Finite Group Databasebeta

← #7697085

Subgroups — #7697085

Order 512.

5273 conjugacy classes of subgroups.

The subgroup lattice has 1516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C211yesmaximal, characteristic, complemented
2#59918C212yesmaximal, complemented
3#59799C212yesmaximal, complemented
4#59779C214yesmaximal, complemented
5#52288C212yesmaximal, complemented
6#52257C211yesmaximal, characteristic, complemented
7#45247C212yesmaximal, complemented
8#45244C211yesmaximal, characteristic, complemented
9#45047C211yesmaximal, characteristic, complemented
10#45028C212yesmaximal, complemented
11#44836C212yesmaximal, complemented
12#44834C212yesmaximal, complemented
13#44426C214yesmaximal, complemented
14#44320C214yesmaximal, complemented
15#40366C214yesmaximal, complemented
16#40054C214yesmaximal, complemented
17#39433C212yesmaximal, complemented
18#38558C214yesmaximal, complemented
19#38249C212yesmaximal, complemented
20#38123C212yesmaximal, complemented
21#36412C211yesmaximal, characteristic, complemented
22#36410C212yesmaximal, complemented
23#36087C211yesmaximal, characteristic, complemented
24#36077C211yesmaximal, characteristic, complemented
25#36000C212yesmaximal, complemented
26#35895C212yesmaximal, complemented
27#34293C212yesmaximal, complemented
28#34284C212yesmaximal, complemented
29#34267C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#548C2212yes—
33C2×#542C2212yes—
34C2×#537C2212yes—
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2212yes—
38#2858C2211yescharacteristic
39#2856C2212yes—
40#2856C2212yes—
41#2854C2214yes—
42#2806C2214yes—
43#2804C2212yes—
44#2803C2214yes—
45#2801C2214yes—
46#2800C2214yes—
47#2799C2212yes—
48#2799C2211yescharacteristic
49#2798C2212yes—
50#2797C2212yes—
51#2797C2214yes—
52#2796C2212yes—
53#2792C2214yes—
54#2789C2211yescharacteristic
55#2786C2212yes—
56#2782C2211yescharacteristic
57#2780C2214yes—
58#2780C2214yes—
59#2778C2212yes—
60#2748C2212yes—
61#2748C2214yes—
62#2730C2214yes—
63#2730C2212yes—
64#2728C2211yescharacteristic
65#2718C2214yes—
66#2717C2214yes—
67#2714C2214yes—
68#2712C2214yes—
69#2712C2212yes—
70#2710C2214yes—
71#2702C2214yes—
72#2701C2214yes—
73#2701C2214yes—
74#2692C2214yes—
75#2692C2214yes—
76#2683C2212yes—
77#2676C2214yes—
78#2676C2214yes—
79#2675C2212yes—
80#2671C2214yes—
81#2671C2214yes—
82#2651C2214yes—
83#2651C2214yes—
84#2644C2212yes—
85#2632C2212yes—
86#2632C2212yes—
87#2624C2212yes—
88#2624C2211yescharacteristic
89#2615C2211yescharacteristic
90#2612C2212yes—
91#2603C2214yes—
92#2602C2214yes—
93#2599C2212yes—
94#2598C2212yes—
95#2594C2214yes—
96#2593C2212yes—
97#2592C2212yes—
98#2589C2214yes—
99#2586C2214yes—
100#2583C2214yes—
101#2582C2212yes—
102#2578C2214yes—
103#2577C2214yes—
104#2567C2211yescharacteristic
105#2560C2214yes—
106#2560C2214yes—
107#2557C2214yes—
108#2555C2214yes—
109#2555C2214yes—
110#2555C2214yes—
111#2555C2212yes—
112#2555C2214yes—
113#2554C2214yes—
114#2549C2214yes—
115#2548C2212yes—
116#2544C2214yes—
117#2543C2214yes—
118#2541C2211yescharacteristic
119#2540C2214yes—
120#2540C2212yes—
121#2532C2214yes—
122#2531C2214yes—
123#2531C2214yes—
124#2525C2214yes—
125#2522C2214yes—
126#2521C2214yes—
127#2521C2214yes—
128#2516C2214yes—
129#2512C2212yes—
130#2507C2214yes—
131#2507C2212yes—
132#2507C2212yes—
133#2502C2214yes—
134#2501C2211yescharacteristic
135#2500C2212yes—
136#2497C2212yes—
137#2491C2212yes—
138#2491C2212yes—
139#2487C2211yescharacteristic
140#2476C2214yes—
141#2476C2214yes—
142#2476C2214yes—
143#2476C2214yes—
144#2474C2214yes—
145#2474C2214yes—
146#2467C2214yes—
147#2464C2214yes—
148#2464C2214yes—
149#2464C2214yes—
150#2464C2214yes—
151#2463C2212yes—
152#2461C2214yes—
153#2461C2214yes—
154#2455C2212yes—
155#2451C2212yes—
156#2451C2212yes—
157#2448C2212yes—
158#2448C2214yes—
159#2445C2212yes—
160#2445C2212yes—
161#2444C2214yes—
162#2443C2214yes—
163#2440C2212yes—
164#2440C2212yes—
165#2436C2211yescharacteristic
166#2431C2212yes—
167#2431C2212yes—
168#2431C2212yes—
169#2428C2212yes—
170#2428C2212yes—
171#2428C2214yes—
172#2427C2214yes—
173#2426C2212yes—
174#2426C2214yes—
175#2426C2212yes—
176#2423C2212yes—
177#2422C2214yes—
178#2416C2214yes—
179#2416C2212yes—
180#2416C2212yes—
181#2414C2214yes—
182#2409C2211yescharacteristic
183#2407C2214yes—
184#2401C2212yes—
185#2396C2214yes—
186#2396C2212yes—
187#2396C2212yes—
188#2396C2214yes—
189#2395C2212yes—
190#2395C2211yescharacteristic
191#2388C2211yescharacteristic
192#2373C2214yes—
193#2373C2214yes—
194#2372C2212yes—
195#2372C2214yes—
196#2369C2212yes—
197#2368C2214yes—
198#2367C2214yes—
199#2367C2212yes—
200#2367C2212yes—
201#2367C2214yes—
202#2367C2212yes—
203#2365C2212yes—
204#2364C2214yes—
205#2364C2214yes—
206#2363C2214yes—
207#2363C2212yes—
208#2363C2212yes—
209#2363C2212yes—
210#2363C2212yes—
211#2362C2214yes—
212#2362C2212yes—
213#2362C2212yes—
214#2361C2212yes—
215#2361C2214yes—
216#2361C2212yes—
217#2361C2214yes—
218#2361C2212yes—
219#2360C2212yes—
220#2360C2212yes—
221#2360C2212yes—
222#2354C2212yes—
223#2354C2214yes—
224#2354C2212yes—
225Q8×C4⋊C4C2212yes—
226#2347C2211yescharacteristic
227#2347C2211yescharacteristic
228#2341C2212yes—
229Q8×C22⋊C4C2212yes—
230#2335C2214yes—
231#2332C2214yes—
232#2326C2214yes—
233#2326C2212yes—
234#2324C2214yes—
235#2324C2214yes—
236#2324C2212yes—
237#2323C2214yes—
238#2319C2212yes—
239#2311C2212yes—
240C4×#124C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2214yes—
244C4×C22⋊Q8C2214yes—
245C4×C22⋊Q8C2214yes—
246C4×#123C2214yes—
247C4×#121C2214yes—
248#2298C2212yes—
249#2297C2212yes—
250#2297C2214yes—
251#2297C2212yes—
252#2295C2212yes—
253C2×#389C2212yes—
254#2290C2212yes—
255#2290C2214yes—
256#2276C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C23×Q8C2311yescharacteristic
263#555—44no—
264#550—44no—
265#548—216no—
266#542—216no—
267#537—216no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2312yes—
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#124C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×#121C2311yescharacteristic
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316#520—44no—
317#519—44no—
318C4×#41—48no—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×#117C2312yes—
344C2×#117C2311yescharacteristic
345C2×#117C2311yescharacteristic
346C2×#117C2312yes—
347C2×#117C2314yes—
348C2×#117C2311yescharacteristic
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2314yes—
356C22×C42C2314yes—
357C22×C42C2312yes—
358C22×C42C2312yes—
359#401C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2312yes—
363#400C2311yescharacteristic
364#400C2312yes—
365#400C2312yes—
366#400C2312yes—
367#399C2314yes—
368#399C2312yes—
369#399C2312yes—
370#399C2314yes—
371#399C2311yescharacteristic
372#399C2312yes—
373#399C2312yes—
374#399C2314yes—
375#399C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2311yescharacteristic
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2311yescharacteristic
396#397C2312yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2312yes—
417#395C2311yescharacteristic
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2311yescharacteristic
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#393C2312yes—
442#393C2314yes—
443#393C2312yes—
444#393C2312yes—
445#393C2312yes—
446#393C2311yescharacteristic
447#393C2314yes—
448#392C2312yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2311yescharacteristic
453#392C2312yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2312yes—
458#392C2312yes—
459#392C2314yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2312yes—
491#390C2314yes—
492#390C2314yes—
493#390C2314yes—
494#390C2312yes—
495#390C2314yes—
496#390C2314yes—
497#390C2311yescharacteristic
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2314yes—
504#390C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
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#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2312yes—
617#386C2312yes—
618#386C2312yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2314yes—
636#385C2312yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#385C2312yes—
645#385C2312yes—
646#384C2312yes—
647#384C2314yes—
648#384C2312yes—
649#384C2312yes—
650#383C2312yes—
651#383C2312yes—
652#382C2311yescharacteristic
653#381C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2311yescharacteristic
663#380C2311yescharacteristic
664#380C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716#376C2314yes—
717#376C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—28no—
724C2×#41—42no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—82no—
728C22×Q8—28no—
729C22×Q8—42no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2412yes—
735C22×Q8C2411yescharacteristic
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2411yescharacteristic
747C22×D4C2414yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2414yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2414yes—
767C4⋊Q8—28no—
768C4⋊Q8—42no—
769#127—44no—
770#127—42no—
771#127—82no—
772#126—216no—
773#126—84no—
774#124—28no—
775#124—28no—
776#124—24no—
777#124—216no—
778#124—216no—
779#124—44no—
780#124—44no—
781#124—84no—
782#124—84no—
783#124—84no—
784#123—216no—
785#123—84no—
786#123—84no—
787#123—84no—
788C22⋊Q8—28no—
789C22⋊Q8—28no—
790C22⋊Q8—216no—
791C22⋊Q8—216no—
792C22⋊Q8—216no—
793C22⋊Q8—84no—
794C22⋊Q8—84no—
795C22⋊Q8#41116yescomplemented
796#121—28no—
797#121—28no—
798#121—28no—
799#121—216no—
800#121—28no—
801#121—216no—
802#121—216no—
803#121—216no—
804#121—44no—
805#121—48no—
806#121—44no—
807#121—42no—
808#121—42no—
809#121—84no—
810#121—84no—
811#121—84no—
812#121—84no—
813#121—84no—
814#121—84no—
815C4×Q8—28no—
816C4×Q8—28no—
817C4×Q8—28no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—42no—
821C4×Q8—44no—
822C4×Q8—44no—
823C4×Q8—44no—
824C4×Q8—84no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—216no—
828C4×D4—28no—
829C4×D4—24no—
830C4×D4—48no—
831C4×D4—48no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—42no—
835C4×D4—48no—
836C4×D4—84no—
837C4×D4—84no—
838C4×D4—84no—
839#117—28no—
840#117—28no—
841#117—24no—
842#117—24no—
843#117—42no—
844#117—44no—
845#117—48no—
846#117—48no—
847#117—84no—
848C2×C4⋊C4—28no—
849C2×C4⋊C4—42no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4—84no—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C42—48no—
962C2×C42—44no—
963C2×C42—82no—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2411yescharacteristic
1030#95C2411yescharacteristic
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2512yes—
1048C24C2514yes—
1049C24C2511yescharacteristic
1050C24C2511yescharacteristic
1051C24C2512yes—
1052#41—416no—
1053#41—432no—
1054#41—816no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—28no—
1058C2×Q8—28no—
1059C2×Q8—24no—
1060C2×Q8—42no—
1061C2×Q8—41no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—42no—
1068C2×Q8—416no—
1069C2×Q8C2×#4118yes—
1070C2×Q82−1+414yes—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—24no—
1075C2×D4—28no—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—28no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—24no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—28no—
1089C2×D4—42no—
1090C2×D4—44no—
1091C2×D4—41no—
1092C2×D4—41no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—41no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—24no—
1121C22×C4—28no—
1122C22×C4—28no—
1123C22×C4—24no—
1124C22×C4—28no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—28no—
1130C22×C4—28no—
1131C22×C4—28no—
1132C22×C4—24no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—42no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—42no—
1147C22×C4—42no—
1148C22×C4—44no—
1149C22×C4—42no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4C2×#4118yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2514yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2514yes—
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—41no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—41no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4C2×#4118yes—
1226C4⋊C4C2×#41116yes—
1227C4⋊C4H(5,𝔽2)14yes—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—24no—
1243C22⋊C4—28no—
1244C22⋊C4—24no—
1245C22⋊C4—28no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4C2×#41116yes—
1288C42—24no—
1289C42—24no—
1290C42—28no—
1291C42—24no—
1292C42—28no—
1293C42—28no—
1294C42—28no—
1295C42—24no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—22no—
1300C42—22no—
1301C42—42no—
1302C42—42no—
1303C42—44no—
1304C42—41no—
1305C42—44no—
1306C42—42no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C42—44no—
1313C42—42no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—24no—
1321C23—24no—
1322C23—22no—
1323C23—24no—
1324C23—22no—
1325C23—21no—
1326C23—21no—
1327C23—22no—
1328C23—24no—
1329C23—21no—
1330C23—21no—
1331C23—22no—
1332C23—24no—
1333C23—24no—
1334C23—24no—
1335C23—22no—
1336C23—21no—
1337C23—22no—
1338C23—24no—
1339C23—24no—
1340C23—22no—
1341C23—21no—
1342C23C22×#4114yes—
1343C23C2611yescharacteristic
1344Q8—216no—
1345Q8—44no—
1346Q8—48no—
1347Q8—44no—
1348Q8—88no—
1349Q8—162no—
1350D4—48no—
1351D4—416no—
1352D4—44no—
1353D4—44no—
1354D4—48no—
1355D4—88no—
1356D4—88no—
1357D4—82no—
1358D4—88no—
1359D4—84no—
1360D4—88no—
1361D4—84no—
1362D4—88no—
1363D4—164no—
1364D4—162no—
1365D4—162no—
1366D4—162no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—21no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—216no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—48no—
1427C2×C4—416no—
1428C2×C4—416no—
1429C2×C4—48no—
1430C2×C4—44no—
1431C2×C4—44no—
1432C2×C4—88no—
1433C2×C4—88no—
1434C2×C4—84no—
1435C2×C4—88no—
1436C2×C4—84no—
1437C2×C4—162no—
1438C2×C4—164no—
1439C2×C4C22×#4118yes—
1440C2×C4C22×#4118yes—
1441C2×C4C22×#4114yes—
1442C2×C4C22×#4114yes—
1443C2×C4C2×H(5,𝔽2)14yes—
1444C2×C4C2×H(5,𝔽2)12yes—
1445C2×C4C2×2−1+412yes—
1446C2×C4C2×2−1+414yes—
1447C22—24no—
1448C22—24no—
1449C22—24no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—44no—
1455C22—44no—
1456C22—42no—
1457C22—44no—
1458C22—42no—
1459C22—44no—
1460C22—41no—
1461C22—42no—
1462C22—41no—
1463C22—44no—
1464C22—42no—
1465C22—42no—
1466C22—44no—
1467C22—44no—
1468C22—42no—
1469C22—44no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—44no—
1474C22—41no—
1475C22—42no—
1476C22C23×#4112yes—
1477C22C22×H(5,𝔽2)11yescharacteristic
1478C22C22×2−1+411yescharacteristic
1479C22H(7,𝔽2)12yes—
1480C22H(7,𝔽2)11yescharacteristic
1481C4—28no—
1482C4—24no—
1483C4—24no—
1484C4—22no—
1485C4—24no—
1486C4—28no—
1487C4—42no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—44no—
1492C4—42no—
1493C4—42no—
1494C4—41no—
1495C4—42no—
1496C4—42no—
1497C4—44no—
1498C4—42no—
1499C4—44no—
1500C4—42no—
1501C4—42no—
1502C4—41no—
1503C4—41no—
1504C4#348114yes—
1505C2—44no—
1506C2—84no—
1507C2—81no—
1508C2—82no—
1509C2—81no—
1510C2C2×#348111yescharacteristic
1511C2#6285812yes—
1512C2#6289411yescharacteristic
1513C2#6299912yes—
1514C2#6306611yescharacteristic
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. #59933C2semidirect
2. #59918C2semidirect
3. #59799C2semidirect
4. #59779C2semidirect
5. #52288C2semidirect
6. #52257C2semidirect
7. #45247C2semidirect
8. #45244C2semidirect
9. #45047C2semidirect
10. #45028C2semidirect
11. #44836C2semidirect
12. #44834C2semidirect
13. #44426C2semidirect
14. #44320C2semidirect
15. #40366C2semidirect
16. #40054C2semidirect
17. #39433C2semidirect
18. #38558C2semidirect
19. #38249C2semidirect
20. #38123C2semidirect
21. #36412C2semidirect
22. #36410C2semidirect
23. #36087C2semidirect
24. #36077C2semidirect
25. #36000C2semidirect
26. #35895C2semidirect
27. #34293C2semidirect
28. #34284C2semidirect
29. #34267C2semidirect
795. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599332
#599182
#597992
#597792
#522882
#522572
#452472
#452442
#450472
#450282
#448362
#448342
#444262
#443202
#403662
#400542
#394332
#385582
#382492
#381232
#364122
#364102
#360872
#360772
#360002
#358952
#342932
#342842
#342672