Finite Group Databasebeta

← #8091821

Subgroups — #8091821

Order 512.

4898 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46072C213yesmaximal, complemented
2#46057C213yesmaximal, complemented
3#46055C213yesmaximal, complemented
4#45700C213yesmaximal, complemented
5#45695C213yesmaximal, complemented
6#45682C213yesmaximal, complemented
7#45664C213yesmaximal, complemented
8#45662C213yesmaximal, complemented
9#45634C213yesmaximal, complemented
10#45626C213yesmaximal, complemented
11#45619C213yesmaximal, complemented
12#45617C213yesmaximal, complemented
13#45525C213yesmaximal, complemented
14#45512C213yesmaximal, complemented
15#45482C213yesmaximal, complemented
16#36578C211yesmaximal, characteristic, complemented
17#36577C211yesmaximal, characteristic, complemented
18Q8×#121C211yesmaximal, characteristic, complemented
19#36482C211yesmaximal, characteristic, complemented
20#36482C211yesmaximal, characteristic, complemented
21#36475C211yesmaximal, characteristic, complemented
22#36467C211yesmaximal, characteristic, complemented
23#36446C211yesmaximal, characteristic, complemented
24#36444C211yesmaximal, characteristic, complemented
25#36435C211yesmaximal, characteristic, complemented
26#36435C211yesmaximal, characteristic, complemented
27#36434C211yesmaximal, characteristic, complemented
28#36434C211yesmaximal, characteristic, complemented
29#36432C211yesmaximal, characteristic, complemented
30#36431C211yesmaximal, characteristic, complemented
31C4×#562C213yesmaximal, complemented
32C2×#562C2213yes—
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2864C2213yes—
46#2862C2213yes—
47#2861C2213yes—
48#2857C2213yes—
49#2857C2213yes—
50#2857C2213yes—
51#2855C2213yes—
52#2855C2213yes—
53#2855C2213yes—
54#2854C2213yes—
55#2851C2213yes—
56#2851C2213yes—
57#2851C2213yes—
58#2850C2213yes—
59#2850C2213yes—
60#2839C2216yes—
61#2831C2216yes—
62#2827C2216yes—
63#2827C2216yes—
64#2814C2216yes—
65#2802C2216yes—
66#2798C2216yes—
67#2788C2216yes—
68#2786C2216yes—
69#2783C2216yes—
70#2783C2216yes—
71#2772C2216yes—
72#2768C2216yes—
73#2761C2216yes—
74#2755C2216yes—
75#2755C2216yes—
76#2754C2216yes—
77#2750C2216yes—
78#2750C2216yes—
79#2747C2216yes—
80#2747C2216yes—
81#2744C2216yes—
82#2744C2216yes—
83#2744C2216yes—
84#2743C2216yes—
85#2741C2216yes—
86#2740C2216yes—
87#2739C2216yes—
88#2739C2216yes—
89#2708C2216yes—
90#2704C2216yes—
91#2701C2216yes—
92#2700C2216yes—
93#2687C2216yes—
94#2686C2216yes—
95#2592C2213yes—
96#2582C2213yes—
97#2581C2213yes—
98#2581C2213yes—
99#2580C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2568C2213yes—
103#2568C2213yes—
104#2566C2213yes—
105#2565C2213yes—
106#2565C2213yes—
107#2562C2213yes—
108#2547C2213yes—
109#2547C2213yes—
110#2546C2213yes—
111#2545C2213yes—
112#2545C2213yes—
113#2538C2213yes—
114#2537C2213yes—
115#2536C2213yes—
116#2536C2213yes—
117#2509C2213yes—
118#2508C2213yes—
119#2507C2213yes—
120#2506C2213yes—
121#2504C2213yes—
122#2503C2213yes—
123#2503C2213yes—
124#2499C2213yes—
125#2492C2213yes—
126#2491C2213yes—
127#2490C2213yes—
128#2489C2213yes—
129#2489C2213yes—
130#2489C2213yes—
131#2489C2213yes—
132#2489C2213yes—
133#2487C2213yes—
134#2486C2213yes—
135#2486C2213yes—
136#2485C2213yes—
137#2454C2213yes—
138#2453C2213yes—
139#2453C2213yes—
140#2453C2213yes—
141#2453C2213yes—
142#2452C2213yes—
143#2451C2213yes—
144#2451C2213yes—
145#2448C2213yes—
146#2448C2213yes—
147#2447C2213yes—
148#2447C2213yes—
149#2446C2213yes—
150#2446C2213yes—
151#2446C2213yes—
152#2446C2213yes—
153#2442C2213yes—
154#2442C2213yes—
155#2442C2213yes—
156#2442C2213yes—
157#2441C2213yes—
158#2440C2213yes—
159#2440C2213yes—
160#2439C2213yes—
161#2429C2213yes—
162#2429C2213yes—
163#2429C2213yes—
164#2429C2213yes—
165#2427C2213yes—
166#2427C2213yes—
167#2426C2213yes—
168#2426C2213yes—
169#2422C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2421C2213yes—
173#2421C2213yes—
174#2421C2213yes—
175#2421C2213yes—
176#2420C2213yes—
177#2417C2213yes—
178#2417C2213yes—
179#2417C2213yes—
180#2417C2213yes—
181#2416C2213yes—
182#2416C2213yes—
183#2415C2213yes—
184#2415C2213yes—
185#2382C2213yes—
186#2379C2213yes—
187#2379C2213yes—
188#2378C2213yes—
189#2378C2213yes—
190#2378C2213yes—
191#2378C2213yes—
192#2377C2211yescharacteristic
193#2377C2213yes—
194#2377C2213yes—
195#2377C2213yes—
196#2376C2213yes—
197#2376C2213yes—
198#2376C2213yes—
199#2376C2213yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
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
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#562—224no—
243#557—44no—
244#557—44no—
245D4×Q8—44no—
246D4×Q8—44no—
247D4×Q8—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×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#123C2313yes—
267C2×#123C2313yes—
268C2×#123C2313yes—
269C2×#123C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2311yescharacteristic
290C4×#41—44no—
291C2×C4×Q8—44no—
292C2×C4×Q8—44no—
293C2×C4×Q8—44no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×Q8C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×#117C2313yes—
322C22×C4⋊C4C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C4⋊C4C2313yes—
325C22×C42C2313yes—
326C22×C42C2313yes—
327C22×C42C2313yes—
328C22×C42C2313yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#400C2316yes—
333#400C2316yes—
334#400C2316yes—
335#400C2316yes—
336#400C2316yes—
337#400C2316yes—
338#400C2316yes—
339#400C2316yes—
340#400C2316yes—
341#400C2316yes—
342#400C2316yes—
343#399C2316yes—
344#399C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2316yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2316yes—
369#397C2316yes—
370#397C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2316yes—
379#395C2316yes—
380#395C2316yes—
381#394C2316yes—
382#394C2316yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#393C2316yes—
388#393C2316yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2316yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2316yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2311yescharacteristic
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2311yescharacteristic
426#390C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2316yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#388C2313yes—
462#388C2316yes—
463#388C2313yes—
464#388C2313yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2311yescharacteristic
484#388C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#387C2311yescharacteristic
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2311yescharacteristic
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#386C2313yes—
528#386C2313yes—
529#386C2316yes—
530#386C2316yes—
531#386C2316yes—
532#386C2311yescharacteristic
533#386C2313yes—
534#386C2313yes—
535#386C2311yescharacteristic
536#386C2311yescharacteristic
537#386C2313yes—
538#386C2313yes—
539#386C2311yescharacteristic
540#386C2313yes—
541#386C2313yes—
542#385C2313yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#385C2311yescharacteristic
554#385C2313yes—
555#385C2313yes—
556#385C2313yes—
557#385C2311yescharacteristic
558#385C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2316yes—
572#382C2316yes—
573#382C2313yes—
574#381C2316yes—
575#381C2316yes—
576#381C2316yes—
577#381C2311yescharacteristic
578#381C2313yes—
579#381C2313yes—
580#381C2313yes—
581#380C2313yes—
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#380C2316yes—
596#380C2316yes—
597#380C2316yes—
598#380C2311yescharacteristic
599#380C2313yes—
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—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2413yes—
646C22×Q8C2413yes—
647C22×Q8C2413yes—
648C22×Q8C2411yescharacteristic
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2411yescharacteristic
654C22×D4C2411yescharacteristic
655C22×D4C2411yescharacteristic
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2413yes—
665C23×C4C2411yescharacteristic
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C4⋊Q8—46no—
669C4⋊Q8—46no—
670C4⋊Q8—46no—
671C4⋊Q8—46no—
672C4⋊Q8—46no—
673#125—212no—
674#125—46no—
675#125—46no—
676#125—46no—
677#125—46no—
678#124—212no—
679#124—212no—
680#124—46no—
681#124—46no—
682#124—46no—
683#123—212no—
684#123—212no—
685#123—212no—
686#123—212no—
687C22⋊Q8—212no—
688C22⋊Q8—212no—
689C22⋊Q8—212no—
690C22⋊Q8—212no—
691C22⋊Q8—46no—
692C22⋊Q8—46no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697C22⋊Q8—46no—
698C22⋊Q8—46no—
699C22⋊Q8—46no—
700#121—212no—
701#121—212no—
702#121—212no—
703#121—46no—
704#121—46no—
705#121—46no—
706#121#4118yescomplemented
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—24no—
715C4×Q8—24no—
716C4×Q8—24no—
717C4×Q8—24no—
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—
730C4×D4—46no—
731C4×D4—46no—
732C4×D4—46no—
733C4×D4—46no—
734#117—46no—
735C2×C4⋊C4—46no—
736C2×C4⋊C4—46no—
737C2×C4⋊C4—46no—
738C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C42—46no—
836C2×C42—46no—
837C2×C42—46no—
838C2×C42—46no—
839C2×C42C2413yes—
840C2×C42C2413yes—
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×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2411yescharacteristic
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910#95C2416yes—
911#95C2416yes—
912#95C2416yes—
913#95C2416yes—
914#95C2416yes—
915#95C2416yes—
916#95C2416yes—
917#95C2416yes—
918#95C2416yes—
919#95C2416yes—
920#95C2416yes—
921#95C2416yes—
922#95C2416yes—
923C24C2513yes—
924C24C2511yescharacteristic
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927#41—416no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—43no—
940C2×Q8—43no—
941C2×Q8—43no—
942C2×Q8—43no—
943C2×Q8—416no—
944C2×Q8—416no—
945C2×Q8—416no—
946C2×Q8H(5,𝔽2)14yes—
947C2×Q8H(5,𝔽2)14yes—
948C2×Q82−1+414yes—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—41no—
959C2×D4—41no—
960C2×D4—41no—
961C2×D4—43no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4C2×#4114yes—
968C2×D4C2×#4114yes—
969C2×D4C2×#4114yes—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—41no—
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—43no—
1002C22×C4—43no—
1003C22×C4—43no—
1004C22×C4—43no—
1005C22×C4C2×#4114yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2513yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2513yes—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
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—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—43no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—46no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—46no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—46no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—46no—
1082C4⋊C4—46no—
1083C4⋊C4—46no—
1084C4⋊C4—46no—
1085C4⋊C4—46no—
1086C4⋊C4C2×#4114yes—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—26no—
1095C22⋊C4—26no—
1096C22⋊C4—26no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—46no—
1106C22⋊C4—46no—
1107C22⋊C4—43no—
1108C22⋊C4—41no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—41no—
1112C22⋊C4—46no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—46no—
1126C22⋊C4—46no—
1127C22⋊C4—46no—
1128C22⋊C4C2×#4114yes—
1129C22⋊C4C2×#4114yes—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—41no—
1143C42—43no—
1144C42—43no—
1145C42—43no—
1146C42—43no—
1147C42—43no—
1148C42—43no—
1149C42—43no—
1150C42—41no—
1151C42—43no—
1152C42—43no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—23no—
1172C23—23no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23C22×#4112yes—
1179C23C22×#4112yes—
1180C23C22×#4112yes—
1181C23C2611yescharacteristic
1182Q8—412no—
1183Q8—412no—
1184Q8—412no—
1185Q8—86no—
1186Q8—86no—
1187Q8#562116yescomplemented
1188D4—44no—
1189D4—44no—
1190D4—44no—
1191D4—412no—
1192D4—86no—
1193D4—86no—
1194D4—86no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
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—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—23no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—412no—
1273C2×C4—412no—
1274C2×C4—412no—
1275C2×C4—412no—
1276C2×C4—86no—
1277C2×C4—86no—
1278C2×C4—86no—
1279C2×C4—86no—
1280C2×C4—86no—
1281C2×C4C22×#4112yes—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C2×H(5,𝔽2)16yes—
1286C2×C4C2×H(5,𝔽2)16yes—
1287C2×C4C2×2−1+416yes—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—43no—
1310C22—43no—
1311C22—43no—
1312C22—43no—
1313C22—43no—
1314C22—43no—
1315C22—43no—
1316C22C23×#4111yescharacteristic
1317C22C22×H(5,𝔽2)11yescharacteristic
1318C22C22×H(5,𝔽2)11yescharacteristic
1319C22C22×2−1+411yescharacteristic
1320C222−1+611yescharacteristic
1321C222−1+611yescharacteristic
1322C222−1+611yescharacteristic
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—43no—
1328C4—43no—
1329C4—43no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—43no—
1334C4—41no—
1335C4—43no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—43no—
1341C4—43no—
1342C4—43no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—43no—
1347C4—43no—
1348C4—43no—
1349C4C2×#562112yes—
1350C2—42no—
1351C2—42no—
1352C2—42no—
1353C2—83no—
1354C2C22×#56211yescharacteristic
1355C2#6298411yescharacteristic
1356C2#6298411yescharacteristic
1357C2#6300111yescharacteristic
1358C2#6304411yescharacteristic
1359C2#6304411yescharacteristic
1360C2#6305711yescharacteristic
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. #46072C2semidirect
2. #46057C2semidirect
3. #46055C2semidirect
4. #45700C2semidirect
5. #45695C2semidirect
6. #45682C2semidirect
7. #45664C2semidirect
8. #45662C2semidirect
9. #45634C2semidirect
10. #45626C2semidirect
11. #45619C2semidirect
12. #45617C2semidirect
13. #45525C2semidirect
14. #45512C2semidirect
15. #45482C2semidirect
16. #36578C2semidirect
17. #36577C2semidirect
18. Q8×#121C2semidirect
19. #36482C2semidirect
20. #36482C2semidirect
21. #36475C2semidirect
22. #36467C2semidirect
23. #36446C2semidirect
24. #36444C2semidirect
25. #36435C2semidirect
26. #36435C2semidirect
27. #36434C2semidirect
28. #36434C2semidirect
29. #36432C2semidirect
30. #36431C2semidirect
31. C4×#562C2semidirect
706. #121#41semidirect
1187. Q8#562semidirect

Maximal subgroups

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

subgroupindex
#460722
#460572
#460552
#457002
#456952
#456822
#456642
#456622
#456342
#456262
#456192
#456172
#455252
#455122
#454822
#365782
#365772
Q8×#1212
#364822
#364752
#364672
#364462
#364442
#364352
#364342
#364322
#364312
C4×#5622