Finite Group Databasebeta

← #7657539

Subgroups — #7657539

Order 512.

4495 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41580C214yesmaximal, complemented
2#41579C214yesmaximal, complemented
3#40741C214yesmaximal, complemented
4#40724C214yesmaximal, complemented
5#40716C214yesmaximal, complemented
6#40701C214yesmaximal, complemented
7#39638C211yesmaximal, characteristic, complemented
8#39628C211yesmaximal, characteristic, complemented
9#38926C212yesmaximal, complemented
10#38074C212yesmaximal, complemented
11#38068C212yesmaximal, complemented
12#37898C211yesmaximal, characteristic, complemented
13#37893C211yesmaximal, characteristic, complemented
14#37889C211yesmaximal, characteristic, complemented
15#37882C211yesmaximal, characteristic, complemented
16#37571C212yesmaximal, complemented
17#37511C212yesmaximal, complemented
18#37505C212yesmaximal, complemented
19#36361C212yesmaximal, complemented
20#36191C211yesmaximal, characteristic, complemented
21#36182C211yesmaximal, characteristic, complemented
22#35889C214yesmaximal, complemented
23#35861C214yesmaximal, complemented
24#35337C211yesmaximal, characteristic, complemented
25#35271C211yesmaximal, characteristic, complemented
26#35271C211yesmaximal, characteristic, complemented
27#34638C211yesmaximal, characteristic, complemented
28#34621C211yesmaximal, characteristic, complemented
29C2×#2647C211yesmaximal, characteristic, complemented
30#34323C212yesmaximal, complemented
31#34123C211yesmaximal, characteristic, complemented
32C2×#553C2212yes—
33C2×C4×#41C2211yescharacteristic
34#2862C2211yescharacteristic
35#2859C2211yescharacteristic
36#2856C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854C2212yes—
39#2854C2212yes—
40#2851C2211yescharacteristic
41#2851C2212yes—
42#2851C2211yescharacteristic
43#2838C2214yes—
44#2837C2214yes—
45#2836C2214yes—
46#2831C2214yes—
47#2827C2214yes—
48#2824C2214yes—
49#2804C2214yes—
50#2802C2214yes—
51#2794C2214yes—
52#2787C2214yes—
53#2779C2214yes—
54#2775C2214yes—
55#2774C2214yes—
56#2772C2214yes—
57#2770C2214yes—
58#2765C2214yes—
59#2761C2214yes—
60#2753C2214yes—
61#2751C2214yes—
62#2750C2214yes—
63#2750C2214yes—
64#2744C2214yes—
65#2732C2214yes—
66#2721C2214yes—
67#2707C2214yes—
68#2703C2214yes—
69#2698C2214yes—
70#2695C2214yes—
71#2691C2214yes—
72#2687C2214yes—
73#2664C2214yes—
74#2663C2214yes—
75#2652C2214yes—
76#2652C2214yes—
77#2652C2214yes—
78#2651C2214yes—
79#2651C2214yes—
80#2650C2214yes—
81#2650C2214yes—
82#2648C2214yes—
83#2647C2211yescharacteristic
84#2647C2211yescharacteristic
85#2647C2211yescharacteristic
86#2647C2211yescharacteristic
87#2647C2211yescharacteristic
88#2647C2214yes—
89#2647C2212yes—
90#2647C2212yes—
91#2647C2214yes—
92#2647C2211yescharacteristic
93#2647C2212yes—
94#2647C2212yes—
95#2647C2211yescharacteristic
96#2646C2214yes—
97#2646C2214yes—
98#2644C2212yes—
99#2644C2212yes—
100#2644C2212yes—
101#2643C2214yes—
102#2641C2211yescharacteristic
103#2639C2214yes—
104#2638C2214yes—
105#2636C2214yes—
106#2629C2211yescharacteristic
107#2628C2212yes—
108#2624C2212yes—
109#2619C2211yescharacteristic
110#2597C2214yes—
111#2589C2214yes—
112#2589C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2585C2214yes—
116#2584C2212yes—
117#2580C2212yes—
118#2577C2214yes—
119#2575C2214yes—
120#2574C2214yes—
121#2570C2212yes—
122#2566C2212yes—
123#2560C2214yes—
124#2554C2214yes—
125#2543C2214yes—
126#2532C2214yes—
127#2531C2214yes—
128#2531C2214yes—
129#2529C2214yes—
130#2529C2214yes—
131#2528C2214yes—
132#2526C2214yes—
133#2526C2214yes—
134#2520C2214yes—
135#2515C2214yes—
136#2513C2212yes—
137#2512C2212yes—
138#2512C2214yes—
139#2509C2212yes—
140#2509C2214yes—
141#2509C2212yes—
142#2508C2212yes—
143#2506C2212yes—
144#2504C2212yes—
145#2500C2212yes—
146#2496C2212yes—
147#2494C2212yes—
148#2493C2214yes—
149#2489C2214yes—
150#2488C2214yes—
151#2487C2212yes—
152#2485C2212yes—
153#2481C2214yes—
154#2481C2214yes—
155#2479C2214yes—
156#2478C2214yes—
157#2475C2214yes—
158#2473C2214yes—
159#2470C2214yes—
160#2469C2214yes—
161#2468C2214yes—
162#2455C2214yes—
163#2452C2212yes—
164#2452C2212yes—
165#2450C2214yes—
166#2450C2214yes—
167#2450C2214yes—
168#2449C2214yes—
169#2444C2214yes—
170#2444C2214yes—
171#2444C2214yes—
172#2443C2214yes—
173#2443C2214yes—
174#2440C2212yes—
175#2439C2212yes—
176#2430C2214yes—
177#2425C2214yes—
178#2425C2214yes—
179#2422C2212yes—
180#2422C2214yes—
181#2420C2212yes—
182#2419C2214yes—
183#2419C2214yes—
184#2417C2214yes—
185#2416C2212yes—
186#2416C2214yes—
187#2414C2212yes—
188#2402C2214yes—
189#2402C2214yes—
190#2395C2214yes—
191C2×#400C2214yes—
192#2392C2214yes—
193C2×#398C2214yes—
194#2373C2214yes—
195#2370C2212yes—
196#2368C2214yes—
197#2363C2212yes—
198#2361C2212yes—
199#2361C2214yes—
200#2361C2214yes—
201#2361C2214yes—
202#2359C2214yes—
203#2359C2214yes—
204#2356C2212yes—
205#2353C2212yes—
206#2353C2212yes—
207#2352C2212yes—
208#2352C2214yes—
209#2349C2212yes—
210#2349C2212yes—
211#2346C2212yes—
212#2346C2212yes—
213#2345C2212yes—
214#2343C2212yes—
215#2343C2212yes—
216#2339C2212yes—
217#2335C2214yes—
218#2334C2214yes—
219#2331C2212yes—
220#2330C2211yescharacteristic
221#2330C2211yescharacteristic
222#2328C2211yescharacteristic
223#2328C2211yescharacteristic
224#2325C2214yes—
225#2319C2212yes—
226#2319C2212yes—
227#2314C2211yescharacteristic
228#2314C2211yescharacteristic
229C4×#127C2211yescharacteristic
230C4×#125C2212yes—
231C4×#125C2211yescharacteristic
232C4×#121C2212yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235#2296C2212yes—
236#2296C2212yes—
237#2295C2211yescharacteristic
238#2295C2211yescharacteristic
239#2293C2212yes—
240C2×#389C2212yes—
241C2×#389C2212yes—
242#2290C2211yescharacteristic
243#2290C2211yescharacteristic
244#2290C2211yescharacteristic
245#2290C2211yescharacteristic
246#2285C2211yescharacteristic
247#2285C2211yescharacteristic
248C2×#384C2211yescharacteristic
249#2283C2211yescharacteristic
250#2283C2211yescharacteristic
251#2283C2211yescharacteristic
252C2×#382C2211yescharacteristic
253#2275C2214yes—
254C42×D4C2211yescharacteristic
255C42×D4C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×#376C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2311yescharacteristic
260#553—216no—
261C2×C4⋊Q8C2312yes—
262C2×#127C2311yescharacteristic
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2312yes—
267C2×#125C2311yescharacteristic
268C2×#125C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C4×#41—28no—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2314yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2311yescharacteristic
310C2×#117C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
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#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
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#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#392C2314yes—
426#392C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#390C2314yes—
435#390C2312yes—
436#390C2314yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#388C2312yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2312yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#386C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2312yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#384C2311yescharacteristic
596#384C2312yes—
597#384C2311yescharacteristic
598#384C2311yescharacteristic
599#384C2312yes—
600#384C2314yes—
601#383C2312yes—
602#383C2312yes—
603#383C2312yes—
604#382C2312yes—
605#382C2311yescharacteristic
606#382C2312yes—
607#382C2311yescharacteristic
608#382C2311yescharacteristic
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#382C2312yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#381C2312yes—
621#381C2312yes—
622#381C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2311yescharacteristic
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2311yescharacteristic
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2311yescharacteristic
678C4×C22⋊C4C2311yescharacteristic
679C4×C22⋊C4C2311yescharacteristic
680C4×C22⋊C4C2311yescharacteristic
681#376C2311yescharacteristic
682#376C2311yescharacteristic
683#376C2311yescharacteristic
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2312yes—
687#376C2312yes—
688#376C2314yes—
689#376C2312yes—
690#376C2312yes—
691#376C2311yescharacteristic
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694C2×#95C2314yes—
695C2×#95C2312yes—
696C2×#95C2312yes—
697C2×#95C2312yes—
698C2×#95C2312yes—
699C2×#95C2314yes—
700C2×#95C2314yes—
701C2×#95C2314yes—
702C43C2311yescharacteristic
703C43C2311yescharacteristic
704C2×#41—24no—
705C2×#41—44no—
706C22×Q8C2411yescharacteristic
707C22×Q8C2414yes—
708C22×D4C2414yes—
709C22×D4C2412yes—
710C22×D4C2411yescharacteristic
711C22×D4C2411yescharacteristic
712C22×D4C2411yescharacteristic
713C22×D4C2414yes—
714C22×D4C2414yes—
715C22×D4C2414yes—
716C23×C4C2411yescharacteristic
717C23×C4C2411yescharacteristic
718C23×C4C2412yes—
719C23×C4C2411yescharacteristic
720C23×C4C2411yescharacteristic
721C23×C4C2414yes—
722C23×C4C2411yescharacteristic
723C23×C4C2414yes—
724C23×C4C2412yes—
725C23×C4C2414yes—
726C23×C4C2411yescharacteristic
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C4⋊Q8—44no—
735#127—24no—
736#126—216no—
737#126—84no—
738#126—84no—
739#125—28no—
740#125—24no—
741#125—84no—
742#123—216no—
743#123—48no—
744#123—84no—
745#123—84no—
746C22⋊Q8—48no—
747C22⋊Q8—84no—
748C22⋊Q8—84no—
749#121—216no—
750#121—28no—
751#121—28no—
752#121—44no—
753#121—48no—
754#121—48no—
755#121—84no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×D4—24no—
759C4×D4—24no—
760C4×D4—24no—
761C4×D4—24no—
762C4×D4—24no—
763C4×D4—216no—
764C4×D4—28no—
765C4×D4—44no—
766C4×D4—44no—
767C4×D4—44no—
768C4×D4—48no—
769C4×D4—44no—
770C4×D4—48no—
771C4×D4—84no—
772C4×D4—84no—
773C4×D4—84no—
774C4×D4#4118yes—
775#117—28no—
776#117—24no—
777#117—24no—
778#117—24no—
779#117—24no—
780#117—42no—
781#117—44no—
782#117—84no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—44no—
785C2×C4⋊C4—84no—
786C2×C4⋊C4—84no—
787C2×C4⋊C4—84no—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2411yescharacteristic
885C2×C42—24no—
886C2×C42—24no—
887C2×C42—24no—
888C2×C42—24no—
889C2×C42—24no—
890C2×C42—42no—
891C2×C42—42no—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994C24C2514yes—
995C24C2511yescharacteristic
996C24C2511yescharacteristic
997C24C2511yescharacteristic
998#41—416no—
999C2×Q8—22no—
1000C2×Q8—42no—
1001C2×Q8—44no—
1002C2×Q8—44no—
1003C2×Q8—44no—
1004C2×D4—24no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—28no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—24no—
1011C2×D4—28no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—28no—
1015C2×D4—24no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4C2×#4114yes—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—24no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—28no—
1045C22×C4—24no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4C2×#4114yes—
1072C22×C4C2×#4114yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4C2×#4114yes—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—28no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—22no—
1161C22⋊C4—22no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4C2×#4114yes—
1196C22⋊C4C2×#4114yes—
1197C42—22no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—22no—
1205C42—22no—
1206C42—28no—
1207C42—24no—
1208C42—24no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—42no—
1217C42—42no—
1218C42—44no—
1219C42—42no—
1220C42—44no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—42no—
1226C42—44no—
1227C42—44no—
1228C42C2×#4114yes—
1229C422−1+414yes—
1230C23—21no—
1231C23—21no—
1232C23—22no—
1233C23—21no—
1234C23—21no—
1235C23—22no—
1236C23—22no—
1237C23—24no—
1238C23—21no—
1239C23—21no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—21no—
1245C23—22no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23C22×#4112yes—
1250C23C22×#4112yes—
1251C23#58514yes—
1252C23C2611yescharacteristic
1253Q8—44no—
1254Q8—164no—
1255D4—28no—
1256D4—44no—
1257D4—416no—
1258D4—44no—
1259D4—48no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—28no—
1272C2×C4—28no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—48no—
1331C2×C4—44no—
1332C2×C4—44no—
1333C2×C4—44no—
1334C2×C4—44no—
1335C2×C4—88no—
1336C2×C4—82no—
1337C2×C4—84no—
1338C2×C4—82no—
1339C2×C4—82no—
1340C2×C4—88no—
1341C2×C4—84no—
1342C2×C4—88no—
1343C2×C4—84no—
1344C2×C4—164no—
1345C2×C4—164no—
1346C2×C4C22×#4112yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C22×#4112yes—
1350C2×C4C22×#4112yes—
1351C2×C4C2×2−1+414yes—
1352C2×C4C2×2−1+412yes—
1353C2×C4#58512yes—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—24no—
1358C22—22no—
1359C22—22no—
1360C22—22no—
1361C22—42no—
1362C22—42no—
1363C22—41no—
1364C22—44no—
1365C22—44no—
1366C22—41no—
1367C22—41no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—42no—
1372C22—44no—
1373C22—44no—
1374C22—42no—
1375C22#345514yes—
1376C22C23×#4111yescharacteristic
1377C22C22×2−1+411yescharacteristic
1378C22C2×#58511yescharacteristic
1379C22C2×#58512yes—
1380C22H(7,𝔽2)12yes—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—24no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—44no—
1390C4—41no—
1391C4—44no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—44no—
1396C4—42no—
1397C4—44no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—44no—
1405C4—44no—
1406C4—42no—
1407C4#351514yes—
1408C2—24no—
1409C2—42no—
1410C2—81no—
1411C2—84no—
1412C2C2×#345511yescharacteristic
1413C2C2×#351511yescharacteristic
1414C2#6285811yescharacteristic
1415C2#6295812yes—
1416C2#6297012yes—
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. #41580C2semidirect
2. #41579C2semidirect
3. #40741C2semidirect
4. #40724C2semidirect
5. #40716C2semidirect
6. #40701C2semidirect
7. #39638C2semidirect
8. #39628C2semidirect
9. #38926C2semidirect
10. #38074C2semidirect
11. #38068C2semidirect
12. #37898C2semidirect
13. #37893C2semidirect
14. #37889C2semidirect
15. #37882C2semidirect
16. #37571C2semidirect
17. #37511C2semidirect
18. #37505C2semidirect
19. #36361C2semidirect
20. #36191C2semidirect
21. #36182C2semidirect
22. #35889C2semidirect
23. #35861C2semidirect
24. #35337C2semidirect
25. #35271C2semidirect
26. #35271C2semidirect
27. #34638C2semidirect
28. #34621C2semidirect
29. C2×#2647C2semidirect
30. #34323C2semidirect
31. #34123C2semidirect

Maximal subgroups

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

subgroupindex
#415802
#415792
#407412
#407242
#407162
#407012
#396382
#396282
#389262
#380742
#380682
#378982
#378932
#378892
#378822
#375712
#375112
#375052
#363612
#361912
#361822
#358892
#358612
#353372
#352712
#346382
#346212
C2×#26472
#343232
#341232