Finite Group Databasebeta

← #7653335

Subgroups — #7653335

Order 512.

4567 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42704C213yesmaximal, complemented
2#42667C213yesmaximal, complemented
3#42509C213yesmaximal, complemented
4#42455C213yesmaximal, complemented
5#40213C213yesmaximal, complemented
6#40178C213yesmaximal, complemented
7#40167C213yesmaximal, complemented
8#40096C213yesmaximal, complemented
9#39661C213yesmaximal, complemented
10#39407C213yesmaximal, complemented
11#39399C213yesmaximal, complemented
12#39217C213yesmaximal, complemented
13#37592C213yesmaximal, complemented
14Q8×#125C211yesmaximal, characteristic, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36458C211yesmaximal, characteristic
17#36458C211yesmaximal, characteristic
18#36458C211yesmaximal, characteristic
19#36458C211yesmaximal, characteristic
20#36447C211yesmaximal, characteristic, complemented
21#36447C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic
25#35748C211yesmaximal, characteristic
26#35209C213yesmaximal, complemented
27#35116C213yesmaximal, complemented
28#34973C213yesmaximal, complemented
29#34263C211yesmaximal, characteristic
30C4×Q82C211yesmaximal, characteristic, complemented
31C4×#557C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#541C2216yes—
35C2×#520C2211yescharacteristic
36#2864C2213yes—
37#2860C2213yes—
38#2860C2213yes—
39#2860C2213yes—
40#2860C2213yes—
41#2859C2213yes—
42#2859C2213yes—
43#2859C2213yes—
44#2839C2216yes—
45#2836C2216yes—
46#2802C2216yes—
47#2758C2216yes—
48#2754C2216yes—
49#2739C2216yes—
50#2725C2216yes—
51#2725C2216yes—
52#2722C2216yes—
53#2719C2216yes—
54#2716C2216yes—
55#2713C2216yes—
56#2704C2216yes—
57#2704C2216yes—
58#2698C2216yes—
59#2698C2216yes—
60#2690C2216yes—
61#2689C2216yes—
62#2666C2216yes—
63#2664C2216yes—
64#2664C2216yes—
65#2660C2213yes—
66#2654C2216yes—
67#2650C2216yes—
68#2647C2213yes—
69#2637C2216yes—
70#2637C2216yes—
71#2634C2216yes—
72#2629C2213yes—
73#2628C2213yes—
74#2584C2213yes—
75#2580C2213yes—
76#2571C2213yes—
77#2571C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2566C2213yes—
82#2552C2213yes—
83#2552C2213yes—
84#2552C2213yes—
85#2552C2213yes—
86#2552C2213yes—
87#2551C2213yes—
88#2551C2213yes—
89#2550C2213yes—
90#2550C2213yes—
91#2546C2213yes—
92#2542C2213yes—
93#2538C2213yes—
94#2524C2213yes—
95#2524C2213yes—
96#2524C2213yes—
97#2524C2213yes—
98#2519C2216yes—
99#2519C2213yes—
100#2519C2213yes—
101#2519C2213yes—
102#2519C2213yes—
103#2513C2213yes—
104#2513C2213yes—
105#2513C2213yes—
106#2513C2213yes—
107#2512C2213yes—
108#2512C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2512C2213yes—
112#2512C2213yes—
113#2512C2213yes—
114#2512C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2508C2213yes—
120#2508C2213yes—
121#2508C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2506C2213yes—
129#2506C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2506C2213yes—
135#2497C2213yes—
136#2497C2213yes—
137#2497C2213yes—
138#2497C2213yes—
139#2496C2213yes—
140#2496C2213yes—
141#2496C2213yes—
142#2496C2213yes—
143#2495C2213yes—
144#2495C2213yes—
145#2495C2213yes—
146#2495C2213yes—
147#2489C2216yes—
148#2478C2216yes—
149#2475C2216yes—
150#2469C2213yes—
151#2469C2213yes—
152#2469C2213yes—
153#2469C2213yes—
154#2462C2211yescharacteristic
155#2462C2213yes—
156#2462C2213yes—
157#2462C2213yes—
158#2454C2213yes—
159#2452C2213yes—
160#2452C2213yes—
161#2452C2213yes—
162#2442C2213yes—
163#2440C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2429C2216yes—
167#2402C2213yes—
168#2399C2213yes—
169#2396C2213yes—
170#2396C2213yes—
171#2370C2213yes—
172#2370C2213yes—
173#2369C2213yes—
174#2369C2213yes—
175#2369C2213yes—
176#2365C2213yes—
177#2357C2213yes—
178#2355C2213yes—
179#2354C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187Q8×C4⋊C4C2213yes—
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
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
201#2345C2213yes—
202#2344C2213yes—
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2334C2216yes—
210#2334C2216yes—
211#2323C2216yes—
212#2319C2213yes—
213#2314C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2293C2213yes—
230#2276C2211yescharacteristic
231C42×Q8C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2213yes—
238C22×#41C2311yescharacteristic
239Q82—28no—
240#557—28no—
241#541—424no—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2316yes—
247C2×#126C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2316yes—
252C2×#126C2316yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2311yescharacteristic
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2316yes—
262C2×#125C2316yes—
263C2×#125C2316yes—
264C2×#125C2316yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268#520—28no—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2316yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×#117C2313yes—
293C2×#117C2316yes—
294C22×C4⋊C4C2313yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#399C2316yes—
313#399C2313yes—
314#399C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2313yes—
319#398C2316yes—
320#398C2316yes—
321#398C2313yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2311yescharacteristic
330#398C2313yes—
331#398C2313yes—
332#398C2316yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#396C2313yes—
350#396C2316yes—
351#396C2316yes—
352#396C2316yes—
353#396C2316yes—
354#396C2313yes—
355#396C2313yes—
356#396C2313yes—
357#396C2316yes—
358#396C2316yes—
359#395C2313yes—
360#395C2316yes—
361#395C2316yes—
362#395C2316yes—
363#395C2311yescharacteristic
364#395C2313yes—
365#395C2311yescharacteristic
366#395C2313yes—
367#395C2313yes—
368#393C2313yes—
369#393C2316yes—
370#393C2313yes—
371#391C2316yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2316yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2316yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2316yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2316yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
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#388C2313yes—
448#388C2313yes—
449#388C2313yes—
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2316yes—
460#388C2316yes—
461#388C2313yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#387C2311yescharacteristic
474#387C2311yescharacteristic
475#387C2311yescharacteristic
476#387C2311yescharacteristic
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2311yescharacteristic
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2311yescharacteristic
515#385C2316yes—
516#385C2316yes—
517#385C2316yes—
518#385C2316yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#383C2313yes—
533#383C2313yes—
534#383C2313yes—
535#383C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2316yes—
548#382C2316yes—
549#381C2316yes—
550#380C2313yes—
551#380C2313yes—
552#380C2316yes—
553#380C2316yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
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×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2311yescharacteristic
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616#376C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C43C2313yes—
622C2×#41—24no—
623C2×#41—24no—
624C2×#41—24no—
625C22×Q8C2411yescharacteristic
626C22×Q8C2413yes—
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C22×D4C2413yes—
630C23×C4C2413yes—
631C23×C4C2416yes—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635C4⋊Q8—212no—
636C4⋊Q8—412no—
637#126—212no—
638#126—212no—
639#126—412no—
640#126—412no—
641#126—412no—
642#126—412no—
643#126—46no—
644#126—46no—
645#125—212no—
646#125—212no—
647#125—24no—
648#125—212no—
649#125—412no—
650#125—412no—
651#125—412no—
652#125—46no—
653#125—46no—
654#125—412no—
655C22⋊Q8—412no—
656C22⋊Q8—412no—
657C22⋊Q8—412no—
658C4×Q8—24no—
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—24no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—412no—
676C4×Q8—46no—
677C4×Q8—46no—
678C4×Q8#4118yes—
679C4×D4—212no—
680C4×D4—212no—
681#117—212no—
682#117—412no—
683C2×C4⋊C4—212no—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C22⋊C4C2413yes—
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⋊C4C2416yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2411yescharacteristic
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2411yescharacteristic
804C2×C42C2413yes—
805C2×C42C2416yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815#95C2411yescharacteristic
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2416yes—
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2416yes—
836#95C2413yes—
837#95C2411yescharacteristic
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2416yes—
850#95C2411yescharacteristic
851#95C2413yes—
852#95C2416yes—
853#95C2416yes—
854#95C2416yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2416yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883C24C2513yes—
884#41—416no—
885C2×Q8—22no—
886C2×Q8—26no—
887C2×Q8—212no—
888C2×Q8—26no—
889C2×Q8—22no—
890C2×Q8—22no—
891C2×Q8—43no—
892C2×Q8—46no—
893C2×Q8—46no—
894C2×Q8C2×#4114yes—
895C2×Q82−1+414yes—
896C2×Q82−1+414yes—
897C2×D4—26no—
898C2×D4—26no—
899C2×D4—26no—
900C22×C4—26no—
901C22×C4—26no—
902C22×C4—26no—
903C22×C4—212no—
904C22×C4—46no—
905C22×C4—46no—
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2511yescharacteristic
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2513yes—
919C22×C4C2513yes—
920C22×C4C2513yes—
921C22×C4C2513yes—
922C22×C4C2513yes—
923C22×C4C2513yes—
924C22×C4C2513yes—
925C22×C4C2511yescharacteristic
926C22×C4C2513yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—212no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—46no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4—46no—
992C4⋊C4—46no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—46no—
1003C4⋊C4—46no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4C2×#41112yes—
1010C4⋊C4H(5,𝔽2)14yes—
1011C4⋊C42−1+414yes—
1012C22⋊C4—26no—
1013C22⋊C4—26no—
1014C22⋊C4—26no—
1015C22⋊C4—26no—
1016C22⋊C4—26no—
1017C22⋊C4—26no—
1018C22⋊C4—26no—
1019C22⋊C4—26no—
1020C22⋊C4—26no—
1021C22⋊C4—26no—
1022C22⋊C4—46no—
1023C22⋊C4—46no—
1024C22⋊C4—46no—
1025C22⋊C4—46no—
1026C22⋊C4—46no—
1027C22⋊C4—46no—
1028C22⋊C4—43no—
1029C22⋊C4—43no—
1030C22⋊C4—43no—
1031C22⋊C4—43no—
1032C42—26no—
1033C42—26no—
1034C42—26no—
1035C42—26no—
1036C42—26no—
1037C42—26no—
1038C42—26no—
1039C42—26no—
1040C42—26no—
1041C42—26no—
1042C42—22no—
1043C42—22no—
1044C42—22no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—22no—
1054C42—26no—
1055C42—22no—
1056C42—26no—
1057C42—46no—
1058C42—43no—
1059C42—43no—
1060C42—43no—
1061C42—43no—
1062C42—43no—
1063C42—43no—
1064C42—43no—
1065C42—43no—
1066C42C2×#41112yes—
1067C23—23no—
1068C23—23no—
1069C23—23no—
1070C23—23no—
1071C23—23no—
1072C23—23no—
1073C23—23no—
1074C23C2611yescharacteristic
1075Q8—28no—
1076Q8—412no—
1077Q8—812no—
1078Q8#541116yescomplemented
1079D4—412no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—23no—
1157C2×C4—412no—
1158C2×C4—812no—
1159C2×C4C22×#4112yes—
1160C2×C4C22×#4116yes—
1161C2×C4C22×#4116yes—
1162C2×C4C2×H(5,𝔽2)12yes—
1163C2×C4C2×H(5,𝔽2)12yes—
1164C2×C4C2×H(5,𝔽2)12yes—
1165C2×C4C2×2−1+412yes—
1166C2×C4C2×2−1+412yes—
1167C2×C4C2×2−1+412yes—
1168C2×C4C2×2−1+416yes—
1169C2×C4C2×2−1+416yes—
1170C2×C4#58512yes—
1171C2×C4#58512yes—
1172C22—43no—
1173C22—43no—
1174C22—43no—
1175C22—43no—
1176C22—43no—
1177C22—43no—
1178C22—43no—
1179C22C23×#4111yescharacteristic
1180C22C22×H(5,𝔽2)11yescharacteristic
1181C22C22×2−1+411yescharacteristic
1182C22C22×2−1+411yescharacteristic
1183C22C22×2−1+411yescharacteristic
1184C22C2×#58511yescharacteristic
1185C22C2×#58511yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—26no—
1195C4—22no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—43no—
1200C4—43no—
1201C4—43no—
1202C4—43no—
1203C4—43no—
1204C4—43no—
1205C4—43no—
1206C4—43no—
1207C4—41no—
1208C4—41no—
1209C4—43no—
1210C4—43no—
1211C4—43no—
1212C4—43no—
1213C4—43no—
1214C4—41no—
1215C4C2×#541112yes—
1216C2—83no—
1217C2C22×#54111yescharacteristic
1218C2#6278811yescharacteristic
1219C2#6280011yescharacteristic
1220C2#6303211yescharacteristic
1221C2#6303311yescharacteristic
1222C2#6303711yescharacteristic
1223C2#6303911yescharacteristic
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. #42704C2semidirect
2. #42667C2semidirect
3. #42509C2semidirect
4. #42455C2semidirect
5. #40213C2semidirect
6. #40178C2semidirect
7. #40167C2semidirect
8. #40096C2semidirect
9. #39661C2semidirect
10. #39407C2semidirect
11. #39399C2semidirect
12. #39217C2semidirect
13. #37592C2semidirect
14. Q8×#125C2semidirect
15. #36475C2semidirect
20. #36447C2semidirect
21. #36447C2semidirect
22. #35937C2semidirect
23. #35868C2semidirect
26. #35209C2semidirect
27. #35116C2semidirect
28. #34973C2semidirect
30. C4×Q82C2semidirect
31. C4×#557C2semidirect
1078. Q8#541semidirect

Maximal subgroups

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

subgroupindex
#427042
#426672
#425092
#424552
#402132
#401782
#401672
#400962
#396612
#394072
#393992
#392172
#375922
Q8×#1252
#364752
#364582
#364472
#359372
#358682
#358162
#357482
#352092
#351162
#349732
#342632
C4×Q822
C4×#5572