Finite Group Databasebeta

← #7715604

Subgroups — #7715604

Order 512.

4248 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51195C212yesmaximal, complemented
2#51043C212yesmaximal, complemented
3#50879C212yesmaximal, complemented
4#50662C212yesmaximal, complemented
5#48792C214yesmaximal, complemented
6#47899C214yesmaximal, complemented
7#47460C214yesmaximal, complemented
8#46853C214yesmaximal, complemented
9#46852C214yesmaximal, complemented
10#46840C214yesmaximal, complemented
11#39082C212yesmaximal, complemented
12#39080C212yesmaximal, complemented
13#39078C212yesmaximal, complemented
14#39077C212yesmaximal, complemented
15#39071C212yesmaximal, complemented
16#39068C212yesmaximal, complemented
17#39067C212yesmaximal, complemented
18#39065C212yesmaximal, complemented
19#37476C211yesmaximal, characteristic, complemented
20#37449C211yesmaximal, characteristic
21#37383C212yesmaximal, complemented
22#37288C212yesmaximal, complemented
23#35321C212yesmaximal, complemented
24#35311C211yesmaximal, characteristic, complemented
25#35290C212yesmaximal, complemented
26#35263C211yesmaximal, characteristic
27#34391C211yesmaximal, characteristic
28#34380C211yesmaximal, characteristic, complemented
29#34048C211yesmaximal, characteristic, complemented
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2863C2212yescomplemented
34#2863C2212yescomplemented
35#2863C2212yescomplemented
36#2860C2212yescomplemented
37#2855C2211yescharacteristic
38#2855C2212yes—
39#2855C2211yescharacteristic
40#2855C2212yes—
41#2854C2211yescharacteristic
42#2854C2211yescharacteristic
43#2841C2214yes—
44#2814C2212yes—
45#2814C2212yes—
46#2794C2214yescomplemented
47#2793C2214yescomplemented
48#2792C2214yescomplemented
49#2791C2214yescomplemented
50#2790C2214yescomplemented
51#2789C2214yescomplemented
52#2787C2214yes—
53#2783C2214yescomplemented
54#2773C2214yescomplemented
55#2770C2214yes—
56#2769C2214yescomplemented
57#2769C2214yescomplemented
58#2767C2214yescomplemented
59#2766C2214yescomplemented
60#2765C2214yes—
61#2764C2214yes—
62#2762C2214yescomplemented
63#2759C2214yescomplemented
64#2758C2214yescomplemented
65#2758C2214yescomplemented
66#2757C2214yes—
67#2755C2214yescomplemented
68#2754C2214yescomplemented
69#2750C2214yes—
70#2750C2214yes—
71#2747C2214yes—
72#2746C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2744C2214yescomplemented
76#2743C2214yes—
77#2743C2214yes—
78#2742C2214yescomplemented
79#2740C2214yes—
80#2740C2214yes—
81#2739C2214yes—
82#2739C2214yescomplemented
83#2738C2214yes—
84#2738C2214yes—
85#2738C2214yes—
86#2738C2214yescomplemented
87#2737C2214yes—
88#2723C2214yes—
89#2722C2214yescomplemented
90#2721C2214yescomplemented
91#2707C2214yes—
92#2695C2214yes—
93#2690C2214yes—
94#2667C2212yes—
95#2665C2212yes—
96#2647C2212yescomplemented
97#2647C2212yescomplemented
98#2642C2212yescomplemented
99#2640C2212yescomplemented
100#2638C2212yes—
101#2638C2212yes—
102#2629C2212yes—
103#2628C2212yes—
104#2626C2214yes—
105#2625C2212yes—
106#2625C2212yes—
107#2625C2212yes—
108#2624C2212yes—
109#2622C2214yes—
110#2621C2212yes—
111#2620C2212yes—
112#2607C2214yescomplemented
113#2606C2214yescomplemented
114#2601C2214yes—
115#2599C2214yes—
116#2595C2214yes—
117#2590C2214yescomplemented
118#2588C2214yescomplemented
119#2588C2214yescomplemented
120#2585C2214yescomplemented
121#2585C2214yescomplemented
122#2579C2214yes—
123#2578C2214yes—
124#2578C2214yes—
125#2577C2214yes—
126#2577C2214yes—
127#2577C2214yescomplemented
128#2576C2214yes—
129#2575C2214yes—
130#2575C2214yescomplemented
131#2574C2214yescomplemented
132#2574C2214yescomplemented
133#2573C2214yes—
134#2573C2214yes—
135#2573C2214yes—
136#2573C2214yescomplemented
137#2572C2214yes—
138#2572C2214yes—
139#2569C2212yes—
140#2569C2214yescomplemented
141#2565C2214yescomplemented
142#2560C2214yes—
143#2553C2214yes—
144#2549C2212yes—
145#2533C2214yescomplemented
146#2525C2214yescomplemented
147#2524C2214yescomplemented
148#2524C2214yescomplemented
149#2524C2214yescomplemented
150#2523C2214yescomplemented
151#2516C2214yes—
152#2515C2214yes—
153#2515C2214yes—
154#2514C2212yescomplemented
155#2514C2212yescomplemented
156#2512C2212yescomplemented
157#2511C2212yescomplemented
158#2509C2212yescomplemented
159#2509C2212yescomplemented
160#2507C2212yescomplemented
161#2506C2212yescomplemented
162#2504C2211yescharacteristic
163#2503C2212yes—
164#2502C2211yescharacteristic
165#2502C2212yes—
166#2499C2214yes—
167#2499C2212yes—
168#2498C2214yes—
169#2496C2214yescomplemented
170#2495C2214yes—
171#2493C2214yescomplemented
172#2487C2212yes—
173#2486C2212yes—
174#2485C2214yes—
175#2484C2214yes—
176#2483C2212yes—
177#2483C2212yes—
178#2479C2214yes—
179#2475C2214yes—
180#2469C2214yescomplemented
181#2462C2214yescomplemented
182#2458C2214yes—
183#2454C2212yescomplemented
184#2453C2212yescomplemented
185#2451C2212yescomplemented
186#2451C2212yescomplemented
187#2448C2212yescomplemented
188#2447C2212yescomplemented
189#2446C2212yescomplemented
190#2446C2212yescomplemented
191#2442C2212yes—
192#2441C2212yes—
193#2440C2212yes—
194#2439C2212yes—
195#2436C2211yescharacteristic
196#2434C2211yescharacteristic
197#2432C2212yes—
198#2421C2214yes—
199#2412C2212yes—
200#2412C2212yes—
201#2378C2212yes—
202#2378C2212yes—
203#2375C2214yes—
204#2363C2212yes—
205#2362C2212yes—
206#2360C2212yes—
207#2360C2212yes—
208#2357C2212yes—
209#2353C2212yes—
210#2347C2211yescharacteristic
211#2346C2211yescharacteristic
212#2344C2212yes—
213#2342C2214yes—
214#2341C2211yescharacteristic
215Q8×C22⋊C4C2212yes—
216#2339C2211yescharacteristic
217#2335C2214yes—
218#2329C2214yes—
219#2324C2212yes—
220#2323C2212yes—
221#2323C2212yes—
222#2323C2212yes—
223#2320C2212yescomplemented
224#2320C2212yescomplemented
225#2320C2212yescomplemented
226#2319C2212yes—
227#2319C2212yescomplemented
228#2318C2212yes—
229#2317C2212yes—
230#2316C2212yes—
231#2316C2212yes—
232#2314C2212yes—
233#2314C2212yes—
234#2314C2212yes—
235#2314C2212yes—
236#2313C2211yescharacteristic
237#2313C2211yescharacteristic
238#2313C2211yescharacteristic
239#2313C2211yescharacteristic
240#2313C2212yes—
241#2312C2212yes—
242#2312C2212yes—
243#2311C2212yes—
244#2310C2212yes—
245C4×C4⋊Q8C2212yescomplemented
246C4×C4⋊Q8C2212yescomplemented
247C4×#125C2212yescomplemented
248C4×#124C2212yescomplemented
249#2298C2212yes—
250#2298C2212yes—
251#2298C2212yes—
252#2298C2212yes—
253#2285C2212yes—
254#2280C2211yescharacteristic
255#2280C2211yescharacteristic
256#2280C2211yescharacteristic
257C2×#380C2211yescharacteristic
258C4×#117C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#124C2312yes—
269#525—28no—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×C22⋊Q8—28no—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2311yescharacteristic
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×#121C2311yescharacteristic
282C2×#121C2311yescharacteristic
283C2×#120C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×#117—28no—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2314yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#401C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2312yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#388C2312yes—
471#388C2314yes—
472#388C2314yes—
473#388C2312yes—
474#388C2312yes—
475#388C2312yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#388C2312yes—
486#388C2312yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
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#388C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2312yes—
518#387C2314yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
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#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2312yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#384C2312yes—
603#384C2312yes—
604#384C2314yes—
605#384C2312yes—
606#384C2312yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2312yes—
613#383C2314yes—
614#383C2314yes—
615#383C2314yes—
616#382C2312yes—
617#382C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2314yes—
621#382C2312yes—
622#382C2314yes—
623#382C2314yes—
624#382C2312yes—
625#381C2314yes—
626#381C2314yes—
627#381C2311yescharacteristic
628#381C2311yescharacteristic
629#381C2311yescharacteristic
630#381C2311yescharacteristic
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2312yes—
636#381C2312yes—
637#381C2312yes—
638#381C2312yes—
639#381C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2311yescharacteristic
647#380C2312yes—
648#380C2311yescharacteristic
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2311yescharacteristic
653#380C2312yes—
654#380C2312yes—
655#380C2311yescharacteristic
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2311yescharacteristic
661#380C2311yescharacteristic
662#380C2312yes—
663#380C2311yescharacteristic
664#380C2312yes—
665#380C2311yescharacteristic
666#380C2312yes—
667#379C2312yes—
668#379C2312yes—
669#379C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2311yescharacteristic
708#376C2312yes—
709#376C2312yes—
710#376C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C43C2312yes—
714C43C2312yes—
715C25C2411yescharacteristic
716C2×#41—24no—
717C2×#41—44no—
718C22×Q8—24no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C23×C4—44no—
729C23×C4#4118yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747#126—84no—
748#126—84no—
749#125—44no—
750#125—84no—
751#124—44no—
752#123—28no—
753#123—82no—
754#123—82no—
755C22⋊Q8—28no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—24no—
760C22⋊Q8—24no—
761C22⋊Q8—84no—
762#121—24no—
763#121—24no—
764#120—28no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×Q8—84no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—44no—
772#117—28no—
773#117—28no—
774#117—28no—
775#117—28no—
776#117—24no—
777#117—44no—
778#117—44no—
779#117—44no—
780#117—84no—
781C2×C4⋊C4—24no—
782C2×C4⋊C4—24no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—44no—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C22⋊C4—24no—
844C2×C22⋊C4—24no—
845C2×C22⋊C4—28no—
846C2×C22⋊C4—82no—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C42—24no—
889C2×C42—24no—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915#95C2411yescharacteristic
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2412yes—
934#95C2411yescharacteristic
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2411yescharacteristic
943#95C2411yescharacteristic
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24—41no—
998C24—42no—
999C24—41no—
1000C24—42no—
1001C24C2×#4114yes—
1002C24C2512yes—
1003C24C2511yescharacteristic
1004C24C2511yescharacteristic
1005C24C2511yescharacteristic
1006#41—88no—
1007C2×Q8—24no—
1008C2×Q8—22no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—88no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—22no—
1022C2×D4—24no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—42no—
1026C2×D4—44no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—416no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—42no—
1046C22×C4—41no—
1047C22×C4—42no—
1048C22×C4—41no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4C2×#4114yes—
1058C22×C4C2×#4114yes—
1059C22×C4C2×#4114yes—
1060C22×C4C2×#4114yes—
1061C22×C4C2×#4114yes—
1062C22×C4C2×#4114yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
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—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—42no—
1196C42—44no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42—42no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—21no—
1223C23—22no—
1224C23—24no—
1225C23—22no—
1226C23—24no—
1227C23—22no—
1228C23—44no—
1229C23—44no—
1230C23—44no—
1231C23—84no—
1232C23—84no—
1233C23C22×#4112yes—
1234C23C22×#4112yes—
1235C23C22×#4112yes—
1236C23C2611yescharacteristic
1237Q8—48no—
1238Q8—44no—
1239Q8—84no—
1240Q8—88no—
1241D4—44no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—28no—
1249C2×C4—28no—
1250C2×C4—28no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—44no—
1313C2×C4—44no—
1314C2×C4—44no—
1315C2×C4—48no—
1316C2×C4—84no—
1317C2×C4—82no—
1318C2×C4—82no—
1319C2×C4—82no—
1320C2×C4—82no—
1321C2×C4—84no—
1322C2×C4—164no—
1323C2×C4—164no—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4#58514yes—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—88no—
1350C22C23×#4111yescharacteristic
1351C22C2×#58512yes—
1352C22H(7,𝔽2)11yescharacteristic
1353C222−1+611yescharacteristic
1354C222−1+612yes—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—42no—
1359C4—44no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4#349114yes—
1380C2—42no—
1381C2—42no—
1382C2—42no—
1383C2—82no—
1384C2C2×#349111yescharacteristic
1385C2#6285611yescharacteristic
1386C2#6286011yescharacteristic
1387C2#6288412yes—
1388C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #51195C2semidirect
2. #51043C2semidirect
3. #50879C2semidirect
4. #50662C2semidirect
5. #48792C2semidirect
6. #47899C2semidirect
7. #47460C2semidirect
8. #46853C2semidirect
9. #46852C2semidirect
10. #46840C2semidirect
11. #39082C2semidirect
12. #39080C2semidirect
13. #39078C2semidirect
14. #39077C2semidirect
15. #39071C2semidirect
16. #39068C2semidirect
17. #39067C2semidirect
18. #39065C2semidirect
19. #37476C2semidirect
21. #37383C2semidirect
22. #37288C2semidirect
23. #35321C2semidirect
24. #35311C2semidirect
25. #35290C2semidirect
28. #34380C2semidirect
29. #34048C2semidirect
33. #2863C22semidirect
34. #2863C22semidirect
35. #2863C22semidirect
36. #2860C22semidirect
46. #2794C22semidirect
47. #2793C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2790C22semidirect
51. #2789C22semidirect
53. #2783C22semidirect
54. #2773C22semidirect
56. #2769C22semidirect
57. #2769C22semidirect
58. #2767C22semidirect
59. #2766C22semidirect
62. #2762C22semidirect
63. #2759C22semidirect
64. #2758C22semidirect
65. #2758C22semidirect
67. #2755C22semidirect
68. #2754C22semidirect
75. #2744C22semidirect
78. #2742C22semidirect
82. #2739C22semidirect
86. #2738C22semidirect
89. #2722C22semidirect
90. #2721C22semidirect
96. #2647C22semidirect
97. #2647C22semidirect
98. #2642C22semidirect
99. #2640C22semidirect
112. #2607C22semidirect
113. #2606C22semidirect
117. #2590C22semidirect
118. #2588C22semidirect
119. #2588C22semidirect
120. #2585C22semidirect
121. #2585C22semidirect
127. #2577C22semidirect
130. #2575C22semidirect
131. #2574C22semidirect
132. #2574C22semidirect
136. #2573C22semidirect
140. #2569C22semidirect
141. #2565C22semidirect
145. #2533C22semidirect
146. #2525C22semidirect
147. #2524C22semidirect
148. #2524C22semidirect
149. #2524C22semidirect
150. #2523C22semidirect
154. #2514C22semidirect
155. #2514C22semidirect
156. #2512C22semidirect
157. #2511C22semidirect
158. #2509C22semidirect
159. #2509C22semidirect
160. #2507C22semidirect
161. #2506C22semidirect
169. #2496C22semidirect
171. #2493C22semidirect
180. #2469C22semidirect
181. #2462C22semidirect
183. #2454C22semidirect
184. #2453C22semidirect
185. #2451C22semidirect
186. #2451C22semidirect
187. #2448C22semidirect
188. #2447C22semidirect
189. #2446C22semidirect
190. #2446C22semidirect
223. #2320C22semidirect
224. #2320C22semidirect
225. #2320C22semidirect
227. #2319C22semidirect
245. C4×C4⋊Q8C22semidirect
246. C4×C4⋊Q8C22semidirect
247. C4×#125C22semidirect
248. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#511952
#510432
#508792
#506622
#487922
#478992
#474602
#468532
#468522
#468402
#390822
#390802
#390782
#390772
#390712
#390682
#390672
#390652
#374762
#374492
#373832
#372882
#353212
#353112
#352902
#352632
#343912
#343802
#340482