Finite Group Databasebeta

← #8097167

Subgroups — #8097167

Order 512.

5473 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53136C212yesmaximal, complemented
2#53045C212yesmaximal, complemented
3#53008C211yesmaximal, characteristic, complemented
4#53007C211yesmaximal, characteristic, complemented
5#52913C212yesmaximal, complemented
6#52913C214yesmaximal, complemented
7#52723C214yesmaximal, complemented
8#52549C212yesmaximal, complemented
9#52297C211yesmaximal, characteristic, complemented
10C2×#2792C212yesmaximal, complemented
11#46342C211yesmaximal, characteristic, complemented
12#46327C212yesmaximal, complemented
13#46040C214yesmaximal, complemented
14#46002C212yesmaximal, complemented
15#45751C214yesmaximal, complemented
16#45751C214yesmaximal, complemented
17#45677C212yesmaximal, complemented
18#45550C214yesmaximal, complemented
19#45503C212yesmaximal, complemented
20#45497C212yesmaximal, complemented
21#36259C212yesmaximal, complemented
22#36259C212yesmaximal, complemented
23#36241C212yesmaximal, complemented
24#36217C212yesmaximal, complemented
25#36179C211yesmaximal, characteristic, complemented
26#36085C211yesmaximal, characteristic, complemented
27#36085C212yesmaximal, complemented
28#36020C212yesmaximal, complemented
29#35998C211yesmaximal, characteristic, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#547C2212yes—
32C2×#547C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#547C2212yes—
35C2×#547C2212yes—
36C2×#547C2212yes—
37C2×#547C2212yes—
38C2×#520C2211yescharacteristic
39C2×C4×#41C2212yes—
40#2868C2211yescharacteristic
41#2863C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2856C2212yes—
45#2855C2212yes—
46#2854C2214yes—
47#2854C2214yes—
48#2853C2214yes—
49#2852C2214yes—
50#2843C2212yes—
51#2843C2214yes—
52#2841C2212yes—
53#2841C2214yes—
54#2841C2214yes—
55#2838C2214yes—
56#2838C2214yes—
57#2838C2214yes—
58#2838C2214yes—
59#2838C2214yes—
60#2837C2214yes—
61#2837C2214yes—
62#2834C2212yes—
63#2830C2212yes—
64#2830C2214yes—
65#2829C2214yes—
66#2829C2214yes—
67#2827C2214yes—
68#2823C2212yes—
69#2807C2212yes—
70#2807C2214yes—
71#2807C2214yes—
72#2803C2214yes—
73#2803C2212yes—
74#2801C2214yes—
75#2797C2214yes—
76#2796C2214yes—
77#2796C2214yes—
78#2795C2214yes—
79#2795C2211yescharacteristic
80#2792C2212yes—
81#2792C2211yescharacteristic
82#2792C2212yes—
83#2792C2212yes—
84#2792C2214yes—
85#2792C2214yes—
86#2792C2214yes—
87#2792C2214yes—
88#2792C2214yes—
89#2792C2214yes—
90#2792C2214yes—
91#2792C2214yes—
92#2792C2214yes—
93#2790C2214yes—
94#2790C2214yes—
95#2790C2214yes—
96#2790C2214yes—
97#2790C2214yes—
98#2784C2211yescharacteristic
99#2784C2214yes—
100#2780C2214yes—
101#2780C2214yes—
102#2757C2214yes—
103#2757C2214yes—
104#2756C2212yes—
105#2752C2212yes—
106#2748C2214yes—
107#2746C2214yes—
108#2742C2214yes—
109#2742C2214yes—
110#2742C2214yes—
111#2737C2214yes—
112#2737C2212yes—
113#2737C2214yes—
114#2714C2212yes—
115#2709C2212yes—
116#2705C2214yes—
117#2705C2212yes—
118#2699C2211yescharacteristic
119#2691C2214yes—
120#2673C2212yes—
121#2625C2211yescharacteristic
122#2623C2212yes—
123#2621C2212yes—
124#2618C2214yes—
125#2616C2212yes—
126#2616C2211yescharacteristic
127#2614C2214yes—
128#2614C2212yes—
129#2546C2212yes—
130#2546C2212yes—
131#2546C2212yes—
132#2543C2214yes—
133#2542C2211yescharacteristic
134#2542C2212yes—
135#2542C2211yescharacteristic
136#2542C2212yes—
137#2538C2212yes—
138#2538C2212yes—
139#2536C2212yes—
140#2514C2212yes—
141#2511C2212yes—
142#2511C2212yes—
143#2510C2214yes—
144#2502C2211yescharacteristic
145#2501C2212yes—
146#2501C2214yes—
147#2501C2212yes—
148#2501C2214yes—
149#2499C2212yes—
150#2498C2214yes—
151#2498C2212yes—
152#2497C2212yes—
153#2496C2212yes—
154#2494C2212yes—
155#2493C2214yes—
156#2493C2214yes—
157#2493C2214yes—
158#2486C2211yescharacteristic
159#2486C2214yes—
160#2486C2214yes—
161#2486C2214yes—
162#2485C2212yes—
163#2484C2214yes—
164#2484C2212yes—
165#2481C2214yes—
166#2481C2214yes—
167#2446C2212yes—
168#2446C2212yes—
169#2446C2212yes—
170#2444C2214yes—
171#2443C2214yes—
172#2443C2214yes—
173#2434C2212yes—
174#2434C2212yes—
175#2434C2212yes—
176#2434C2212yes—
177#2434C2211yescharacteristic
178#2430C2214yes—
179#2430C2214yes—
180#2430C2214yes—
181#2430C2214yes—
182#2430C2212yes—
183#2429C2212yes—
184#2429C2212yes—
185#2429C2212yes—
186#2429C2212yes—
187#2429C2212yes—
188#2429C2212yes—
189#2425C2214yes—
190#2425C2214yes—
191#2425C2214yes—
192#2425C2214yes—
193#2425C2214yes—
194#2425C2214yes—
195#2423C2212yes—
196#2423C2212yes—
197#2421C2212yes—
198#2419C2214yes—
199#2419C2214yes—
200#2419C2214yes—
201#2417C2212yes—
202#2417C2212yes—
203#2416C2214yes—
204#2416C2214yes—
205#2415C2212yes—
206#2415C2212yes—
207#2415C2212yes—
208#2415C2212yes—
209#2413C2214yes—
210#2413C2214yes—
211#2413C2214yes—
212#2413C2214yes—
213#2413C2214yes—
214#2413C2214yes—
215#2409C2211yescharacteristic
216#2409C2212yes—
217#2409C2212yes—
218#2409C2212yes—
219#2409C2212yes—
220#2406C2212yes—
221#2406C2214yes—
222#2406C2214yes—
223#2406C2214yes—
224#2406C2214yes—
225#2395C2211yescharacteristic
226#2392C2212yes—
227C2×#398C2212yes—
228C2×#398C2214yes—
229#2388C2211yescharacteristic
230#2388C2212yes—
231C2×#395C2212yes—
232C2×#395C2214yes—
233#2383C2214yes—
234#2383C2214yes—
235#2377C2214yes—
236#2376C2212yes—
237#2376C2214yes—
238#2349C2212yes—
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2212yes—
241#2339C2211yescharacteristic
242#2339C2212yes—
243#2339C2212yes—
244#2339C2212yes—
245#2339C2212yes—
246#2339C2212yes—
247#2339C2211yescharacteristic
248C4×#127C2211yescharacteristic
249C4×#126C2212yes—
250C4×#123C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253C2×#389C2214yes—
254C2×#389C2214yes—
255C2×#387C2214yes—
256C2×#387C2214yes—
257C2×#384C2212yes—
258C42×D4C2211yescharacteristic
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263C22×#41C2312yes—
264C22×#41C2311yescharacteristic
265C22×#41C2311yescharacteristic
266C22×#41C2312yes—
267C22×#41C2314yes—
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270C23×Q8C2312yes—
271#547—48no—
272#547—48no—
273#547—48no—
274#547—48no—
275#547—44no—
276#547—44no—
277#547—48no—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2312yes—
285C2×#127C2311yescharacteristic
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2311yescharacteristic
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2312yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325#520—44no—
326C4×#41—48no—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×#117C2311yescharacteristic
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2314yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2311yescharacteristic
359C22×C4⋊C4C2312yes—
360C22×C42C2312yes—
361C22×C42C2314yes—
362C22×C42C2312yes—
363#401C2314yes—
364#401C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2311yescharacteristic
377#400C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2312yes—
382#399C2314yes—
383#399C2314yes—
384#399C2312yes—
385#399C2314yes—
386#399C2314yes—
387#399C2311yescharacteristic
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2311yescharacteristic
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2311yescharacteristic
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2312yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2312yes—
445#396C2314yes—
446#396C2314yes—
447#396C2312yes—
448#395C2312yes—
449#395C2314yes—
450#395C2312yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2312yes—
459#395C2314yes—
460#395C2312yes—
461#395C2311yescharacteristic
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2314yes—
467#394C2311yescharacteristic
468#394C2314yes—
469#394C2312yes—
470#394C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2312yes—
482#394C2312yes—
483#394C2312yes—
484#394C2312yes—
485#394C2312yes—
486#394C2312yes—
487#393C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2312yes—
491#393C2312yes—
492#393C2314yes—
493#393C2311yescharacteristic
494#392C2312yes—
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#392C2311yescharacteristic
499#392C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#390C2311yescharacteristic
513#390C2311yescharacteristic
514#390C2312yes—
515#390C2312yes—
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2314yes—
553#389C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2312yes—
631#386C2312yes—
632#386C2312yes—
633#386C2312yes—
634#386C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2312yes—
658#384C2311yescharacteristic
659#384C2312yes—
660#384C2314yes—
661#384C2312yes—
662#384C2312yes—
663#384C2312yes—
664#384C2312yes—
665#384C2312yes—
666#384C2314yes—
667#384C2314yes—
668#383C2312yes—
669#383C2314yes—
670#383C2314yes—
671#382C2312yes—
672#381C2312yes—
673#381C2314yes—
674#381C2312yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#381C2314yes—
679#381C2314yes—
680#381C2312yes—
681#381C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686#380C2314yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2311yescharacteristic
692#380C2312yes—
693#380C2311yescharacteristic
694#380C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2314yes—
698#380C2314yes—
699#380C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C2×#95C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C2×#95C2314yes—
720C2×#95C2312yes—
721C2×#95C2314yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—28no—
727C2×#41—28no—
728C2×#41—28no—
729C2×#41—28no—
730C2×#41—28no—
731C2×#41—28no—
732C2×#41—28no—
733C2×#41—24no—
734C2×#41—44no—
735C2×#41—42no—
736C2×#41—48no—
737C2×#41—44no—
738C2×#41—48no—
739C2×#41—48no—
740C2×#41—48no—
741C22×Q8—48no—
742C22×Q8—44no—
743C22×Q8—44no—
744C22×Q8—42no—
745C22×Q8—44no—
746C22×Q8—44no—
747C22×Q8—44no—
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2414yes—
754C22×Q8C2412yes—
755C22×D4C2414yes—
756C22×D4C2412yes—
757C22×D4C2414yes—
758C22×D4C2412yes—
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2411yescharacteristic
764C22×D4C2412yes—
765C22×D4C2412yes—
766C22×D4C2412yes—
767C22×D4C2411yescharacteristic
768C22×D4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2412yes—
775C23×C4C2411yescharacteristic
776C23×C4C2412yes—
777C23×C4C2412yes—
778C23×C4C2414yes—
779C23×C4C2414yes—
780C23×C4C2414yes—
781C23×C4C2414yes—
782C23×C4C2412yes—
783C23×C4C2412yes—
784C23×C4C2412yes—
785C23×C4C2414yes—
786C23×C4C2412yes—
787C4⋊Q8—44no—
788C4⋊Q8—44no—
789C4⋊Q8—44no—
790C4⋊Q8—42no—
791C4⋊Q8—44no—
792C4⋊Q8—44no—
793C4⋊Q8—42no—
794#127—42no—
795#126—28no—
796#126—48no—
797#123—28no—
798#123—48no—
799#123—48no—
800#123—48no—
801#123—48no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—44no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—44no—
810#123—48no—
811#123—44no—
812C22⋊Q8—44no—
813C22⋊Q8—44no—
814C22⋊Q8—44no—
815C22⋊Q8—44no—
816C22⋊Q8—44no—
817C22⋊Q8—44no—
818C22⋊Q8—44no—
819C22⋊Q8—42no—
820C22⋊Q8—44no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824C22⋊Q8—42no—
825#121—28no—
826#121—44no—
827#121—48no—
828#121—48no—
829#121—44no—
830#121—48no—
831#121—44no—
832#121—48no—
833#121—48no—
834C4×Q8—44no—
835C4×Q8—44no—
836C4×Q8—44no—
837C4×D4—28no—
838C4×D4—28no—
839C4×D4—28no—
840C4×D4—24no—
841C4×D4—28no—
842C4×D4—44no—
843C4×D4—44no—
844C4×D4—44no—
845C4×D4—44no—
846C4×D4—42no—
847C4×D4—44no—
848C4×D4—42no—
849C4×D4—48no—
850C4×D4—48no—
851C4×D4—48no—
852#117—42no—
853#117—48no—
854#117—44no—
855#117—44no—
856C2×C4⋊C4—216no—
857C2×C4⋊C4—48no—
858C2×C4⋊C4—42no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4—48no—
861C2×C4⋊C4—48no—
862C2×C4⋊C4—48no—
863C2×C4⋊C4—44no—
864C2×C4⋊C4—48no—
865C2×C4⋊C4—44no—
866C2×C4⋊C4—48no—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2411yescharacteristic
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2411yescharacteristic
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C42—44no—
981C2×C42—44no—
982C2×C42—48no—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2411yescharacteristic
997C2×C42C2414yes—
998C2×C42C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2411yescharacteristic
1002#95C2411yescharacteristic
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2411yescharacteristic
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2411yescharacteristic
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060C24C2512yes—
1061C24C2511yescharacteristic
1062C24C2512yes—
1063C24C2511yescharacteristic
1064C24C2512yes—
1065#41—432no—
1066#41—464no—
1067#41—416no—
1068#41—432no—
1069#41—416no—
1070#41—432no—
1071#41—416no—
1072C2×Q8—24no—
1073C2×Q8—22no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—24no—
1081C2×Q8—22no—
1082C2×Q8—42no—
1083C2×Q8—41no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×Q8—44no—
1087C2×Q8—44no—
1088C2×Q8—42no—
1089C2×Q8—416no—
1090C2×Q8—432no—
1091C2×Q8—432no—
1092C2×D4—28no—
1093C2×D4—24no—
1094C2×D4—28no—
1095C2×D4—28no—
1096C2×D4—28no—
1097C2×D4—28no—
1098C2×D4—28no—
1099C2×D4—28no—
1100C2×D4—24no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—22no—
1107C2×D4—22no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D4—41no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—41no—
1116C2×D4—42no—
1117C2×D4—41no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—41no—
1125C2×D4—41no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4H(5,𝔽2)18yes—
1129C2×D4H(5,𝔽2)14yes—
1130C22×C4—28no—
1131C22×C4—28no—
1132C22×C4—28no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—28no—
1138C22×C4—28no—
1139C22×C4—28no—
1140C22×C4—28no—
1141C22×C4—28no—
1142C22×C4—24no—
1143C22×C4—28no—
1144C22×C4—28no—
1145C22×C4—24no—
1146C22×C4—22no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—22no—
1155C22×C4—28no—
1156C22×C4—28no—
1157C22×C4—28no—
1158C22×C4—24no—
1159C22×C4—24no—
1160C22×C4—24no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—42no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—42no—
1170C22×C4—42no—
1171C22×C4—42no—
1172C22×C4—44no—
1173C22×C4—42no—
1174C22×C4—42no—
1175C22×C4—44no—
1176C22×C4—42no—
1177C22×C4—42no—
1178C22×C4—42no—
1179C22×C4C2512yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2514yes—
1187C22×C4C2514yes—
1188C22×C4C2514yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2512yes—
1191C22×C4C2514yes—
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2514yes—
1196C22×C4C2512yes—
1197C22×C4C2511yescharacteristic
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C22×C4C2511yescharacteristic
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—28no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—41no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—41no—
1222C4⋊C4—42no—
1223C4⋊C4—41no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—41no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C42−1+418yescomplemented
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—24no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—24no—
1274C22⋊C4—24no—
1275C22⋊C4—24no—
1276C22⋊C4—24no—
1277C22⋊C4—24no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—22no—
1323C42—24no—
1324C42—42no—
1325C42—44no—
1326C42—42no—
1327C42—44no—
1328C42—44no—
1329C42—44no—
1330C42—41no—
1331C42—44no—
1332C23—24no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—21no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—21no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23—21no—
1353C23—21no—
1354C23—22no—
1355C23—21no—
1356C23—22no—
1357C23—22no—
1358C23—21no—
1359C23C2×H(5,𝔽2)18yes—
1360C23C2×H(5,𝔽2)14yes—
1361C23C2611yescharacteristic
1362Q8—44no—
1363Q8—416no—
1364Q8—48no—
1365Q8—48no—
1366Q8—44no—
1367Q8—48no—
1368Q8—44no—
1369D4—48no—
1370D4—44no—
1371D4—416no—
1372D4—48no—
1373D4—48no—
1374D4—416no—
1375D4—84no—
1376D4—84no—
1377D4—84no—
1378D4—82no—
1379D4—82no—
1380D4—84no—
1381D4—84no—
1382D4#560116yes—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—416no—
1444C2×C4—416no—
1445C2×C4—48no—
1446C2×C4—416no—
1447C2×C4—48no—
1448C2×C4—416no—
1449C2×C4—48no—
1450C2×C4—416no—
1451C2×C4—416no—
1452C2×C4—48no—
1453C2×C4—44no—
1454C2×C4—48no—
1455C2×C4—48no—
1456C2×C4—44no—
1457C2×C4—84no—
1458C2×C4—84no—
1459C2×C4—88no—
1460C2×C4—162no—
1461C2×C4C2×H(5,𝔽2)14yes—
1462C2×C4C2×H(5,𝔽2)12yes—
1463C2×C4C2×2−1+414yes—
1464C2×C4C2×2−1+414yes—
1465C2×C4C2×2−1+414yes—
1466C2×C4#58512yes—
1467C22—28no—
1468C22—24no—
1469C22—24no—
1470C22—28no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—41no—
1479C22—42no—
1480C22—41no—
1481C22—41no—
1482C22—42no—
1483C22—41no—
1484C22—42no—
1485C22—42no—
1486C22—42no—
1487C22—42no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—41no—
1492C22—42no—
1493C22—42no—
1494C22—41no—
1495C22C2×#56018yes—
1496C22C22×H(5,𝔽2)12yes—
1497C22C22×H(5,𝔽2)11yescharacteristic
1498C22C22×2−1+412yes—
1499C22C2×#58511yescharacteristic
1500C222−1+611yescharacteristic
1501C4—24no—
1502C4—24no—
1503C4—22no—
1504C4—24no—
1505C4—44no—
1506C4—44no—
1507C4—42no—
1508C4—42no—
1509C4—41no—
1510C4—42no—
1511C4—42no—
1512C4—44no—
1513C4—42no—
1514C4—44no—
1515C4—42no—
1516C4—42no—
1517C4—41no—
1518C4—42no—
1519C4—41no—
1520C4—44no—
1521C4—42no—
1522C4—44no—
1523C4—42no—
1524C4C2×#56014yes—
1525C2—28no—
1526C2—82no—
1527C2—81no—
1528C2—81no—
1529C2—82no—
1530C2C22×#56011yescharacteristic
1531C2#6289811yescharacteristic
1532C2#6291512yes—
1533C2#6301312yes—
1534C2#6303711yescharacteristic
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. #53136C2semidirect
2. #53045C2semidirect
3. #53008C2semidirect
4. #53007C2semidirect
5. #52913C2semidirect
6. #52913C2semidirect
7. #52723C2semidirect
8. #52549C2semidirect
9. #52297C2semidirect
10. C2×#2792C2semidirect
11. #46342C2semidirect
12. #46327C2semidirect
13. #46040C2semidirect
14. #46002C2semidirect
15. #45751C2semidirect
16. #45751C2semidirect
17. #45677C2semidirect
18. #45550C2semidirect
19. #45503C2semidirect
20. #45497C2semidirect
21. #36259C2semidirect
22. #36259C2semidirect
23. #36241C2semidirect
24. #36217C2semidirect
25. #36179C2semidirect
26. #36085C2semidirect
27. #36085C2semidirect
28. #36020C2semidirect
29. #35998C2semidirect
1263. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#531362
#530452
#530082
#530072
#529132
#527232
#525492
#522972
C2×#27922
#463422
#463272
#460402
#460022
#457512
#456772
#455502
#455032
#454972
#362592
#362412
#362172
#361792
#360852
#360202
#359982