Finite Group Databasebeta

← #7696322

Subgroups — #7696322

Order 512.

4825 conjugacy classes of subgroups.

The subgroup lattice has 1411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C211yesmaximal, characteristic, complemented
2#59922C212yesmaximal, complemented
3#59722C214yesmaximal, complemented
4#59673C212yesmaximal, complemented
5#52302C212yesmaximal, complemented
6#52257C211yesmaximal, characteristic
7#45322C212yesmaximal, complemented
8#45321C211yesmaximal, characteristic
9#45226C211yesmaximal, characteristic, complemented
10#45184C212yesmaximal, complemented
11#44863C212yesmaximal, complemented
12#44617C214yesmaximal, complemented
13#43807C214yesmaximal, complemented
14#43803C212yesmaximal, complemented
15#40363C214yesmaximal, complemented
16#40039C214yesmaximal, complemented
17#39435C212yesmaximal, complemented
18#38553C214yesmaximal, complemented
19#38251C212yesmaximal, complemented
20#38128C212yesmaximal, complemented
21#36545C212yesmaximal, complemented
22#36508C211yesmaximal, characteristic, complemented
23#36007C211yesmaximal, characteristic, complemented
24#35899C212yesmaximal, complemented
25#35803C212yesmaximal, complemented
26#35759C211yesmaximal, characteristic
27#34291C212yesmaximal, complemented
28#34286C212yesmaximal, complemented
29#34266C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×#541C2212yes—
34C2×#536C2212yes—
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2857C2212yes—
41#2851C2214yes—
42#2807C2212yes—
43#2802C2214yes—
44#2799C2211yescharacteristic
45#2799C2212yes—
46#2799C2214yes—
47#2798C2212yes—
48#2797C2212yes—
49#2796C2212yes—
50#2794C2212yes—
51#2789C2214yes—
52#2789C2211yescharacteristic
53#2787C2214yes—
54#2786C2212yes—
55#2782C2211yescharacteristic
56#2781C2214yes—
57#2779C2214yes—
58#2778C2212yes—
59#2776C2214yes—
60#2773C2214yes—
61#2770C2214yes—
62#2768C2214yes—
63#2766C2214yes—
64#2765C2214yes—
65#2748C2212yes—
66#2745C2214yes—
67#2744C2214yes—
68#2730C2212yes—
69#2729C2214yes—
70#2728C2211yescharacteristic
71#2715C2214yes—
72#2713C2214yes—
73#2713C2214yes—
74#2698C2214yes—
75#2695C2214yes—
76#2694C2214yes—
77#2690C2214yes—
78#2689C2214yes—
79#2680C2212yes—
80#2677C2212yes—
81#2674C2214yes—
82#2654C2214yes—
83#2649C2214yes—
84#2645C2212yes—
85#2637C2212yes—
86#2636C2212yes—
87#2625C2212yes—
88#2625C2211yescharacteristic
89#2616C2211yescharacteristic
90#2612C2212yes—
91#2608C2214yes—
92#2605C2214yes—
93#2604C2212yes—
94#2604C2212yes—
95#2597C2214yes—
96#2596C2214yes—
97#2596C2214yes—
98#2594C2214yes—
99#2594C2214yes—
100#2594C2214yes—
101#2590C2214yes—
102#2589C2214yes—
103#2589C2214yes—
104#2587C2214yes—
105#2585C2214yes—
106#2585C2214yes—
107#2584C2214yes—
108#2582C2212yes—
109#2581C2212yes—
110#2581C2212yes—
111#2581C2214yes—
112#2573C2214yes—
113#2571C2212yes—
114#2565C2212yes—
115#2558C2214yes—
116#2556C2214yes—
117#2553C2214yes—
118#2551C2212yes—
119#2550C2214yes—
120#2550C2214yes—
121#2546C2212yes—
122#2546C2211yescharacteristic
123#2545C2212yes—
124#2542C2211yescharacteristic
125#2533C2214yes—
126#2529C2214yes—
127#2528C2214yes—
128#2528C2214yes—
129#2527C2214yes—
130#2525C2214yes—
131#2522C2214yes—
132#2521C2214yes—
133#2520C2214yes—
134#2520C2214yes—
135#2519C2214yes—
136#2519C2214yes—
137#2518C2214yes—
138#2517C2214yes—
139#2517C2212yes—
140#2515C2214yes—
141#2515C2214yes—
142#2514C2212yes—
143#2509C2212yes—
144#2509C2214yes—
145#2509C2214yes—
146#2508C2214yes—
147#2508C2214yes—
148#2507C2212yes—
149#2503C2211yescharacteristic
150#2497C2212yes—
151#2489C2212yes—
152#2489C2212yes—
153#2487C2211yescharacteristic
154#2478C2214yes—
155#2474C2214yes—
156#2473C2214yes—
157#2473C2214yes—
158#2468C2214yes—
159#2466C2214yes—
160#2466C2214yes—
161#2462C2214yes—
162#2462C2214yes—
163#2461C2214yes—
164#2459C2214yes—
165#2455C2212yes—
166#2453C2212yes—
167#2451C2212yes—
168#2446C2212yes—
169#2446C2212yes—
170#2446C2212yes—
171#2441C2212yes—
172#2439C2212yes—
173#2434C2212yes—
174#2434C2211yescharacteristic
175#2434C2212yes—
176#2429C2212yes—
177#2429C2212yes—
178#2429C2212yes—
179#2429C2212yes—
180#2423C2212yes—
181#2415C2212yes—
182#2415C2212yes—
183#2409C2211yescharacteristic
184#2402C2214yes—
185#2401C2214yes—
186#2401C2212yes—
187#2399C2212yes—
188#2398C2212yes—
189#2395C2212yes—
190#2395C2211yescharacteristic
191#2388C2211yescharacteristic
192#2373C2214yes—
193#2373C2214yes—
194#2372C2212yes—
195#2371C2214yes—
196#2370C2212yes—
197#2370C2214yes—
198#2370C2212yes—
199#2369C2214yes—
200#2367C2214yes—
201#2367C2214yes—
202#2365C2212yes—
203#2365C2214yes—
204#2365C2214yes—
205#2365C2212yes—
206#2365C2214yes—
207#2365C2212yes—
208#2362C2212yes—
209#2362C2212yes—
210#2362C2212yes—
211#2362C2212yes—
212#2362C2212yes—
213#2362C2214yes—
214#2362C2212yes—
215#2362C2212yes—
216#2360C2214yes—
217#2360C2212yes—
218#2360C2212yes—
219#2360C2212yes—
220#2360C2212yes—
221#2360C2212yes—
222#2355C2212yes—
223#2352C2214yes—
224#2352C2212yes—
225#2351C2212yes—
226#2346C2211yescharacteristic
227#2346C2211yescharacteristic
228Q8×C22⋊C4C2212yes—
229Q8×C22⋊C4C2212yes—
230#2336C2214yes—
231#2334C2214yes—
232#2327C2214yes—
233#2327C2212yes—
234#2323C2214yes—
235#2323C2212yes—
236#2322C2214yes—
237#2322C2214yes—
238#2320C2212yes—
239#2310C2212yes—
240C4×C4⋊Q8C2212yes—
241C4×#125C2214yes—
242C4×#126C2214yes—
243C4×#124C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2214yes—
247C4×C22⋊Q8C2214yes—
248C4×#123C2214yes—
249C4×#123C2214yes—
250#2298C2212yes—
251#2297C2212yes—
252#2296C2212yes—
253#2295C2212yes—
254#2290C2212yes—
255#2290C2214yes—
256#2276C2212yes—
257#2274C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2312yes—
261C23×Q8C2311yescharacteristic
262#557—44no—
263#556—44no—
264D4×Q8—216no—
265#541—216no—
266#536—216no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#126C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2314yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2312yes—
300#520—44no—
301#519—44no—
302C2×C4×Q8—48no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2311yescharacteristic
325C2×#117C2312yes—
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C2×#117C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2314yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C42C2314yes—
336C22×C42C2312yes—
337#401C2314yes—
338#401C2314yes—
339#401C2312yes—
340#400C2311yescharacteristic
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2311yescharacteristic
367#399C2312yes—
368#399C2312yes—
369#399C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2311yescharacteristic
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2311yescharacteristic
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2314yes—
414#395C2311yescharacteristic
415#395C2312yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2314yes—
424#394C2312yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2311yescharacteristic
429#394C2312yes—
430#394C2312yes—
431#394C2314yes—
432#394C2312yes—
433#393C2312yes—
434#393C2314yes—
435#393C2311yescharacteristic
436#392C2311yescharacteristic
437#392C2312yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#390C2312yes—
467#390C2311yescharacteristic
468#390C2312yes—
469#390C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
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#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#387C2312yes—
604#386C2312yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2312yes—
612#386C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2312yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#385C2314yes—
632#384C2312yes—
633#384C2312yes—
634#383C2314yes—
635#383C2314yes—
636#382C2314yes—
637#382C2311yescharacteristic
638#382C2314yes—
639#382C2314yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#380C2312yes—
650#380C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2311yescharacteristic
657#380C2311yescharacteristic
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716#376C2312yes—
717#376C2314yes—
718C43C2312yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—42no—
722C22×Q8—28no—
723C22×Q8—28no—
724C22×Q8—28no—
725C22×Q8—44no—
726C22×Q8—42no—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2412yes—
734C22×Q8C2411yescharacteristic
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C4⋊Q8—28no—
749C4⋊Q8—28no—
750C4⋊Q8—28no—
751C4⋊Q8—216no—
752C4⋊Q8—216no—
753C4⋊Q8—42no—
754C4⋊Q8—44no—
755C4⋊Q8—42no—
756#126—216no—
757#126—216no—
758#126—44no—
759#126—44no—
760#125—28no—
761#125—216no—
762#125—216no—
763#125—48no—
764#125—44no—
765#124—24no—
766#124—216no—
767#124—44no—
768#123—216no—
769#123—216no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—216no—
776C22⋊Q8—28no—
777C22⋊Q8—216no—
778C22⋊Q8—42no—
779C22⋊Q8—42no—
780C22⋊Q8#41116yes—
781C4×Q8—28no—
782C4×Q8—28no—
783C4×Q8—28no—
784C4×Q8—28no—
785C4×Q8—28no—
786C4×Q8—24no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—42no—
791C4×Q8—48no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×D4—28no—
799C4×D4—216no—
800C4×D4—44no—
801C4×D4—42no—
802C4×D4—48no—
803#117—28no—
804#117—28no—
805#117—24no—
806#117—24no—
807#117—42no—
808#117—48no—
809#117—44no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—48no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C42—48no—
916C2×C42—44no—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2411yescharacteristic
987#95C2412yes—
988#95C2411yescharacteristic
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023C24C2511yescharacteristic
1024C24C2511yescharacteristic
1025C24C2512yes—
1026#41—416no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—28no—
1032C2×Q8—24no—
1033C2×Q8—28no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—432no—
1047C2×Q8—416no—
1048C2×Q8C2×#4118yes—
1049C2×Q82−1+414yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—42no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—41no—
1060C2×D4—41no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—24no—
1071C22×C4—28no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—44no—
1083C22×C4C2×#4118yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—41no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4C2×#4118yes—
1173C4⋊C4C2×#41116yes—
1174C4⋊C4H(5,𝔽2)14yes—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—41no—
1208C22⋊C4—41no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4C2×#41116yes—
1212C42—24no—
1213C42—28no—
1214C42—24no—
1215C42—28no—
1216C42—24no—
1217C42—28no—
1218C42—28no—
1219C42—28no—
1220C42—24no—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—22no—
1226C42—24no—
1227C42—22no—
1228C42—24no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—41no—
1239C42—42no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—21no—
1252C23—21no—
1253C23—21no—
1254C23—21no—
1255C23—22no—
1256C23—21no—
1257C23—22no—
1258C23—21no—
1259C23C22×#4114yes—
1260C23C2611yescharacteristic
1261Q8—216no—
1262Q8—44no—
1263Q8—416no—
1264Q8—48no—
1265Q8—44no—
1266Q8—44no—
1267Q8—48no—
1268Q8—84no—
1269D4—48no—
1270D4—44no—
1271D4—48no—
1272D4—82no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—216no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—48no—
1339C2×C4—416no—
1340C2×C4—48no—
1341C2×C4—44no—
1342C2×C4—44no—
1343C2×C4—88no—
1344C2×C4—84no—
1345C2×C4—162no—
1346C2×C4C22×#4118yes—
1347C2×C4C22×#4118yes—
1348C2×C4C22×#4114yes—
1349C2×C4C22×#4114yes—
1350C2×C4C2×H(5,𝔽2)14yes—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4C2×2−1+412yes—
1353C2×C4C2×2−1+414yes—
1354C22—24no—
1355C22—24no—
1356C22—24no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—42no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22C23×#4112yes—
1372C22C22×H(5,𝔽2)11yescharacteristic
1373C22C22×2−1+411yescharacteristic
1374C222−1+612yes—
1375C222−1+611yescharacteristic
1376C4—28no—
1377C4—24no—
1378C4—24no—
1379C4—22no—
1380C4—24no—
1381C4—28no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—41no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—41no—
1398C4—44no—
1399C4—41no—
1400C4—42no—
1401C4#348114yes—
1402C2—44no—
1403C2—81no—
1404C2—81no—
1405C2C2×#348111yescharacteristic
1406C2#6285012yes—
1407C2#6289311yescharacteristic
1408C2#6300112yes—
1409C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2388C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59933C2semidirect
2. #59922C2semidirect
3. #59722C2semidirect
4. #59673C2semidirect
5. #52302C2semidirect
7. #45322C2semidirect
9. #45226C2semidirect
10. #45184C2semidirect
11. #44863C2semidirect
12. #44617C2semidirect
13. #43807C2semidirect
14. #43803C2semidirect
15. #40363C2semidirect
16. #40039C2semidirect
17. #39435C2semidirect
18. #38553C2semidirect
19. #38251C2semidirect
20. #38128C2semidirect
21. #36545C2semidirect
22. #36508C2semidirect
23. #36007C2semidirect
24. #35899C2semidirect
25. #35803C2semidirect
27. #34291C2semidirect
28. #34286C2semidirect
29. #34266C2semidirect

Maximal subgroups

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

subgroupindex
#599332
#599222
#597222
#596732
#523022
#522572
#453222
#453212
#452262
#451842
#448632
#446172
#438072
#438032
#403632
#400392
#394352
#385532
#382512
#381282
#365452
#365082
#360072
#358992
#358032
#357592
#342912
#342862
#342662