Finite Group Databasebeta

← #7898363

Subgroups — #7898363

Order 512.

4517 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59695C212yesmaximal, complemented
3#52272C211yesmaximal, characteristic, complemented
4#52029C214yesmaximal, complemented
5#51732C214yesmaximal, complemented
6#48648C214yesmaximal, complemented
7#46691C214yesmaximal, complemented
8#46286C212yesmaximal, complemented
9#45227C212yesmaximal, complemented
10#45167C212yesmaximal, complemented
11#45068C212yesmaximal, complemented
12#44202C214yesmaximal, complemented
13#42853C212yesmaximal, complemented
14#42812C212yesmaximal, complemented
15#41127C214yesmaximal, complemented
16#39809C212yesmaximal, complemented
17#39740C211yesmaximal, characteristic, complemented
18#39509C212yesmaximal, complemented
19#39381C211yesmaximal, characteristic
20#39248C212yesmaximal, complemented
21#38474C212yesmaximal, complemented
22#38289C212yesmaximal, complemented
23#37200C212yesmaximal, complemented
24#36271C211yesmaximal, characteristic, complemented
25#35817C212yesmaximal, complemented
26#35669C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34499C212yesmaximal, complemented
29#34311C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×#556C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#542C2212yes—
34C2×#519C2212yes—
35#2863C2212yes—
36#2861C2212yes—
37#2860C2212yes—
38#2859C2212yes—
39#2858C2211yescharacteristic
40#2833C2214yes—
41#2821C2214yes—
42#2810C2211yescharacteristic
43#2810C2212yes—
44#2810C2212yes—
45#2808C2214yes—
46#2808C2211yescharacteristic
47#2808C2214yes—
48#2807C2214yes—
49#2805C2214yes—
50#2805C2211yescharacteristic
51#2803C2214yes—
52#2800C2212yes—
53#2798C2214yes—
54#2798C2212yes—
55#2797C2214yes—
56#2795C2214yes—
57#2793C2212yes—
58#2787C2214yes—
59#2783C2214yes—
60#2781C2214yes—
61#2778C2214yes—
62#2778C2214yes—
63#2776C2212yes—
64#2774C2214yes—
65#2773C2214yes—
66#2771C2214yes—
67#2770C2214yes—
68#2766C2214yes—
69#2759C2212yes—
70#2756C2214yes—
71#2756C2214yes—
72#2751C2214yes—
73#2751C2214yes—
74#2746C2214yes—
75#2744C2214yes—
76#2733C2212yes—
77#2732C2212yes—
78#2732C2212yes—
79#2732C2212yes—
80#2727C2212yes—
81#2727C2211yescharacteristic
82#2727C2212yes—
83#2727C2212yes—
84#2725C2214yes—
85#2723C2214yes—
86#2723C2214yes—
87#2718C2214yes—
88#2716C2212yes—
89#2715C2214yes—
90#2711C2214yes—
91#2698C2214yes—
92#2692C2214yes—
93#2692C2214yes—
94#2689C2214yes—
95#2682C2212yes—
96#2666C2214yes—
97#2666C2214yes—
98#2658C2212yes—
99#2653C2214yes—
100#2652C2214yes—
101#2642C2212yes—
102#2637C2214yes—
103#2636C2214yes—
104#2628C2214yes—
105#2620C2212yes—
106#2609C2214yes—
107#2606C2214yes—
108#2601C2214yes—
109#2601C2214yes—
110#2598C2214yes—
111#2597C2214yes—
112#2597C2214yes—
113#2596C2214yes—
114#2596C2214yes—
115#2596C2214yes—
116#2594C2214yes—
117#2593C2214yes—
118#2592C2212yes—
119#2590C2214yes—
120#2589C2214yes—
121#2587C2214yes—
122#2582C2211yescharacteristic
123#2575C2214yes—
124#2575C2214yes—
125#2572C2214yes—
126#2568C2212yes—
127#2568C2212yes—
128#2568C2212yes—
129#2567C2211yescharacteristic
130#2567C2211yescharacteristic
131#2562C2214yes—
132#2560C2214yes—
133#2559C2214yes—
134#2554C2214yes—
135#2552C2211yescharacteristic
136#2548C2211yescharacteristic
137#2546C2212yes—
138#2546C2211yescharacteristic
139#2545C2212yes—
140#2545C2212yes—
141#2544C2212yes—
142#2540C2212yes—
143#2529C2214yes—
144#2529C2214yes—
145#2526C2214yes—
146#2525C2214yes—
147#2514C2212yes—
148#2514C2214yes—
149#2514C2212yes—
150#2514C2214yes—
151#2513C2214yes—
152#2512C2212yes—
153#2511C2212yes—
154#2510C2214yes—
155#2507C2212yes—
156#2506C2212yes—
157#2500C2212yes—
158#2499C2212yes—
159#2497C2214yes—
160#2496C2214yes—
161#2490C2212yes—
162#2489C2212yes—
163#2488C2214yes—
164#2479C2214yes—
165#2479C2214yes—
166#2479C2214yes—
167#2477C2214yes—
168#2474C2214yes—
169#2474C2214yes—
170#2474C2214yes—
171#2470C2214yes—
172#2470C2214yes—
173#2469C2214yes—
174#2469C2214yes—
175#2469C2214yes—
176#2465C2214yes—
177#2465C2214yes—
178#2465C2214yes—
179#2462C2214yes—
180#2453C2212yes—
181#2452C2212yes—
182#2448C2212yes—
183#2447C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2444C2214yes—
187#2438C2214yes—
188#2436C2212yes—
189#2436C2212yes—
190#2434C2212yes—
191#2434C2212yes—
192#2429C2212yes—
193#2429C2212yes—
194#2429C2212yes—
195#2428C2212yes—
196#2427C2212yes—
197#2427C2212yes—
198#2426C2214yes—
199#2421C2212yes—
200#2420C2212yes—
201#2401C2212yes—
202#2398C2212yes—
203#2396C2212yes—
204#2396C2214yes—
205#2383C2214yes—
206#2378C2214yes—
207#2373C2214yes—
208#2370C2214yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2366C2211yescharacteristic
213#2365C2211yescharacteristic
214#2365C2212yes—
215#2365C2211yescharacteristic
216#2365C2212yes—
217#2363C2212yes—
218#2362C2214yes—
219#2362C2212yes—
220#2362C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2355C2212yes—
224#2354C2212yes—
225#2354C2211yescharacteristic
226#2351C2212yes—
227Q8×C4⋊C4C2211yescharacteristic
228#2349C2212yes—
229#2343C2214yes—
230Q8×C22⋊C4C2212yes—
231#2334C2214yes—
232#2334C2214yes—
233#2333C2214yes—
234#2330C2212yes—
235#2329C2214yes—
236#2327C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2323C2214yes—
240#2323C2212yes—
241#2320C2212yes—
242#2319C2212yes—
243#2314C2214yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2211yescharacteristic
248C4×C4⋊Q8C2211yescharacteristic
249C4×#126C2212yes—
250C4×#124C2212yes—
251#2298C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2293C2211yescharacteristic
256#2293C2212yes—
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260#556—216no—
261#556—48no—
262D4×Q8—28no—
263#542—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×#127C2311yescharacteristic
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298#519—48no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×#117C2314yes—
320C2×#117C2312yes—
321C2×#117C2314yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325#401C2312yes—
326#401C2314yes—
327#401C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2312yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2314yes—
388#396C2312yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2312yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2312yes—
414#394C2314yes—
415#394C2312yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2312yes—
427#393C2312yes—
428#393C2312yes—
429#392C2314yes—
430#392C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2311yescharacteristic
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2312yes—
473#390C2314yes—
474#390C2311yescharacteristic
475#389C2311yescharacteristic
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2311yescharacteristic
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2311yescharacteristic
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2311yescharacteristic
509#389C2314yes—
510#389C2312yes—
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2311yescharacteristic
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
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#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
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#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
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#384C2312yes—
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#383C2312yes—
646#383C2314yes—
647#383C2314yes—
648#383C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2314yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8—28no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2412yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—24no—
741C4⋊Q8—24no—
742C4⋊Q8—42no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746#127—42no—
747#126—216no—
748#126—216no—
749#126—48no—
750#126—44no—
751#126—48no—
752#126—48no—
753#125—48no—
754#125—44no—
755#124—28no—
756#124—28no—
757#124—28no—
758#124—44no—
759#124—44no—
760#124—48no—
761#123—48no—
762C22⋊Q8—28no—
763C22⋊Q8—216no—
764C22⋊Q8—216no—
765C22⋊Q8—48no—
766C22⋊Q8—48no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769#121—48no—
770#121—44no—
771#121—44no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—24no—
775C4×Q8—28no—
776C4×Q8—24no—
777C4×Q8—44no—
778C4×Q8—48no—
779C4×Q8—48no—
780C4×Q8—42no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8#4118yes—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—24no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—44no—
792#117—216no—
793#117—28no—
794#117—48no—
795#117—48no—
796#117—48no—
797#117—44no—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009C24C2514yes—
1010C24C2512yes—
1011C2×Q8—24no—
1012C2×Q8—28no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—432no—
1032C2×Q8C2×#4114yes—
1033C2×D4—22no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—41no—
1039C2×D4—41no—
1040C2×D4—42no—
1041C2×D4—42no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—42no—
1047C2×D4—44no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C22×C4—28no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—28no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—42no—
1124C4⋊C4—41no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4C2×#4114yes—
1159C4⋊C4C2×#4118yes—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C42—28no—
1202C42—24no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—28no—
1207C42—24no—
1208C42—24no—
1209C42—22no—
1210C42—22no—
1211C42—24no—
1212C42—41no—
1213C42—42no—
1214C42—42no—
1215C42—41no—
1216C42—41no—
1217C42—44no—
1218C42—42no—
1219C42—44no—
1220C42—42no—
1221C42—42no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—42no—
1228C42—44no—
1229C42—42no—
1230C42C2×#4118yes—
1231C42C2×#4114yes—
1232C42H(5,𝔽2)14yes—
1233C23—24no—
1234C23—22no—
1235C23—24no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—22no—
1246C23—22no—
1247C23C2611yescharacteristic
1248Q8—28no—
1249Q8—416no—
1250Q8—48no—
1251Q8—48no—
1252Q8—84no—
1253Q8—82no—
1254Q8—84no—
1255D4—44no—
1256D4—48no—
1257D4—84no—
1258D4—162no—
1259D4—164no—
1260D4—164no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
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—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—416no—
1333C2×C4—48no—
1334C2×C4—88no—
1335C2×C4—88no—
1336C2×C4—164no—
1337C2×C4C22×#4114yes—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4112yes—
1340C2×C4C22×#4114yes—
1341C2×C4C22×#4112yes—
1342C2×C4C2×H(5,𝔽2)12yes—
1343C2×C4C2×H(5,𝔽2)12yes—
1344C2×C4C2×H(5,𝔽2)12yes—
1345C2×C4#58512yes—
1346C2×C4#58512yes—
1347C22—44no—
1348C22—42no—
1349C22—42no—
1350C22—44no—
1351C22—44no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—44no—
1356C22—42no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22C23×#4111yescharacteristic
1362C22C22×H(5,𝔽2)11yescharacteristic
1363C22C2×#58511yescharacteristic
1364C22C2×#58511yescharacteristic
1365C222−1+611yescharacteristic
1366C222−1+611yescharacteristic
1367C222−1+611yescharacteristic
1368C4—24no—
1369C4—22no—
1370C4—24no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—22no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—41no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—44no—
1392C4—42no—
1393C4—44no—
1394C4#350614yes—
1395C2—84no—
1396C2—82no—
1397C2C2×#350611yescharacteristic
1398C2#6285011yescharacteristic
1399C2#6288811yescharacteristic
1400C2#6293111yescharacteristic
1401C2#6296411yescharacteristic
1402C2#6300911yescharacteristic
1403C2#6306211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39381C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59695C2semidirect
3. #52272C2semidirect
4. #52029C2semidirect
5. #51732C2semidirect
6. #48648C2semidirect
7. #46691C2semidirect
8. #46286C2semidirect
9. #45227C2semidirect
10. #45167C2semidirect
11. #45068C2semidirect
12. #44202C2semidirect
13. #42853C2semidirect
14. #42812C2semidirect
15. #41127C2semidirect
16. #39809C2semidirect
17. #39740C2semidirect
18. #39509C2semidirect
20. #39248C2semidirect
21. #38474C2semidirect
22. #38289C2semidirect
23. #37200C2semidirect
24. #36271C2semidirect
25. #35817C2semidirect
26. #35669C2semidirect
27. #35208C2semidirect
28. #34499C2semidirect
29. #34311C2semidirect

Maximal subgroups

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

subgroupindex
#598752
#596952
#522722
#520292
#517322
#486482
#466912
#462862
#452272
#451672
#450682
#442022
#428532
#428122
#411272
#398092
#397402
#395092
#393812
#392482
#384742
#382892
#372002
#362712
#358172
#356692
#352082
#344992
#343112