Finite Group Databasebeta

← #8091825

Subgroups — #8091825

Order 512.

5148 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46083C213yesmaximal, complemented
2#46044C213yesmaximal, complemented
3#46042C213yesmaximal, complemented
4#45718C213yesmaximal, complemented
5#45717C213yesmaximal, complemented
6#45689C213yesmaximal, complemented
7#45676C213yesmaximal, complemented
8#45670C213yesmaximal, complemented
9#45653C213yesmaximal, complemented
10#45650C213yesmaximal, complemented
11#45609C213yesmaximal, complemented
12#45602C213yesmaximal, complemented
13#45524C213yesmaximal, complemented
14#45514C213yesmaximal, complemented
15#45484C213yesmaximal, complemented
16#36578C211yesmaximal, characteristic, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36467C211yesmaximal, characteristic, complemented
21#36457C211yesmaximal, characteristic, complemented
22#36456C211yesmaximal, characteristic, complemented
23#36455C211yesmaximal, characteristic, complemented
24#36445C211yesmaximal, characteristic, complemented
25#36433C211yesmaximal, characteristic, complemented
26#36433C211yesmaximal, characteristic, complemented
27#36432C211yesmaximal, characteristic, complemented
28#36431C211yesmaximal, characteristic, complemented
29#36430C211yesmaximal, characteristic, complemented
30#36430C211yesmaximal, characteristic, complemented
31C4×#562C213yesmaximal, complemented
32C2×#562C2213yes—
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2864C2213yes—
46#2861C2213yes—
47#2858C2213yes—
48#2857C2213yes—
49#2857C2213yes—
50#2857C2213yes—
51#2856C2213yes—
52#2856C2213yes—
53#2855C2213yes—
54#2854C2213yes—
55#2854C2213yes—
56#2854C2213yes—
57#2851C2213yes—
58#2850C2213yes—
59#2850C2213yes—
60#2837C2216yes—
61#2832C2216yes—
62#2830C2216yes—
63#2829C2216yes—
64#2813C2216yes—
65#2800C2216yes—
66#2800C2216yes—
67#2798C2216yes—
68#2788C2216yes—
69#2783C2216yes—
70#2779C2216yes—
71#2761C2216yes—
72#2751C2216yes—
73#2741C2216yes—
74#2740C2216yes—
75#2730C2216yes—
76#2730C2216yes—
77#2730C2216yes—
78#2711C2216yes—
79#2710C2216yes—
80#2708C2216yes—
81#2706C2216yes—
82#2701C2216yes—
83#2700C2216yes—
84#2696C2216yes—
85#2696C2216yes—
86#2692C2216yes—
87#2686C2216yes—
88#2686C2216yes—
89#2681C2216yes—
90#2681C2216yes—
91#2676C2216yes—
92#2676C2216yes—
93#2672C2216yes—
94#2671C2216yes—
95#2592C2213yes—
96#2582C2213yes—
97#2580C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2567C2213yes—
101#2566C2213yes—
102#2563C2213yes—
103#2563C2213yes—
104#2562C2213yes—
105#2548C2213yes—
106#2548C2213yes—
107#2544C2213yes—
108#2544C2213yes—
109#2542C2213yes—
110#2541C2213yes—
111#2538C2213yes—
112#2538C2213yes—
113#2538C2213yes—
114#2537C2213yes—
115#2535C2213yes—
116#2535C2213yes—
117#2509C2213yes—
118#2508C2213yes—
119#2507C2213yes—
120#2506C2213yes—
121#2504C2213yes—
122#2500C2213yes—
123#2500C2213yes—
124#2499C2213yes—
125#2492C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2491C2213yes—
129#2491C2213yes—
130#2491C2213yes—
131#2490C2213yes—
132#2489C2213yes—
133#2487C2213yes—
134#2485C2213yes—
135#2485C2213yes—
136#2485C2213yes—
137#2454C2213yes—
138#2454C2213yes—
139#2454C2213yes—
140#2452C2213yes—
141#2452C2213yes—
142#2452C2213yes—
143#2451C2213yes—
144#2451C2213yes—
145#2448C2213yes—
146#2448C2213yes—
147#2447C2213yes—
148#2447C2213yes—
149#2445C2213yes—
150#2445C2213yes—
151#2445C2213yes—
152#2445C2213yes—
153#2441C2213yes—
154#2441C2213yes—
155#2441C2213yes—
156#2440C2213yes—
157#2440C2213yes—
158#2439C2213yes—
159#2439C2213yes—
160#2439C2213yes—
161#2428C2213yes—
162#2428C2213yes—
163#2428C2213yes—
164#2428C2213yes—
165#2427C2213yes—
166#2427C2213yes—
167#2426C2213yes—
168#2426C2213yes—
169#2422C2213yes—
170#2422C2213yes—
171#2422C2213yes—
172#2421C2213yes—
173#2421C2213yes—
174#2420C2213yes—
175#2420C2213yes—
176#2420C2213yes—
177#2416C2213yes—
178#2416C2213yes—
179#2415C2213yes—
180#2415C2213yes—
181#2414C2213yes—
182#2414C2213yes—
183#2414C2213yes—
184#2414C2213yes—
185#2382C2213yes—
186#2379C2213yes—
187#2379C2213yes—
188#2378C2213yes—
189#2378C2211yescharacteristic
190#2378C2213yes—
191#2378C2213yes—
192#2377C2213yes—
193#2377C2213yes—
194#2377C2213yes—
195#2377C2213yes—
196#2376C2213yes—
197#2376C2213yes—
198#2376C2213yes—
199#2376C2213yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222C4×#125C2213yes—
223C4×#124C2213yes—
224C4×#124C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#123C2213yes—
231C4×#123C2213yes—
232C4×#123C2213yes—
233C4×#121C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#562—224no—
243Q82—44no—
244#557—44no—
245#550—44no—
246#550—44no—
247#550—44no—
248#548—44no—
249#548—44no—
250#548—44no—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#124C2316yes—
267C2×#124C2316yes—
268C2×#123C2313yes—
269C2×#123C2313yes—
270C2×#123C2313yes—
271C2×#123C2313yes—
272C2×#123C2316yes—
273C2×#123C2316yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2316yes—
281C2×C22⋊Q8C2316yes—
282C2×C22⋊Q8C2316yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2313yes—
296C2×#121C2313yes—
297C2×#121C2316yes—
298C2×#121C2316yes—
299C2×#121C2316yes—
300C4×#41—44no—
301C4×#41—44no—
302C4×#41—44no—
303C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2313yes—
316C2×C4×Q8C2313yes—
317C2×C4×Q8C2313yes—
318C2×C4×Q8C2313yes—
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×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C2×#117C2313yes—
334C22×C4⋊C4C2313yes—
335C22×C42C2313yes—
336C22×C42C2313yes—
337C22×C42C2313yes—
338C22×C42C2313yes—
339#400C2316yes—
340#400C2316yes—
341#400C2316yes—
342#400C2316yes—
343#399C2316yes—
344#399C2316yes—
345#399C2316yes—
346#399C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#396C2316yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2316yes—
368#396C2316yes—
369#395C2316yes—
370#395C2316yes—
371#394C2316yes—
372#394C2316yes—
373#394C2316yes—
374#394C2316yes—
375#394C2316yes—
376#394C2316yes—
377#394C2316yes—
378#394C2316yes—
379#394C2316yes—
380#394C2316yes—
381#394C2316yes—
382#394C2316yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2316yes—
388#394C2316yes—
389#393C2316yes—
390#393C2316yes—
391#393C2316yes—
392#393C2316yes—
393#393C2316yes—
394#393C2316yes—
395#392C2316yes—
396#392C2316yes—
397#392C2316yes—
398#392C2316yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2316yes—
408#391C2316yes—
409#391C2311yescharacteristic
410#391C2313yes—
411#391C2311yescharacteristic
412#391C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2316yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2316yes—
435#390C2316yes—
436#390C2316yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2316yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2311yescharacteristic
468#389C2313yes—
469#389C2311yescharacteristic
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#388C2313yes—
474#388C2316yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2311yescharacteristic
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2311yescharacteristic
497#388C2311yescharacteristic
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2311yescharacteristic
504#388C2313yes—
505#388C2313yes—
506#387C2311yescharacteristic
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2311yescharacteristic
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2311yescharacteristic
528#387C2311yescharacteristic
529#387C2313yes—
530#387C2313yes—
531#386C2316yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2313yes—
539#386C2313yes—
540#386C2313yes—
541#386C2313yes—
542#386C2313yes—
543#386C2313yes—
544#386C2313yes—
545#386C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2313yes—
549#386C2313yes—
550#385C2313yes—
551#385C2316yes—
552#385C2313yes—
553#385C2316yes—
554#385C2316yes—
555#385C2313yes—
556#385C2313yes—
557#385C2313yes—
558#385C2313yes—
559#385C2313yes—
560#385C2313yes—
561#385C2313yes—
562#385C2313yes—
563#385C2313yes—
564#385C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#382C2313yes—
575#382C2313yes—
576#382C2313yes—
577#382C2313yes—
578#381C2316yes—
579#381C2311yescharacteristic
580#381C2313yes—
581#381C2313yes—
582#381C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2316yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2316yes—
599#380C2311yescharacteristic
600#380C2313yes—
601#380C2313yes—
602#380C2313yes—
603#380C2313yes—
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—
630C43C2313yes—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2416yes—
646C22×Q8C2411yescharacteristic
647C22×Q8C2411yescharacteristic
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2413yes—
657C22×D4C2416yes—
658C22×D4C2416yes—
659C22×D4C2416yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2413yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C4⋊Q8—46no—
673C4⋊Q8—46no—
674C4⋊Q8—46no—
675C4⋊Q8—46no—
676#127—46no—
677#127—46no—
678#127—46no—
679#125—212no—
680#125—46no—
681#125—46no—
682#124—212no—
683#124—212no—
684#124—46no—
685#124—46no—
686#124—46no—
687#124—86no—
688#124—86no—
689#123—212no—
690#123—212no—
691#123—212no—
692#123—212no—
693#123—86no—
694#123—86no—
695C22⋊Q8—212no—
696C22⋊Q8—212no—
697C22⋊Q8—212no—
698C22⋊Q8—46no—
699C22⋊Q8—46no—
700C22⋊Q8—46no—
701C22⋊Q8—86no—
702C22⋊Q8—86no—
703C22⋊Q8—86no—
704C22⋊Q8#4118yescomplemented
705#121—212no—
706#121—212no—
707#121—212no—
708#121—212no—
709#121—46no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—46no—
716#121—46no—
717#121—46no—
718#121—86no—
719#121—86no—
720#121—86no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—46no—
733C4×Q8—46no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×D4—46no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748#117—46no—
749#117—46no—
750#117—46no—
751C2×C4⋊C4—46no—
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⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2416yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C42—46no—
854C2×C42—46no—
855C2×C42—46no—
856C2×C42—46no—
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×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
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#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2416yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930#95C2416yes—
931#95C2416yes—
932#95C2416yes—
933C24C2513yes—
934C24C2513yes—
935C24C2513yes—
936C24C2511yescharacteristic
937#41—416no—
938#41—416no—
939#41—416no—
940C2×Q8—26no—
941C2×Q8—26no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—41no—
945C2×Q8—41no—
946C2×Q8—43no—
947C2×Q8—43no—
948C2×Q8—46no—
949C2×Q8—46no—
950C2×Q8—46no—
951C2×Q8—416no—
952C2×Q8C2×#4114yes—
953C2×Q8H(5,𝔽2)14yes—
954C2×Q8H(5,𝔽2)14yes—
955C2×Q82−1+414yes—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
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—26no—
971C2×D4—43no—
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—43no—
983C2×D4—46no—
984C2×D4—46no—
985C2×D4—46no—
986C2×D4—46no—
987C2×D4—46no—
988C2×D4—46no—
989C2×D4—46no—
990C2×D4—46no—
991C2×D4—46no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—26no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—43no—
1010C22×C4—43no—
1011C22×C4—43no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—43no—
1017C22×C4—43no—
1018C22×C4—43no—
1019C22×C4—43no—
1020C22×C4—43no—
1021C22×C4—43no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4C2×#4114yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2513yes—
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—46no—
1074C4⋊C4—43no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—43no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—41no—
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—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—46no—
1097C4⋊C4—46no—
1098C4⋊C4—46no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—46no—
1102C4⋊C4C2×#4114yes—
1103C4⋊C4C2×#4114yes—
1104C4⋊C4C2×#4114yes—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—26no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—43no—
1116C22⋊C4—41no—
1117C22⋊C4—46no—
1118C22⋊C4—46no—
1119C22⋊C4—46no—
1120C22⋊C4—46no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—46no—
1134C22⋊C4—46no—
1135C22⋊C4—46no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—46no—
1139C22⋊C4—46no—
1140C22⋊C4—46no—
1141C22⋊C4—46no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—46no—
1145C22⋊C4—46no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—46no—
1149C22⋊C4—46no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4C2×#4114yes—
1155C22⋊C4C2×#4114yes—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—41no—
1169C42—41no—
1170C42—41no—
1171C42—43no—
1172C42—43no—
1173C42—43no—
1174C42—43no—
1175C42—43no—
1176C42—41no—
1177C42—43no—
1178C42—43no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23C22×#4112yes—
1207C23C2611yescharacteristic
1208Q8—44no—
1209Q8—412no—
1210Q8—86no—
1211Q8—166no—
1212Q8#562116yescomplemented
1213D4—412no—
1214D4—412no—
1215D4—412no—
1216D4—86no—
1217D4—86no—
1218D4—86no—
1219D4—86no—
1220D4—86no—
1221D4—86no—
1222D4—166no—
1223D4—166no—
1224D4—166no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
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—21no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—23no—
1297C2×C4—44no—
1298C2×C4—412no—
1299C2×C4—412no—
1300C2×C4—412no—
1301C2×C4—412no—
1302C2×C4—86no—
1303C2×C4—86no—
1304C2×C4—86no—
1305C2×C4—86no—
1306C2×C4—86no—
1307C2×C4—86no—
1308C2×C4—86no—
1309C2×C4C22×#4112yes—
1310C2×C4C22×#4112yes—
1311C2×C4C22×#4112yes—
1312C2×C4C22×#4112yes—
1313C2×C4C22×#4112yes—
1314C2×C4C22×#4112yes—
1315C2×C4C2×H(5,𝔽2)16yes—
1316C2×C4C2×H(5,𝔽2)16yes—
1317C2×C4C2×2−1+416yes—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22—43no—
1331C22—43no—
1332C22—43no—
1333C22—43no—
1334C22—43no—
1335C22—43no—
1336C22—43no—
1337C22—43no—
1338C22—43no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22—43no—
1346C22C23×#4111yescharacteristic
1347C22C22×H(5,𝔽2)11yescharacteristic
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22H(7,𝔽2)11yescharacteristic
1351C22H(7,𝔽2)11yescharacteristic
1352C222−1+611yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—43no—
1360C4—43no—
1361C4—43no—
1362C4—43no—
1363C4—43no—
1364C4—41no—
1365C4—43no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4—41no—
1370C4—41no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4—43no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—43no—
1379C4C2×#562112yes—
1380C2—42no—
1381C2—83no—
1382C2—83no—
1383C2—83no—
1384C2C22×#56211yescharacteristic
1385C2#6298411yescharacteristic
1386C2#6298611yescharacteristic
1387C2#6299911yescharacteristic
1388C2#6305211yescharacteristic
1389C2#6306111yescharacteristic
1390C2#6306611yescharacteristic
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. #46083C2semidirect
2. #46044C2semidirect
3. #46042C2semidirect
4. #45718C2semidirect
5. #45717C2semidirect
6. #45689C2semidirect
7. #45676C2semidirect
8. #45670C2semidirect
9. #45653C2semidirect
10. #45650C2semidirect
11. #45609C2semidirect
12. #45602C2semidirect
13. #45524C2semidirect
14. #45514C2semidirect
15. #45484C2semidirect
16. #36578C2semidirect
17. #36576C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. #36475C2semidirect
20. #36467C2semidirect
21. #36457C2semidirect
22. #36456C2semidirect
23. #36455C2semidirect
24. #36445C2semidirect
25. #36433C2semidirect
26. #36433C2semidirect
27. #36432C2semidirect
28. #36431C2semidirect
29. #36430C2semidirect
30. #36430C2semidirect
31. C4×#562C2semidirect
704. C22⋊Q8#41semidirect
1212. Q8#562semidirect

Maximal subgroups

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

subgroupindex
#460832
#460442
#460422
#457182
#457172
#456892
#456762
#456702
#456532
#456502
#456092
#456022
#455242
#455142
#454842
#365782
#365762
Q8×C22⋊Q82
#364752
#364672
#364572
#364562
#364552
#364452
#364332
#364322
#364312
#364302
C4×#5622