Finite Group Databasebeta

← #7698952

Subgroups — #7698952

Order 512.

5459 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59693C213yesmaximal, complemented
2#59392C213yesmaximal, complemented
3#59304C213yesmaximal, complemented
4#52242C213yesmaximal, complemented
5#45374C213yesmaximal, complemented
6#45372C213yesmaximal, complemented
7#45257C213yesmaximal, complemented
8#45203C213yesmaximal, complemented
9#45069C213yesmaximal, complemented
10#44970C213yesmaximal, complemented
11#39730C213yesmaximal, complemented
12#39280C213yesmaximal, complemented
13#39256C213yesmaximal, complemented
14#39052C213yesmaximal, complemented
15#38212C213yesmaximal, complemented
16#37892C213yesmaximal, complemented
17#36483C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#36430C211yesmaximal, characteristic, complemented
20#36029C211yesmaximal, characteristic, complemented
21#36005C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35831C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#34313C211yesmaximal, characteristic, complemented
27#34295C211yesmaximal, characteristic, complemented
28#34294C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31#34183C211yesmaximal, characteristic, complemented
32C2×#553C2216yes—
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2863C2213yes—
46#2854C2213yes—
47#2850C2213yes—
48#2796C2216yes—
49#2795C2216yes—
50#2795C2213yes—
51#2793C2213yes—
52#2790C2216yes—
53#2790C2211yescharacteristic
54#2787C2216yes—
55#2786C2213yes—
56#2778C2213yes—
57#2778C2216yes—
58#2778C2216yes—
59#2772C2213yes—
60#2766C2213yes—
61#2761C2213yes—
62#2757C2216yes—
63#2756C2213yes—
64#2756C2216yes—
65#2753C2213yes—
66#2750C2213yes—
67#2747C2213yes—
68#2746C2216yes—
69#2741C2213yes—
70#2718C2216yes—
71#2718C2213yes—
72#2711C2216yes—
73#2708C2216yes—
74#2703C2213yes—
75#2691C2213yes—
76#2688C2216yes—
77#2647C2213yes—
78#2644C2213yes—
79#2624C2213yes—
80#2620C2213yes—
81#2620C2213yes—
82#2619C2213yes—
83#2602C2216yes—
84#2600C2216yes—
85#2598C2216yes—
86#2591C2216yes—
87#2579C2216yes—
88#2578C2216yes—
89#2576C2216yes—
90#2570C2213yes—
91#2552C2213yes—
92#2544C2213yes—
93#2544C2213yes—
94#2544C2213yes—
95#2541C2213yes—
96#2537C2213yes—
97#2537C2213yes—
98#2535C2213yes—
99#2535C2213yes—
100#2518C2216yes—
101#2514C2213yes—
102#2514C2213yes—
103#2513C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2511C2213yes—
107#2509C2213yes—
108#2507C2213yes—
109#2506C2213yes—
110#2506C2213yes—
111#2501C2213yes—
112#2501C2213yes—
113#2497C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2495C2213yes—
117#2494C2213yes—
118#2494C2213yes—
119#2487C2216yes—
120#2487C2213yes—
121#2486C2213yes—
122#2481C2216yes—
123#2476C2216yes—
124#2467C2216yes—
125#2464C2216yes—
126#2460C2216yes—
127#2457C2216yes—
128#2456C2216yes—
129#2448C2213yes—
130#2448C2213yes—
131#2445C2213yes—
132#2445C2213yes—
133#2443C2216yes—
134#2443C2216yes—
135#2443C2216yes—
136#2441C2216yes—
137#2428C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2428C2213yes—
141#2428C2213yes—
142#2427C2213yes—
143#2427C2213yes—
144#2427C2213yes—
145#2423C2213yes—
146#2423C2213yes—
147#2422C2213yes—
148#2422C2213yes—
149#2422C2216yes—
150#2417C2213yes—
151#2417C2213yes—
152#2416C2213yes—
153#2416C2213yes—
154#2416C2213yes—
155#2416C2213yes—
156#2415C2213yes—
157#2414C2213yes—
158#2402C2213yes—
159#2401C2213yes—
160#2395C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2392C2213yes—
164#2367C2213yes—
165#2367C2213yes—
166#2366C2213yes—
167#2366C2213yes—
168#2363C2213yes—
169#2361C2213yes—
170#2361C2213yes—
171#2361C2213yes—
172#2361C2213yes—
173#2361C2213yes—
174#2360C2213yes—
175#2360C2213yes—
176#2357C2213yes—
177#2354C2213yes—
178#2352C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189D4×C4⋊C4C2213yes—
190D4×C4⋊C4C2213yes—
191D4×C4⋊C4C2213yes—
192D4×C4⋊C4C2213yes—
193D4×C4⋊C4C2213yes—
194D4×C4⋊C4C2213yes—
195D4×C4⋊C4C2213yes—
196#2345C2213yes—
197#2344C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2328C2213yes—
209#2326C2213yes—
210#2326C2213yes—
211#2324C2213yes—
212#2324C2213yes—
213#2324C2213yes—
214#2323C2213yes—
215#2323C2213yes—
216#2319C2213yes—
217#2317C2213yes—
218#2317C2213yes—
219#2314C2213yes—
220C4×#127C2213yes—
221C4×#126C2213yes—
222C4×#123C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225C4×#121C2213yes—
226C4×#121C2213yes—
227#2298C2213yes—
228#2293C2213yes—
229#2293C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232#2290C2213yes—
233#2285C2213yes—
234C2×#384C2213yes—
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#553—424no—
243#550—28no—
244#550—28no—
245#550—44no—
246#548—28no—
247#548—28no—
248#548—44no—
249C2×#127C2313yes—
250C2×#127C2313yes—
251C2×#127C2313yes—
252C2×#126C2313yes—
253C2×#126C2316yes—
254C2×#125C2316yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#124C2313yes—
258C2×#123C2313yes—
259C2×#123C2316yes—
260C2×#123C2316yes—
261C2×#123C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276C2×#121C2316yes—
277C2×#121C2316yes—
278C2×#121C2316yes—
279#520—28no—
280#520—44no—
281#520—44no—
282#520—44no—
283C4×#41—28no—
284C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2316yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2316yes—
312C2×C4×D4C2316yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2316yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2316yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2316yes—
325C22×C4⋊C4C2313yes—
326C22×C4⋊C4C2313yes—
327C22×C4⋊C4C2313yes—
328C22×C4⋊C4C2313yes—
329C22×C4⋊C4C2313yes—
330C22×C4⋊C4C2316yes—
331C22×C4⋊C4C2316yes—
332C22×C42C2313yes—
333C22×C42C2313yes—
334#401C2316yes—
335#401C2313yes—
336#400C2313yes—
337#400C2316yes—
338#400C2313yes—
339#400C2316yes—
340#400C2313yes—
341#400C2313yes—
342#400C2311yescharacteristic
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2316yes—
347#399C2316yes—
348#399C2316yes—
349#399C2313yes—
350#399C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2316yes—
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2313yes—
357#398C2311yescharacteristic
358#398C2311yescharacteristic
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#397C2316yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2313yes—
367#397C2316yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2316yes—
376#396C2316yes—
377#396C2313yes—
378#396C2316yes—
379#396C2313yes—
380#396C2316yes—
381#396C2311yescharacteristic
382#396C2311yescharacteristic
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#394C2313yes—
387#394C2316yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2313yes—
392#394C2313yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#392C2313yes—
407#392C2316yes—
408#392C2316yes—
409#392C2316yes—
410#392C2313yes—
411#392C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#390C2313yes—
419#390C2316yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2316yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2311yescharacteristic
463#388C2311yescharacteristic
464#388C2313yes—
465#388C2313yes—
466#388C2316yes—
467#388C2316yes—
468#388C2313yes—
469#388C2316yes—
470#388C2316yes—
471#388C2313yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2313yes—
478#388C2316yes—
479#388C2313yes—
480#388C2313yes—
481#388C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2311yescharacteristic
495#388C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2311yescharacteristic
516#387C2311yescharacteristic
517#386C2316yes—
518#386C2316yes—
519#386C2316yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2316yes—
525#386C2316yes—
526#386C2313yes—
527#386C2316yes—
528#386C2316yes—
529#386C2316yes—
530#386C2313yes—
531#386C2316yes—
532#386C2313yes—
533#386C2313yes—
534#386C2313yes—
535#386C2316yes—
536#386C2313yes—
537#386C2313yes—
538#386C2313yes—
539#386C2313yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2313yes—
546#385C2316yes—
547#385C2316yes—
548#385C2316yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2313yes—
553#385C2313yes—
554#385C2313yes—
555#385C2311yescharacteristic
556#385C2311yescharacteristic
557#385C2311yescharacteristic
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2316yes—
562#384C2313yes—
563#384C2313yes—
564#384C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2311yescharacteristic
568#383C2313yes—
569#383C2316yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#382C2313yes—
575#381C2316yes—
576#381C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2316yes—
580#380C2316yes—
581#380C2313yes—
582#380C2313yes—
583#380C2316yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
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×C4⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628#376C2313yes—
629#376C2313yes—
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#4118yes—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8C2413yes—
644C22×Q8C2411yescharacteristic
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2416yes—
653C22×D4C2416yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2416yes—
665C23×C4C2416yes—
666C23×C4C2416yes—
667C23×C4C2416yes—
668C23×C4C2411yescharacteristic
669#127—212no—
670#127—212no—
671#127—46no—
672#126—212no—
673#126—412no—
674#125—412no—
675#124—212no—
676#124—212no—
677#124—46no—
678#123—212no—
679#123—412no—
680#123—86no—
681#123—86no—
682C22⋊Q8—212no—
683C22⋊Q8—212no—
684C22⋊Q8—46no—
685#121—212no—
686#121—212no—
687#121—212no—
688#121—212no—
689#121—212no—
690#121—212no—
691#121—212no—
692#121—412no—
693#121—412no—
694#121—412no—
695#121—46no—
696#121—46no—
697#121—46no—
698#121—86no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8#4118yes—
712C4×D4—212no—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—412no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—412no—
730C4×D4—412no—
731C4×D4—412no—
732C4×D4—86no—
733#117—212no—
734#117—212no—
735#117—46no—
736#117—46no—
737#117—46no—
738#117—412no—
739C2×C4⋊C4—212no—
740C2×C4⋊C4—46no—
741C2×C4⋊C4—46no—
742C2×C4⋊C4—46no—
743C2×C4⋊C4—46no—
744C2×C4⋊C4—412no—
745C2×C4⋊C4—86no—
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⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
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⋊C4C2416yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2416yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2411yescharacteristic
850C2×C42—212no—
851C2×C42—46no—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2411yescharacteristic
865C2×C42C2416yes—
866C2×C42C2416yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2411yescharacteristic
871C2×C42C2413yes—
872C2×C42C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2411yescharacteristic
882#95C2413yes—
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#95C2416yes—
897#95C2413yes—
898#95C2416yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2416yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2411yescharacteristic
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#95C2413yes—
926#95C2416yes—
927#95C2416yes—
928C24C2513yes—
929C24C2513yes—
930C24C2513yes—
931C24C2511yescharacteristic
932#41—232no—
933#41—416no—
934#41—416no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—416no—
939C2×Q8C2×#4114yes—
940C2×Q8C2×#4114yes—
941C2×Q8H(5,𝔽2)14yes—
942C2×D4—26no—
943C2×D4—26no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—212no—
948C2×D4—212no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—43no—
961C2×D4—43no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—46no—
965C2×D4—43no—
966C2×D4—46no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—46no—
970C2×D4—46no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—46no—
975C2×D4—46no—
976C2×D4—46no—
977C2×D4C2×#41112yes—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—212no—
994C22×C4—41no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—43no—
1001C22×C4—46no—
1002C22×C4—43no—
1003C22×C4—46no—
1004C22×C4—46no—
1005C22×C4—46no—
1006C22×C4—46no—
1007C22×C4—46no—
1008C22×C4—46no—
1009C22×C4—46no—
1010C22×C4—46no—
1011C22×C4—46no—
1012C22×C4—46no—
1013C22×C4C2×#41112yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C22×C4C2513yes—
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—22no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
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—26no—
1062C4⋊C4—26no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—46no—
1067C4⋊C4—46no—
1068C4⋊C4—46no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—46no—
1072C4⋊C4—46no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—43no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—43no—
1088C4⋊C4—46no—
1089C4⋊C4—46no—
1090C4⋊C4—46no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4C2×#41112yes—
1094C22⋊C4—26no—
1095C22⋊C4—26no—
1096C22⋊C4—26no—
1097C22⋊C4—212no—
1098C22⋊C4—26no—
1099C22⋊C4—26no—
1100C22⋊C4—26no—
1101C22⋊C4—212no—
1102C22⋊C4—26no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—212no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—26no—
1112C22⋊C4—41no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—41no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—46no—
1128C22⋊C4—41no—
1129C22⋊C4—46no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—46no—
1133C22⋊C4—46no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—46no—
1138C22⋊C4—43no—
1139C22⋊C4—46no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—46no—
1144C22⋊C4H(5,𝔽2)14yes—
1145C42—22no—
1146C42—26no—
1147C42—26no—
1148C42—26no—
1149C42—26no—
1150C42—26no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—26no—
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—43no—
1159C42—43no—
1160C42—41no—
1161C42—43no—
1162C42—46no—
1163C42—46no—
1164C42—43no—
1165C42C2×#41112yes—
1166C23—23no—
1167C23—21no—
1168C23—21no—
1169C23—23no—
1170C23—23no—
1171C23—21no—
1172C23—21no—
1173C23—23no—
1174C23—21no—
1175C23—21no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23C22×#4116yes—
1193C23C2×H(5,𝔽2)12yes—
1194C23C2611yescharacteristic
1195Q8—412no—
1196Q8#553116yescomplemented
1197D4—224no—
1198D4—412no—
1199D4—412no—
1200D4—412no—
1201D4—412no—
1202D4—412no—
1203D4—812no—
1204D4—812no—
1205D4—86no—
1206D4—86no—
1207D4—86no—
1208D4—166no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—224no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
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—23no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—23no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—412no—
1284C2×C4—412no—
1285C2×C4—44no—
1286C2×C4—412no—
1287C2×C4—412no—
1288C2×C4—412no—
1289C2×C4—812no—
1290C2×C4—86no—
1291C2×C4—166no—
1292C2×C4—166no—
1293C2×C4—166no—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4116yes—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4116yes—
1298C2×C4C22×#4116yes—
1299C2×C4C2×H(5,𝔽2)12yes—
1300C2×C4C2×H(5,𝔽2)12yes—
1301C2×C4C2×H(5,𝔽2)16yes—
1302C22—22no—
1303C22—22no—
1304C22—26no—
1305C22—26no—
1306C22—22no—
1307C22—26no—
1308C22—43no—
1309C22—41no—
1310C22—43no—
1311C22—43no—
1312C22—41no—
1313C22—41no—
1314C22—43no—
1315C22—41no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22C23×#4111yescharacteristic
1331C22C23×#4111yescharacteristic
1332C22C22×H(5,𝔽2)11yescharacteristic
1333C22C22×H(5,𝔽2)11yescharacteristic
1334C22H(7,𝔽2)11yescharacteristic
1335C222−1+611yescharacteristic
1336C222−1+611yescharacteristic
1337C4—22no—
1338C4—26no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—43no—
1352C4—41no—
1353C4—43no—
1354C4—41no—
1355C4—43no—
1356C4—43no—
1357C4—43no—
1358C4—43no—
1359C4—43no—
1360C4—41no—
1361C4—41no—
1362C4—43no—
1363C4C2×#553112yes—
1364C2—42no—
1365C2—46no—
1366C2—83no—
1367C2—83no—
1368C2C22×#55311yescharacteristic
1369C2#6285111yescharacteristic
1370C2#6285711yescharacteristic
1371C2#6291611yescharacteristic
1372C2#6298511yescharacteristic
1373C2#6298511yescharacteristic
1374C2#6304411yescharacteristic
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. #59693C2semidirect
2. #59392C2semidirect
3. #59304C2semidirect
4. #52242C2semidirect
5. #45374C2semidirect
6. #45372C2semidirect
7. #45257C2semidirect
8. #45203C2semidirect
9. #45069C2semidirect
10. #44970C2semidirect
11. #39730C2semidirect
12. #39280C2semidirect
13. #39256C2semidirect
14. #39052C2semidirect
15. #38212C2semidirect
16. #37892C2semidirect
17. #36483C2semidirect
18. #36448C2semidirect
19. #36430C2semidirect
20. #36029C2semidirect
21. #36005C2semidirect
22. #35898C2semidirect
23. #35868C2semidirect
24. #35831C2semidirect
25. #35831C2semidirect
26. #34313C2semidirect
27. #34295C2semidirect
28. #34294C2semidirect
29. #34294C2semidirect
30. #34263C2semidirect
31. #34183C2semidirect
1196. Q8#553semidirect

Maximal subgroups

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

subgroupindex
#596932
#593922
#593042
#522422
#453742
#453722
#452572
#452032
#450692
#449702
#397302
#392802
#392562
#390522
#382122
#378922
#364832
#364482
#364302
#360292
#360052
#358982
#358682
#358312
#343132
#342952
#342942
#342632
#341832