Finite Group Databasebeta

← #7671698

Subgroups — #7671698

Order 512.

5150 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60046C212yesmaximal, complemented
2#60044C212yesmaximal, complemented
3#59993C214yesmaximal, complemented
4#59879C212yesmaximal, complemented
5#59835C212yesmaximal, complemented
6#59517C214yesmaximal, complemented
7#39749C211yesmaximal, characteristic, complemented
8#39611C211yesmaximal, characteristic, complemented
9#39509C211yesmaximal, characteristic, complemented
10#39372C211yesmaximal, characteristic, complemented
11#38789C212yesmaximal, complemented
12#38788C212yesmaximal, complemented
13#38781C212yesmaximal, complemented
14#38780C212yesmaximal, complemented
15#37961C212yesmaximal, complemented
16#37764C212yesmaximal, complemented
17#36640C211yesmaximal, characteristic, complemented
18#36492C212yesmaximal, complemented
19#36372C212yesmaximal, complemented
20#36372C212yesmaximal, complemented
21#36323C214yesmaximal, complemented
22#36272C212yesmaximal, complemented
23#36227C214yesmaximal, complemented
24#35553C212yesmaximal, complemented
25#35551C212yesmaximal, complemented
26#35282C212yesmaximal, complemented
27#35218C212yesmaximal, complemented
28#34333C212yesmaximal, complemented
29#34280C212yesmaximal, complemented
30C4×#532C211yesmaximal, characteristic, complemented
31#34026C211yesmaximal, characteristic, complemented
32C2×#554C2212yes—
33C2×#552C2214yes—
34C2×#540C2212yes—
35C2×#532C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2212yes—
38#2864C2212yes—
39#2864C2212yes—
40#2864C2212yes—
41#2859C2211yescharacteristic
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2857C2212yes—
47#2853C2214yes—
48#2852C2214yes—
49#2851C2212yes—
50#2851C2212yes—
51#2851C2212yes—
52#2851C2212yes—
53#2851C2212yes—
54#2810C2212yes—
55#2809C2212yes—
56#2808C2212yes—
57#2806C2212yes—
58#2805C2212yes—
59#2805C2212yes—
60#2788C2214yes—
61#2786C2214yes—
62#2775C2214yes—
63#2767C2214yes—
64#2732C2212yes—
65#2732C2212yes—
66#2727C2212yes—
67#2726C2212yes—
68#2724C2212yes—
69#2724C2212yes—
70#2717C2214yes—
71#2708C2214yes—
72#2686C2214yes—
73#2683C2212yes—
74#2683C2212yes—
75#2682C2212yes—
76#2682C2212yes—
77#2671C2214yes—
78#2660C2212yes—
79#2660C2212yes—
80#2652C2214yes—
81#2648C2214yes—
82#2629C2212yes—
83#2628C2212yes—
84#2611C2214yes—
85#2611C2214yes—
86#2609C2214yes—
87#2609C2214yes—
88#2601C2214yes—
89#2599C2214yes—
90#2597C2214yes—
91#2596C2214yes—
92#2595C2214yes—
93#2590C2214yes—
94#2586C2214yes—
95#2585C2214yes—
96#2577C2214yes—
97#2575C2214yes—
98#2574C2214yes—
99#2573C2214yes—
100#2573C2214yes—
101#2573C2214yes—
102#2570C2212yes—
103#2570C2212yes—
104#2566C2212yes—
105#2566C2212yes—
106#2563C2212yes—
107#2562C2212yes—
108#2562C2212yes—
109#2560C2214yes—
110#2558C2214yes—
111#2556C2214yes—
112#2554C2214yes—
113#2553C2214yes—
114#2553C2214yes—
115#2552C2212yes—
116#2542C2212yes—
117#2537C2212yes—
118#2535C2212yes—
119#2535C2212yes—
120#2530C2214yes—
121#2530C2214yes—
122#2524C2214yes—
123#2522C2214yes—
124#2520C2214yes—
125#2518C2214yes—
126#2517C2214yes—
127#2505C2214yes—
128#2497C2212yes—
129#2497C2212yes—
130#2496C2212yes—
131#2496C2212yes—
132#2495C2212yes—
133#2495C2212yes—
134#2489C2214yes—
135#2488C2214yes—
136#2477C2214yes—
137#2477C2214yes—
138#2477C2214yes—
139#2476C2214yes—
140#2475C2214yes—
141#2475C2214yes—
142#2471C2214yes—
143#2470C2214yes—
144#2470C2214yes—
145#2470C2214yes—
146#2469C2214yes—
147#2469C2214yes—
148#2467C2214yes—
149#2465C2214yes—
150#2463C2214yes—
151#2463C2214yes—
152#2462C2214yes—
153#2462C2214yes—
154#2460C2214yes—
155#2460C2214yes—
156#2460C2214yes—
157#2450C2214yes—
158#2449C2214yes—
159#2449C2214yes—
160#2443C2214yes—
161#2430C2214yes—
162#2425C2214yes—
163#2425C2214yes—
164#2425C2214yes—
165#2422C2212yes—
166#2422C2212yes—
167#2422C2212yes—
168#2422C2212yes—
169#2421C2214yes—
170#2420C2212yes—
171#2420C2212yes—
172#2419C2214yes—
173#2415C2214yes—
174#2407C2214yes—
175#2406C2214yes—
176#2374C2214yes—
177#2374C2214yes—
178#2370C2212yes—
179#2370C2212yes—
180#2368C2214yes—
181#2368C2214yes—
182#2365C2212yes—
183#2364C2214yes—
184#2364C2214yes—
185#2363C2214yes—
186#2363C2214yes—
187#2361C2214yes—
188#2360C2214yes—
189#2360C2214yes—
190#2359C2214yes—
191#2359C2214yes—
192#2359C2214yes—
193#2359C2214yes—
194#2355C2212yes—
195#2352C2214yes—
196#2349C2212yes—
197#2349C2212yes—
198D4×C4⋊C4C2212yes—
199#2345C2214yes—
200#2343C2214yes—
201#2343C2214yes—
202#2331C2212yes—
203#2330C2212yes—
204#2330C2212yes—
205#2329C2214yes—
206#2329C2214yes—
207#2328C2212yes—
208#2324C2212yes—
209#2324C2212yes—
210#2314C2212yes—
211#2314C2212yes—
212#2314C2212yes—
213C4×C4⋊Q8C2211yescharacteristic
214C4×C4⋊Q8C2211yescharacteristic
215C4×#127C2211yescharacteristic
216C4×#127C2211yescharacteristic
217C4×#125C2212yes—
218C4×#125C2212yes—
219C4×#125C2212yes—
220C4×#125C2212yes—
221C4×#124C2212yes—
222C4×#124C2212yes—
223C4×C22⋊Q8C2214yes—
224C4×#121C2212yes—
225C4×#121C2212yes—
226C4×#121C2212yes—
227C4×#121C2212yes—
228C4×#121C2212yes—
229C4×#121C2212yes—
230#2298C2212yes—
231#2298C2212yes—
232#2297C2211yescharacteristic
233#2297C2211yescharacteristic
234#2297C2212yes—
235#2296C2212yes—
236#2296C2212yes—
237#2296C2211yescharacteristic
238#2296C2211yescharacteristic
239#2295C2211yescharacteristic
240#2295C2211yescharacteristic
241#2295C2211yescharacteristic
242#2295C2211yescharacteristic
243#2293C2212yes—
244#2293C2212yes—
245#2293C2212yes—
246#2293C2211yescharacteristic
247#2293C2211yescharacteristic
248#2293C2211yescharacteristic
249#2293C2211yescharacteristic
250#2293C2212yes—
251#2290C2212yes—
252#2290C2212yes—
253#2290C2212yes—
254#2290C2212yes—
255C2×#387C2214yes—
256#2285C2211yescharacteristic
257#2285C2211yescharacteristic
258#2285C2211yescharacteristic
259#2275C2212yes—
260#2275C2212yes—
261C42×D4C2212yes—
262C42×D4C2212yes—
263C4×#117C2211yescharacteristic
264C4×#117C2212yes—
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2311yescharacteristic
269#554—216no—
270#552—416no—
271#540—216no—
272#532—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2314yes—
305C4×#41—28no—
306C4×#41—48no—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2311yescharacteristic
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2311yescharacteristic
341C2×#117C2314yes—
342C2×#117C2312yes—
343C2×#117C2311yescharacteristic
344C2×#117C2312yes—
345C2×#117C2312yes—
346C22×C4⋊C4C2314yes—
347C22×C4⋊C4C2314yes—
348C22×C42C2311yescharacteristic
349C22×C42C2311yescharacteristic
350C22×C42C2311yescharacteristic
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353C22×C42C2311yescharacteristic
354C22×C42C2314yes—
355C22×C42C2311yescharacteristic
356C22×C42C2311yescharacteristic
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2314yes—
420#392C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2311yescharacteristic
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2311yescharacteristic
462#389C2312yes—
463#389C2314yes—
464#389C2311yescharacteristic
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2311yescharacteristic
486#389C2311yescharacteristic
487#389C2311yescharacteristic
488#389C2311yescharacteristic
489#389C2311yescharacteristic
490#389C2311yescharacteristic
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2314yes—
512#388C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2312yes—
522#388C2312yes—
523#388C2314yes—
524#388C2312yes—
525#387C2314yes—
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#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2312yes—
592#386C2312yes—
593#386C2314yes—
594#386C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2312yes—
620#385C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#383C2314yes—
631#383C2314yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#381C2314yes—
645#381C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722#376C2312yes—
723#376C2312yes—
724#376C2312yes—
725#376C2312yes—
726#376C2312yes—
727C2×#95C2314yes—
728C2×#95C2314yes—
729C2×#95C2314yes—
730C2×#95C2314yes—
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—24no—
741C2×#41—28no—
742C2×#41—44no—
743C2×#41—42no—
744C2×#41—42no—
745C2×#41—44no—
746C22×Q8C2412yes—
747C22×Q8C2414yes—
748C22×Q8C2411yescharacteristic
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2412yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2411yescharacteristic
774C4⋊Q8—24no—
775C4⋊Q8—28no—
776#127#4118yescomplemented
777#126—48no—
778#126—48no—
779#125—28no—
780#125—28no—
781#125—28no—
782#125—28no—
783#125—44no—
784#125—48no—
785#125—48no—
786#124—28no—
787#123—216no—
788#123—216no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—48no—
793C22⋊Q8—216no—
794C22⋊Q8—216no—
795C22⋊Q8—216no—
796C22⋊Q8—48no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799#121—28no—
800#121—28no—
801#121—216no—
802#121—216no—
803#121—28no—
804#121—28no—
805#121—48no—
806C4×Q8—24no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—48no—
810C4×Q8#4118yescomplemented
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—24no—
817C4×D4—24no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—44no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—48no—
828C4×D4—48no—
829C4×D4—48no—
830C4×D4—48no—
831#117—28no—
832#117—24no—
833#117—28no—
834#117—216no—
835#117—28no—
836#117—28no—
837#117—42no—
838#117—44no—
839#117—44no—
840#117—48no—
841#117—48no—
842#117—44no—
843#117—42no—
844#117—44no—
845C2×C4⋊C4—216no—
846C2×C4⋊C4—48no—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2411yescharacteristic
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C42—24no—
949C2×C42—28no—
950C2×C42—24no—
951C2×C42—24no—
952C2×C42—24no—
953C2×C42—48no—
954C2×C42—42no—
955C2×C42—42no—
956C2×C42—42no—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063C24C2512yes—
1064C24C2514yes—
1065C24C2511yescharacteristic
1066#41—416no—
1067#41—432no—
1068C2×Q8—24no—
1069C2×Q8—28no—
1070C2×Q8—42no—
1071C2×Q8—41no—
1072C2×Q8—41no—
1073C2×Q8—42no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8C2×#4114yes—
1077C2×D4—28no—
1078C2×D4—24no—
1079C2×D4—28no—
1080C2×D4—28no—
1081C2×D4—28no—
1082C2×D4—24no—
1083C2×D4—22no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4C2×#4118yes—
1099C2×D4C2×#4118yes—
1100C2×D4C2×#4118yes—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—22no—
1110C22×C4—28no—
1111C22×C4—28no—
1112C22×C4—28no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—24no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—24no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—28no—
1124C22×C4—24no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—28no—
1130C22×C4—28no—
1131C22×C4—28no—
1132C22×C4—28no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2514yes—
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2514yes—
1165C22×C4C2514yes—
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—28no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—24no—
1203C4⋊C4—28no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—28no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4C2×#4118yes—
1240C4⋊C4C2×#4114yes—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—24no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—24no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—24no—
1266C22⋊C4—28no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C42—22no—
1282C42—24no—
1283C42—22no—
1284C42—22no—
1285C42—22no—
1286C42—22no—
1287C42—24no—
1288C42—22no—
1289C42—24no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—28no—
1294C42—24no—
1295C42—22no—
1296C42—22no—
1297C42—22no—
1298C42—24no—
1299C42—22no—
1300C42—22no—
1301C42—22no—
1302C42—22no—
1303C42—24no—
1304C42—41no—
1305C42—41no—
1306C42—41no—
1307C42—41no—
1308C42—41no—
1309C42—41no—
1310C42—41no—
1311C42—41no—
1312C42—44no—
1313C42—44no—
1314C42—42no—
1315C42—44no—
1316C42—44no—
1317C42—42no—
1318C42—44no—
1319C42—44no—
1320C42—44no—
1321C42—44no—
1322C42C2×#4114yes—
1323C42C2×#4114yes—
1324C42C2×#4118yes—
1325C42H(5,𝔽2)14yes—
1326C422−1+414yes—
1327C23—24no—
1328C23—21no—
1329C23—21no—
1330C23—24no—
1331C23—21no—
1332C23—24no—
1333C23—21no—
1334C23—24no—
1335C23—24no—
1336C23—21no—
1337C23—21no—
1338C23—24no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23C22×#4118yes—
1347C23#58512yes—
1348C23C2611yescharacteristic
1349Q8—44no—
1350Q8—48no—
1351Q8—88no—
1352D4—216no—
1353D4—48no—
1354D4—48no—
1355D4—48no—
1356D4—44no—
1357D4—416no—
1358D4—88no—
1359D4—88no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—28no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—44no—
1432C2×C4—48no—
1433C2×C4—44no—
1434C2×C4—48no—
1435C2×C4—416no—
1436C2×C4—44no—
1437C2×C4—44no—
1438C2×C4—48no—
1439C2×C4—88no—
1440C2×C4—88no—
1441C2×C4—88no—
1442C2×C4—88no—
1443C2×C4—88no—
1444C2×C4—88no—
1445C2×C4C22×#4112yes—
1446C2×C4C22×#4114yes—
1447C2×C4C22×#4112yes—
1448C2×C4C22×#4112yes—
1449C2×C4C22×#4114yes—
1450C2×C4C22×#4112yes—
1451C2×C4C22×#4112yes—
1452C2×C4C22×#4112yes—
1453C2×C4C2×H(5,𝔽2)12yes—
1454C2×C4C2×H(5,𝔽2)12yes—
1455C2×C4C2×H(5,𝔽2)12yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+412yes—
1459C2×C4#58512yes—
1460C2×C4#58512yes—
1461C22—22no—
1462C22—28no—
1463C22—28no—
1464C22—22no—
1465C22—22no—
1466C22—28no—
1467C22—41no—
1468C22—41no—
1469C22—44no—
1470C22—44no—
1471C22—44no—
1472C22—41no—
1473C22—44no—
1474C22—41no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22C23×#4111yescharacteristic
1483C22C23×#4111yescharacteristic
1484C22C22×H(5,𝔽2)11yescharacteristic
1485C22C22×2−1+411yescharacteristic
1486C22C2×#58511yescharacteristic
1487C22C2×#58511yescharacteristic
1488C22C2×#58511yescharacteristic
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—24no—
1495C4—22no—
1496C4—22no—
1497C4—24no—
1498C4—22no—
1499C4—22no—
1500C4—22no—
1501C4—22no—
1502C4—44no—
1503C4—42no—
1504C4—44no—
1505C4—41no—
1506C4—42no—
1507C4—44no—
1508C4—44no—
1509C4—44no—
1510C4—44no—
1511C4—42no—
1512C4—42no—
1513C4—44no—
1514C4—41no—
1515C4—42no—
1516C4#348214yes—
1517C2—42no—
1518C2—48no—
1519C2—82no—
1520C2C2×#348211yescharacteristic
1521C2#6277311yescharacteristic
1522C2#6278111yescharacteristic
1523C2#6280011yescharacteristic
1524C2#6281411yescharacteristic
1525C2#6282511yescharacteristic
1526C2#6283511yescharacteristic
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. #60046C2semidirect
2. #60044C2semidirect
3. #59993C2semidirect
4. #59879C2semidirect
5. #59835C2semidirect
6. #59517C2semidirect
7. #39749C2semidirect
8. #39611C2semidirect
9. #39509C2semidirect
10. #39372C2semidirect
11. #38789C2semidirect
12. #38788C2semidirect
13. #38781C2semidirect
14. #38780C2semidirect
15. #37961C2semidirect
16. #37764C2semidirect
17. #36640C2semidirect
18. #36492C2semidirect
19. #36372C2semidirect
20. #36372C2semidirect
21. #36323C2semidirect
22. #36272C2semidirect
23. #36227C2semidirect
24. #35553C2semidirect
25. #35551C2semidirect
26. #35282C2semidirect
27. #35218C2semidirect
28. #34333C2semidirect
29. #34280C2semidirect
30. C4×#532C2semidirect
31. #34026C2semidirect
776. #127#41semidirect
810. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600462
#600442
#599932
#598792
#598352
#595172
#397492
#396112
#395092
#393722
#387892
#387882
#387812
#387802
#379612
#377642
#366402
#364922
#363722
#363232
#362722
#362272
#355532
#355512
#352822
#352182
#343332
#342802
C4×#5322
#340262