Finite Group Databasebeta

← #7898115

Subgroups — #7898115

Order 512.

4661 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic
2#59276C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#51179C214yesmaximal, complemented
5#50626C214yesmaximal, complemented
6#50365C214yesmaximal, complemented
7#47255C214yesmaximal, complemented
8#45958C212yesmaximal, complemented
9#45335C212yesmaximal, complemented
10#45300C212yesmaximal, complemented
11#44918C212yesmaximal, complemented
12#43682C214yesmaximal, complemented
13#42835C212yesmaximal, complemented
14#42693C212yesmaximal, complemented
15#41498C214yesmaximal, complemented
16#39756C211yesmaximal, characteristic, complemented
17#39612C211yesmaximal, characteristic, complemented
18#39215C212yesmaximal, complemented
19#38829C212yesmaximal, complemented
20#38495C212yesmaximal, complemented
21#38093C212yesmaximal, complemented
22#37952C212yesmaximal, complemented
23#37152C212yesmaximal, complemented
24#36270C211yesmaximal, characteristic, complemented
25#36049C212yesmaximal, complemented
26#35609C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34473C212yesmaximal, complemented
29#34328C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#552C2212yes—
33C2×#550C2212yes—
34C2×#547C2212yes—
35#2861C2212yes—
36#2860C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2850C2212yes—
40#2832C2214yes—
41#2830C2214yes—
42#2808C2212yes—
43#2808C2211yescharacteristic
44#2808C2211yescharacteristic
45#2808C2212yes—
46#2804C2211yescharacteristic
47#2803C2214yes—
48#2800C2214yes—
49#2797C2214yes—
50#2796C2212yes—
51#2796C2212yes—
52#2794C2212yes—
53#2788C2214yes—
54#2787C2214yes—
55#2786C2214yes—
56#2785C2214yes—
57#2781C2214yes—
58#2780C2214yes—
59#2757C2214yes—
60#2751C2212yes—
61#2751C2212yes—
62#2748C2214yes—
63#2747C2214yes—
64#2745C2214yes—
65#2744C2214yes—
66#2737C2214yes—
67#2734C2212yes—
68#2734C2212yes—
69#2727C2212yes—
70#2727C2212yes—
71#2727C2214yes—
72#2726C2212yes—
73#2726C2212yes—
74#2725C2214yes—
75#2724C2211yescharacteristic
76#2722C2214yes—
77#2719C2214yes—
78#2716C2214yes—
79#2715C2214yes—
80#2711C2214yes—
81#2711C2214yes—
82#2709C2214yes—
83#2709C2212yes—
84#2709C2214yes—
85#2707C2214yes—
86#2705C2214yes—
87#2694C2214yes—
88#2694C2214yes—
89#2691C2214yes—
90#2691C2214yes—
91#2691C2214yes—
92#2686C2214yes—
93#2686C2214yes—
94#2682C2212yes—
95#2682C2212yes—
96#2662C2214yes—
97#2660C2212yes—
98#2653C2214yes—
99#2651C2214yes—
100#2651C2214yes—
101#2651C2214yes—
102#2649C2214yes—
103#2641C2214yes—
104#2641C2212yes—
105#2620C2212yes—
106#2610C2214yes—
107#2603C2214yes—
108#2601C2214yes—
109#2601C2214yes—
110#2594C2214yes—
111#2593C2214yes—
112#2590C2214yes—
113#2587C2214yes—
114#2582C2211yescharacteristic
115#2580C2212yes—
116#2578C2214yes—
117#2576C2214yes—
118#2574C2214yes—
119#2574C2214yes—
120#2567C2212yes—
121#2565C2212yes—
122#2565C2212yes—
123#2562C2212yes—
124#2562C2214yes—
125#2558C2214yes—
126#2554C2214yes—
127#2552C2211yescharacteristic
128#2548C2211yescharacteristic
129#2548C2211yescharacteristic
130#2548C2214yes—
131#2541C2212yes—
132#2538C2212yes—
133#2538C2211yescharacteristic
134#2538C2211yescharacteristic
135#2537C2212yes—
136#2536C2212yes—
137#2531C2214yes—
138#2530C2214yes—
139#2528C2214yes—
140#2522C2214yes—
141#2521C2214yes—
142#2521C2214yes—
143#2519C2214yes—
144#2518C2214yes—
145#2512C2212yes—
146#2512C2212yes—
147#2512C2212yes—
148#2506C2212yes—
149#2504C2212yes—
150#2500C2212yes—
151#2496C2212yes—
152#2494C2212yes—
153#2492C2212yes—
154#2491C2212yes—
155#2491C2212yes—
156#2491C2214yes—
157#2491C2214yes—
158#2490C2214yes—
159#2490C2212yes—
160#2490C2212yes—
161#2490C2214yes—
162#2489C2212yes—
163#2479C2214yes—
164#2476C2214yes—
165#2476C2214yes—
166#2476C2214yes—
167#2475C2214yes—
168#2475C2214yes—
169#2474C2214yes—
170#2473C2214yes—
171#2473C2214yes—
172#2468C2214yes—
173#2467C2214yes—
174#2466C2214yes—
175#2466C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2460C2214yes—
179#2460C2214yes—
180#2458C2214yes—
181#2458C2214yes—
182#2458C2214yes—
183#2454C2212yes—
184#2453C2214yes—
185#2448C2212yes—
186#2447C2212yes—
187#2445C2214yes—
188#2445C2212yes—
189#2442C2212yes—
190#2439C2212yes—
191#2439C2214yes—
192#2432C2212yes—
193#2432C2212yes—
194#2429C2212yes—
195#2429C2212yes—
196#2423C2212yes—
197#2423C2212yes—
198#2416C2214yes—
199#2407C2212yes—
200#2407C2212yes—
201#2398C2212yes—
202#2398C2214yes—
203#2398C2212yes—
204#2395C2212yes—
205#2377C2214yes—
206#2376C2214yes—
207#2374C2214yes—
208#2373C2214yes—
209#2371C2214yes—
210#2370C2212yes—
211#2365C2212yes—
212#2365C2211yescharacteristic
213#2362C2212yes—
214#2360C2212yes—
215#2357C2212yes—
216#2356C2212yes—
217#2356C2212yes—
218#2355C2211yescharacteristic
219#2355C2211yescharacteristic
220#2354C2211yescharacteristic
221#2352C2212yes—
222D4×C4⋊C4C2211yescharacteristic
223D4×C4⋊C4C2212yes—
224#2345C2214yes—
225#2341C2212yes—
226#2341C2212yes—
227#2341C2212yes—
228#2341C2212yes—
229#2336C2214yes—
230#2335C2214yes—
231#2335C2214yes—
232#2334C2214yes—
233#2333C2214yes—
234#2330C2212yes—
235#2327C2212yes—
236#2327C2212yes—
237#2326C2212yes—
238#2323C2212yes—
239#2319C2212yes—
240#2314C2212yes—
241#2313C2214yes—
242#2311C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×#123C2212yes—
249#2297C2212yes—
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2293C2212yes—
254#2290C2212yes—
255#2290C2212yes—
256#2285C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261#557—28no—
262#557—48no—
263#552—48no—
264#550—48no—
265#547—216no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×#117C2312yes—
326C2×#117C2314yes—
327C2×#117C2312yes—
328C2×#117C2314yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C42C2312yes—
332#401C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2312yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#397C2312yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2312yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2312yes—
379#397C2312yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2312yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2312yes—
435#393C2312yes—
436#392C2314yes—
437#392C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2311yescharacteristic
452#390C2312yes—
453#390C2311yescharacteristic
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2311yescharacteristic
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2314yes—
483#389C2311yescharacteristic
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2312yes—
615#386C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2312yes—
642#383C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2312yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—28no—
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C4⋊Q8—28no—
748C4⋊Q8—44no—
749C4⋊Q8—48no—
750C4⋊Q8#4118yes—
751#127—24no—
752#127—42no—
753#127—48no—
754#126—48no—
755#126—48no—
756#126—48no—
757#126—84no—
758#126—84no—
759#125—216no—
760#125—28no—
761#125—28no—
762#125—48no—
763#125—44no—
764#125—48no—
765#125—48no—
766#125—82no—
767#124—44no—
768#124—84no—
769#124—82no—
770#124—84no—
771#123—216no—
772#123—216no—
773#123—44no—
774#123—48no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779#121—216no—
780#121—48no—
781#121—48no—
782#121—44no—
783#121—44no—
784#121—84no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—24no—
789C4×Q8—28no—
790C4×Q8—24no—
791C4×Q8—24no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—42no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×D4—28no—
798C4×D4—28no—
799C4×D4—28no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—48no—
803C4×D4—42no—
804C4×D4—42no—
805C4×D4—82no—
806#117—44no—
807#117—48no—
808#117—44no—
809#117—84no—
810C2×C4⋊C4—216no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C42—44no—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2411yescharacteristic
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018C24C2512yes—
1019C24C2512yes—
1020C24C2514yes—
1021#41—816no—
1022#41—816no—
1023C2×Q8—22no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—22no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—44no—
1033C2×Q8—41no—
1034C2×Q8—44no—
1035C2×Q8—41no—
1036C2×Q8—44no—
1037C2×Q8C2×#4118yes—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—28no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—41no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—28no—
1078C22×C4—28no—
1079C22×C4—28no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—41no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4C2×#4118yes—
1183C4⋊C4C2×#4118yes—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C42—28no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—28no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—22no—
1245C42—22no—
1246C42—24no—
1247C42—42no—
1248C42—42no—
1249C42—41no—
1250C42—42no—
1251C42—41no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—41no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—42no—
1261C42—44no—
1262C42—44no—
1263C42C2×#4114yes—
1264C42H(5,𝔽2)14yes—
1265C23—22no—
1266C23—22no—
1267C23—24no—
1268C23—22no—
1269C23—22no—
1270C23—24no—
1271C23—24no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—22no—
1278C23—24no—
1279C23—22no—
1280C23—24no—
1281C23—22no—
1282C23—22no—
1283C23—24no—
1284C23—22no—
1285C23—22no—
1286C23C2611yescharacteristic
1287Q8—216no—
1288Q8—44no—
1289Q8—44no—
1290Q8—82no—
1291Q8—88no—
1292D4—44no—
1293D4—48no—
1294D4—48no—
1295D4—84no—
1296D4—84no—
1297D4—82no—
1298D4—84no—
1299D4—88no—
1300D4—88no—
1301D4—164no—
1302D4—164no—
1303C2×C4—24no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—21no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—48no—
1373C2×C4—48no—
1374C2×C4—48no—
1375C2×C4—88no—
1376C2×C4—88no—
1377C2×C4—88no—
1378C2×C4—84no—
1379C2×C4—88no—
1380C2×C4C22×#4112yes—
1381C2×C4C22×#4118yes—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4C2×H(5,𝔽2)12yes—
1385C2×C4C2×H(5,𝔽2)12yes—
1386C2×C4C2×H(5,𝔽2)12yes—
1387C2×C4#58512yes—
1388C2×C4#58512yes—
1389C22—44no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—44no—
1395C22—42no—
1396C22—42no—
1397C22—44no—
1398C22—42no—
1399C22—42no—
1400C22—44no—
1401C22—44no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—44no—
1407C22—42no—
1408C22—44no—
1409C22—42no—
1410C22C23×#4111yescharacteristic
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C2×#58511yescharacteristic
1413C22C2×#58511yescharacteristic
1414C22H(7,𝔽2)11yescharacteristic
1415C222−1+611yescharacteristic
1416C222−1+611yescharacteristic
1417C4—22no—
1418C4—28no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—41no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—44no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4#351414yes—
1443C2—84no—
1444C2—82no—
1445C2—82no—
1446C2C2×#351411yescharacteristic
1447C2#6285011yescharacteristic
1448C2#6287811yescharacteristic
1449C2#6290711yescharacteristic
1450C2#6292511yescharacteristic
1451C2#6300611yescharacteristic
1452C2#6304711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59815C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59276C2semidirect
3. #52273C2semidirect
4. #51179C2semidirect
5. #50626C2semidirect
6. #50365C2semidirect
7. #47255C2semidirect
8. #45958C2semidirect
9. #45335C2semidirect
10. #45300C2semidirect
11. #44918C2semidirect
12. #43682C2semidirect
13. #42835C2semidirect
14. #42693C2semidirect
15. #41498C2semidirect
16. #39756C2semidirect
17. #39612C2semidirect
18. #39215C2semidirect
19. #38829C2semidirect
20. #38495C2semidirect
21. #38093C2semidirect
22. #37952C2semidirect
23. #37152C2semidirect
24. #36270C2semidirect
25. #36049C2semidirect
26. #35609C2semidirect
27. #35186C2semidirect
28. #34473C2semidirect
29. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#592762
#522732
#511792
#506262
#503652
#472552
#459582
#453352
#453002
#449182
#436822
#428352
#426932
#414982
#397562
#396122
#392152
#388292
#384952
#380932
#379522
#371522
#362702
#360492
#356092
#351862
#344732
#343282