Finite Group Databasebeta

← #7659114

Subgroups — #7659114

Order 512.

5342 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52288C213yesmaximal, complemented
2#42954C213yesmaximal, complemented
3#42931C213yesmaximal, complemented
4#42930C213yesmaximal, complemented
5#42930C213yesmaximal, complemented
6#42817C213yesmaximal, complemented
7#42816C213yesmaximal, complemented
8#39984C213yesmaximal, complemented
9#39981C213yesmaximal, complemented
10#39981C213yesmaximal, complemented
11#39980C213yesmaximal, complemented
12#39624C213yesmaximal, complemented
13#39179C213yesmaximal, complemented
14#37310C213yesmaximal, complemented
15#37310C213yesmaximal, complemented
16#37306C213yesmaximal, complemented
17#36577C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36456C211yesmaximal, characteristic, complemented
21#36435C211yesmaximal, characteristic, complemented
22#36431C211yesmaximal, characteristic, complemented
23#35845C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#35786C211yesmaximal, characteristic, complemented
26#35748C211yesmaximal, characteristic, complemented
27#35711C211yesmaximal, characteristic, complemented
28#35711C211yesmaximal, characteristic, complemented
29#34259C211yesmaximal, characteristic
30#34257C211yesmaximal, characteristic
31#34257C211yesmaximal, characteristic
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43#2857C2213yes—
44#2857C2213yes—
45#2857C2213yes—
46#2857C2213yes—
47#2851C2213yes—
48#2851C2213yes—
49#2841C2216yes—
50#2841C2216yes—
51#2811C2216yes—
52#2809C2216yes—
53#2806C2216yes—
54#2806C2213yes—
55#2806C2216yes—
56#2806C2213yes—
57#2804C2216yes—
58#2804C2213yes—
59#2799C2213yes—
60#2799C2216yes—
61#2799C2216yes—
62#2799C2213yes—
63#2784C2216yes—
64#2784C2216yes—
65#2780C2213yes—
66#2780C2216yes—
67#2780C2216yes—
68#2780C2213yes—
69#2780C2213yes—
70#2780C2213yes—
71#2748C2213yes—
72#2748C2213yes—
73#2732C2216yes—
74#2732C2216yes—
75#2692C2216yes—
76#2692C2216yes—
77#2692C2216yes—
78#2692C2213yes—
79#2692C2211yescharacteristic
80#2692C2213yes—
81#2692C2213yes—
82#2692C2216yes—
83#2692C2216yes—
84#2683C2213yes—
85#2683C2216yes—
86#2667C2216yes—
87#2665C2216yes—
88#2665C2216yes—
89#2665C2216yes—
90#2659C2216yes—
91#2646C2216yes—
92#2629C2213yes—
93#2629C2213yes—
94#2628C2213yes—
95#2628C2213yes—
96#2628C2213yes—
97#2628C2213yes—
98#2608C2216yes—
99#2607C2216yes—
100#2582C2213yes—
101#2582C2213yes—
102#2582C2213yes—
103#2582C2213yes—
104#2581C2213yes—
105#2581C2213yes—
106#2581C2213yes—
107#2581C2213yes—
108#2580C2213yes—
109#2580C2213yes—
110#2569C2216yes—
111#2568C2213yes—
112#2568C2213yes—
113#2568C2213yes—
114#2567C2213yes—
115#2567C2213yes—
116#2567C2213yes—
117#2566C2213yes—
118#2566C2213yes—
119#2565C2213yes—
120#2565C2213yes—
121#2563C2213yes—
122#2549C2216yes—
123#2549C2216yes—
124#2549C2216yes—
125#2542C2213yes—
126#2538C2213yes—
127#2538C2213yes—
128#2454C2213yes—
129#2454C2213yes—
130#2453C2213yes—
131#2453C2213yes—
132#2453C2213yes—
133#2453C2213yes—
134#2453C2213yes—
135#2453C2213yes—
136#2452C2213yes—
137#2452C2213yes—
138#2452C2213yes—
139#2452C2213yes—
140#2452C2213yes—
141#2452C2213yes—
142#2451C2213yes—
143#2451C2213yes—
144#2451C2213yes—
145#2451C2213yes—
146#2451C2213yes—
147#2451C2213yes—
148#2451C2213yes—
149#2451C2213yes—
150#2451C2213yes—
151#2451C2213yes—
152#2442C2213yes—
153#2442C2213yes—
154#2442C2213yes—
155#2442C2213yes—
156#2441C2213yes—
157#2441C2213yes—
158#2441C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2440C2213yes—
163#2440C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2440C2213yes—
168#2439C2213yes—
169#2439C2213yes—
170#2439C2213yes—
171#2439C2213yes—
172#2439C2213yes—
173#2439C2213yes—
174#2439C2213yes—
175#2439C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2396C2213yes—
179#2396C2213yes—
180#2396C2213yes—
181#2396C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194#2341C2213yes—
195#2341C2213yes—
196#2341C2213yes—
197#2341C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2213yes—
205Q8×C22⋊C4C2213yes—
206Q8×C22⋊C4C2213yes—
207Q8×C22⋊C4C2213yes—
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2339C2213yes—
215#2339C2213yes—
216#2339C2213yes—
217#2339C2213yes—
218#2329C2216yes—
219#2329C2216yes—
220#2311C2213yes—
221#2311C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224#2311C2213yes—
225#2310C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×C22⋊Q8C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2297C2213yes—
235#2297C2213yes—
236#2297C2213yes—
237C2×#391C2213yes—
238C2×2−1+4—44no—
239C2×2−1+4—44no—
240C2×2−1+4Q8116yescomplemented
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×Q8C2313yes—
248Q82—44no—
249Q82—44no—
250#557—44no—
251#557—44no—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×C4⋊Q8C2313yes—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2316yes—
272C2×C22⋊Q8C2316yes—
273C2×C22⋊Q8C2316yes—
274C2×C22⋊Q8C2316yes—
275C2×C22⋊Q8C2316yes—
276#520—44no—
277#519—44no—
278#519—44no—
279C4×#41—44no—
280C2×C4×Q8—44no—
281C2×C4×Q8—44no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C2×#117C2313yes—
315C2×#117C2313yes—
316C22×C4⋊C4C2313yes—
317C22×C4⋊C4C2313yes—
318C22×C4⋊C4C2313yes—
319C22×C42C2313yes—
320C22×C42C2313yes—
321C22×C42C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2313yes—
329#400C2316yes—
330#400C2313yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#399C2316yes—
335#399C2316yes—
336#399C2313yes—
337#399C2313yes—
338#399C2313yes—
339#399C2316yes—
340#399C2311yescharacteristic
341#399C2313yes—
342#399C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2316yes—
349#398C2313yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2313yes—
356#398C2313yes—
357#398C2316yes—
358#398C2313yes—
359#398C2316yes—
360#398C2311yescharacteristic
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#396C2313yes—
367#396C2316yes—
368#396C2316yes—
369#396C2316yes—
370#396C2313yes—
371#396C2316yes—
372#396C2313yes—
373#396C2316yes—
374#396C2313yes—
375#396C2316yes—
376#396C2316yes—
377#396C2311yescharacteristic
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#395C2313yes—
386#395C2316yes—
387#395C2316yes—
388#395C2316yes—
389#395C2316yes—
390#395C2316yes—
391#395C2313yes—
392#395C2313yes—
393#395C2316yes—
394#395C2316yes—
395#395C2316yes—
396#395C2316yes—
397#395C2311yescharacteristic
398#395C2313yes—
399#395C2313yes—
400#393C2316yes—
401#393C2316yes—
402#393C2313yes—
403#393C2316yes—
404#393C2313yes—
405#393C2313yes—
406#393C2316yes—
407#393C2316yes—
408#393C2316yes—
409#393C2311yescharacteristic
410#393C2311yescharacteristic
411#393C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2316yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2316yes—
425#391C2316yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2316yes—
433#391C2313yes—
434#391C2316yes—
435#391C2316yes—
436#391C2316yes—
437#391C2316yes—
438#391C2313yes—
439#391C2313yes—
440#391C2316yes—
441#391C2316yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2316yes—
447#391C2316yes—
448#391C2313yes—
449#391C2311yescharacteristic
450#391C2313yes—
451#391C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2316yes—
461#390C2316yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2311yescharacteristic
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2316yes—
472#389C2316yes—
473#389C2316yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2316yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2316yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#387C2313yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2316yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2313yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2311yescharacteristic
526#387C2313yes—
527#386C2316yes—
528#386C2313yes—
529#386C2313yes—
530#386C2313yes—
531#386C2313yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2313yes—
536#386C2313yes—
537#386C2313yes—
538#386C2313yes—
539#386C2313yes—
540#386C2311yescharacteristic
541#386C2311yescharacteristic
542#386C2313yes—
543#385C2313yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#385C2316yes—
549#385C2313yes—
550#385C2316yes—
551#385C2313yes—
552#385C2313yes—
553#385C2316yes—
554#385C2313yes—
555#385C2313yes—
556#385C2313yes—
557#385C2313yes—
558#385C2311yescharacteristic
559#385C2313yes—
560#385C2313yes—
561#385C2313yes—
562#384C2313yes—
563#384C2313yes—
564#384C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#381C2316yes—
575#381C2316yes—
576#380C2313yes—
577#380C2316yes—
578#380C2316yes—
579#380C2316yes—
580#380C2316yes—
581#380C2316yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2316yes—
595#380C2313yes—
596#380C2313yes—
597#380C2316yes—
598#380C2313yes—
599#380C2313yes—
600#380C2311yescharacteristic
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
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×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊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—
629C2×#95C2316yes—
630C2×#95C2316yes—
6312−1+4—464no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—46no—
635C2×#41—46no—
636C2×#41—46no—
637C2×#41—46no—
638C2×#41—46no—
639C2×#41—46no—
640C2×#41C2×Q818yes—
641C2×#41C2×Q8124yes—
642C2×#41C2×Q8124yes—
643C2×#41C2×Q8124yes—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—46no—
649C22×Q8—46no—
650C22×Q8C2×Q818yes—
651C22×Q8C2×Q818yes—
652C22×Q8C2×Q8124yes—
653C22×Q8C2411yescharacteristic
654C22×Q8C2413yes—
655C22×Q8C2413yes—
656C22×Q8C2411yescharacteristic
657C22×Q8C2413yes—
658C22×Q8C2413yes—
659C22×Q8C2416yes—
660C22×Q8C2416yes—
661C22×Q8C2413yes—
662C22×Q8C2411yescharacteristic
663C22×D4C2413yes—
664C22×D4C2411yescharacteristic
665C22×D4C2413yes—
666C22×D4C2413yes—
667C23×C4C2411yescharacteristic
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2411yescharacteristic
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2416yes—
676C23×C4C2413yes—
677C23×C4C2416yes—
678C4⋊Q8—46no—
679C4⋊Q8—46no—
680C4⋊Q8—46no—
681C4⋊Q8—46no—
682C4⋊Q8—46no—
683C4⋊Q8—46no—
684C4⋊Q8—46no—
685C4⋊Q8—46no—
686#125—46no—
687#125—46no—
688#125—46no—
689#125—46no—
690C22⋊Q8—24no—
691C22⋊Q8—24no—
692C22⋊Q8—212no—
693C22⋊Q8—46no—
694C22⋊Q8—412no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697C22⋊Q8—86no—
698C22⋊Q8—86no—
699C22⋊Q8—86no—
700C22⋊Q8—86no—
701C22⋊Q8—86no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×Q8—46no—
719C4×Q8—46no—
720C4×Q8—46no—
721C4×Q8—46no—
722C4×Q8—46no—
723C4×Q8—46no—
724C4×Q8—46no—
725C4×Q8—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—46no—
730#117—46no—
731#117—46no—
732#117—46no—
733#117—46no—
734#117—46no—
735#117—46no—
736C2×C4⋊C4—46no—
737C2×C4⋊C4—46no—
738C2×C4⋊C4—46no—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2416yes—
838C2×C42—46no—
839C2×C42—46no—
840C2×C42—46no—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2416yes—
855C2×C42C2416yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2411yescharacteristic
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2413yes—
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2416yes—
883#95C2416yes—
884#95C2413yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
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#95C2416yes—
918#95C2416yes—
919#95C2416yes—
920#95C2416yes—
921#95C2416yes—
922#95C2416yes—
923C24C2511yescharacteristic
924C24C2511yescharacteristic
925C24C2513yes—
926#41—232no—
927#41—448no—
928#41—448no—
929#41—448no—
930C2×Q8—232no—
931C2×Q8—232no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—22no—
937C2×Q8—22no—
938C2×Q8—26no—
939C2×Q8—22no—
940C2×Q8—41no—
941C2×Q8—41no—
942C2×Q8—43no—
943C2×Q8—43no—
944C2×Q8—41no—
945C2×Q8—43no—
946C2×Q8—43no—
947C2×Q8—43no—
948C2×Q8—43no—
949C2×Q8—43no—
950C2×Q8—46no—
951C2×Q8—46no—
952C2×Q8—46no—
953C2×Q8—46no—
954C2×Q8—46no—
955C2×Q8—46no—
956C2×Q8—448no—
957C2×Q8C22×Q8112yes—
958C2×Q8C22×Q8112yes—
959C2×Q8C22×Q8112yes—
960C2×Q8C22×Q814yes—
961C2×Q8H(5,𝔽2)14yes—
962C2×Q8H(5,𝔽2)14yes—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—41no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—41no—
971C2×D4C22×Q8112yes—
972C2×D4C22×Q814yes—
973C2×D4C22×Q8112yes—
974C2×D4C22×Q8112yes—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—26no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—46no—
989C22×C4—46no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—43no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—43no—
999C22×C4—43no—
1000C22×C4—43no—
1001C22×C4—46no—
1002C22×C4—46no—
1003C22×C4—46no—
1004C22×C4C22×Q8112yes—
1005C22×C4C22×Q8112yes—
1006C22×C4C22×Q8112yes—
1007C22×C4C22×Q8124yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2513yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C22×C4C2513yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—43no—
1058C4⋊C4—46no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—41no—
1064C4⋊C4—43no—
1065C4⋊C4—41no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—46no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—46no—
1092C4⋊C4—46no—
1093C4⋊C4—46no—
1094C4⋊C4—46no—
1095C4⋊C4—43no—
1096C4⋊C4—46no—
1097C4⋊C4—46no—
1098C4⋊C4—46no—
1099C4⋊C42−1+414yescomplemented
1100C22⋊C4—26no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—26no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—26no—
1107C22⋊C4—22no—
1108C22⋊C4—41no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—46no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—46no—
1130C22⋊C4—43no—
1131C22⋊C4—46no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—41no—
1148C42—43no—
1149C42—43no—
1150C42—43no—
1151C42—43no—
1152C42—43no—
1153C42—46no—
1154C42—46no—
1155C23—21no—
1156C23—21no—
1157C23—23no—
1158C23—23no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—23no—
1163C23—21no—
1164C23—23no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—23no—
1169C23—21no—
1170C23—23no—
1171C23—21no—
1172C23—21no—
1173C23C23×Q812yes—
1174C23C23×Q812yes—
1175C23C23×Q816yes—
1176C23C2611yescharacteristic
1177Q8—224no—
1178Q8—224no—
1179Q8—412no—
1180Q8—44no—
1181Q8—44no—
1182Q8—86no—
1183Q8—86no—
1184Q8—166no—
1185Q8—166no—
1186Q8#543116yes—
1187D4—224no—
1188D4—44no—
1189D4—412no—
1190D4—412no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—224no—
1206C2×C4—224no—
1207C2×C4—224no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—21no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—424no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—86no—
1272C2×C4—86no—
1273C2×C4—86no—
1274C2×C4—86no—
1275C2×C4—166no—
1276C2×C4C23×Q812yes—
1277C2×C4C23×Q816yes—
1278C2×C4C23×Q816yes—
1279C2×C4C23×Q816yes—
1280C2×C4C2×H(5,𝔽2)16yes—
1281C2×C4C2×H(5,𝔽2)16yes—
1282C2×C4C2×2−1+412yes—
1283C2×C4C2×2−1+412yes—
1284C2×C4C2×2−1+412yes—
1285C2×C4#58512yes—
1286C22—22no—
1287C22—22no—
1288C22—26no—
1289C22—22no—
1290C22—26no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—26no—
1295C22—41no—
1296C22—43no—
1297C22—41no—
1298C22—41no—
1299C22—43no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—43no—
1304C22—41no—
1305C22—43no—
1306C22—41no—
1307C22C24×Q811yescharacteristic
1308C22C22×H(5,𝔽2)11yescharacteristic
1309C22C22×H(5,𝔽2)11yescharacteristic
1310C22C22×2−1+411yescharacteristic
1311C22C2×#58511yescharacteristic
1312C22H(7,𝔽2)11yescharacteristic
1313C222−1+611yescharacteristic
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—26no—
1320C4—26no—
1321C4—43no—
1322C4—41no—
1323C4—43no—
1324C4—41no—
1325C4—43no—
1326C4—41no—
1327C4—43no—
1328C4—43no—
1329C4—43no—
1330C4—41no—
1331C4—43no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—43no—
1336C4—43no—
1337C4—43no—
1338C4—43no—
1339C4—41no—
1340C4—43no—
1341C4C2×#543112yes—
1342C2—42no—
1343C2—42no—
1344C2—46no—
1345C2C22×#54311yescharacteristic
1346C2#6291311yescharacteristic
1347C2#6292311yescharacteristic
1348C2Q8×2−1+411yescharacteristic
1349C2#6300411yescharacteristic
1350C2#6301511yescharacteristic
1351C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×2−1+4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52288C2semidirect
2. #42954C2semidirect
3. #42931C2semidirect
4. #42930C2semidirect
5. #42930C2semidirect
6. #42817C2semidirect
7. #42816C2semidirect
8. #39984C2semidirect
9. #39981C2semidirect
10. #39981C2semidirect
11. #39980C2semidirect
12. #39624C2semidirect
13. #39179C2semidirect
14. #37310C2semidirect
15. #37310C2semidirect
16. #37306C2semidirect
17. #36577C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36456C2semidirect
21. #36435C2semidirect
22. #36431C2semidirect
23. #35845C2semidirect
24. #35816C2semidirect
25. #35786C2semidirect
26. #35748C2semidirect
27. #35711C2semidirect
28. #35711C2semidirect
240. C2×2−1+4Q8semidirect
1099. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#522882
#429542
#429312
#429302
#428172
#428162
#399842
#399812
#399802
#396242
#391792
#373102
#373062
#365772
Q8×C22⋊Q82
#364562
#364352
#364312
#358452
#358162
#357862
#357482
#357112
#342592
#342572