Finite Group Databasebeta

← #7680407

Subgroups — #7680407

Order 512.

4775 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59954C214yesmaximal, complemented
2#59690C214yesmaximal, complemented
3#59686C214yesmaximal, complemented
4#59677C214yesmaximal, complemented
5#44722C214yesmaximal, complemented
6#44628C214yesmaximal, complemented
7#44356C214yesmaximal, complemented
8#44196C214yesmaximal, complemented
9#39763C211yesmaximal, characteristic, complemented
10#39638C211yesmaximal, characteristic, complemented
11#39298C212yesmaximal, complemented
12#38266C212yesmaximal, complemented
13#38042C212yesmaximal, complemented
14#37889C211yesmaximal, characteristic, complemented
15#37882C211yesmaximal, characteristic, complemented
16#37706C211yesmaximal, characteristic, complemented
17#37706C211yesmaximal, characteristic, complemented
18#36294C212yesmaximal, complemented
19#36182C211yesmaximal, characteristic, complemented
20D4×#125C211yesmaximal, characteristic, complemented
21#35612C212yesmaximal, complemented
22#35588C212yesmaximal, complemented
23#35345C211yesmaximal, characteristic, complemented
24#35295C211yesmaximal, characteristic, complemented
25#35271C211yesmaximal, characteristic, complemented
26#34788C212yesmaximal, complemented
27#34305C212yesmaximal, complemented
28#34280C211yesmaximal, characteristic, complemented
29#34217C211yesmaximal, characteristic, complemented
30#34149C211yesmaximal, characteristic, complemented
31C2×#2330C211yesmaximal, characteristic, complemented
32C2×#553C2212yes—
33C2×#540C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#125C2211yescharacteristic
37#2864C2212yes—
38#2860C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2856C2211yescharacteristic
42#2856C2211yescharacteristic
43#2854C2212yes—
44#2851C2211yescharacteristic
45#2851C2211yescharacteristic
46#2802C2214yes—
47#2800C2214yes—
48#2800C2214yes—
49#2800C2214yes—
50#2794C2214yes—
51#2793C2214yes—
52#2787C2214yes—
53#2787C2214yes—
54#2786C2214yes—
55#2779C2214yes—
56#2779C2214yes—
57#2774C2214yes—
58#2773C2214yes—
59#2772C2214yes—
60#2741C2214yes—
61#2727C2214yes—
62#2725C2214yes—
63#2721C2214yes—
64#2711C2214yes—
65#2711C2214yes—
66#2707C2214yes—
67#2707C2214yes—
68#2695C2214yes—
69#2672C2214yes—
70#2647C2211yescharacteristic
71#2647C2211yescharacteristic
72#2644C2212yes—
73#2641C2211yescharacteristic
74#2641C2211yescharacteristic
75#2629C2211yescharacteristic
76#2629C2211yescharacteristic
77#2629C2212yes—
78#2624C2212yes—
79#2611C2214yes—
80#2608C2214yes—
81#2608C2214yes—
82#2608C2214yes—
83#2606C2214yes—
84#2606C2214yes—
85#2601C2214yes—
86#2597C2214yes—
87#2596C2214yes—
88#2595C2214yes—
89#2594C2214yes—
90#2587C2214yes—
91#2585C2214yes—
92#2584C2212yes—
93#2578C2214yes—
94#2573C2214yes—
95#2569C2214yes—
96#2566C2212yes—
97#2559C2214yes—
98#2559C2214yes—
99#2556C2214yes—
100#2552C2212yes—
101#2538C2212yes—
102#2531C2214yes—
103#2531C2214yes—
104#2530C2214yes—
105#2530C2214yes—
106#2529C2214yes—
107#2529C2214yes—
108#2529C2214yes—
109#2528C2214yes—
110#2526C2214yes—
111#2525C2214yes—
112#2522C2214yes—
113#2516C2214yes—
114#2513C2212yes—
115#2513C2212yes—
116#2512C2214yes—
117#2512C2214yes—
118#2510C2214yes—
119#2509C2212yes—
120#2509C2214yes—
121#2509C2212yes—
122#2508C2212yes—
123#2506C2214yes—
124#2506C2212yes—
125#2504C2212yes—
126#2500C2212yes—
127#2498C2214yes—
128#2497C2214yes—
129#2496C2212yes—
130#2494C2212yes—
131#2490C2212yes—
132#2490C2212yes—
133#2487C2212yes—
134#2485C2212yes—
135#2485C2214yes—
136#2485C2214yes—
137#2481C2214yes—
138#2481C2214yes—
139#2479C2214yes—
140#2478C2214yes—
141#2478C2214yes—
142#2476C2214yes—
143#2473C2214yes—
144#2473C2214yes—
145#2473C2214yes—
146#2468C2214yes—
147#2460C2214yes—
148#2454C2212yes—
149#2454C2212yes—
150#2449C2214yes—
151#2444C2214yes—
152#2444C2214yes—
153#2443C2214yes—
154#2443C2214yes—
155#2442C2212yes—
156#2442C2212yes—
157#2441C2214yes—
158#2438C2214yes—
159#2425C2214yes—
160#2425C2214yes—
161#2425C2214yes—
162#2422C2214yes—
163#2420C2214yes—
164#2416C2212yes—
165#2416C2214yes—
166#2416C2214yes—
167#2416C2214yes—
168#2416C2214yes—
169#2416C2212yes—
170#2415C2214yes—
171#2401C2214yes—
172#2395C2214yes—
173#2374C2214yes—
174#2373C2214yes—
175#2373C2212yes—
176#2373C2212yes—
177#2372C2212yes—
178#2371C2212yes—
179#2370C2212yes—
180#2370C2214yes—
181#2370C2214yes—
182#2368C2212yes—
183#2364C2214yes—
184#2364C2212yes—
185#2364C2214yes—
186#2363C2214yes—
187#2361C2212yes—
188#2361C2212yes—
189#2361C2214yes—
190#2359C2214yes—
191#2359C2212yes—
192#2359C2214yes—
193#2359C2212yes—
194#2359C2214yes—
195#2354C2212yes—
196#2352C2214yes—
197#2349C2214yes—
198D4×C4⋊C4C2212yes—
199D4×C4⋊C4C2214yes—
200#2346C2212yes—
201#2345C2212yes—
202#2345C2214yes—
203#2345C2214yes—
204#2335C2214yes—
205#2334C2214yes—
206#2330C2212yes—
207#2330C2211yescharacteristic
208#2330C2212yes—
209#2330C2211yescharacteristic
210#2330C2211yescharacteristic
211#2330C2214yes—
212#2330C2211yescharacteristic
213#2330C2214yes—
214#2330C2212yes—
215#2330C2211yescharacteristic
216#2330C2211yescharacteristic
217#2330C2211yescharacteristic
218#2328C2211yescharacteristic
219#2324C2212yes—
220#2324C2212yes—
221#2319C2212yes—
222#2316C2212yes—
223#2314C2211yescharacteristic
224C4×#127C2211yescharacteristic
225C4×#125C2211yescharacteristic
226C4×#125C2212yes—
227C4×#125C2212yes—
228C4×#121C2214yes—
229C4×#121C2212yes—
230C4×#121C2212yes—
231C4×#121C2214yes—
232#2298C2211yescharacteristic
233#2298C2211yescharacteristic
234#2295C2211yescharacteristic
235#2295C2211yescharacteristic
236#2293C2212yes—
237#2293C2212yes—
238C2×#389C2214yes—
239C2×#389C2212yes—
240#2290C2211yescharacteristic
241#2290C2214yes—
242#2290C2211yescharacteristic
243#2290C2211yescharacteristic
244#2290C2214yes—
245#2290C2211yescharacteristic
246C2×#387C2214yes—
247#2285C2211yescharacteristic
248C2×#384C2211yescharacteristic
249#2283C2212yes—
250#2275C2212yes—
251#2274C2212yes—
252C42×D4C2211yescharacteristic
253C42×D4C2211yescharacteristic
254C4×#117C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×#376C2211yescharacteristic
259#553—216no—
260#540—28no—
261C2×#127C2311yescharacteristic
262#529—28no—
263C2×#126C2314yes—
264C2×#126C2311yescharacteristic
265C2×#126C2311yescharacteristic
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#125—28no—
269C2×#125—28no—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2311yescharacteristic
278C2×#125C2314yes—
279C2×#125C2311yescharacteristic
280C2×#124C2311yescharacteristic
281C2×#123C2314yes—
282C2×#123C2311yescharacteristic
283C2×#123C2311yescharacteristic
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2311yescharacteristic
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2314yes—
322C2×#117C2314yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2314yes—
328C22×C4⋊C4C2314yes—
329C22×C4⋊C4C2314yes—
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2314yes—
336#401C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#391C2312yes—
409#391C2312yes—
410#390C2314yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2314yes—
417#390C2312yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2312yes—
423#390C2312yes—
424#390C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2312yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2312yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2312yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2312yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2312yes—
570#386C2312yes—
571#386C2314yes—
572#386C2312yes—
573#386C2312yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2312yes—
593#385C2312yes—
594#385C2312yes—
595#385C2314yes—
596#384C2311yescharacteristic
597#384C2312yes—
598#384C2311yescharacteristic
599#384C2311yescharacteristic
600#384C2314yes—
601#384C2312yes—
602#384C2314yes—
603#383C2314yes—
604#382C2312yes—
605#382C2311yescharacteristic
606#382C2314yes—
607#382C2312yes—
608#382C2312yes—
609#382C2314yes—
610#381C2314yes—
611#381C2314yes—
612#380C2314yes—
613#380C2314yes—
614#380C2314yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2312yes—
619#380C2314yes—
620#380C2312yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2311yescharacteristic
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2311yescharacteristic
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2311yescharacteristic
687#376C2311yescharacteristic
688#376C2311yescharacteristic
689#376C2312yes—
690#376C2312yes—
691#376C2311yescharacteristic
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2314yes—
696#376C2314yes—
697#376C2312yes—
698C2×#95C2314yes—
699C2×#95C2314yes—
700C2×#95C2312yes—
701C2×#95C2314yes—
702C2×#95C2312yes—
703C43C2311yescharacteristic
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C22×Q8C2411yescharacteristic
708C22×D4C2414yes—
709C22×D4C2411yescharacteristic
710C22×D4C2412yes—
711C22×D4C2411yescharacteristic
712C22×D4C2414yes—
713C22×D4C2411yescharacteristic
714C22×D4C2414yes—
715C22×D4C2414yes—
716C23×C4C2411yescharacteristic
717C23×C4C2411yescharacteristic
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2414yes—
724C23×C4C2411yescharacteristic
725C23×C4C2414yes—
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2412yes—
731#127—24no—
732#126—24no—
733#126—216no—
734#126—24no—
735#126—84no—
736#126—84no—
737#125—28no—
738#125—28no—
739#125—216no—
740#125—216no—
741#125—24no—
742#125—24no—
743#125—24no—
744#125—28no—
745#125—84no—
746#125#4118yes—
747#124—24no—
748#123—24no—
749#123—216no—
750#123—24no—
751#123—216no—
752#123—48no—
753C22⋊Q8—24no—
754C22⋊Q8—84no—
755#121—24no—
756#121—216no—
757#121—28no—
758#121—28no—
759#121—216no—
760#121—28no—
761#121—48no—
762#121—48no—
763#121—84no—
764#121—84no—
765C4×Q8—24no—
766C4×D4—24no—
767C4×D4—24no—
768C4×D4—28no—
769C4×D4—216no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—44no—
773C4×D4—48no—
774C4×D4—44no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—84no—
778C4×D4—84no—
779C4×D4—84no—
780C4×D4#4118yes—
781#117—24no—
782#117—28no—
783#117—24no—
784#117—24no—
785#117—24no—
786#117—44no—
787#117—84no—
788#117—84no—
789#117—84no—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—216no—
794C2×C4⋊C4—216no—
795C2×C4⋊C4—84no—
796C2×C4⋊C4—84no—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2411yescharacteristic
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2411yescharacteristic
903C2×C42—24no—
904C2×C42—24no—
905C2×C42—24no—
906C2×C42—24no—
907C2×C42—24no—
908C2×C42—84no—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24C2511yescharacteristic
1007C24C2514yes—
1008C24C2511yescharacteristic
1009C24C2511yescharacteristic
1010C2×Q8—22no—
1011C2×Q8—42no—
1012C2×D4—24no—
1013C2×D4—28no—
1014C2×D4—22no—
1015C2×D4—28no—
1016C2×D4—24no—
1017C2×D4—28no—
1018C2×D4—22no—
1019C2×D4—28no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—28no—
1023C2×D4—28no—
1024C2×D4—24no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—42no—
1032C2×D4C2×#4114yes—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—22no—
1043C22×C4—28no—
1044C22×C4—24no—
1045C22×C4—28no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—22no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—28no—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4C2×#4114yes—
1075C22×C4C2×#4114yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—28no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4C2×#4118yes—
1161C4⋊C4C2×#41116yes—
1162C4⋊C4C2×#4114yes—
1163C22⋊C4—28no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—22no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—22no—
1173C22⋊C4—22no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—22no—
1178C22⋊C4—22no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4C2×#4114yes—
1208C22⋊C4C2×#4114yes—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—24no—
1213C42—24no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—22no—
1218C42—22no—
1219C42—28no—
1220C42—24no—
1221C42—24no—
1222C42—22no—
1223C42—22no—
1224C42—22no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—42no—
1237C42—42no—
1238C42—44no—
1239C42—44no—
1240C42—42no—
1241C42—42no—
1242C42C2×#4114yes—
1243C42C2×#4114yes—
1244C422−1+414yes—
1245C23—21no—
1246C23—21no—
1247C23—22no—
1248C23—21no—
1249C23—21no—
1250C23—22no—
1251C23—22no—
1252C23—21no—
1253C23—24no—
1254C23—24no—
1255C23—21no—
1256C23—24no—
1257C23—21no—
1258C23—24no—
1259C23—24no—
1260C23—22no—
1261C23—24no—
1262C23—22no—
1263C23—24no—
1264C23C22×#4112yes—
1265C23C22×#4112yes—
1266C23#58514yes—
1267C23C2611yescharacteristic
1268Q8—82no—
1269D4—28no—
1270D4—416no—
1271D4—44no—
1272D4—48no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—82no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—28no—
1290C2×C4—28no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—416no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—44no—
1346C2×C4—44no—
1347C2×C4—88no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—88no—
1351C2×C4—84no—
1352C2×C4—88no—
1353C2×C4—82no—
1354C2×C4—88no—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4114yes—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4118yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4C2×2−1+412yes—
1365C22—24no—
1366C22—22no—
1367C22—24no—
1368C22—22no—
1369C22—22no—
1370C22—22no—
1371C22—22no—
1372C22—42no—
1373C22—42no—
1374C22—44no—
1375C22—44no—
1376C22—42no—
1377C22—41no—
1378C22—44no—
1379C22—44no—
1380C22—41no—
1381C22—44no—
1382C22—42no—
1383C22—44no—
1384C22—41no—
1385C22—44no—
1386C22#351214yes—
1387C22C23×#4111yescharacteristic
1388C22C23×#4111yescharacteristic
1389C22C22×2−1+411yescharacteristic
1390C22C2×#58512yes—
1391C22H(7,𝔽2)12yes—
1392C4—28no—
1393C4—24no—
1394C4—22no—
1395C4—22no—
1396C4—24no—
1397C4—22no—
1398C4—22no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—44no—
1403C4—42no—
1404C4—41no—
1405C4—41no—
1406C4—44no—
1407C4—41no—
1408C4—41no—
1409C4—44no—
1410C4—44no—
1411C4—41no—
1412C4—41no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—41no—
1418C4#348214yes—
1419C2—24no—
1420C2—42no—
1421C2—84no—
1422C2—81no—
1423C2C2×#348211yescharacteristic
1424C2C2×#351211yescharacteristic
1425C2#6285811yescharacteristic
1426C2#6295812yes—
1427C2#6300812yes—
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. #59954C2semidirect
2. #59690C2semidirect
3. #59686C2semidirect
4. #59677C2semidirect
5. #44722C2semidirect
6. #44628C2semidirect
7. #44356C2semidirect
8. #44196C2semidirect
9. #39763C2semidirect
10. #39638C2semidirect
11. #39298C2semidirect
12. #38266C2semidirect
13. #38042C2semidirect
14. #37889C2semidirect
15. #37882C2semidirect
16. #37706C2semidirect
17. #37706C2semidirect
18. #36294C2semidirect
19. #36182C2semidirect
20. D4×#125C2semidirect
21. #35612C2semidirect
22. #35588C2semidirect
23. #35345C2semidirect
24. #35295C2semidirect
25. #35271C2semidirect
26. #34788C2semidirect
27. #34305C2semidirect
28. #34280C2semidirect
29. #34217C2semidirect
30. #34149C2semidirect
31. C2×#2330C2semidirect

Maximal subgroups

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

subgroupindex
#599542
#596902
#596862
#596772
#447222
#446282
#443562
#441962
#397632
#396382
#392982
#382662
#380422
#378892
#378822
#377062
#362942
#361822
D4×#1252
#356122
#355882
#353452
#352952
#352712
#347882
#343052
#342802
#342172
#341492
C2×#23302