Finite Group Databasebeta

← #7653902

Subgroups — #7653902

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42905C213yesmaximal, complemented
2#42904C213yesmaximal, complemented
3#42902C213yesmaximal, complemented
4#42901C213yesmaximal, complemented
5#40220C213yesmaximal, complemented
6#40123C213yesmaximal, complemented
7#39787C213yesmaximal, complemented
8#39759C213yesmaximal, complemented
9#39219C213yesmaximal, complemented
10#39155C213yesmaximal, complemented
11#38982C213yesmaximal, complemented
12#38939C213yesmaximal, complemented
13#37505C213yesmaximal, complemented
14#36584C211yesmaximal, characteristic, complemented
15#36578C211yesmaximal, characteristic, complemented
16Q8×#123C211yesmaximal, characteristic, complemented
17Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
18#36456C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic, complemented
20#36434C211yesmaximal, characteristic
21#36432C211yesmaximal, characteristic, complemented
22#35971C211yesmaximal, characteristic, complemented
23#35898C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35711C211yesmaximal, characteristic, complemented
26#35083C213yesmaximal, complemented
27#35017C213yesmaximal, complemented
28#34960C213yesmaximal, complemented
29#34291C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C2×#2351C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2863C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2855C2213yes—
47#2854C2213yes—
48#2850C2213yes—
49#2838C2216yes—
50#2837C2216yes—
51#2810C2216yes—
52#2798C2216yes—
53#2798C2216yes—
54#2789C2216yes—
55#2787C2216yes—
56#2785C2216yes—
57#2783C2216yes—
58#2783C2216yes—
59#2781C2216yes—
60#2777C2216yes—
61#2775C2216yes—
62#2775C2216yes—
63#2767C2216yes—
64#2744C2216yes—
65#2727C2216yes—
66#2689C2216yes—
67#2667C2216yes—
68#2666C2216yes—
69#2663C2216yes—
70#2654C2216yes—
71#2652C2216yes—
72#2650C2216yes—
73#2647C2213yes—
74#2644C2213yes—
75#2643C2216yes—
76#2639C2216yes—
77#2628C2213yes—
78#2624C2213yes—
79#2596C2213yes—
80#2594C2213yes—
81#2590C2213yes—
82#2588C2213yes—
83#2585C2216yes—
84#2582C2213yes—
85#2581C2213yes—
86#2577C2213yes—
87#2575C2213yes—
88#2571C2213yes—
89#2571C2213yes—
90#2571C2213yes—
91#2570C2213yes—
92#2568C2213yes—
93#2567C2213yes—
94#2563C2213yes—
95#2560C2213yes—
96#2558C2213yes—
97#2556C2216yes—
98#2545C2213yes—
99#2538C2213yes—
100#2536C2213yes—
101#2514C2213yes—
102#2514C2213yes—
103#2513C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2511C2213yes—
107#2509C2213yes—
108#2509C2213yes—
109#2509C2213yes—
110#2509C2213yes—
111#2509C2213yes—
112#2508C2213yes—
113#2508C2213yes—
114#2507C2213yes—
115#2504C2213yes—
116#2502C2213yes—
117#2500C2213yes—
118#2499C2213yes—
119#2497C2213yes—
120#2496C2213yes—
121#2496C2213yes—
122#2495C2213yes—
123#2494C2213yes—
124#2494C2213yes—
125#2493C2213yes—
126#2488C2216yes—
127#2488C2211yescharacteristic
128#2487C2213yes—
129#2487C2213yes—
130#2485C2213yes—
131#2485C2213yes—
132#2481C2216yes—
133#2481C2213yes—
134#2473C2213yes—
135#2452C2213yes—
136#2452C2213yes—
137#2451C2213yes—
138#2451C2213yes—
139#2451C2213yes—
140#2451C2213yes—
141#2449C2216yes—
142#2449C2213yes—
143#2448C2213yes—
144#2448C2213yes—
145#2448C2213yes—
146#2448C2213yes—
147#2447C2213yes—
148#2447C2213yes—
149#2446C2213yes—
150#2446C2213yes—
151#2443C2213yes—
152#2440C2213yes—
153#2440C2213yes—
154#2439C2213yes—
155#2439C2213yes—
156#2439C2213yes—
157#2439C2213yes—
158#2429C2213yes—
159#2426C2213yes—
160#2425C2213yes—
161#2423C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2422C2213yes—
165#2421C2213yes—
166#2421C2213yes—
167#2421C2213yes—
168#2420C2213yes—
169#2419C2213yes—
170#2417C2213yes—
171#2416C2213yes—
172#2402C2213yes—
173#2401C2213yes—
174#2396C2213yes—
175#2395C2213yes—
176#2367C2213yes—
177#2365C2213yes—
178#2362C2213yes—
179#2362C2213yes—
180#2361C2213yes—
181#2360C2213yes—
182#2352C2213yes—
183#2352C2213yes—
184#2351C2213yes—
185#2351C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2213yes—
191#2351C2213yes—
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#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2334C2216yes—
213#2332C2216yes—
214#2329C2216yes—
215#2327C2213yes—
216#2323C2213yes—
217#2318C2216yes—
218C4×#125C2213yes—
219C4×#126C2213yes—
220C4×#124C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C2×#389C2213yes—
231C2×#389C2213yes—
232#2290C2213yes—
233C2×#382C2213yes—
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242D4×Q8—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×#126C2313yes—
250C2×#126C2316yes—
251C2×#125C2313yes—
252C2×#124C2313yes—
253C2×#124C2313yes—
254C2×#123C2311yescharacteristic
255C2×#123C2313yes—
256C2×#123C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268#519—44no—
269C4×#41—44no—
270C2×C4×Q8—28no—
271C2×C4×Q8—44no—
272C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C4⋊C4C2313yes—
307C22×C4⋊C4C2313yes—
308C22×C4⋊C4C2313yes—
309C22×C42C2313yes—
310C22×C42C2313yes—
311C22×C42C2313yes—
312C22×C42C2313yes—
313#401C2316yes—
314#401C2313yes—
315#400C2313yes—
316#400C2316yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2311yescharacteristic
325#400C2316yes—
326#400C2316yes—
327#400C2313yes—
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2313yes—
331#400C2313yes—
332#400C2316yes—
333#400C2316yes—
334#400C2316yes—
335#399C2313yes—
336#399C2313yes—
337#399C2316yes—
338#399C2316yes—
339#399C2316yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2311yescharacteristic
363#397C2316yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2313yes—
372#396C2313yes—
373#396C2316yes—
374#396C2313yes—
375#396C2316yes—
376#395C2316yes—
377#395C2316yes—
378#395C2313yes—
379#395C2316yes—
380#394C2313yes—
381#394C2316yes—
382#394C2316yes—
383#394C2316yes—
384#394C2313yes—
385#393C2311yescharacteristic
386#393C2316yes—
387#393C2316yes—
388#393C2316yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2316yes—
393#391C2316yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2316yes—
402#391C2316yes—
403#391C2311yescharacteristic
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2316yes—
456#389C2313yes—
457#389C2313yes—
458#388C2311yescharacteristic
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2313yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2311yescharacteristic
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2313yes—
482#388C2316yes—
483#388C2316yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#386C2313yes—
519#386C2316yes—
520#386C2316yes—
521#386C2313yes—
522#386C2313yes—
523#386C2316yes—
524#386C2313yes—
525#386C2313yes—
526#386C2311yescharacteristic
527#386C2311yescharacteristic
528#385C2313yes—
529#385C2313yes—
530#385C2313yes—
531#385C2313yes—
532#385C2313yes—
533#385C2316yes—
534#385C2313yes—
535#385C2316yes—
536#385C2313yes—
537#385C2316yes—
538#385C2313yes—
539#385C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#383C2313yes—
546#383C2316yes—
547#382C2311yescharacteristic
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2316yes—
555#382C2313yes—
556#382C2316yes—
557#382C2313yes—
558#382C2313yes—
559#382C2316yes—
560#382C2316yes—
561#381C2316yes—
562#381C2313yes—
563#381C2313yes—
564#381C2311yescharacteristic
565#380C2313yes—
566#380C2316yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
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⋊C4C2316yes—
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×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2311yescharacteristic
622#376C2313yes—
623C2×#95C2316yes—
624C2×#95C2311yescharacteristic
625C2×#95C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C4⋊Q8—212no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660#126—412no—
661#126—46no—
662#125—46no—
663#124—212no—
664#124—46no—
665#123—24no—
666#123—46no—
667#123—46no—
668C22⋊Q8—212no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8—24no—
672C22⋊Q8—412no—
673C22⋊Q8—46no—
674C22⋊Q8—412no—
675C22⋊Q8—46no—
676#121—212no—
677#121—46no—
678#121—46no—
679C4×Q8—212no—
680C4×Q8—212no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8—46no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×D4—212no—
701C4×D4—212no—
702C4×D4—212no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707#117—46no—
708#117—46no—
709#117—46no—
710C2×C4⋊C4—212no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4—46no—
713C2×C4⋊C4—46no—
714C2×C4⋊C4—46no—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2411yescharacteristic
807C2×C42—212no—
808C2×C42—46no—
809C2×C42—46no—
810C2×C42—46no—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2411yescharacteristic
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2416yes—
836C2×C42C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2416yes—
846#95C2416yes—
847#95C2416yes—
848#95C2416yes—
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868#95C2413yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2416yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2416yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2416yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2416yes—
901#95C2416yes—
902#95C2416yes—
903#95C2416yes—
904#95C2416yes—
905C24C2511yescharacteristic
906C24C2513yes—
907C24C2511yescharacteristic
908#41—416no—
909C2×Q8—232no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—22no—
915C2×Q8—26no—
916C2×Q8—22no—
917C2×Q8—41no—
918C2×Q8—46no—
919C2×Q8—46no—
920C2×Q8—46no—
921C2×Q8—416no—
922C2×Q8C2×#41112yes—
923C2×Q8C2×#4114yes—
924C2×Q8H(5,𝔽2)14yes—
925C2×Q82−1+414yes—
926C2×D4—22no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—22no—
930C2×D4—26no—
931C2×D4—22no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—43no—
936C2×D4—43no—
937C2×D4—43no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—22no—
941C22×C4—26no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—43no—
964C22×C4—43no—
965C22×C4—43no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4C2×#41112yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2513yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2513yes—
999C4⋊C4—212no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—212no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—46no—
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⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—46no—
1044C4⋊C4—46no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—46no—
1056C22⋊C4—22no—
1057C22⋊C4—26no—
1058C22⋊C4—22no—
1059C22⋊C4—26no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—26no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—26no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—41no—
1071C22⋊C4—43no—
1072C22⋊C4—46no—
1073C22⋊C4—43no—
1074C22⋊C4—41no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—46no—
1081C22⋊C4—46no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—46no—
1088C22⋊C4—46no—
1089C22⋊C4—43no—
1090C22⋊C42−1+414yes—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—22no—
1107C42—41no—
1108C42—43no—
1109C42—43no—
1110C42—43no—
1111C42—43no—
1112C42—43no—
1113C42—46no—
1114C42—43no—
1115C42—43no—
1116C42—46no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—23no—
1123C23—21no—
1124C23—23no—
1125C23—21no—
1126C23—23no—
1127C23—21no—
1128C23—23no—
1129C23—21no—
1130C23—23no—
1131C23—21no—
1132C23—23no—
1133C23—23no—
1134C23—21no—
1135C23C22×#4112yes—
1136C23C2×2−1+412yes—
1137C23#58512yes—
1138C23C2611yescharacteristic
1139Q8—224no—
1140Q8—44no—
1141Q8—412no—
1142Q8—166no—
1143Q8#539116yes—
1144D4—44no—
1145D4—412no—
1146D4—412no—
1147D4—86no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—224no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—412no—
1228C2×C4—44no—
1229C2×C4—412no—
1230C2×C4—412no—
1231C2×C4—86no—
1232C2×C4—86no—
1233C2×C4—86no—
1234C2×C4—86no—
1235C2×C4C22×#4116yes—
1236C2×C4C22×#4116yes—
1237C2×C4C2×H(5,𝔽2)16yes—
1238C2×C4C2×2−1+412yes—
1239C2×C4C2×2−1+412yes—
1240C2×C4C2×2−1+416yes—
1241C2×C4#58512yes—
1242C2×C4#58512yes—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—43no—
1250C22—41no—
1251C22—43no—
1252C22—41no—
1253C22—41no—
1254C22—43no—
1255C22—41no—
1256C22—43no—
1257C22—41no—
1258C22—43no—
1259C22—41no—
1260C22—43no—
1261C22—41no—
1262C22—43no—
1263C22#351814yes—
1264C22C23×#4111yescharacteristic
1265C22C22×H(5,𝔽2)11yescharacteristic
1266C22C22×2−1+411yescharacteristic
1267C22C22×2−1+411yescharacteristic
1268C22C2×#58511yescharacteristic
1269C22C2×#58511yescharacteristic
1270C22C2×#58511yescharacteristic
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—26no—
1276C4—41no—
1277C4—43no—
1278C4—43no—
1279C4—41no—
1280C4—41no—
1281C4—43no—
1282C4—43no—
1283C4—43no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—43no—
1292C4—41no—
1293C4—43no—
1294C4—43no—
1295C4—43no—
1296C4—41no—
1297C4—43no—
1298C4C2×#539112yes—
1299C2—24no—
1300C2—83no—
1301C2—81no—
1302C2C22×#53911yescharacteristic
1303C2C2×#351811yescharacteristic
1304C2#6279311yescharacteristic
1305C2#6301511yescharacteristic
1306C2#6302011yescharacteristic
1307C2#6303211yescharacteristic
1308C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36434C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42905C2semidirect
2. #42904C2semidirect
3. #42902C2semidirect
4. #42901C2semidirect
5. #40220C2semidirect
6. #40123C2semidirect
7. #39787C2semidirect
8. #39759C2semidirect
9. #39219C2semidirect
10. #39155C2semidirect
11. #38982C2semidirect
12. #38939C2semidirect
13. #37505C2semidirect
14. #36584C2semidirect
15. #36578C2semidirect
16. Q8×#123C2semidirect
17. Q8×C22⋊Q8C2semidirect
18. #36456C2semidirect
19. #36448C2semidirect
21. #36432C2semidirect
22. #35971C2semidirect
23. #35898C2semidirect
24. #35801C2semidirect
25. #35711C2semidirect
26. #35083C2semidirect
27. #35017C2semidirect
28. #34960C2semidirect
29. #34291C2semidirect
30. C4×#548C2semidirect
31. C2×#2351C2semidirect

Maximal subgroups

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

subgroupindex
#429052
#429042
#429022
#429012
#402202
#401232
#397872
#397592
#392192
#391552
#389822
#389392
#375052
#365842
#365782
Q8×#1232
Q8×C22⋊Q82
#364562
#364482
#364342
#364322
#359712
#358982
#358012
#357112
#350832
#350172
#349602
#342912
C4×#5482
C2×#23512