Finite Group Databasebeta

← #8096123

Subgroups — #8096123

Order 512.

5061 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53130C213yesmaximal, complemented
2#53127C213yesmaximal, complemented
3#53126C213yesmaximal, complemented
4#53097C213yesmaximal, complemented
5#53025C213yesmaximal, complemented
6#52992C213yesmaximal, complemented
7#52295C213yesmaximal, complemented
8#45718C213yesmaximal, complemented
9#45675C213yesmaximal, complemented
10#45653C213yesmaximal, complemented
11#45650C213yesmaximal, complemented
12#45631C213yesmaximal, complemented
13#45501C213yesmaximal, complemented
14#45486C213yesmaximal, complemented
15#45482C213yesmaximal, complemented
16#45482C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36483C211yesmaximal, characteristic, complemented
21#36482C211yesmaximal, characteristic, complemented
22#36456C211yesmaximal, characteristic, complemented
23#36444C211yesmaximal, characteristic, complemented
24#36434C211yesmaximal, characteristic, complemented
25#36433C211yesmaximal, characteristic, complemented
26#35996C211yesmaximal, characteristic, complemented
27#35948C211yesmaximal, characteristic, complemented
28#35948C211yesmaximal, characteristic, complemented
29#35868C211yesmaximal, characteristic, complemented
30#35831C211yesmaximal, characteristic, complemented
31#35748C211yesmaximal, characteristic, complemented
32C2×#562C2216yes—
33C2×Q82C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2857C2213yes—
46#2857C2213yes—
47#2857C2213yes—
48#2857C2213yes—
49#2856C2213yes—
50#2855C2213yes—
51#2854C2213yes—
52#2854C2213yes—
53#2850C2213yes—
54#2841C2216yes—
55#2836C2216yes—
56#2836C2216yes—
57#2832C2216yes—
58#2832C2216yes—
59#2831C2216yes—
60#2830C2216yes—
61#2827C2216yes—
62#2816C2216yes—
63#2814C2216yes—
64#2814C2216yes—
65#2806C2216yes—
66#2802C2213yes—
67#2800C2216yes—
68#2798C2213yes—
69#2788C2213yes—
70#2788C2216yes—
71#2786C2213yes—
72#2779C2213yes—
73#2751C2216yes—
74#2751C2213yes—
75#2747C2213yes—
76#2743C2213yes—
77#2741C2216yes—
78#2739C2213yes—
79#2710C2216yes—
80#2708C2216yes—
81#2708C2213yes—
82#2704C2216yes—
83#2704C2216yes—
84#2701C2213yes—
85#2701C2216yes—
86#2700C2216yes—
87#2700C2216yes—
88#2696C2213yes—
89#2694C2216yes—
90#2692C2216yes—
91#2692C2211yescharacteristic
92#2692C2216yes—
93#2687C2213yes—
94#2687C2216yes—
95#2687C2216yes—
96#2686C2216yes—
97#2686C2216yes—
98#2681C2216yes—
99#2681C2213yes—
100#2672C2216yes—
101#2671C2213yes—
102#2647C2213yes—
103#2640C2213yes—
104#2640C2213yes—
105#2628C2213yes—
106#2625C2213yes—
107#2620C2213yes—
108#2592C2213yes—
109#2592C2213yes—
110#2582C2213yes—
111#2582C2213yes—
112#2580C2213yes—
113#2570C2213yes—
114#2567C2213yes—
115#2567C2213yes—
116#2563C2213yes—
117#2552C2213yes—
118#2548C2213yes—
119#2547C2213yes—
120#2547C2213yes—
121#2547C2213yes—
122#2545C2213yes—
123#2544C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2537C2213yes—
128#2537C2213yes—
129#2536C2213yes—
130#2509C2213yes—
131#2507C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2503C2213yes—
135#2502C2213yes—
136#2501C2213yes—
137#2500C2213yes—
138#2492C2213yes—
139#2492C2213yes—
140#2492C2213yes—
141#2492C2213yes—
142#2491C2213yes—
143#2491C2213yes—
144#2491C2213yes—
145#2491C2213yes—
146#2486C2213yes—
147#2486C2213yes—
148#2486C2213yes—
149#2485C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2451C2213yes—
157#2451C2213yes—
158#2448C2213yes—
159#2448C2213yes—
160#2447C2213yes—
161#2447C2213yes—
162#2446C2213yes—
163#2446C2213yes—
164#2445C2213yes—
165#2445C2213yes—
166#2440C2213yes—
167#2440C2213yes—
168#2440C2213yes—
169#2440C2213yes—
170#2440C2213yes—
171#2440C2213yes—
172#2439C2213yes—
173#2439C2213yes—
174#2429C2213yes—
175#2428C2213yes—
176#2427C2213yes—
177#2427C2213yes—
178#2427C2213yes—
179#2426C2213yes—
180#2426C2213yes—
181#2426C2213yes—
182#2423C2213yes—
183#2423C2213yes—
184#2422C2213yes—
185#2422C2213yes—
186#2422C2213yes—
187#2421C2213yes—
188#2421C2213yes—
189#2420C2213yes—
190#2417C2213yes—
191#2417C2213yes—
192#2416C2213yes—
193#2416C2213yes—
194#2416C2213yes—
195#2416C2213yes—
196#2415C2213yes—
197#2415C2213yes—
198#2402C2213yes—
199#2398C2213yes—
200#2398C2213yes—
201#2396C2213yes—
202#2395C2213yes—
203#2392C2213yes—
204#2378C2216yes—
205#2376C2216yes—
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×#123C2213yes—
232C4×#123C2213yes—
233C4×#123C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237#2276C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#562—424no—
243Q82—44no—
244Q82—44no—
245#550—44no—
246D4×Q8—44no—
247#548—44no—
248#548—44no—
249#548—44no—
250#548—44no—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×C4⋊Q8C2313yes—
258C2×#127C2313yes—
259C2×#125C2316yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2316yes—
266C2×#123C2313yes—
267C2×#123C2313yes—
268C2×#123C2316yes—
269C2×#123C2316yes—
270C2×#123C2313yes—
271C2×#123C2316yes—
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2316yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2316yes—
280C2×C22⋊Q8C2316yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2316yes—
284C2×C22⋊Q8C2313yes—
285C2×C22⋊Q8C2316yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2316yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2313yes—
296C2×#121C2316yes—
297#520—44no—
298C4×#41—44no—
299C2×C4×Q8—44no—
300C2×C4×Q8—44no—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2313yes—
313C2×C4×Q8C2313yes—
314C2×C4×Q8C2313yes—
315C2×C4×Q8C2313yes—
316C2×C4×Q8C2313yes—
317C2×C4×Q8C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×#117C2313yes—
329C2×#117C2313yes—
330C22×C4⋊C4C2313yes—
331C22×C4⋊C4C2313yes—
332C22×C4⋊C4C2313yes—
333C22×C42C2313yes—
334C22×C42C2313yes—
335C22×C42C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2316yes—
339#400C2313yes—
340#400C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#399C2316yes—
350#399C2316yes—
351#399C2316yes—
352#399C2311yescharacteristic
353#399C2313yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#398C2316yes—
358#398C2313yes—
359#398C2316yes—
360#398C2313yes—
361#398C2316yes—
362#398C2316yes—
363#398C2316yes—
364#398C2316yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2311yescharacteristic
369#398C2313yes—
370#398C2313yes—
371#398C2316yes—
372#397C2313yes—
373#397C2313yes—
374#397C2316yes—
375#397C2316yes—
376#397C2316yes—
377#397C2316yes—
378#397C2316yes—
379#397C2316yes—
380#397C2313yes—
381#397C2316yes—
382#397C2313yes—
383#397C2316yes—
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#397C2316yes—
389#396C2316yes—
390#396C2316yes—
391#396C2313yes—
392#396C2316yes—
393#396C2316yes—
394#396C2316yes—
395#396C2316yes—
396#396C2311yescharacteristic
397#396C2313yes—
398#396C2313yes—
399#396C2316yes—
400#395C2316yes—
401#395C2316yes—
402#395C2316yes—
403#395C2316yes—
404#395C2316yes—
405#395C2311yescharacteristic
406#394C2313yes—
407#394C2313yes—
408#394C2316yes—
409#394C2316yes—
410#394C2316yes—
411#394C2316yes—
412#394C2316yes—
413#394C2313yes—
414#394C2316yes—
415#394C2316yes—
416#394C2316yes—
417#394C2316yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2316yes—
425#393C2316yes—
426#393C2316yes—
427#393C2316yes—
428#393C2316yes—
429#393C2316yes—
430#393C2313yes—
431#393C2313yes—
432#393C2316yes—
433#393C2316yes—
434#393C2313yes—
435#393C2311yescharacteristic
436#393C2311yescharacteristic
437#392C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2316yes—
443#391C2313yes—
444#391C2316yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2316yes—
455#391C2316yes—
456#391C2316yes—
457#391C2311yescharacteristic
458#390C2313yes—
459#390C2313yes—
460#390C2316yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2316yes—
472#390C2313yes—
473#390C2311yescharacteristic
474#390C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2316yes—
478#389C2316yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2316yes—
503#389C2313yes—
504#389C2313yes—
505#388C2316yes—
506#388C2313yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2313yes—
511#388C2316yes—
512#388C2316yes—
513#388C2316yes—
514#388C2316yes—
515#388C2313yes—
516#388C2316yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2316yes—
530#387C2313yes—
531#387C2316yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2311yescharacteristic
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#386C2316yes—
543#386C2313yes—
544#386C2316yes—
545#386C2313yes—
546#386C2316yes—
547#386C2316yes—
548#386C2311yescharacteristic
549#386C2313yes—
550#386C2313yes—
551#386C2313yes—
552#386C2313yes—
553#386C2313yes—
554#386C2311yescharacteristic
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2313yes—
559#385C2316yes—
560#385C2313yes—
561#385C2313yes—
562#385C2313yes—
563#385C2313yes—
564#385C2313yes—
565#385C2313yes—
566#385C2311yescharacteristic
567#385C2313yes—
568#384C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2313yes—
572#384C2313yes—
573#384C2313yes—
574#384C2313yes—
575#382C2313yes—
576#382C2313yes—
577#382C2313yes—
578#381C2313yes—
579#381C2313yes—
580#381C2316yes—
581#381C2316yes—
582#381C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2316yes—
601#380C2316yes—
602#380C2313yes—
603#380C2311yescharacteristic
604#380C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630#376C2313yes—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2411yescharacteristic
646C22×Q8C2411yescharacteristic
647C22×Q8C2416yes—
648C22×Q8C2416yes—
649C22×Q8C2411yescharacteristic
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2413yes—
657C22×D4C2416yes—
658C22×D4C2411yescharacteristic
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2411yescharacteristic
664C23×C4C2413yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2411yescharacteristic
669C23×C4C2416yes—
670C4⋊Q8—46no—
671C4⋊Q8—46no—
672C4⋊Q8—46no—
673C4⋊Q8—46no—
674C4⋊Q8—46no—
675C4⋊Q8—46no—
676C4⋊Q8—46no—
677#127—46no—
678#125—412no—
679#124—46no—
680#124—46no—
681#124—46no—
682#124—46no—
683#124—412no—
684#124—412no—
685#123—212no—
686#123—212no—
687#123—46no—
688#123—412no—
689#123—412no—
690#123—412no—
691C22⋊Q8—24no—
692C22⋊Q8—24no—
693C22⋊Q8—412no—
694C22⋊Q8—412no—
695C22⋊Q8—412no—
696C22⋊Q8—412no—
697C22⋊Q8—46no—
698C22⋊Q8—412no—
699C22⋊Q8—46no—
700C22⋊Q8—46no—
701C22⋊Q8—46no—
702C22⋊Q8—46no—
703C22⋊Q8—46no—
704C22⋊Q8—46no—
705#121—212no—
706#121—212no—
707#121—46no—
708#121—412no—
709#121—46no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—412no—
716C4×Q8—24no—
717C4×Q8—24no—
718C4×Q8—24no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—46no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8—46no—
733C4×D4—46no—
734C4×D4—46no—
735C4×D4—46no—
736C4×D4—46no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743#117—46no—
744#117—46no—
745C2×C4⋊C4—46no—
746C2×C4⋊C4—46no—
747C2×C4⋊C4—46no—
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⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2416yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2416yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2416yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C42—46no—
853C2×C42—46no—
854C2×C42—46no—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2416yes—
872C2×C42C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2416yes—
922#95C2416yes—
923#95C2416yes—
924#95C2416yes—
925#95C2416yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930C24C2513yes—
931C24C2513yes—
932C24C2511yescharacteristic
933C24C2511yescharacteristic
934#41—416no—
935#41—416no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—22no—
941C2×Q8—22no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—22no—
945C2×Q8—41no—
946C2×Q8—41no—
947C2×Q8—41no—
948C2×Q8—46no—
949C2×Q8—46no—
950C2×Q8—46no—
951C2×Q8—46no—
952C2×Q8—46no—
953C2×Q8—46no—
954C2×Q8—416no—
955C2×Q8—416no—
956C2×Q8H(5,𝔽2)14yes—
957C2×Q8H(5,𝔽2)14yes—
958C2×Q82−1+414yes—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—41no—
971C2×D4—41no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—46no—
983C2×D4—46no—
984C2×D4—46no—
985C2×D4H(5,𝔽2)14yes—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—22no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—43no—
1009C22×C4—43no—
1010C22×C4—43no—
1011C22×C4—43no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—46no—
1017C22×C4—46no—
1018C22×C4—46no—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2513yes—
1028C22×C4C2513yes—
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2513yes—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—43no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—43no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—43no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—46no—
1090C4⋊C4—46no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—46no—
1094C4⋊C4—46no—
1095C4⋊C4—46no—
1096C4⋊C4—46no—
1097C4⋊C4—46no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C4⋊C42−1+414yes—
1101C22⋊C4—26no—
1102C22⋊C4—26no—
1103C22⋊C4—26no—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—22no—
1118C22⋊C4—41no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—46no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—46no—
1139C22⋊C4—46no—
1140C22⋊C4—46no—
1141C22⋊C4—46no—
1142C22⋊C4—46no—
1143C22⋊C4—46no—
1144C22⋊C4—46no—
1145C22⋊C4—46no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—46no—
1149C22⋊C4—46no—
1150C42—26no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—26no—
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—41no—
1162C42—43no—
1163C42—43no—
1164C42—43no—
1165C42—43no—
1166C42—43no—
1167C42—46no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23C2×H(5,𝔽2)12yes—
1195C23C2×H(5,𝔽2)12yes—
1196C23C2611yescharacteristic
1197Q8—44no—
1198Q8—44no—
1199Q8—412no—
1200Q8—412no—
1201Q8—166no—
1202Q8—166no—
1203Q8#562116yescomplemented
1204D4—44no—
1205D4—412no—
1206D4—412no—
1207D4—86no—
1208D4—86no—
1209D4—86no—
1210D4—86no—
1211D4—86no—
1212D4—166no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—21no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—412no—
1289C2×C4—412no—
1290C2×C4—412no—
1291C2×C4—412no—
1292C2×C4—86no—
1293C2×C4—86no—
1294C2×C4—86no—
1295C2×C4—86no—
1296C2×C4—166no—
1297C2×C4C2×H(5,𝔽2)12yes—
1298C2×C4C2×H(5,𝔽2)16yes—
1299C2×C4C2×H(5,𝔽2)16yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4C2×2−1+412yes—
1302C2×C4C2×2−1+412yes—
1303C2×C4C2×2−1+416yes—
1304C2×C4#58512yes—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22—43no—
1331C22—43no—
1332C22—43no—
1333C22C22×H(5,𝔽2)11yescharacteristic
1334C22C22×H(5,𝔽2)11yescharacteristic
1335C22C22×H(5,𝔽2)11yescharacteristic
1336C22C22×2−1+411yescharacteristic
1337C22C22×2−1+411yescharacteristic
1338C22C2×#58511yescharacteristic
1339C222−1+611yescharacteristic
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—43no—
1346C4—43no—
1347C4—43no—
1348C4—43no—
1349C4—43no—
1350C4—43no—
1351C4—41no—
1352C4—43no—
1353C4—43no—
1354C4—43no—
1355C4—43no—
1356C4—43no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—43no—
1364C4—43no—
1365C4—41no—
1366C4C2×#562112yes—
1367C2—42no—
1368C2—42no—
1369C2—83no—
1370C2—83no—
1371C2C22×#56211yescharacteristic
1372C2#6289511yescharacteristic
1373C2#6291311yescharacteristic
1374C2#6295311yescharacteristic
1375C2#6301411yescharacteristic
1376C2#6301511yescharacteristic
1377C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53130C2semidirect
2. #53127C2semidirect
3. #53126C2semidirect
4. #53097C2semidirect
5. #53025C2semidirect
6. #52992C2semidirect
7. #52295C2semidirect
8. #45718C2semidirect
9. #45675C2semidirect
10. #45653C2semidirect
11. #45650C2semidirect
12. #45631C2semidirect
13. #45501C2semidirect
14. #45486C2semidirect
15. #45482C2semidirect
16. #45482C2semidirect
17. #36576C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36483C2semidirect
21. #36482C2semidirect
22. #36456C2semidirect
23. #36444C2semidirect
24. #36434C2semidirect
25. #36433C2semidirect
26. #35996C2semidirect
27. #35948C2semidirect
28. #35948C2semidirect
29. #35868C2semidirect
30. #35831C2semidirect
31. #35748C2semidirect
1203. Q8#562semidirect

Maximal subgroups

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

subgroupindex
#531302
#531272
#531262
#530972
#530252
#529922
#522952
#457182
#456752
#456532
#456502
#456312
#455012
#454862
#454822
#365762
Q8×C22⋊Q82
#364832
#364822
#364562
#364442
#364342
#364332
#359962
#359482
#358682
#358312
#357482