Finite Group Databasebeta

← #7716057

Subgroups — #7716057

Order 512.

4734 conjugacy classes of subgroups.

The subgroup lattice has 1461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50626C214yesmaximal, complemented
2#50566C214yesmaximal, complemented
3#49536C214yesmaximal, complemented
4#49436C214yesmaximal, complemented
5#45048C212yesmaximal, complemented
6#45039C212yesmaximal, complemented
7#45029C212yesmaximal, complemented
8#45007C212yesmaximal, complemented
9#44954C212yesmaximal, complemented
10#44945C212yesmaximal, complemented
11#44919C212yesmaximal, complemented
12#44911C212yesmaximal, complemented
13#39767C211yesmaximal, characteristic, complemented
14#39759C211yesmaximal, characteristic, complemented
15#38907C212yesmaximal, complemented
16#38247C214yesmaximal, complemented
17#37708C212yesmaximal, complemented
18#37698C212yesmaximal, complemented
19#36823C214yesmaximal, complemented
20#36257C212yesmaximal, complemented
21#36133C211yesmaximal, characteristic, complemented
22#36126C211yesmaximal, characteristic
23#35230C212yesmaximal, complemented
24#35180C212yesmaximal, complemented
25#35042C212yesmaximal, complemented
26#35006C211yesmaximal, characteristic, complemented
27#34584C211yesmaximal, characteristic, complemented
28#34460C212yesmaximal, complemented
29C2×#2370C211yesmaximal, characteristic, complemented
30C2×#547C2212yes—
31C2×#539C2212yes—
32C2×#533C2212yes—
33C2×#532C2212yes—
34C22×#125C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2855C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2852C2214yes—
41#2850C2214yes—
42#2850C2214yes—
43#2810C2212yes—
44#2808C2212yes—
45#2806C2214yes—
46#2803C2214yes—
47#2800C2214yes—
48#2799C2214yes—
49#2798C2214yes—
50#2798C2214yes—
51#2797C2214yes—
52#2796C2214yes—
53#2788C2214yes—
54#2788C2214yes—
55#2786C2214yes—
56#2780C2214yes—
57#2779C2214yes—
58#2775C2214yes—
59#2774C2214yes—
60#2770C2214yes—
61#2768C2214yes—
62#2768C2214yes—
63#2748C2214yes—
64#2747C2214yes—
65#2745C2214yes—
66#2743C2214yes—
67#2729C2214yes—
68#2727C2212yes—
69#2727C2214yes—
70#2724C2212yes—
71#2719C2214yes—
72#2716C2214yes—
73#2715C2214yes—
74#2715C2214yes—
75#2713C2214yes—
76#2710C2214yes—
77#2709C2214yes—
78#2707C2214yes—
79#2700C2214yes—
80#2695C2214yes—
81#2694C2214yes—
82#2694C2214yes—
83#2690C2214yes—
84#2690C2214yes—
85#2655C2212yes—
86#2654C2212yes—
87#2651C2212yes—
88#2651C2214yes—
89#2650C2212yes—
90#2650C2214yes—
91#2646C2211yescharacteristic
92#2643C2212yes—
93#2639C2211yescharacteristic
94#2639C2212yes—
95#2639C2212yes—
96#2639C2212yes—
97#2627C2211yescharacteristic
98#2623C2212yes—
99#2623C2214yes—
100#2618C2211yescharacteristic
101#2618C2212yes—
102#2601C2214yes—
103#2597C2214yes—
104#2596C2214yes—
105#2593C2214yes—
106#2592C2214yes—
107#2592C2214yes—
108#2590C2214yes—
109#2589C2214yes—
110#2580C2212yes—
111#2574C2214yes—
112#2570C2212yes—
113#2568C2214yes—
114#2563C2214yes—
115#2562C2214yes—
116#2562C2214yes—
117#2560C2214yes—
118#2558C2214yes—
119#2557C2214yes—
120#2551C2211yescharacteristic
121#2551C2211yescharacteristic
122#2550C2212yes—
123#2550C2212yes—
124#2548C2214yes—
125#2547C2214yes—
126#2546C2211yescharacteristic
127#2541C2211yescharacteristic
128#2533C2214yes—
129#2532C2214yes—
130#2530C2214yes—
131#2529C2214yes—
132#2527C2214yes—
133#2521C2214yes—
134#2521C2214yes—
135#2520C2214yes—
136#2515C2214yes—
137#2513C2212yes—
138#2513C2212yes—
139#2512C2212yes—
140#2512C2212yes—
141#2509C2212yes—
142#2508C2212yes—
143#2508C2212yes—
144#2506C2212yes—
145#2506C2212yes—
146#2505C2214yes—
147#2504C2212yes—
148#2498C2214yes—
149#2497C2212yes—
150#2496C2212yes—
151#2495C2212yes—
152#2491C2212yes—
153#2491C2212yes—
154#2491C2212yes—
155#2490C2212yes—
156#2490C2212yes—
157#2488C2214yes—
158#2487C2212yes—
159#2485C2212yes—
160#2481C2214yes—
161#2479C2214yes—
162#2478C2214yes—
163#2474C2214yes—
164#2469C2214yes—
165#2466C2214yes—
166#2462C2214yes—
167#2461C2214yes—
168#2460C2214yes—
169#2458C2214yes—
170#2454C2212yes—
171#2454C2212yes—
172#2453C2214yes—
173#2452C2212yes—
174#2452C2212yes—
175#2451C2212yes—
176#2450C2214yes—
177#2450C2214yes—
178#2446C2212yes—
179#2445C2212yes—
180#2445C2212yes—
181#2445C2212yes—
182#2444C2214yes—
183#2443C2214yes—
184#2442C2212yes—
185#2442C2212yes—
186#2440C2212yes—
187#2439C2212yes—
188#2438C2214yes—
189#2430C2214yes—
190#2425C2214yes—
191#2421C2214yes—
192#2419C2214yes—
193#2416C2212yes—
194#2413C2214yes—
195#2406C2214yes—
196#2402C2212yes—
197#2401C2212yes—
198#2396C2212yes—
199#2395C2212yes—
200#2378C2214yes—
201#2376C2214yes—
202#2370C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2370C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2369C2212yes—
209#2369C2212yes—
210#2366C2211yescharacteristic
211#2365C2212yes—
212#2365C2211yescharacteristic
213#2363C2212yes—
214#2363C2212yes—
215#2361C2212yes—
216#2361C2212yes—
217#2359C2214yes—
218#2354C2212yes—
219#2352C2212yes—
220Q8×C4⋊C4C2211yescharacteristic
221#2349C2212yes—
222D4×C4⋊C4C2211yescharacteristic
223#2346C2212yes—
224#2345C2212yes—
225#2344C2212yes—
226#2339C2214yes—
227#2335C2214yes—
228#2331C2212yes—
229#2331C2212yes—
230#2329C2214yes—
231#2329C2212yes—
232#2325C2212yes—
233#2325C2212yes—
234#2324C2212yes—
235#2324C2212yes—
236#2322C2214yes—
237#2319C2212yes—
238#2319C2212yes—
239#2316C2212yes—
240#2314C2212yes—
241#2311C2214yes—
242#2311C2214yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×#123C2212yes—
245C4×#121C2211yescharacteristic
246C4×#121C2212yes—
247C2×#389C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#389C2212yes—
250#2290C2212yes—
251#2290C2214yes—
252C2×#387C2212yes—
253C2×#387C2212yes—
254C2×C4×C4⋊C4C2211yescharacteristic
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2314yes—
260#547—216no—
261#539—48no—
262#533—48no—
263#532—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×#127C2311yescharacteristic
271C2×#127C2312yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125—28no—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2311yescharacteristic
316C2×#117C2314yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2311yescharacteristic
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2312yes—
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2312yes—
337#401C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2312yes—
365#399C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#396C2314yes—
404#396C2312yes—
405#396C2314yes—
406#396C2312yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#393C2314yes—
434#393C2312yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#392C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2311yescharacteristic
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2311yescharacteristic
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2314yes—
513#389C2314yes—
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#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
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#387C2314yes—
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#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2312yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#384C2312yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#383C2314yes—
635#382C2314yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2312yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2311yescharacteristic
661#380C2312yes—
662#380C2311yescharacteristic
663#380C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2314yes—
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2311yescharacteristic
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#41—216no—
718C2×#41—48no—
719C2×#41—48no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×D4C2412yes—
725C22×D4C2414yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2414yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2411yescharacteristic
748C4⋊Q8—28no—
749C4⋊Q8—28no—
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—44no—
754#127—42no—
755#127—44no—
756#126—48no—
757#126—84no—
758#126—84no—
759#125—28no—
760#125—28no—
761#125—216no—
762#125—48no—
763#125—48no—
764#124—48no—
765#124—84no—
766#124—84no—
767#123—216no—
768#123—216no—
769#123—44no—
770#123—48no—
771#123—48no—
772#123—84no—
773C22⋊Q8—24no—
774C22⋊Q8—28no—
775C22⋊Q8—216no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778#121—28no—
779#121—24no—
780#121—28no—
781#121—28no—
782#121—28no—
783#121—44no—
784#121—48no—
785C4×Q8—42no—
786C4×Q8—48no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—48no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—42no—
797C4×D4—48no—
798C4×D4—48no—
799#117—44no—
800#117—48no—
801#117—44no—
802#117—84no—
803C2×C4⋊C4—28no—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—24no—
806C2×C4⋊C4—24no—
807C2×C4⋊C4—28no—
808C2×C4⋊C4—24no—
809C2×C4⋊C4—42no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4—42no—
812C2×C4⋊C4—82no—
813C2×C4⋊C4#4118yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C42—24no—
923C2×C42—28no—
924C2×C42—42no—
925C2×C42—42no—
926C2×C42—82no—
927C2×C42—82no—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021C24C2514yes—
1022C24C2512yes—
1023C24C2511yescharacteristic
1024#41—832no—
1025C2×Q8—28no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—28no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×D4—24no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—24no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—28no—
1049C2×D4—24no—
1050C2×D4—41no—
1051C2×D4—41no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—28no—
1080C22×C4—28no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—42no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—42no—
1087C22×C4—41no—
1088C22×C4—42no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—41no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—41no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4C2×#4114yes—
1107C22×C4C2×#4118yes—
1108C22×C4H(5,𝔽2)14yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—22no—
1155C4⋊C4—28no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—41no—
1167C4⋊C4—41no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—41no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—41no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4C2×#4114yes—
1197C4⋊C4C2×#4114yes—
1198C4⋊C4C2×#4118yes—
1199C4⋊C42−1+414yes—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—24no—
1252C42—22no—
1253C42—22no—
1254C42—24no—
1255C42—41no—
1256C42—41no—
1257C42—42no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—21no—
1272C23—24no—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—24no—
1277C23—22no—
1278C23—22no—
1279C23—24no—
1280C23—22no—
1281C23—24no—
1282C23—22no—
1283C23—24no—
1284C23—22no—
1285C23—24no—
1286C23C22×#4112yes—
1287C23C2×H(5,𝔽2)12yes—
1288C23#58512yes—
1289C23C2611yescharacteristic
1290Q8—44no—
1291Q8—84no—
1292Q8—88no—
1293Q8—88no—
1294D4—44no—
1295D4—416no—
1296D4—48no—
1297D4—48no—
1298D4—84no—
1299D4—88no—
1300D4—88no—
1301D4—162no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—216no—
1315C2×C4—28no—
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—24no—
1325C2×C4—22no—
1326C2×C4—22no—
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—24no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—44no—
1374C2×C4—48no—
1375C2×C4—44no—
1376C2×C4—48no—
1377C2×C4—44no—
1378C2×C4—44no—
1379C2×C4—48no—
1380C2×C4—88no—
1381C2×C4—88no—
1382C2×C4—82no—
1383C2×C4—82no—
1384C2×C4—84no—
1385C2×C4—88no—
1386C2×C4—164no—
1387C2×C4C22×#4112yes—
1388C2×C4C22×#4114yes—
1389C2×C4C22×#4114yes—
1390C2×C4C22×#4112yes—
1391C2×C4C2×H(5,𝔽2)12yes—
1392C2×C4C2×H(5,𝔽2)12yes—
1393C2×C4C2×2−1+414yes—
1394C2×C4C2×2−1+412yes—
1395C2×C4#58512yes—
1396C22—22no—
1397C22—22no—
1398C22—22no—
1399C22—22no—
1400C22—22no—
1401C22—22no—
1402C22—42no—
1403C22—44no—
1404C22—42no—
1405C22—44no—
1406C22—44no—
1407C22—42no—
1408C22—44no—
1409C22—42no—
1410C22—44no—
1411C22—42no—
1412C22—42no—
1413C22—44no—
1414C22—44no—
1415C22—42no—
1416C22#351414yes—
1417C22C23×#4111yescharacteristic
1418C22C22×H(5,𝔽2)11yescharacteristic
1419C22C22×2−1+411yescharacteristic
1420C22C2×#58511yescharacteristic
1421C22C2×#58511yescharacteristic
1422C22H(7,𝔽2)11yescharacteristic
1423C222−1+611yescharacteristic
1424C4—22no—
1425C4—24no—
1426C4—24no—
1427C4—22no—
1428C4—22no—
1429C4—24no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4—42no—
1438C4—44no—
1439C4—42no—
1440C4—42no—
1441C4—41no—
1442C4—42no—
1443C4—44no—
1444C4—41no—
1445C4—42no—
1446C4—44no—
1447C4—42no—
1448C4—42no—
1449C4#350714yes—
1450C2—24no—
1451C2—82no—
1452C2—84no—
1453C2C2×#350711yescharacteristic
1454C2C2×#351411yescharacteristic
1455C2#6285111yescharacteristic
1456C2#6290111yescharacteristic
1457C2#6293511yescharacteristic
1458C2#6294411yescharacteristic
1459C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36126C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50626C2semidirect
2. #50566C2semidirect
3. #49536C2semidirect
4. #49436C2semidirect
5. #45048C2semidirect
6. #45039C2semidirect
7. #45029C2semidirect
8. #45007C2semidirect
9. #44954C2semidirect
10. #44945C2semidirect
11. #44919C2semidirect
12. #44911C2semidirect
13. #39767C2semidirect
14. #39759C2semidirect
15. #38907C2semidirect
16. #38247C2semidirect
17. #37708C2semidirect
18. #37698C2semidirect
19. #36823C2semidirect
20. #36257C2semidirect
21. #36133C2semidirect
23. #35230C2semidirect
24. #35180C2semidirect
25. #35042C2semidirect
26. #35006C2semidirect
27. #34584C2semidirect
28. #34460C2semidirect
29. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#506262
#505662
#495362
#494362
#450482
#450392
#450292
#450072
#449542
#449452
#449192
#449112
#397672
#397592
#389072
#382472
#377082
#376982
#368232
#362572
#361332
#361262
#352302
#351802
#350422
#350062
#345842
#344602
C2×#23702