Finite Group Databasebeta

← #7657585

Subgroups — #7657585

Order 512.

4332 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41707C214yesmaximal, complemented
2#41698C214yesmaximal, complemented
3#41616C214yesmaximal, complemented
4#41604C214yesmaximal, complemented
5#41440C212yesmaximal, complemented
6#41439C212yesmaximal, complemented
7#41396C214yesmaximal, complemented
8#39077C212yesmaximal, complemented
9#39071C212yesmaximal, complemented
10#38264C212yesmaximal, complemented
11#38251C212yesmaximal, complemented
12#38075C212yesmaximal, complemented
13#38063C212yesmaximal, complemented
14#37526C212yesmaximal, complemented
15#37521C212yesmaximal, complemented
16#37480C211yesmaximal, characteristic, complemented
17#37449C211yesmaximal, characteristic
18#36390C212yesmaximal, complemented
19#36380C212yesmaximal, complemented
20#36064C212yesmaximal, complemented
21#35857C212yesmaximal, complemented
22#35760C214yesmaximal, complemented
23#35314C212yesmaximal, complemented
24#35311C211yesmaximal, characteristic, complemented
25#34635C211yesmaximal, characteristic
26#34619C212yesmaximal, complemented
27#34245C211yesmaximal, characteristic, complemented
28#34223C211yesmaximal, characteristic
29#34109C211yesmaximal, characteristic, complemented
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2864C2212yescomplemented
34#2863C2212yescomplemented
35#2863C2212yescomplemented
36#2862C2212yescomplemented
37#2855C2212yes—
38#2855C2212yes—
39#2842C2212yes—
40#2840C2212yes—
41#2838C2214yescomplemented
42#2836C2214yescomplemented
43#2835C2214yes—
44#2834C2214yes—
45#2814C2214yes—
46#2799C2214yescomplemented
47#2793C2214yescomplemented
48#2791C2214yescomplemented
49#2789C2214yescomplemented
50#2765C2214yes—
51#2765C2214yes—
52#2764C2214yes—
53#2764C2214yes—
54#2762C2214yescomplemented
55#2761C2214yes—
56#2761C2214yes—
57#2759C2214yescomplemented
58#2754C2214yescomplemented
59#2754C2214yescomplemented
60#2751C2214yes—
61#2751C2214yes—
62#2745C2214yes—
63#2745C2214yes—
64#2744C2214yes—
65#2744C2214yes—
66#2740C2214yes—
67#2740C2214yes—
68#2737C2214yes—
69#2737C2214yes—
70#2666C2214yescomplemented
71#2666C2214yescomplemented
72#2665C2212yes—
73#2665C2212yes—
74#2665C2214yes—
75#2655C2214yescomplemented
76#2655C2214yescomplemented
77#2654C2214yescomplemented
78#2653C2214yes—
79#2653C2214yes—
80#2650C2214yescomplemented
81#2649C2214yes—
82#2649C2214yes—
83#2647C2212yescomplemented
84#2645C2212yescomplemented
85#2644C2212yescomplemented
86#2640C2212yescomplemented
87#2638C2214yes—
88#2638C2214yes—
89#2633C2214yes—
90#2628C2212yes—
91#2628C2212yes—
92#2625C2212yes—
93#2625C2212yes—
94#2625C2211yescharacteristic
95#2625C2211yescharacteristic
96#2625C2212yes—
97#2624C2211yescharacteristic
98#2624C2212yes—
99#2624C2211yescharacteristic
100#2623C2212yes—
101#2623C2212yes—
102#2622C2212yes—
103#2622C2212yes—
104#2622C2214yes—
105#2621C2212yes—
106#2620C2212yes—
107#2609C2214yes—
108#2609C2214yes—
109#2607C2214yes—
110#2607C2214yescomplemented
111#2605C2214yescomplemented
112#2599C2214yes—
113#2599C2214yes—
114#2579C2212yes—
115#2579C2212yes—
116#2577C2214yescomplemented
117#2576C2214yes—
118#2576C2214yes—
119#2574C2214yescomplemented
120#2573C2214yescomplemented
121#2572C2214yes—
122#2572C2214yes—
123#2565C2214yescomplemented
124#2556C2214yescomplemented
125#2528C2214yescomplemented
126#2527C2214yes—
127#2527C2214yes—
128#2527C2214yescomplemented
129#2524C2214yescomplemented
130#2524C2214yescomplemented
131#2524C2214yescomplemented
132#2524C2214yescomplemented
133#2524C2214yescomplemented
134#2523C2214yes—
135#2523C2214yes—
136#2523C2214yes—
137#2523C2214yescomplemented
138#2523C2214yescomplemented
139#2520C2214yescomplemented
140#2520C2214yescomplemented
141#2520C2214yescomplemented
142#2520C2214yescomplemented
143#2520C2214yescomplemented
144#2517C2214yes—
145#2517C2214yes—
146#2517C2214yes—
147#2517C2214yescomplemented
148#2517C2214yescomplemented
149#2515C2214yes—
150#2515C2214yes—
151#2515C2214yescomplemented
152#2514C2214yescomplemented
153#2514C2212yescomplemented
154#2514C2212yescomplemented
155#2514C2212yescomplemented
156#2513C2212yescomplemented
157#2508C2212yescomplemented
158#2508C2212yescomplemented
159#2507C2212yescomplemented
160#2506C2212yescomplemented
161#2504C2211yescharacteristic
162#2503C2212yes—
163#2502C2211yescharacteristic
164#2502C2212yes—
165#2499C2212yes—
166#2499C2214yes—
167#2499C2214yescomplemented
168#2484C2212yes—
169#2484C2212yes—
170#2483C2214yes—
171#2477C2214yes—
172#2477C2214yes—
173#2475C2214yes—
174#2475C2214yes—
175#2452C2212yescomplemented
176#2451C2212yescomplemented
177#2451C2212yescomplemented
178#2451C2212yescomplemented
179#2448C2212yescomplemented
180#2447C2212yescomplemented
181#2446C2212yescomplemented
182#2446C2212yescomplemented
183#2439C2212yes—
184#2439C2212yes—
185#2439C2212yes—
186#2439C2212yes—
187#2436C2211yescharacteristic
188#2434C2211yescharacteristic
189#2432C2212yes—
190#2401C2214yescomplemented
191#2398C2214yes—
192#2396C2214yescomplemented
193#2395C2212yes—
194#2395C2214yes—
195#2395C2214yes—
196#2395C2212yes—
197#2374C2214yes—
198#2371C2214yescomplemented
199#2368C2212yes—
200#2368C2212yes—
201#2368C2214yescomplemented
202#2363C2212yes—
203#2362C2212yes—
204#2362C2212yes—
205#2362C2212yes—
206#2357C2212yes—
207#2356C2214yescomplemented
208#2353C2212yes—
209#2347C2211yescharacteristic
210#2347C2211yescharacteristic
211#2347C2211yescharacteristic
212#2346C2211yescharacteristic
213#2346C2211yescharacteristic
214#2346C2211yescharacteristic
215#2345C2212yes—
216#2344C2212yes—
217#2344C2212yes—
218#2343C2212yes—
219#2343C2212yes—
220#2343C2214yescomplemented
221#2342C2212yes—
222#2342C2212yes—
223#2342C2214yes—
224#2341C2211yescharacteristic
225Q8×C22⋊C4C2212yes—
226#2339C2211yescharacteristic
227#2332C2214yes—
228#2331C2212yescomplemented
229#2327C2212yescomplemented
230#2321C2214yes—
231#2320C2212yescomplemented
232#2320C2212yescomplemented
233#2318C2212yes—
234#2317C2212yes—
235#2313C2212yes—
236#2310C2212yes—
237C4×C4⋊Q8C2212yescomplemented
238C4×#124C2212yescomplemented
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×#121C2212yes—
243#2298C2212yes—
244#2298C2212yes—
245#2297C2212yes—
246#2296C2212yes—
247#2296C2212yes—
248#2295C2212yescomplemented
249#2293C2212yescomplemented
250#2283C2212yes—
251#2280C2211yescharacteristic
252#2280C2211yescharacteristic
253#2280C2211yescharacteristic
254#2275C2212yes—
255#2274C2212yes—
256C4×#117C2212yes—
257C4×#117C2212yes—
258C2×C4×C22⋊C4C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×#125C2314yes—
266C2×#124C2312yes—
267#525—28no—
268C2×#123C2312yes—
269C2×C22⋊Q8—28no—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2311yescharacteristic
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2311yescharacteristic
278C2×#121C2311yescharacteristic
279C2×#120C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×#117—28no—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2314yes—
299C2×#117C2312yes—
300C2×#117C2314yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C42C2312yes—
311C22×C42C2312yes—
312#401C2314yes—
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
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#400C2312yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#399C2314yes—
337#399C2312yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2312yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
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#398C2312yes—
360#398C2312yes—
361#398C2314yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
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#397C2312yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#387C2312yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
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#386C2312yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2312yes—
570#386C2312yes—
571#386C2312yes—
572#386C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2312yes—
581#385C2314yes—
582#385C2312yes—
583#385C2312yes—
584#385C2312yes—
585#385C2312yes—
586#385C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#384C2312yes—
595#384C2314yes—
596#383C2314yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#383C2312yes—
602#383C2314yes—
603#383C2312yes—
604#383C2312yes—
605#383C2314yes—
606#382C2314yes—
607#382C2314yes—
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2314yes—
619#381C2314yes—
620#381C2314yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2312yes—
625#381C2312yes—
626#381C2312yes—
627#381C2312yes—
628#381C2312yes—
629#381C2314yes—
630#381C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2311yescharacteristic
634#380C2311yescharacteristic
635#380C2311yescharacteristic
636#380C2312yes—
637#380C2311yescharacteristic
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2311yescharacteristic
642#380C2311yescharacteristic
643#380C2312yes—
644#379C2312yes—
645#379C2311yescharacteristic
646#379C2312yes—
647#379C2311yescharacteristic
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C22⋊C4C2311yescharacteristic
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2311yescharacteristic
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710C2×#95C2311yescharacteristic
711C2×#95C2312yes—
712C2×#95C2311yescharacteristic
713C43C2312yes—
714C43C2312yes—
715C25C2411yescharacteristic
716C2×#41—24no—
717C2×#41—44no—
718C22×Q8—24no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×D4C2411yescharacteristic
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C23×C4—44no—
730C23×C4#4118yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748#125—48no—
749#124—44no—
750#123—28no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—48no—
758#121—24no—
759#121—24no—
760#120—28no—
761C4×Q8—48no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—44no—
768C4×D4—48no—
769#117—28no—
770#117—24no—
771#117—24no—
772#117—24no—
773#117—24no—
774#117—28no—
775#117—24no—
776#117—48no—
777#117—44no—
778#117—44no—
779#117—48no—
780#117—44no—
781#117—44no—
782#117—44no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
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×C22⋊C4—28no—
841C2×C22⋊C4—28no—
842C2×C22⋊C4—44no—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C42—28no—
886C2×C42—44no—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2412yes—
919#95C2411yescharacteristic
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
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—42no—
998C24—42no—
999C24—41no—
1000C24—41no—
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—44no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—88no—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—22no—
1025C2×D4—24no—
1026C2×D4—44no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—44no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—416no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4C2×#4114yes—
1059C22×C4C2×#4114yes—
1060C22×C4C2×#4114yes—
1061C22×C4C2×#4114yes—
1062C22×C4C2×#4114yes—
1063C22×C4C2×#4114yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
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—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—42no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
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—44no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—24no—
1191C42—24no—
1192C42—28no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—28no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—42no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—22no—
1225C23—24no—
1226C23—24no—
1227C23—22no—
1228C23—22no—
1229C23—44no—
1230C23—44no—
1231C23—44no—
1232C23—84no—
1233C23—84no—
1234C23C22×#4112yes—
1235C23C22×#4112yes—
1236C23C22×#4112yes—
1237C23C2611yescharacteristic
1238Q8—48no—
1239Q8—44no—
1240Q8—84no—
1241Q8—88no—
1242Q8—164no—
1243D4—48no—
1244D4—44no—
1245D4—84no—
1246D4—84no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—28no—
1253C2×C4—28no—
1254C2×C4—28no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
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—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—44no—
1314C2×C4—44no—
1315C2×C4—44no—
1316C2×C4—48no—
1317C2×C4—48no—
1318C2×C4—84no—
1319C2×C4—88no—
1320C2×C4—84no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—84no—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4#58514yes—
1329C2×C4#58514yes—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—42no—
1350C22—88no—
1351C22C23×#4111yescharacteristic
1352C22C2×#58512yes—
1353C22C2×#58512yes—
1354C222−1+611yescharacteristic
1355C222−1+611yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—44no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—44no—
1374C4—44no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4#349114yes—
1381C2—42no—
1382C2—42no—
1383C2—42no—
1384C2—82no—
1385C2#6268611yescharacteristic
1386C2C2×#349111yescharacteristic
1387C2#6286011yescharacteristic
1388C2#6293612yes—
1389C2#6294012yes—
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. #41707C2semidirect
2. #41698C2semidirect
3. #41616C2semidirect
4. #41604C2semidirect
5. #41440C2semidirect
6. #41439C2semidirect
7. #41396C2semidirect
8. #39077C2semidirect
9. #39071C2semidirect
10. #38264C2semidirect
11. #38251C2semidirect
12. #38075C2semidirect
13. #38063C2semidirect
14. #37526C2semidirect
15. #37521C2semidirect
16. #37480C2semidirect
18. #36390C2semidirect
19. #36380C2semidirect
20. #36064C2semidirect
21. #35857C2semidirect
22. #35760C2semidirect
23. #35314C2semidirect
24. #35311C2semidirect
26. #34619C2semidirect
27. #34245C2semidirect
29. #34109C2semidirect
33. #2864C22semidirect
34. #2863C22semidirect
35. #2863C22semidirect
36. #2862C22semidirect
41. #2838C22semidirect
42. #2836C22semidirect
46. #2799C22semidirect
47. #2793C22semidirect
48. #2791C22semidirect
49. #2789C22semidirect
54. #2762C22semidirect
57. #2759C22semidirect
58. #2754C22semidirect
59. #2754C22semidirect
70. #2666C22semidirect
71. #2666C22semidirect
75. #2655C22semidirect
76. #2655C22semidirect
77. #2654C22semidirect
80. #2650C22semidirect
83. #2647C22semidirect
84. #2645C22semidirect
85. #2644C22semidirect
86. #2640C22semidirect
110. #2607C22semidirect
111. #2605C22semidirect
116. #2577C22semidirect
119. #2574C22semidirect
120. #2573C22semidirect
123. #2565C22semidirect
124. #2556C22semidirect
125. #2528C22semidirect
128. #2527C22semidirect
129. #2524C22semidirect
130. #2524C22semidirect
131. #2524C22semidirect
132. #2524C22semidirect
133. #2524C22semidirect
137. #2523C22semidirect
138. #2523C22semidirect
139. #2520C22semidirect
140. #2520C22semidirect
141. #2520C22semidirect
142. #2520C22semidirect
143. #2520C22semidirect
147. #2517C22semidirect
148. #2517C22semidirect
151. #2515C22semidirect
152. #2514C22semidirect
153. #2514C22semidirect
154. #2514C22semidirect
155. #2514C22semidirect
156. #2513C22semidirect
157. #2508C22semidirect
158. #2508C22semidirect
159. #2507C22semidirect
160. #2506C22semidirect
167. #2499C22semidirect
175. #2452C22semidirect
176. #2451C22semidirect
177. #2451C22semidirect
178. #2451C22semidirect
179. #2448C22semidirect
180. #2447C22semidirect
181. #2446C22semidirect
182. #2446C22semidirect
190. #2401C22semidirect
192. #2396C22semidirect
198. #2371C22semidirect
201. #2368C22semidirect
207. #2356C22semidirect
220. #2343C22semidirect
228. #2331C22semidirect
229. #2327C22semidirect
231. #2320C22semidirect
232. #2320C22semidirect
237. C4×C4⋊Q8C22semidirect
238. C4×#124C22semidirect
248. #2295C22semidirect
249. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#417072
#416982
#416162
#416042
#414402
#414392
#413962
#390772
#390712
#382642
#382512
#380752
#380632
#375262
#375212
#374802
#374492
#363902
#363802
#360642
#358572
#357602
#353142
#353112
#346352
#346192
#342452
#342232
#341092