Finite Group Databasebeta

← #8418648

Subgroups — #8418648

Order 512.

4372 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58787C212yesmaximal, complemented
2#58375C214yesmaximal, complemented
3#57901C214yesmaximal, complemented
4#57603C214yesmaximal, complemented
5#57048C214yesmaximal, complemented
6#55913C214yesmaximal, complemented
7#53487C212yesmaximal, complemented
8#53113C212yesmaximal, complemented
9#53037C212yesmaximal, complemented
10#52913C212yesmaximal, complemented
11#52593C214yesmaximal, complemented
12#52414C212yesmaximal, complemented
13#45413C212yesmaximal, complemented
14#45376C212yesmaximal, complemented
15#45097C212yesmaximal
16#44964C212yesmaximal, complemented
17#42983C211yesmaximal, characteristic, complemented
18#42837C212yesmaximal, complemented
19#42698C212yesmaximal, complemented
20#42536C212yesmaximal, complemented
21#42490C211yesmaximal, characteristic, complemented
22#42481C212yesmaximal, complemented
23#38060C212yesmaximal, complemented
24#38054C212yesmaximal, complemented
25#37383C211yesmaximal, characteristic, complemented
26#36691C211yesmaximal, characteristic, complemented
27#35846C211yesmaximal, characteristic, complemented
28#35739C211yesmaximal, characteristic, complemented
29#35531C211yesmaximal, characteristic
30C2×#559C2212yes—
31C2×#556C2211yescharacteristic, complemented
32C2×D4×Q8C2211yescharacteristic, complemented
33C2×#535C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2855C2212yes—
36#2845C2212yescomplemented
37#2844C2211yescharacteristic, complemented
38#2844C2211yescharacteristic, complemented
39#2843C2212yescomplemented
40#2843C2211yescharacteristic, complemented
41#2843C2211yescharacteristic, complemented
42#2842C2212yes—
43#2841C2212yes—
44#2841C2212yes—
45#2841C2212yes—
46#2841C2212yes—
47#2841C2214yescomplemented
48#2838C2214yescomplemented
49#2838C2214yescomplemented
50#2838C2214yescomplemented
51#2836C2214yescomplemented
52#2836C2214yescomplemented
53#2831C2214yescomplemented
54#2831C2214yescomplemented
55#2831C2214yescomplemented
56#2830C2212yes—
57#2827C2214yescomplemented
58#2817C2214yescomplemented
59#2814C2214yescomplemented
60#2798C2214yescomplemented
61#2794C2212yescomplemented
62#2793C2214yescomplemented
63#2792C2212yescomplemented
64#2792C2214yescomplemented
65#2790C2214yes—
66#2790C2214yescomplemented
67#2789C2212yescomplemented
68#2788C2214yescomplemented
69#2784C2212yes—
70#2780C2214yes—
71#2774C2214yescomplemented
72#2771C2214yescomplemented
73#2769C2212yescomplemented
74#2761C2214yes—
75#2757C2214yes—
76#2757C2214yescomplemented
77#2750C2214yes—
78#2750C2214yescomplemented
79#2750C2214yescomplemented
80#2747C2214yescomplemented
81#2747C2214yescomplemented
82#2746C2214yes—
83#2746C2214yescomplemented
84#2745C2214yes—
85#2745C2214yescomplemented
86#2745C2214yescomplemented
87#2743C2214yes—
88#2743C2214yes—
89#2743C2214yescomplemented
90#2742C2214yescomplemented
91#2741C2214yescomplemented
92#2739C2214yescomplemented
93#2738C2214yes—
94#2738C2214yescomplemented
95#2737C2214yes—
96#2736C2212yes—
97#2735C2214yes—
98#2735C2212yes—
99#2723C2214yes—
100#2720C2214yes—
101#2720C2214yescomplemented
102#2720C2214yescomplemented
103#2718C2214yescomplemented
104#2715C2214yescomplemented
105#2707C2214yescomplemented
106#2701C2214yes—
107#2700C2214yescomplemented
108#2700C2214yescomplemented
109#2697C2214yes—
110#2695C2214yescomplemented
111#2694C2214yescomplemented
112#2690C2214yescomplemented
113#2689C2214yescomplemented
114#2686C2214yes—
115#2684C2214yes—
116#2683C2212yes—
117#2680C2214yescomplemented
118#2680C2214yescomplemented
119#2680C2214yescomplemented
120#2664C2214yescomplemented
121#2654C2214yescomplemented
122#2651C2214yes—
123#2650C2214yescomplemented
124#2650C2214yescomplemented
125#2645C2212yescomplemented
126#2644C2212yes—
127#2643C2214yescomplemented
128#2642C2212yescomplemented
129#2640C2212yes—
130#2638C2212yes—
131#2638C2214yescomplemented
132#2633C2214yescomplemented
133#2628C2211yescharacteristic
134#2627C2212yescomplemented
135#2626C2214yes—
136#2621C2211yescharacteristic
137#2614C2214yescomplemented
138#2594C2214yescomplemented
139#2593C2212yes—
140#2592C2212yes—
141#2592C2212yes—
142#2589C2214yes—
143#2583C2212yescomplemented
144#2582C2212yescomplemented
145#2581C2211yescharacteristic, complemented
146#2581C2211yescharacteristic, complemented
147#2575C2214yescomplemented
148#2573C2214yescomplemented
149#2567C2211yescharacteristic, complemented
150#2567C2212yescomplemented
151#2566C2212yes—
152#2564C2212yes—
153#2561C2214yes—
154#2558C2214yescomplemented
155#2556C2214yes—
156#2552C2214yescomplemented
157#2547C2212yes—
158#2546C2211yescharacteristic, complemented
159#2545C2212yes—
160#2545C2212yes—
161#2544C2212yes—
162#2538C2212yes—
163#2534C2214yes—
164#2525C2214yescomplemented
165#2520C2214yescomplemented
166#2514C2212yescomplemented
167#2513C2212yes—
168#2512C2212yes—
169#2511C2212yescomplemented
170#2509C2212yescomplemented
171#2506C2212yescomplemented
172#2506C2212yescomplemented
173#2505C2214yescomplemented
174#2504C2212yes—
175#2501C2212yes—
176#2500C2212yes—
177#2500C2212yes—
178#2493C2214yescomplemented
179#2486C2214yescomplemented
180#2484C2212yescomplemented
181#2483C2214yes—
182#2481C2214yescomplemented
183#2480C2214yes—
184#2478C2214yescomplemented
185#2474C2214yescomplemented
186#2468C2214yescomplemented
187#2468C2214yescomplemented
188#2466C2214yes—
189#2454C2212yes—
190#2454C2212yescomplemented
191#2453C2212yescomplemented
192#2452C2212yes—
193#2452C2212yes—
194#2451C2212yescomplemented
195#2451C2212yescomplemented
196#2451C2212yescomplemented
197#2449C2214yes—
198#2449C2214yescomplemented
199#2448C2212yes—
200#2448C2212yes—
201#2448C2212yes—
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2447C2212yescomplemented
206#2447C2212yescomplemented
207#2446C2212yescomplemented
208#2446C2212yescomplemented
209#2445C2212yes—
210#2445C2212yes—
211#2445C2212yes—
212#2444C2214yes—
213#2441C2212yes—
214#2440C2212yes—
215#2438C2214yescomplemented
216#2437C2214yes—
217#2437C2212yes—
218#2435C2212yes—
219#2432C2212yes—
220#2425C2214yes—
221#2419C2214yescomplemented
222#2418C2214yes—
223#2418C2214yes—
224#2418C2214yes—
225#2413C2214yescomplemented
226#2409C2212yes—
227#2409C2214yescomplemented
228#2402C2212yescomplemented
229#2402C2212yescomplemented
230#2399C2212yescomplemented
231#2399C2212yescomplemented
232#2396C2211yescharacteristic
233#2396C2212yes—
234#2396C2211yescharacteristic
235#2395C2212yes—
236C2×#395C2212yescomplemented
237#2370C2212yescomplemented
238#2366C2212yes—
239#2365C2212yescomplemented
240#2362C2212yes—
241#2360C2212yes—
242#2357C2211yescharacteristic, complemented
243Q8×C4⋊C4C2212yescomplemented
244#2349C2211yescharacteristic, complemented
245D4×C4⋊C4C2212yescomplemented
246#2339C2212yes—
247D4×C22⋊C4C2212yes—
248#2326C2212yes—
249#2326C2212yescomplemented
250#2323C2212yes—
251#2319C2212yes—
252#2319C2212yescomplemented
253#2317C2211yescharacteristic
254#2309C2211yescharacteristic
255#2297C2211yescharacteristic
256C2×#390C2211yescharacteristic
257#2285C2211yescharacteristic
258#2283C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2312yes—
261C23×D4C2311yescharacteristic
262#559—48no—
263#556—44no—
264D4×Q8—44no—
265#535—44no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#120C2314yes—
297#520—44no—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C22⋊C4C2314yes—
325C22×C22⋊C4C2314yes—
326C22×C42C2311yescharacteristic
327#401C2314yes—
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2311yescharacteristic
356#400C2312yes—
357#400C2311yescharacteristic
358#400C2312yes—
359#400C2314yes—
360#399C2311yescharacteristic
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2311yescharacteristic
368#399C2312yes—
369#399C2314yes—
370#399C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2312yes—
445#396C2312yes—
446#396C2312yes—
447#396C2312yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#395C2312yes—
452#395C2312yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#395C2314yes—
457#395C2312yes—
458#395C2311yescharacteristic
459#395C2312yes—
460#395C2312yes—
461#395C2312yes—
462#395C2314yes—
463#395C2311yescharacteristic
464#395C2312yes—
465#395C2312yes—
466#395C2312yes—
467#395C2312yes—
468#395C2312yes—
469#395C2314yes—
470#395C2312yes—
471#395C2312yes—
472#395C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2312yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2312yes—
492#393C2311yescharacteristic
493#393C2311yescharacteristic
494#393C2314yes—
495#391C2314yes—
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2312yes—
643#384C2312yes—
644#384C2314yes—
645#384C2312yes—
646#384C2311yescharacteristic
647#384C2311yescharacteristic
648#384C2314yes—
649#383C2312yes—
650#383C2312yes—
651#383C2314yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#382C2311yescharacteristic
656#382C2311yescharacteristic
657#382C2312yes—
658#382C2311yescharacteristic
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2312yes—
666#381C2314yes—
667#381C2312yes—
668#381C2314yes—
669#381C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#379C2314yes—
685#379C2314yes—
686#379C2312yes—
687#379C2312yes—
688#379C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2312yes—
716C2×#95C2314yes—
717C25C2412yes—
718C2×#41—24no—
719C2×#41—24no—
720C2×#41—42no—
721C22×Q8—44no—
722C22×Q8—84no—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×D4—24no—
731C22×D4—42no—
732C22×D4—42no—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753#127—28no—
754#126—48no—
755#126—84no—
756#125—44no—
757#125—84no—
758#125—84no—
759#124—28no—
760#124—44no—
761#124—44no—
762#124—44no—
763#124—48no—
764#123—48no—
765#123—48no—
766#123—84no—
767#123—84no—
768#123—84no—
769C22⋊Q8—28no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—84no—
774C22⋊Q8—84no—
775C22⋊Q8—84no—
776C22⋊Q8—84no—
777#121—44no—
778#121—44no—
779#120—48no—
780C4×Q8—42no—
781C4×Q8—42no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—42no—
785C4×Q8—42no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×D4—24no—
789C4×D4—24no—
790C4×D4—28no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—48no—
797C4×D4—84no—
798#117—42no—
799#117—42no—
800#117—44no—
801#117—44no—
802#117—42no—
803C2×C4⋊C4—42no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—84no—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C22⋊C4—84no—
875C2×C22⋊C4—84no—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C42—24no—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940#95C2412yes—
941#95C2411yescharacteristic
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014C24—24no—
1015C24—42no—
1016C24—44no—
1017C24—44no—
1018C24—42no—
1019C24C2514yes—
1020C24C2512yes—
1021C24C2511yescharacteristic
1022#41—416no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—41no—
1030C2×Q8—42no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—44no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—816no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—28no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—24no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—88no—
1060C2×D4H(5,𝔽2)14yes—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—28no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C42−1+414yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—41no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—41no—
1207C22⋊C4—41no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C42—22no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—22no—
1232C42—22no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—44no—
1237C42—42no—
1238C42—42no—
1239C42—42no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C23—21no—
1246C23—22no—
1247C23—21no—
1248C23—22no—
1249C23—22no—
1250C23—24no—
1251C23—24no—
1252C23—22no—
1253C23—24no—
1254C23—24no—
1255C23—24no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—24no—
1260C23—84no—
1261C23—88no—
1262C23—88no—
1263C23—162no—
1264C23—162no—
1265C23C2×H(5,𝔽2)14yes—
1266C23C2×2−1+412yes—
1267C23C2611yescharacteristic
1268Q8—44no—
1269Q8—48no—
1270Q8—44no—
1271Q8—82no—
1272Q8—84no—
1273Q8—88no—
1274Q8—84no—
1275D4—28no—
1276D4—48no—
1277D4—48no—
1278D4—84no—
1279D4—88no—
1280D4—88no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—28no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
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—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—48no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—162no—
1357C2×C4—164no—
1358C2×C4—164no—
1359C2×C4C2×H(5,𝔽2)12yes—
1360C2×C4C2×2−1+412yes—
1361C2×C4C2×2−1+412yes—
1362C2×C4#58512yes—
1363C22—22no—
1364C22—24no—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—41no—
1369C22—44no—
1370C22—42no—
1371C22—41no—
1372C22—44no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—168no—
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C22×2−1+411yescharacteristic
1383C22C2×#58511yescharacteristic
1384C22H(7,𝔽2)12yes—
1385C222−1+612yes—
1386C4—22no—
1387C4—42no—
1388C4—44no—
1389C4—42no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—44no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—41no—
1404C4—41no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—44no—
1409C4—42no—
1410C4—42no—
1411C4#353514yes—
1412C2—44no—
1413C2—42no—
1414C2—84no—
1415C2C2×#353511yescharacteristic
1416C2#6287912yes—
1417C2#6304111yescharacteristic
1418C2#6305612yes—
1419C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58787C2semidirect
2. #58375C2semidirect
3. #57901C2semidirect
4. #57603C2semidirect
5. #57048C2semidirect
6. #55913C2semidirect
7. #53487C2semidirect
8. #53113C2semidirect
9. #53037C2semidirect
10. #52913C2semidirect
11. #52593C2semidirect
12. #52414C2semidirect
13. #45413C2semidirect
14. #45376C2semidirect
16. #44964C2semidirect
17. #42983C2semidirect
18. #42837C2semidirect
19. #42698C2semidirect
20. #42536C2semidirect
21. #42490C2semidirect
22. #42481C2semidirect
23. #38060C2semidirect
24. #38054C2semidirect
25. #37383C2semidirect
26. #36691C2semidirect
27. #35846C2semidirect
28. #35739C2semidirect
31. C2×#556C22semidirect
32. C2×D4×Q8C22semidirect
36. #2845C22semidirect
37. #2844C22semidirect
38. #2844C22semidirect
39. #2843C22semidirect
40. #2843C22semidirect
41. #2843C22semidirect
47. #2841C22semidirect
48. #2838C22semidirect
49. #2838C22semidirect
50. #2838C22semidirect
51. #2836C22semidirect
52. #2836C22semidirect
53. #2831C22semidirect
54. #2831C22semidirect
55. #2831C22semidirect
57. #2827C22semidirect
58. #2817C22semidirect
59. #2814C22semidirect
60. #2798C22semidirect
61. #2794C22semidirect
62. #2793C22semidirect
63. #2792C22semidirect
64. #2792C22semidirect
66. #2790C22semidirect
67. #2789C22semidirect
68. #2788C22semidirect
71. #2774C22semidirect
72. #2771C22semidirect
73. #2769C22semidirect
76. #2757C22semidirect
78. #2750C22semidirect
79. #2750C22semidirect
80. #2747C22semidirect
81. #2747C22semidirect
83. #2746C22semidirect
85. #2745C22semidirect
86. #2745C22semidirect
89. #2743C22semidirect
90. #2742C22semidirect
91. #2741C22semidirect
92. #2739C22semidirect
94. #2738C22semidirect
101. #2720C22semidirect
102. #2720C22semidirect
103. #2718C22semidirect
104. #2715C22semidirect
105. #2707C22semidirect
107. #2700C22semidirect
108. #2700C22semidirect
110. #2695C22semidirect
111. #2694C22semidirect
112. #2690C22semidirect
113. #2689C22semidirect
117. #2680C22semidirect
118. #2680C22semidirect
119. #2680C22semidirect
120. #2664C22semidirect
121. #2654C22semidirect
123. #2650C22semidirect
124. #2650C22semidirect
125. #2645C22semidirect
127. #2643C22semidirect
128. #2642C22semidirect
131. #2638C22semidirect
132. #2633C22semidirect
134. #2627C22semidirect
137. #2614C22semidirect
138. #2594C22semidirect
143. #2583C22semidirect
144. #2582C22semidirect
145. #2581C22semidirect
146. #2581C22semidirect
147. #2575C22semidirect
148. #2573C22semidirect
149. #2567C22semidirect
150. #2567C22semidirect
154. #2558C22semidirect
156. #2552C22semidirect
158. #2546C22semidirect
164. #2525C22semidirect
165. #2520C22semidirect
166. #2514C22semidirect
169. #2511C22semidirect
170. #2509C22semidirect
171. #2506C22semidirect
172. #2506C22semidirect
173. #2505C22semidirect
178. #2493C22semidirect
179. #2486C22semidirect
180. #2484C22semidirect
182. #2481C22semidirect
184. #2478C22semidirect
185. #2474C22semidirect
186. #2468C22semidirect
187. #2468C22semidirect
190. #2454C22semidirect
191. #2453C22semidirect
194. #2451C22semidirect
195. #2451C22semidirect
196. #2451C22semidirect
198. #2449C22semidirect
205. #2447C22semidirect
206. #2447C22semidirect
207. #2446C22semidirect
208. #2446C22semidirect
215. #2438C22semidirect
221. #2419C22semidirect
225. #2413C22semidirect
227. #2409C22semidirect
228. #2402C22semidirect
229. #2402C22semidirect
230. #2399C22semidirect
231. #2399C22semidirect
236. C2×#395C22semidirect
237. #2370C22semidirect
239. #2365C22semidirect
242. #2357C22semidirect
243. Q8×C4⋊C4C22semidirect
244. #2349C22semidirect
245. D4×C4⋊C4C22semidirect
249. #2326C22semidirect
252. #2319C22semidirect

Maximal subgroups

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

subgroupindex
#587872
#583752
#579012
#576032
#570482
#559132
#534872
#531132
#530372
#529132
#525932
#524142
#454132
#453762
#450972
#449642
#429832
#428372
#426982
#425362
#424902
#424812
#380602
#380542
#373832
#366912
#358462
#357392
#355312