristic
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2316yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2311yescharacteristic
500#387C2313yes—
501#387C2311yescharacteristic
502#387C2311yescharacteristic
503#387C2311yescharacteristic
504#387C2311yescharacteristic
505#386C2316yes—
506#386C2313yes—
507#386C2316yes—
508#386C2316yes—
509#386C2316yes—
510#386C2316yes—
511#386C2313yes—
512#386C2316yes—
513#385C2316yes—
514#385C2316yes—
515#385C2316yes—
516#385C2316yes—
517#385C2316yes—
518#385C2313yes—
519#385C2316yes—
520#385C2313yes—
521#385C2313yes—
522#385C2313yes—
523#385C2316yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#383C2313yes—
534#382C2311yescharacteristic
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2316yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2316yes—
547#382C2311yescharacteristic
548#382C2313yes—
549#381C2316yes—
550#381C2316yes—
551#381C2316yes—
552#381C2316yes—
553#380C2313yes—
554#380C2316yes—
555#380C2316yes—
556#380C2316yes—
557#380C2316yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2316yes—
564#380C2316yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
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×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620C2×#95C2316yes—
621C2×#95C2316yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×D4C2413yes—
633C22×D4C2413yes—
634C22×D4C2416yes—
635C22×D4C2413yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2416yes—
639C23×C4C2416yes—
640C23×C4C2416yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C4⋊Q8—212no—
644#127—212no—
645#126—46no—
646#126—86no—
647#126—86no—
648#125—212no—
649#125—212no—
650#125—46no—
651#125—86no—
652#123—412no—
653#123—86no—
654#123—86no—
655C22⋊Q8—46no—
656C22⋊Q8—86no—
657#121—212no—
658#121—212no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—212no—
672C4×Q8#4118yes—
673C4×D4—212no—
674C4×D4—212no—
675C4×D4—212no—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682C4×D4—86no—
683#117—212no—
684#117—212no—
685#117—212no—
686#117—212no—
687#117—86no—
688#117—86no—
689#117—86no—
690C2×C4⋊C4—212no—
691C2×C4⋊C4—212no—
692C2×C4⋊C4—212no—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
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⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2416yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2416yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C42—212no—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2416yes—
809C2×C42C2416yes—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2411yescharacteristic
814C2×C42C2413yes—
815C2×C42C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2416yes—
821#95C2416yes—
822#95C2416yes—
823#95C2416yes—
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2416yes—
863#95C2416yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887C24C2513yes—
888C24C2513yes—
889#41—232no—
890#41—416no—
891C2×Q8—26no—
892C2×Q8—43no—
893C2×Q8—43no—
894C2×Q8C2×#4114yes—
895C2×Q8C2×#4114yes—
896C2×Q82−1+414yes—
897C2×D4—26no—
898C2×D4—212no—
899C2×D4—26no—
900C2×D4—26no—
901C2×D4—26no—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—46no—
905C2×D4—46no—
906C2×D4—43no—
907C2×D4—43no—
908C2×D4C2×#41112yes—
909C22×C4—26no—
910C22×C4—26no—
911C22×C4—212no—
912C22×C4—212no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—212no—
919C22×C4—46no—
920C22×C4—46no—
921C22×C4—46no—
922C22×C4—43no—
923C22×C4—43no—
924C22×C4—43no—
925C22×C4—46no—
926C22×C4—46no—
927C22×C4—43no—
928C22×C4—46no—
929C22×C4C2×#41112yes—
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2513yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C22×C4C2511yescharacteristic
958C22×C4C2513yes—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—26no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—212no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—22no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—22no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—41no—
991C4⋊C4—43no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—46no—
998C4⋊C4—46no—
999C4⋊C4—46no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
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—43no—
1020C4⋊C4—43no—
1021C4⋊C4C2×#41112yes—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—212no—
1029C22⋊C4—26no—
1030C22⋊C4—26no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—43no—
1034C22⋊C4—43no—
1035C22⋊C4—43no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—46no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—46no—
1045C22⋊C4—46no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—46no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—43no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C42—22no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—22no—
1070C42—43no—
1071C42—41no—
1072C42—43no—
1073C42—43no—
1074C42—43no—
1075C42—46no—
1076C42—46no—
1077C42—46no—
1078C42—43no—
1079C42—43no—
1080C42C2×#41112yes—
1081C23—23no—
1082C23—23no—
1083C23—23no—
1084C23—23no—
1085C23—23no—
1086C23—23no—
1087C23—23no—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23C22×#4116yes—
1095C23C2611yescharacteristic
1096Q8—86no—
1097Q8#552116yes—
1098D4—224no—
1099D4—412no—
1100D4—812no—
1101D4—86no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—224no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—412no—
1184C2×C4—86no—
1185C2×C4—812no—
1186C2×C4—86no—
1187C2×C4—812no—
1188C2×C4—812no—
1189C2×C4C22×#4112yes—
1190C2×C4C22×#4116yes—
1191C2×C4C22×#4112yes—
1192C2×C4C22×#4116yes—
1193C2×C4C22×#4116yes—
1194C2×C4C2×2−1+416yes—
1195C2×C4#58512yes—
1196C22—26no—
1197C22—26no—
1198C22—26no—
1199C22—43no—
1200C22—43no—
1201C22—43no—
1202C22—43no—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22C23×#4111yescharacteristic
1211C22C23×#4111yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C2×#58511yescharacteristic
1214C22H(7,𝔽2)11yescharacteristic
1215C22H(7,𝔽2)11yescharacteristic
1216C222−1+611yescharacteristic
1217C4—22no—
1218C4—26no—
1219C4—22no—
1220C4—22no—
1221C4—41no—
1222C4—43no—
1223C4—43no—
1224C4—43no—
1225C4—41no—
1226C4—41no—
1227C4—43no—
1228C4—43no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—43no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4C2×#552112yes—
1246C2—46no—
1247C2—83no—
1248C2C22×#55211yescharacteristic
1249C2#6285711yescharacteristic
1250C2#6285711yescharacteristic
1251C2#6294911yescharacteristic
1252C2#6300611yescharacteristic
1253C2#6301011yescharacteristic
1254C2#6307011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59962C2semidirect
2. #59507C2semidirect
3. #59332C2semidirect
4. #52240C2semidirect
5. #45253C2semidirect
6. #45211C2semidirect
7. #45191C2semidirect
8. #45118C2semidirect
9. #45050C2semidirect
10. #45007C2semidirect
11. #39479C2semidirect
12. #39080C2semidirect
13. #38272C2semidirect
14. #38260C2semidirect
15. #38228C2semidirect
16. #37884C2semidirect
17. #36584C2semidirect
18. #36458C2semidirect
19. #36445C2semidirect
21. #36040C2semidirect
23. #35971C2semidirect
24. #35898C2semidirect
25. #35868C2semidirect
26. #34336C2semidirect
28. #34263C2semidirect
29. #34263C2semidirect
30. #34263C2semidirect
31. #34184C2semidirect

Maximal subgroups

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

subgroupindex
#599622
#595072
#593322
#522402
#452532
#452112
#451912
#451182
#450502
#450072
#394792
#390802
#382722
#382602
#382282
#378842
#365842
#364582
#364452
#360762
#360402
#360052
#359712
#358982
#358682
#343362
#342952
#342632
#341842