Finite Group Databasebeta

← #7656481

Subgroups — #7656481

Order 512.

4697 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42865C213yesmaximal, complemented
2#42856C213yesmaximal, complemented
3#42841C213yesmaximal, complemented
4#42830C213yesmaximal, complemented
5#42516C213yesmaximal, complemented
6#42506C213yesmaximal, complemented
7#42451C213yesmaximal, complemented
8#42450C213yesmaximal, complemented
9#40219C213yesmaximal, complemented
10#40197C213yesmaximal, complemented
11#39782C213yesmaximal, complemented
12#39662C213yesmaximal, complemented
13#37521C213yesmaximal, complemented
14#37510C213yesmaximal, complemented
15#36585C211yesmaximal, characteristic, complemented
16Q8×#125C211yesmaximal, characteristic, complemented
17#36483C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#35996C211yesmaximal, characteristic, complemented
20#35883C211yesmaximal, characteristic, complemented
21#35868C211yesmaximal, characteristic, complemented
22#35845C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35771C211yesmaximal, characteristic
26#35723C211yesmaximal, characteristic, complemented
27#35047C213yesmaximal, complemented
28#34592C213yesmaximal, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34249C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2860C2213yes—
42#2859C2213yes—
43#2854C2213yes—
44#2851C2213yes—
45#2838C2216yes—
46#2836C2216yes—
47#2834C2216yes—
48#2827C2216yes—
49#2807C2216yes—
50#2807C2216yes—
51#2793C2216yes—
52#2792C2216yes—
53#2787C2216yes—
54#2783C2216yes—
55#2777C2216yes—
56#2776C2216yes—
57#2765C2216yes—
58#2765C2216yes—
59#2744C2216yes—
60#2726C2216yes—
61#2724C2216yes—
62#2720C2216yes—
63#2694C2216yes—
64#2680C2216yes—
65#2667C2213yes—
66#2666C2213yes—
67#2664C2213yes—
68#2663C2213yes—
69#2655C2213yes—
70#2655C2216yes—
71#2654C2213yes—
72#2654C2216yes—
73#2653C2213yes—
74#2652C2213yes—
75#2652C2213yes—
76#2652C2213yes—
77#2649C2213yes—
78#2649C2213yes—
79#2649C2216yes—
80#2647C2213yes—
81#2645C2213yes—
82#2638C2213yes—
83#2638C2216yes—
84#2636C2213yes—
85#2633C2211yescharacteristic
86#2633C2216yes—
87#2630C2213yes—
88#2629C2213yes—
89#2628C2213yes—
90#2625C2213yes—
91#2625C2213yes—
92#2624C2213yes—
93#2620C2213yes—
94#2596C2216yes—
95#2594C2216yes—
96#2590C2216yes—
97#2581C2213yes—
98#2581C2213yes—
99#2573C2216yes—
100#2570C2213yes—
101#2567C2213yes—
102#2566C2213yes—
103#2565C2213yes—
104#2558C2216yes—
105#2556C2216yes—
106#2552C2213yes—
107#2552C2213yes—
108#2552C2213yes—
109#2545C2213yes—
110#2538C2213yes—
111#2538C2213yes—
112#2514C2213yes—
113#2514C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2513C2213yes—
117#2511C2213yes—
118#2509C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2507C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2506C2213yes—
125#2506C2213yes—
126#2502C2213yes—
127#2501C2213yes—
128#2500C2213yes—
129#2499C2213yes—
130#2497C2213yes—
131#2495C2213yes—
132#2494C2213yes—
133#2494C2213yes—
134#2494C2213yes—
135#2494C2213yes—
136#2486C2213yes—
137#2486C2213yes—
138#2485C2213yes—
139#2485C2213yes—
140#2460C2216yes—
141#2455C2216yes—
142#2454C2213yes—
143#2453C2213yes—
144#2453C2213yes—
145#2453C2213yes—
146#2452C2213yes—
147#2451C2213yes—
148#2448C2213yes—
149#2448C2213yes—
150#2448C2213yes—
151#2448C2213yes—
152#2447C2213yes—
153#2447C2213yes—
154#2446C2213yes—
155#2446C2213yes—
156#2442C2213yes—
157#2442C2213yes—
158#2441C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2429C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2423C2213yes—
167#2423C2213yes—
168#2422C2213yes—
169#2422C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2367C2213yes—
183#2365C2213yes—
184#2361C2213yes—
185#2360C2213yes—
186#2360C2213yes—
187#2360C2213yes—
188#2351C2211yescharacteristic
189#2351C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2213yes—
194#2351C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2213yes—
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2213yes—
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2335C2216yes—
219#2334C2216yes—
220#2326C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242D4×Q8—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#126C2313yes—
248C2×#125C2311yescharacteristic
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2316yes—
252C2×#125C2316yes—
253C2×#124C2313yes—
254C2×#124C2313yes—
255C2×#123C2316yes—
256C2×#123C2313yes—
257C2×#123C2316yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2316yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266#520—44no—
267#519—28no—
268#519—44no—
269C2×C4×Q8—44no—
270C2×C4×Q8—44no—
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×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2316yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C4⋊C4C2313yes—
307C22×C4⋊C4C2313yes—
308C22×C42C2313yes—
309C22×C42C2313yes—
310#401C2316yes—
311#401C2316yes—
312#401C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2313yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#399C2316yes—
332#399C2316yes—
333#399C2316yes—
334#399C2316yes—
335#399C2313yes—
336#399C2311yescharacteristic
337#399C2311yescharacteristic
338#399C2313yes—
339#399C2313yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2313yes—
354#398C2313yes—
355#398C2311yescharacteristic
356#398C2311yescharacteristic
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#397C2313yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2313yes—
369#397C2313yes—
370#397C2316yes—
371#397C2313yes—
372#397C2316yes—
373#397C2316yes—
374#397C2316yes—
375#397C2316yes—
376#397C2313yes—
377#397C2313yes—
378#397C2311yescharacteristic
379#397C2311yescharacteristic
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#396C2313yes—
386#396C2316yes—
387#396C2313yes—
388#396C2316yes—
389#396C2316yes—
390#396C2316yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#395C2313yes—
397#395C2316yes—
398#395C2316yes—
399#395C2313yes—
400#394C2316yes—
401#394C2316yes—
402#394C2313yes—
403#394C2313yes—
404#394C2311yescharacteristic
405#394C2313yes—
406#394C2311yescharacteristic
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#393C2313yes—
412#393C2313yes—
413#392C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2316yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2316yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2313yes—
490#388C2316yes—
491#388C2316yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2313yes—
530#386C2313yes—
531#386C2313yes—
532#386C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2316yes—
537#385C2313yes—
538#385C2313yes—
539#385C2313yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2313yes—
544#385C2316yes—
545#385C2316yes—
546#385C2311yescharacteristic
547#385C2311yescharacteristic
548#385C2311yescharacteristic
549#385C2311yescharacteristic
550#385C2316yes—
551#385C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2316yes—
560#384C2313yes—
561#384C2313yes—
562#383C2311yescharacteristic
563#383C2316yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2316yes—
570#382C2313yes—
571#381C2316yes—
572#381C2313yes—
573#380C2313yes—
574#380C2316yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
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⋊C4C2316yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2316yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
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⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625#376C2313yes—
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×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2411yescharacteristic
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2413yes—
651C23×C4C2416yes—
652C4⋊Q8—212no—
653C4⋊Q8—46no—
654#126—212no—
655#125—24no—
656#125—46no—
657#125—46no—
658#125—86no—
659#125—86no—
660#124—212no—
661#124—46no—
662#123—412no—
663#123—46no—
664#123—86no—
665C22⋊Q8—212no—
666C22⋊Q8—212no—
667C22⋊Q8—212no—
668C22⋊Q8—46no—
669C22⋊Q8—46no—
670C22⋊Q8—86no—
671#121—212no—
672#121—46no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—24no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—86no—
702#117—212no—
703#117—212no—
704#117—46no—
705#117—46no—
706#117—46no—
707C2×C4⋊C4—46no—
708C2×C4⋊C4—46no—
709C2×C4⋊C4—46no—
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⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2416yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C42—46no—
814C2×C42—46no—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2416yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2416yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2416yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2416yes—
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2413yes—
874#95C2416yes—
875#95C2416yes—
876#95C2413yes—
877#95C2416yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2416yes—
899#95C2416yes—
900#95C2416yes—
901#95C2416yes—
902C24C2513yes—
903C24C2511yescharacteristic
904C24C2511yescharacteristic
905#41—416no—
906C2×Q8—232no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—43no—
915C2×Q8—416no—
916C2×Q8C2×#41112yes—
917C2×Q8C2×#4114yes—
918C2×Q8H(5,𝔽2)14yes—
919C2×Q82−1+414yes—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—22no—
927C2×D4—26no—
928C2×D4—43no—
929C2×D4—43no—
930C2×D4—43no—
931C2×D4—43no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—43no—
948C22×C4—43no—
949C22×C4—43no—
950C22×C4—43no—
951C22×C4—43no—
952C22×C4—46no—
953C22×C4—46no—
954C22×C4—46no—
955C22×C4C2×#41112yes—
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—212no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—22no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—43no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—46no—
1027C4⋊C4—41no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—46no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—46no—
1040C4⋊C4—46no—
1041C4⋊C4—46no—
1042C4⋊C4—46no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C22⋊C4—22no—
1050C22⋊C4—26no—
1051C22⋊C4—22no—
1052C22⋊C4—26no—
1053C22⋊C4—26no—
1054C22⋊C4—22no—
1055C22⋊C4—26no—
1056C22⋊C4—22no—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—212no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—46no—
1066C22⋊C4—43no—
1067C22⋊C4—41no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—41no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—46no—
1080C22⋊C4—46no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C42—212no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—43no—
1101C42—43no—
1102C42—43no—
1103C42—43no—
1104C42—43no—
1105C42—46no—
1106C42—43no—
1107C42—46no—
1108C42—43no—
1109C422−1+414yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—23no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
1128C23—23no—
1129C23C22×#4112yes—
1130C23#58512yes—
1131C23C2611yescharacteristic
1132Q8—224no—
1133Q8—412no—
1134Q8—86no—
1135Q8#539116yes—
1136D4—28no—
1137D4—412no—
1138D4—412no—
1139D4—86no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—224no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—21no—
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—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
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—21no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—412no—
1221C2×C4—412no—
1222C2×C4—86no—
1223C2×C4—86no—
1224C2×C4—166no—
1225C2×C4C22×#4116yes—
1226C2×C4C22×#4116yes—
1227C2×C4C2×H(5,𝔽2)16yes—
1228C2×C4C2×2−1+412yes—
1229C2×C4C2×2−1+412yes—
1230C2×C4C2×2−1+412yes—
1231C2×C4C2×2−1+416yes—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—43no—
1247C22—43no—
1248C22—43no—
1249C22—43no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22C23×#4111yescharacteristic
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C22×2−1+411yescharacteristic
1256C22C22×2−1+411yescharacteristic
1257C22C2×#58511yescharacteristic
1258C22H(7,𝔽2)11yescharacteristic
1259C222−1+611yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—26no—
1263C4—22no—
1264C4—41no—
1265C4—43no—
1266C4—41no—
1267C4—43no—
1268C4—41no—
1269C4—43no—
1270C4—43no—
1271C4—43no—
1272C4—43no—
1273C4—43no—
1274C4—43no—
1275C4—43no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—43no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—43no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4C2×#539112yes—
1288C2—42no—
1289C2—42no—
1290C2—83no—
1291C2C22×#53911yescharacteristic
1292C2#6278811yescharacteristic
1293C2#6285111yescharacteristic
1294C2#6289911yescharacteristic
1295C2#6291311yescharacteristic
1296C2#6294311yescharacteristic
1297C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35771C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42865C2semidirect
2. #42856C2semidirect
3. #42841C2semidirect
4. #42830C2semidirect
5. #42516C2semidirect
6. #42506C2semidirect
7. #42451C2semidirect
8. #42450C2semidirect
9. #40219C2semidirect
10. #40197C2semidirect
11. #39782C2semidirect
12. #39662C2semidirect
13. #37521C2semidirect
14. #37510C2semidirect
15. #36585C2semidirect
16. Q8×#125C2semidirect
17. #36483C2semidirect
18. #36435C2semidirect
19. #35996C2semidirect
20. #35883C2semidirect
21. #35868C2semidirect
22. #35845C2semidirect
23. #35816C2semidirect
24. #35801C2semidirect
26. #35723C2semidirect
27. #35047C2semidirect
28. #34592C2semidirect
29. #34294C2semidirect
30. #34249C2semidirect
31. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#428652
#428562
#428412
#428302
#425162
#425062
#424512
#424502
#402192
#401972
#397822
#396622
#375212
#375102
#365852
Q8×#1252
#364832
#364352
#359962
#358832
#358682
#358452
#358162
#358012
#357712
#357232
#350472
#345922
#342942
#342492
C4×D4×Q82