Finite Group Databasebeta

← #7715323

Subgroups — #7715323

Order 512.

4906 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49808C214yesmaximal, complemented
2#49756C214yesmaximal, complemented
3#48256C214yesmaximal, complemented
4#48187C214yesmaximal, complemented
5#47624C214yesmaximal, complemented
6#47098C214yesmaximal, complemented
7#46803C214yesmaximal, complemented
8#46551C214yesmaximal, complemented
9#39803C212yesmaximal, complemented
10#39634C211yesmaximal, characteristic, complemented
11#39628C211yesmaximal, characteristic, complemented
12#39507C211yesmaximal, characteristic, complemented
13#39500C211yesmaximal, characteristic, complemented
14#39426C212yesmaximal, complemented
15#37898C211yesmaximal, characteristic, complemented
16#37898C211yesmaximal, characteristic, complemented
17#37893C211yesmaximal, characteristic, complemented
18#37893C211yesmaximal, characteristic, complemented
19#37764C212yesmaximal, complemented
20#37756C212yesmaximal, complemented
21#37591C212yesmaximal, complemented
22#37292C212yesmaximal, complemented
23#37276C212yesmaximal, complemented
24#35337C211yesmaximal, characteristic, complemented
25#35336C211yesmaximal, characteristic, complemented
26#35330C211yesmaximal, characteristic, complemented
27#35293C211yesmaximal, characteristic, complemented
28#35278C211yesmaximal, characteristic, complemented
29#35278C211yesmaximal, characteristic, complemented
30#34431C212yesmaximal, complemented
31#34081C211yesmaximal, characteristic, complemented
32C2×#544C2212yes—
33C2×#540C2212yes—
34C2×#540C2212yes—
35C2×#532C2212yes—
36C2×#529C2211yescharacteristic
37#2867C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2858C2212yes—
44#2856C2211yescharacteristic
45#2856C2211yescharacteristic
46#2856C2212yes—
47#2851C2212yes—
48#2851C2212yes—
49#2830C2214yes—
50#2829C2214yes—
51#2808C2214yes—
52#2804C2214yes—
53#2803C2214yes—
54#2803C2214yes—
55#2786C2214yes—
56#2780C2214yes—
57#2780C2214yes—
58#2761C2214yes—
59#2761C2214yes—
60#2761C2214yes—
61#2757C2214yes—
62#2753C2214yes—
63#2753C2214yes—
64#2740C2214yes—
65#2737C2214yes—
66#2733C2214yes—
67#2732C2214yes—
68#2731C2214yes—
69#2730C2214yes—
70#2723C2214yes—
71#2717C2214yes—
72#2715C2214yes—
73#2711C2214yes—
74#2711C2214yes—
75#2708C2214yes—
76#2707C2214yes—
77#2705C2214yes—
78#2703C2214yes—
79#2703C2214yes—
80#2701C2214yes—
81#2700C2214yes—
82#2696C2214yes—
83#2691C2214yes—
84#2691C2214yes—
85#2691C2214yes—
86#2691C2214yes—
87#2686C2214yes—
88#2686C2214yes—
89#2682C2214yes—
90#2681C2214yes—
91#2676C2214yes—
92#2676C2214yes—
93#2676C2214yes—
94#2675C2214yes—
95#2674C2214yes—
96#2672C2214yes—
97#2671C2214yes—
98#2671C2214yes—
99#2662C2214yes—
100#2660C2212yes—
101#2660C2212yes—
102#2651C2214yes—
103#2647C2211yescharacteristic
104#2647C2211yescharacteristic
105#2647C2211yescharacteristic
106#2647C2211yescharacteristic
107#2641C2212yes—
108#2641C2212yes—
109#2638C2214yes—
110#2630C2214yes—
111#2629C2212yes—
112#2628C2212yes—
113#2619C2212yes—
114#2619C2211yescharacteristic
115#2619C2211yescharacteristic
116#2619C2211yescharacteristic
117#2619C2211yescharacteristic
118#2619C2212yes—
119#2601C2214yes—
120#2597C2214yes—
121#2597C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2589C2214yes—
125#2589C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2587C2214yes—
129#2587C2214yes—
130#2580C2212yes—
131#2560C2214yes—
132#2558C2214yes—
133#2554C2214yes—
134#2554C2214yes—
135#2550C2214yes—
136#2550C2214yes—
137#2549C2214yes—
138#2549C2214yes—
139#2544C2214yes—
140#2544C2214yes—
141#2543C2214yes—
142#2543C2214yes—
143#2540C2214yes—
144#2538C2212yes—
145#2537C2212yes—
146#2535C2212yes—
147#2521C2214yes—
148#2513C2212yes—
149#2513C2212yes—
150#2512C2212yes—
151#2512C2212yes—
152#2491C2212yes—
153#2491C2214yes—
154#2491C2212yes—
155#2490C2212yes—
156#2490C2212yes—
157#2487C2214yes—
158#2485C2214yes—
159#2474C2214yes—
160#2468C2214yes—
161#2463C2214yes—
162#2461C2214yes—
163#2461C2214yes—
164#2460C2214yes—
165#2459C2214yes—
166#2459C2214yes—
167#2454C2212yes—
168#2454C2212yes—
169#2452C2212yes—
170#2452C2212yes—
171#2450C2214yes—
172#2450C2214yes—
173#2445C2214yes—
174#2445C2214yes—
175#2445C2214yes—
176#2445C2214yes—
177#2444C2214yes—
178#2444C2214yes—
179#2443C2214yes—
180#2432C2214yes—
181#2431C2214yes—
182#2431C2214yes—
183#2430C2214yes—
184#2428C2214yes—
185#2428C2214yes—
186#2428C2214yes—
187#2428C2214yes—
188#2422C2212yes—
189#2422C2212yes—
190#2420C2212yes—
191#2420C2212yes—
192#2419C2214yes—
193#2417C2214yes—
194#2416C2212yes—
195#2416C2212yes—
196#2414C2212yes—
197#2414C2214yes—
198#2414C2212yes—
199#2407C2214yes—
200#2406C2214yes—
201#2377C2214yes—
202#2376C2214yes—
203#2363C2212yes—
204#2363C2212yes—
205#2361C2212yes—
206#2361C2212yes—
207#2361C2214yes—
208#2359C2214yes—
209#2357C2212yes—
210#2354C2212yes—
211#2349C2212yes—
212D4×C4⋊C4C2212yes—
213#2337C2212yes—
214#2336C2212yes—
215#2335C2212yes—
216#2335C2212yes—
217#2335C2214yes—
218#2334C2212yes—
219#2334C2212yes—
220#2333C2212yes—
221#2332C2212yes—
222#2331C2212yes—
223#2330C2212yes—
224#2328C2211yescharacteristic
225#2328C2211yescharacteristic
226#2328C2211yescharacteristic
227#2328C2211yescharacteristic
228#2328C2212yes—
229#2328C2212yes—
230#2325C2214yes—
231#2324C2214yes—
232#2322C2214yes—
233#2317C2212yes—
234#2314C2211yescharacteristic
235#2314C2211yescharacteristic
236#2314C2211yescharacteristic
237#2314C2211yescharacteristic
238C4×#127C2211yescharacteristic
239C4×#127C2211yescharacteristic
240C4×#127C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243#2298C2211yescharacteristic
244#2298C2211yescharacteristic
245#2295C2211yescharacteristic
246#2295C2211yescharacteristic
247#2293C2211yescharacteristic
248#2293C2211yescharacteristic
249#2290C2211yescharacteristic
250#2290C2211yescharacteristic
251#2290C2211yescharacteristic
252#2290C2211yescharacteristic
253#2285C2211yescharacteristic
254#2283C2211yescharacteristic
255C2×#382C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C22×#41C2314yes—
260#544—48no—
261#540—216no—
262#540—48no—
263#532—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×#127C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2312yes—
270C2×#127C2312yes—
271C2×#127C2314yes—
272C2×#127C2314yes—
273#529—28no—
274C2×#126C2311yescharacteristic
275C2×#126C2311yescharacteristic
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#124C2311yescharacteristic
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#123C2314yes—
290C2×#123C2311yescharacteristic
291C2×#123C2311yescharacteristic
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×#121C2314yes—
304C2×#121C2311yescharacteristic
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2311yescharacteristic
342C2×#117C2311yescharacteristic
343C2×#117C2311yescharacteristic
344C2×#117C2312yes—
345C2×#117C2314yes—
346C2×#117C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2314yes—
349C22×C42C2311yescharacteristic
350C22×C42C2311yescharacteristic
351C22×C42C2311yescharacteristic
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
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#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2312yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2312yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2312yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2312yes—
617#385C2312yes—
618#385C2312yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2312yes—
630#384C2312yes—
631#383C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2311yescharacteristic
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#381C2314yes—
643#381C2312yes—
644#381C2314yes—
645#381C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2311yescharacteristic
699#376C2311yescharacteristic
700#376C2311yescharacteristic
701C2×#95C2314yes—
702C2×#95C2314yes—
703C43C2311yescharacteristic
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C2×#41—48no—
708C2×#41—84no—
709C2×#41—84no—
710C22×Q8C2411yescharacteristic
711C22×Q8C2414yes—
712C22×Q8C2414yes—
713C22×D4C2412yes—
714C22×D4C2412yes—
715C22×D4C2414yes—
716C22×D4C2414yes—
717C22×D4C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2411yescharacteristic
720C22×D4C2414yes—
721C22×D4C2414yes—
722C22×D4C2414yes—
723C22×D4C2414yes—
724C22×D4C2414yes—
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C4⋊Q8—28no—
745C4⋊Q8—44no—
746C4⋊Q8—48no—
747#127—28no—
748#127—28no—
749#127—24no—
750#127—24no—
751#127—84no—
752#127—84no—
753#126—24no—
754#126—24no—
755#126—84no—
756#126—84no—
757#125—24no—
758#125—28no—
759#125—28no—
760#125—44no—
761#125—48no—
762#124—24no—
763#124—48no—
764#124—84no—
765#124—84no—
766#124—84no—
767#124—84no—
768#123—24no—
769#123—216no—
770#123—216no—
771#123—24no—
772#123—48no—
773#123—48no—
774#123—84no—
775#123—84no—
776C22⋊Q8—24no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—84no—
780C22⋊Q8—84no—
781C22⋊Q8—84no—
782#121—28no—
783#121—28no—
784#121—24no—
785#121—216no—
786#121—216no—
787#121—48no—
788#121—48no—
789#121—44no—
790#121—44no—
791#121—48no—
792#121—44no—
793#121—44no—
794#121—84no—
795#121—84no—
796#121—84no—
797#121—84no—
798#121—84no—
799#121—84no—
800#121—84no—
801C4×Q8—24no—
802C4×D4—24no—
803C4×D4—24no—
804C4×D4—24no—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—48no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—84no—
813C4×D4—84no—
814C4×D4—84no—
815C4×D4—84no—
816C4×D4—84no—
817C4×D4—84no—
818#117—24no—
819#117—24no—
820#117—24no—
821#117—24no—
822#117—24no—
823#117—44no—
824#117—84no—
825#117#4118yescomplemented
826C2×C4⋊C4—44no—
827C2×C4⋊C4—84no—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2411yescharacteristic
939C2×C22⋊C4C2411yescharacteristic
940C2×C42—24no—
941C2×C42—24no—
942C2×C42—24no—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024C24C2511yescharacteristic
1025C24C2511yescharacteristic
1026C24C2514yes—
1027C24C2514yes—
1028C24C2511yescharacteristic
1029#41—832no—
1030C2×Q8—22no—
1031C2×Q8—28no—
1032C2×Q8—42no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×D4—22no—
1039C2×D4—22no—
1040C2×D4—28no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—22no—
1045C2×D4—28no—
1046C2×D4—28no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—28no—
1050C2×D4—28no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—22no—
1089C22×C4—22no—
1090C22×C4—22no—
1091C22×C4—24no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—24no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—42no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4C2×#4114yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2514yes—
1136C22×C4C2514yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2514yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—28no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4C2×#4114yes—
1202C4⋊C4C2×#4114yes—
1203C22⋊C4—22no—
1204C22⋊C4—22no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—22no—
1210C22⋊C4—22no—
1211C22⋊C4—22no—
1212C22⋊C4—22no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4C2×#4114yes—
1263C22⋊C4C2×#4114yes—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—24no—
1270C42—22no—
1271C42—22no—
1272C42—24no—
1273C42—22no—
1274C42—22no—
1275C42—22no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42—42no—
1281C42—42no—
1282C42—42no—
1283C42—44no—
1284C42—42no—
1285C42—42no—
1286C42—44no—
1287C42—42no—
1288C42—42no—
1289C42C2×#4114yes—
1290C42C2×#4114yes—
1291C42H(5,𝔽2)14yes—
1292C422−1+414yes—
1293C23—21no—
1294C23—21no—
1295C23—22no—
1296C23—22no—
1297C23—21no—
1298C23—21no—
1299C23—24no—
1300C23—24no—
1301C23—21no—
1302C23—24no—
1303C23—24no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—24no—
1308C23—24no—
1309C23—24no—
1310C23—24no—
1311C23—22no—
1312C23—24no—
1313C23—24no—
1314C23—22no—
1315C23—22no—
1316C23—24no—
1317C23—24no—
1318C23—24no—
1319C23—22no—
1320C23—24no—
1321C23C22×#4112yes—
1322C23C2611yescharacteristic
1323Q8—82no—
1324Q8—88no—
1325Q8—164no—
1326D4—48no—
1327D4—48no—
1328D4—82no—
1329D4—88no—
1330D4—88no—
1331D4—88no—
1332D4—88no—
1333D4—88no—
1334D4—88no—
1335D4—88no—
1336D4—88no—
1337D4—82no—
1338D4—82no—
1339D4—88no—
1340D4—88no—
1341D4—164no—
1342D4—164no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—28no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—21no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—48no—
1405C2×C4—44no—
1406C2×C4—44no—
1407C2×C4—88no—
1408C2×C4—88no—
1409C2×C4—82no—
1410C2×C4—82no—
1411C2×C4—84no—
1412C2×C4—88no—
1413C2×C4—88no—
1414C2×C4—164no—
1415C2×C4—164no—
1416C2×C4—164no—
1417C2×C4C22×#4112yes—
1418C2×C4C22×#4112yes—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C22×#4112yes—
1422C2×C4C22×#4112yes—
1423C2×C4C2×H(5,𝔽2)14yes—
1424C2×C4C2×H(5,𝔽2)12yes—
1425C2×C4C2×2−1+414yes—
1426C2×C4C2×2−1+412yes—
1427C22—22no—
1428C22—22no—
1429C22—22no—
1430C22—42no—
1431C22—42no—
1432C22—41no—
1433C22—41no—
1434C22—44no—
1435C22—44no—
1436C22—41no—
1437C22—44no—
1438C22—44no—
1439C22—41no—
1440C22—44no—
1441C22—44no—
1442C22—41no—
1443C22—41no—
1444C22—42no—
1445C22—44no—
1446C22—44no—
1447C22—44no—
1448C22—44no—
1449C22—42no—
1450C22—44no—
1451C22—44no—
1452C22—44no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22C23×#4111yescharacteristic
1457C22C22×H(5,𝔽2)11yescharacteristic
1458C22C22×2−1+411yescharacteristic
1459C22H(7,𝔽2)12yes—
1460C22H(7,𝔽2)12yes—
1461C4—22no—
1462C4—22no—
1463C4—22no—
1464C4—22no—
1465C4—22no—
1466C4—24no—
1467C4—24no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—44no—
1472C4—44no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—42no—
1477C4—44no—
1478C4—44no—
1479C4—42no—
1480C4—44no—
1481C4—44no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4#351114yes—
1487C2—42no—
1488C2—81no—
1489C2—81no—
1490C2—84no—
1491C2—84no—
1492C2C2×#351111yescharacteristic
1493C2#6285811yescharacteristic
1494C2#6285811yescharacteristic
1495C2#6287612yes—
1496C2#6288112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49808C2semidirect
2. #49756C2semidirect
3. #48256C2semidirect
4. #48187C2semidirect
5. #47624C2semidirect
6. #47098C2semidirect
7. #46803C2semidirect
8. #46551C2semidirect
9. #39803C2semidirect
10. #39634C2semidirect
11. #39628C2semidirect
12. #39507C2semidirect
13. #39500C2semidirect
14. #39426C2semidirect
15. #37898C2semidirect
16. #37898C2semidirect
17. #37893C2semidirect
18. #37893C2semidirect
19. #37764C2semidirect
20. #37756C2semidirect
21. #37591C2semidirect
22. #37292C2semidirect
23. #37276C2semidirect
24. #35337C2semidirect
25. #35336C2semidirect
26. #35330C2semidirect
27. #35293C2semidirect
28. #35278C2semidirect
29. #35278C2semidirect
30. #34431C2semidirect
31. #34081C2semidirect
825. #117#41semidirect

Maximal subgroups

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

subgroupindex
#498082
#497562
#482562
#481872
#476242
#470982
#468032
#465512
#398032
#396342
#396282
#395072
#395002
#394262
#378982
#378932
#377642
#377562
#375912
#372922
#372762
#353372
#353362
#353302
#352932
#352782
#344312
#340812