Finite Group Databasebeta

← #7898474

Subgroups — #7898474

Order 512.

4969 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59096C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#51058C214yesmaximal, complemented
5#49151C214yesmaximal, complemented
6#48286C214yesmaximal, complemented
7#47132C214yesmaximal, complemented
8#46013C212yesmaximal, complemented
9#45307C212yesmaximal, complemented
10#45168C212yesmaximal, complemented
11#44891C212yesmaximal, complemented
12#44428C214yesmaximal, complemented
13#42815C212yesmaximal, complemented
14#42776C212yesmaximal, complemented
15#41114C214yesmaximal, complemented
16#40146C212yesmaximal, complemented
17#39765C211yesmaximal, characteristic, complemented
18#39740C211yesmaximal, characteristic, complemented
19#39628C212yesmaximal, complemented
20#39573C212yesmaximal, complemented
21#38083C212yesmaximal, complemented
22#37773C212yesmaximal, complemented
23#37145C212yesmaximal, complemented
24#36465C211yesmaximal, characteristic
25#35909C212yesmaximal, complemented
26#35573C212yesmaximal, complemented
27#35199C211yesmaximal, characteristic, complemented
28#34472C212yesmaximal, complemented
29#34328C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2212yes—
32C2×#554C2212yes—
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#548C2212yes—
37C2×#542C2212yes—
38C2×#533C2212yes—
39#2863C2212yes—
40#2862C2212yes—
41#2858C2212yes—
42#2858C2211yescharacteristic
43#2850C2212yes—
44#2836C2214yes—
45#2820C2214yes—
46#2808C2211yescharacteristic
47#2808C2211yescharacteristic
48#2808C2212yes—
49#2808C2212yes—
50#2804C2212yes—
51#2804C2211yescharacteristic
52#2804C2214yes—
53#2798C2214yes—
54#2796C2212yes—
55#2796C2212yes—
56#2794C2212yes—
57#2791C2214yes—
58#2777C2214yes—
59#2771C2214yes—
60#2761C2214yes—
61#2761C2214yes—
62#2756C2214yes—
63#2751C2214yes—
64#2751C2212yes—
65#2751C2212yes—
66#2749C2214yes—
67#2738C2214yes—
68#2732C2212yes—
69#2732C2212yes—
70#2732C2212yes—
71#2732C2214yes—
72#2732C2212yes—
73#2730C2214yes—
74#2727C2212yes—
75#2727C2212yes—
76#2724C2211yescharacteristic
77#2724C2212yes—
78#2721C2214yes—
79#2720C2214yes—
80#2720C2214yes—
81#2715C2214yes—
82#2713C2214yes—
83#2711C2214yes—
84#2711C2214yes—
85#2709C2214yes—
86#2709C2212yes—
87#2709C2214yes—
88#2704C2214yes—
89#2700C2214yes—
90#2700C2214yes—
91#2700C2214yes—
92#2694C2214yes—
93#2691C2214yes—
94#2691C2214yes—
95#2690C2214yes—
96#2690C2214yes—
97#2689C2214yes—
98#2686C2214yes—
99#2672C2214yes—
100#2667C2214yes—
101#2666C2214yes—
102#2664C2214yes—
103#2658C2212yes—
104#2647C2214yes—
105#2640C2212yes—
106#2633C2214yes—
107#2632C2214yes—
108#2630C2214yes—
109#2621C2212yes—
110#2611C2214yes—
111#2610C2214yes—
112#2604C2214yes—
113#2603C2214yes—
114#2601C2214yes—
115#2600C2214yes—
116#2597C2214yes—
117#2597C2214yes—
118#2592C2212yes—
119#2582C2211yescharacteristic
120#2580C2214yes—
121#2568C2211yescharacteristic
122#2560C2214yes—
123#2560C2214yes—
124#2558C2214yes—
125#2556C2214yes—
126#2552C2212yes—
127#2551C2211yescharacteristic
128#2549C2214yes—
129#2546C2212yes—
130#2546C2211yescharacteristic
131#2545C2212yes—
132#2545C2214yes—
133#2544C2212yes—
134#2544C2214yes—
135#2542C2211yescharacteristic
136#2542C2212yes—
137#2542C2212yes—
138#2541C2212yes—
139#2541C2211yescharacteristic
140#2540C2214yes—
141#2540C2212yes—
142#2540C2212yes—
143#2540C2214yes—
144#2538C2214yes—
145#2538C2212yes—
146#2531C2214yes—
147#2526C2214yes—
148#2520C2214yes—
149#2508C2212yes—
150#2504C2212yes—
151#2503C2212yes—
152#2492C2212yes—
153#2491C2212yes—
154#2479C2214yes—
155#2479C2214yes—
156#2479C2214yes—
157#2476C2214yes—
158#2471C2214yes—
159#2468C2214yes—
160#2466C2214yes—
161#2465C2214yes—
162#2461C2214yes—
163#2459C2214yes—
164#2458C2214yes—
165#2457C2214yes—
166#2454C2214yes—
167#2452C2214yes—
168#2452C2214yes—
169#2452C2214yes—
170#2451C2212yes—
171#2451C2212yes—
172#2451C2214yes—
173#2450C2214yes—
174#2450C2214yes—
175#2450C2214yes—
176#2450C2214yes—
177#2450C2214yes—
178#2448C2214yes—
179#2447C2214yes—
180#2446C2212yes—
181#2446C2212yes—
182#2445C2212yes—
183#2444C2214yes—
184#2444C2214yes—
185#2438C2214yes—
186#2438C2214yes—
187#2434C2212yes—
188#2434C2212yes—
189#2432C2212yes—
190#2432C2212yes—
191#2429C2212yes—
192#2429C2212yes—
193#2429C2212yes—
194#2429C2212yes—
195#2427C2212yes—
196#2426C2212yes—
197#2426C2212yes—
198#2426C2212yes—
199#2425C2214yes—
200#2423C2214yes—
201#2421C2212yes—
202#2420C2212yes—
203#2417C2212yes—
204#2417C2212yes—
205#2398C2212yes—
206#2398C2212yes—
207#2395C2212yes—
208#2392C2214yes—
209#2379C2214yes—
210#2378C2214yes—
211#2371C2214yes—
212#2370C2212yes—
213#2367C2212yes—
214#2366C2212yes—
215#2365C2212yes—
216#2365C2211yescharacteristic
217#2364C2214yes—
218#2361C2212yes—
219#2361C2212yes—
220#2360C2212yes—
221#2360C2212yes—
222#2359C2214yes—
223#2356C2212yes—
224#2356C2212yes—
225#2355C2211yescharacteristic
226#2355C2211yescharacteristic
227#2349C2214yes—
228D4×C4⋊C4C2212yes—
229Q8×C22⋊C4C2212yes—
230#2339C2212yes—
231#2337C2214yes—
232#2336C2214yes—
233#2331C2212yes—
234#2329C2214yes—
235#2328C2214yes—
236#2327C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2325C2214yes—
240#2323C2212yes—
241#2320C2212yes—
242#2318C2214yes—
243#2311C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#127C2212yes—
248C4×#125C2212yes—
249C4×#123C2212yes—
250C4×#121C2212yes—
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2290C2212yes—
256#2290C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#557—28no—
262#556—48no—
263#554—48no—
264#550—44no—
265D4×Q8—44no—
266#548—216no—
267#548—48no—
268#542—48no—
269#533—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282C2×#127C2311yescharacteristic
283C2×#127C2312yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#123C2312yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2314yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C42C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2312yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2312yes—
458#393C2312yes—
459#393C2312yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2311yescharacteristic
482#391C2314yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2314yes—
487#391C2311yescharacteristic
488#391C2314yes—
489#391C2311yescharacteristic
490#390C2314yes—
491#390C2314yes—
492#390C2311yescharacteristic
493#390C2314yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2311yescharacteristic
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2314yes—
539#389C2311yescharacteristic
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#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
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#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2312yes—
625#386C2312yes—
626#386C2314yes—
627#386C2314yes—
628#386C2312yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2312yes—
645#385C2312yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#384C2312yes—
654#384C2311yescharacteristic
655#384C2311yescharacteristic
656#384C2311yescharacteristic
657#384C2314yes—
658#383C2314yes—
659#383C2314yes—
660#382C2312yes—
661#382C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#381C2314yes—
669#381C2312yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2314yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2314yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2312yes—
720C43C2311yescharacteristic
721C2×#41—28no—
722C2×#41—44no—
723C2×#41—44no—
724C22×Q8—28no—
725C22×Q8—44no—
726C22×Q8—44no—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2412yes—
745C22×D4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C4⋊Q8—28no—
757C4⋊Q8—28no—
758C4⋊Q8—24no—
759C4⋊Q8—24no—
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762C4⋊Q8—42no—
763C4⋊Q8—44no—
764C4⋊Q8—82no—
765C4⋊Q8—82no—
766#127—24no—
767#127—28no—
768#127—42no—
769#127—44no—
770#126—48no—
771#126—48no—
772#126—48no—
773#125—216no—
774#125—28no—
775#125—48no—
776#125—48no—
777#124—216no—
778#124—28no—
779#124—28no—
780#124—48no—
781#124—44no—
782#124—48no—
783#124—44no—
784#124—84no—
785#123—28no—
786#123—48no—
787#123—84no—
788C22⋊Q8—28no—
789C22⋊Q8—216no—
790C22⋊Q8—28no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—48no—
795C22⋊Q8—48no—
796C22⋊Q8—48no—
797C22⋊Q8—48no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803#121—28no—
804#121—216no—
805#121—28no—
806#121—48no—
807#121—48no—
808#121—44no—
809C4×Q8—28no—
810C4×Q8—28no—
811C4×Q8—24no—
812C4×Q8—28no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—28no—
816C4×Q8—24no—
817C4×Q8—44no—
818C4×Q8—48no—
819C4×Q8—44no—
820C4×Q8—82no—
821C4×Q8#4118yes—
822C4×D4—216no—
823C4×D4—28no—
824C4×D4—28no—
825C4×D4—48no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—48no—
830C4×D4—44no—
831C4×D4—42no—
832C4×D4—42no—
833C4×D4—84no—
834C4×D4—84no—
835C4×D4—84no—
836C4×D4—84no—
837#117—44no—
838#117—48no—
839#117—48no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4—44no—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C42—44no—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2411yescharacteristic
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2411yescharacteristic
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043C24C2514yes—
1044C24C2512yes—
1045C24C2512yes—
1046#41—816no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—24no—
1050C2×Q8—28no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—22no—
1058C2×Q8—28no—
1059C2×Q8—24no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—41no—
1067C2×Q8—41no—
1068C2×Q8—42no—
1069C2×Q8—44no—
1070C2×Q8—816no—
1071C2×Q8C2×#4114yes—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—24no—
1075C2×D4—28no—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—28no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—28no—
1084C2×D4—22no—
1085C2×D4—24no—
1086C2×D4—41no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—41no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—41no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D42−1+414yes—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—28no—
1113C22×C4—28no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2514yes—
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2514yes—
1152C22×C4C2512yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—22no—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—22no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—22no—
1183C4⋊C4—28no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—41no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—41no—
1200C4⋊C4—44no—
1201C4⋊C4—41no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—41no—
1220C4⋊C4C2×#4114yes—
1221C4⋊C4C2×#4118yes—
1222C4⋊C4H(5,𝔽2)14yes—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C42—28no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—28no—
1278C42—28no—
1279C42—24no—
1280C42—24no—
1281C42—22no—
1282C42—24no—
1283C42—22no—
1284C42—24no—
1285C42—42no—
1286C42—42no—
1287C42—41no—
1288C42—42no—
1289C42—41no—
1290C42—44no—
1291C42—44no—
1292C42—44no—
1293C42—44no—
1294C42—44no—
1295C42—41no—
1296C42—42no—
1297C42C2×#4118yes—
1298C42C2×#4114yes—
1299C42H(5,𝔽2)14yes—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—24no—
1308C23—24no—
1309C23—22no—
1310C23—24no—
1311C23—22no—
1312C23—22no—
1313C23—24no—
1314C23—24no—
1315C23—22no—
1316C23—24no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23C2×2−1+414yes—
1321C23C2611yescharacteristic
1322Q8—28no—
1323Q8—44no—
1324Q8—48no—
1325Q8—48no—
1326Q8—88no—
1327Q8—82no—
1328Q8—84no—
1329Q8—88no—
1330D4—44no—
1331D4—48no—
1332D4—416no—
1333D4—48no—
1334D4—48no—
1335D4—88no—
1336D4—84no—
1337D4—82no—
1338D4—88no—
1339D4—88no—
1340D4—162no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—21no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—48no—
1409C2×C4—48no—
1410C2×C4—48no—
1411C2×C4—88no—
1412C2×C4—88no—
1413C2×C4—84no—
1414C2×C4—88no—
1415C2×C4—164no—
1416C2×C4—164no—
1417C2×C4—164no—
1418C2×C4C22×#4114yes—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C22×#4114yes—
1422C2×C4C22×#4112yes—
1423C2×C4C2×H(5,𝔽2)12yes—
1424C2×C4C2×H(5,𝔽2)14yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×H(5,𝔽2)12yes—
1427C2×C4C2×H(5,𝔽2)12yes—
1428C2×C4C2×2−1+412yes—
1429C22—24no—
1430C22—24no—
1431C22—24no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—44no—
1437C22—42no—
1438C22—44no—
1439C22—42no—
1440C22—42no—
1441C22—44no—
1442C22—44no—
1443C22—42no—
1444C22—44no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22C23×#4111yescharacteristic
1451C22C22×H(5,𝔽2)11yescharacteristic
1452C22C22×H(5,𝔽2)11yescharacteristic
1453C22C22×2−1+411yescharacteristic
1454C22H(7,𝔽2)11yescharacteristic
1455C222−1+611yescharacteristic
1456C222−1+611yescharacteristic
1457C4—22no—
1458C4—24no—
1459C4—24no—
1460C4—24no—
1461C4—22no—
1462C4—22no—
1463C4—22no—
1464C4—22no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—41no—
1470C4—42no—
1471C4—42no—
1472C4—44no—
1473C4—44no—
1474C4—42no—
1475C4—42no—
1476C4—44no—
1477C4—44no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4#350814yes—
1483C2—44no—
1484C2—84no—
1485C2—82no—
1486C2C2×#350811yescharacteristic
1487C2#6285011yescharacteristic
1488C2#6287811yescharacteristic
1489C2#6289311yescharacteristic
1490C2#6294211yescharacteristic
1491C2#6300011yescharacteristic
1492C2#6304911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36465C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59096C2semidirect
3. #52273C2semidirect
4. #51058C2semidirect
5. #49151C2semidirect
6. #48286C2semidirect
7. #47132C2semidirect
8. #46013C2semidirect
9. #45307C2semidirect
10. #45168C2semidirect
11. #44891C2semidirect
12. #44428C2semidirect
13. #42815C2semidirect
14. #42776C2semidirect
15. #41114C2semidirect
16. #40146C2semidirect
17. #39765C2semidirect
18. #39740C2semidirect
19. #39628C2semidirect
20. #39573C2semidirect
21. #38083C2semidirect
22. #37773C2semidirect
23. #37145C2semidirect
25. #35909C2semidirect
26. #35573C2semidirect
27. #35199C2semidirect
28. #34472C2semidirect
29. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#590962
#522732
#510582
#491512
#482862
#471322
#460132
#453072
#451682
#448912
#444282
#428152
#427762
#411142
#401462
#397652
#397402
#396282
#395732
#380832
#377732
#371452
#364652
#359092
#355732
#351992
#344722
#343282