Finite Group Databasebeta

← #7895376

Subgroups — #7895376

Order 512.

4611 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59902C212yesmaximal, complemented
2#59821C211yesmaximal, characteristic, complemented
3#52162C211yesmaximal, characteristic, complemented
4#50377C214yesmaximal, complemented
5#50139C214yesmaximal, complemented
6#49663C214yesmaximal, complemented
7#46760C214yesmaximal, complemented
8#45963C212yesmaximal, complemented
9#45395C212yesmaximal, complemented
10#44962C212yesmaximal, complemented
11#44958C212yesmaximal, complemented
12#43228C214yesmaximal, complemented
13#42525C212yesmaximal, complemented
14#42521C212yesmaximal, complemented
15#41176C214yesmaximal, complemented
16#39756C211yesmaximal, characteristic, complemented
17#39719C212yesmaximal, complemented
18#39573C212yesmaximal, complemented
19#39484C211yesmaximal, characteristic, complemented
20#38982C212yesmaximal, complemented
21#38791C212yesmaximal, complemented
22#38093C212yesmaximal
23#37254C212yesmaximal, complemented
24#36535C211yesmaximal, characteristic, complemented
25#35846C212yesmaximal, complemented
26#35519C212yesmaximal, complemented
27#35187C211yesmaximal, characteristic, complemented
28#34465C212yesmaximal, complemented
29#34313C211yesmaximal, characteristic
30C2×#556C2212yes—
31C2×#552C2212yes—
32C2×#550C2211yescharacteristic
33C2×#533C2212yes—
34C2×#520C2212yes—
35#2864C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2859C2211yescharacteristic
39#2850C2212yes—
40#2830C2214yes—
41#2827C2214yes—
42#2808C2212yes—
43#2808C2212yes—
44#2792C2214yes—
45#2792C2214yes—
46#2791C2214yes—
47#2791C2214yes—
48#2790C2214yes—
49#2787C2214yes—
50#2786C2214yes—
51#2783C2214yes—
52#2777C2214yes—
53#2775C2214yes—
54#2772C2214yes—
55#2765C2214yes—
56#2761C2214yes—
57#2761C2214yes—
58#2761C2214yes—
59#2757C2214yes—
60#2751C2214yes—
61#2747C2214yes—
62#2743C2214yes—
63#2737C2214yes—
64#2734C2211yescharacteristic
65#2732C2211yescharacteristic
66#2729C2214yes—
67#2729C2212yes—
68#2728C2214yes—
69#2727C2212yes—
70#2727C2212yes—
71#2727C2212yes—
72#2727C2212yes—
73#2726C2212yes—
74#2726C2212yes—
75#2726C2211yescharacteristic
76#2724C2212yes—
77#2724C2212yes—
78#2723C2214yes—
79#2723C2214yes—
80#2723C2214yes—
81#2722C2214yes—
82#2721C2214yes—
83#2720C2212yes—
84#2716C2214yes—
85#2713C2212yes—
86#2709C2214yes—
87#2709C2214yes—
88#2704C2212yes—
89#2698C2214yes—
90#2692C2212yes—
91#2691C2214yes—
92#2691C2214yes—
93#2689C2214yes—
94#2683C2211yescharacteristic
95#2677C2212yes—
96#2655C2214yes—
97#2653C2214yes—
98#2651C2214yes—
99#2643C2214yes—
100#2641C2212yes—
101#2638C2214yes—
102#2638C2214yes—
103#2633C2214yes—
104#2621C2212yes—
105#2620C2212yes—
106#2601C2214yes—
107#2601C2214yes—
108#2597C2214yes—
109#2595C2214yes—
110#2592C2212yes—
111#2592C2212yes—
112#2590C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2583C2214yes—
119#2582C2212yes—
120#2582C2212yes—
121#2582C2211yescharacteristic
122#2581C2212yes—
123#2581C2212yes—
124#2581C2212yes—
125#2580C2212yes—
126#2580C2212yes—
127#2574C2214yes—
128#2574C2214yes—
129#2571C2211yescharacteristic
130#2571C2211yescharacteristic
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2568C2211yescharacteristic
135#2565C2212yes—
136#2565C2212yes—
137#2560C2214yes—
138#2552C2211yescharacteristic
139#2550C2212yes—
140#2548C2212yes—
141#2546C2211yescharacteristic
142#2542C2212yes—
143#2538C2212yes—
144#2538C2212yes—
145#2530C2214yes—
146#2530C2214yes—
147#2529C2214yes—
148#2524C2214yes—
149#2522C2214yes—
150#2519C2214yes—
151#2517C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2513C2212yes—
155#2512C2212yes—
156#2512C2212yes—
157#2512C2212yes—
158#2512C2214yes—
159#2508C2212yes—
160#2504C2212yes—
161#2502C2212yes—
162#2500C2212yes—
163#2499C2212yes—
164#2484C2214yes—
165#2481C2214yes—
166#2479C2214yes—
167#2478C2214yes—
168#2478C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2477C2214yes—
172#2477C2214yes—
173#2476C2214yes—
174#2476C2214yes—
175#2475C2214yes—
176#2468C2214yes—
177#2466C2214yes—
178#2466C2214yes—
179#2466C2214yes—
180#2466C2214yes—
181#2466C2214yes—
182#2460C2214yes—
183#2460C2214yes—
184#2450C2214yes—
185#2450C2214yes—
186#2449C2214yes—
187#2449C2214yes—
188#2449C2214yes—
189#2448C2212yes—
190#2448C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2442C2214yes—
195#2441C2214yes—
196#2440C2214yes—
197#2439C2214yes—
198#2432C2212yes—
199#2432C2212yes—
200#2415C2214yes—
201#2399C2212yes—
202#2396C2212yes—
203#2396C2212yes—
204#2395C2214yes—
205#2383C2214yes—
206#2382C2214yes—
207#2373C2214yes—
208#2370C2212yes—
209#2366C2211yescharacteristic
210#2366C2212yes—
211#2365C2212yes—
212#2365C2212yes—
213#2361C2212yes—
214#2361C2214yes—
215#2360C2212yes—
216#2360C2212yes—
217#2359C2214yes—
218#2357C2212yes—
219#2355C2212yes—
220#2355C2211yescharacteristic
221#2355C2211yescharacteristic
222#2354C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227#2346C2212yes—
228#2344C2212yes—
229#2343C2214yes—
230#2341C2212yes—
231#2334C2214yes—
232#2330C2212yes—
233#2330C2214yes—
234#2327C2212yes—
235#2324C2212yes—
236#2324C2214yes—
237#2323C2212yes—
238#2322C2214yes—
239#2320C2212yes—
240#2318C2214yes—
241#2317C2212yes—
242#2317C2212yes—
243#2317C2214yes—
244#2311C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#127C2212yes—
249C4×#125C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252#2297C2212yes—
253#2295C2211yescharacteristic
254#2293C2211yescharacteristic
255#2293C2212yes—
256C2×#389C2212yes—
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260#556—48no—
261#552—216no—
262#550—28no—
263#533—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270C2×#127C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297#520—48no—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2312yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#399C2314yes—
346#399C2314yes—
347#399C2312yes—
348#399C2314yes—
349#399C2312yes—
350#399C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2312yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2312yes—
437#393C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#391C2314yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#390C2314yes—
457#390C2311yescharacteristic
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2312yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2314yes—
473#390C2312yes—
474#389C2311yescharacteristic
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2311yescharacteristic
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2311yescharacteristic
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
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#387C2312yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
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#385C2312yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2312yes—
643#384C2312yes—
644#384C2311yescharacteristic
645#384C2314yes—
646#384C2314yes—
647#384C2311yescharacteristic
648#383C2314yes—
649#383C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2314yes—
659#382C2312yes—
660#382C2314yes—
661#382C2312yes—
662#381C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—28no—
719C2×#41—44no—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C4⋊Q8—28no—
741C4⋊Q8—24no—
742C4⋊Q8—42no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745#127—28no—
746#127—24no—
747#126—216no—
748#126—48no—
749#126—48no—
750#126—48no—
751#126—84no—
752#126—84no—
753#125—216no—
754#125—28no—
755#125—44no—
756#125—44no—
757#125—44no—
758#124—44no—
759#124—44no—
760#123—216no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—48no—
769C22⋊Q8—84no—
770C22⋊Q8—84no—
771#121—28no—
772#121—216no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—28no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—28no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×D4—28no—
785C4×D4—28no—
786C4×D4—48no—
787C4×D4—44no—
788C4×D4—48no—
789C4×D4—44no—
790C4×D4—48no—
791C4×D4—82no—
792C4×D4—82no—
793C4×D4—82no—
794C4×D4#4118yes—
795#117—28no—
796#117—216no—
797#117—28no—
798#117—44no—
799#117—48no—
800#117—48no—
801#117—84no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—84no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C42—44no—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2411yescharacteristic
948C2×C42C2414yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2514yes—
1017C24C2512yes—
1018#41—432no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q82−1+414yes—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—28no—
1044C2×D4—24no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4C2×#4114yes—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—28no—
1058C22×C4—28no—
1059C22×C4—28no—
1060C22×C4—28no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4C2×#4118yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—22no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4C2×#4114yes—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4C2×#4118yes—
1221C42—28no—
1222C42—28no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—24no—
1230C42—22no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—42no—
1235C42—42no—
1236C42—41no—
1237C42—42no—
1238C42—41no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—41no—
1246C42—42no—
1247C42—44no—
1248C42C2×#4114yes—
1249C42H(5,𝔽2)14yes—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—24no—
1260C23—24no—
1261C23—24no—
1262C23—24no—
1263C23C22×#4114yes—
1264C23C2611yescharacteristic
1265Q8—28no—
1266Q8—48no—
1267Q8—82no—
1268Q8—84no—
1269Q8—84no—
1270Q8—84no—
1271D4—44no—
1272D4—416no—
1273D4—48no—
1274D4—48no—
1275D4—84no—
1276D4—88no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—216no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—416no—
1350C2×C4—416no—
1351C2×C4—88no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—164no—
1355C2×C4—164no—
1356C2×C4C22×#4112yes—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4114yes—
1359C2×C4C22×#4112yes—
1360C2×C4C2×H(5,𝔽2)12yes—
1361C2×C4C2×H(5,𝔽2)12yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4C2×2−1+412yes—
1365C2×C4#58512yes—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22C23×#4111yescharacteristic
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C22×2−1+411yescharacteristic
1383C22C2×#58511yescharacteristic
1384C22H(7,𝔽2)11yescharacteristic
1385C222−1+611yescharacteristic
1386C222−1+611yescharacteristic
1387C4—22no—
1388C4—24no—
1389C4—24no—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—44no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—41no—
1400C4—44no—
1401C4—44no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4#352014yes—
1414C2—44no—
1415C2—84no—
1416C2C2×#352011yescharacteristic
1417C2#6284511yescharacteristic
1418C2#6288811yescharacteristic
1419C2#6294911yescharacteristic
1420C2#6295511yescharacteristic
1421C2#6299511yescharacteristic
1422C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59902C2semidirect
2. #59821C2semidirect
3. #52162C2semidirect
4. #50377C2semidirect
5. #50139C2semidirect
6. #49663C2semidirect
7. #46760C2semidirect
8. #45963C2semidirect
9. #45395C2semidirect
10. #44962C2semidirect
11. #44958C2semidirect
12. #43228C2semidirect
13. #42525C2semidirect
14. #42521C2semidirect
15. #41176C2semidirect
16. #39756C2semidirect
17. #39719C2semidirect
18. #39573C2semidirect
19. #39484C2semidirect
20. #38982C2semidirect
21. #38791C2semidirect
23. #37254C2semidirect
24. #36535C2semidirect
25. #35846C2semidirect
26. #35519C2semidirect
27. #35187C2semidirect
28. #34465C2semidirect

Maximal subgroups

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

subgroupindex
#599022
#598212
#521622
#503772
#501392
#496632
#467602
#459632
#453952
#449622
#449582
#432282
#425252
#425212
#411762
#397562
#397192
#395732
#394842
#389822
#387912
#380932
#372542
#365352
#358462
#355192
#351872
#344652
#343132