Finite Group Databasebeta

← #7727015

Subgroups — #7727015

Order 512.

4316 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50189C212yesmaximal, complemented
2#49597C212yesmaximal
3#48799C212yesmaximal, complemented
4#47885C212yesmaximal, complemented
5#47202C214yesmaximal, complemented
6#46840C214yesmaximal, complemented
7#45124C212yesmaximal, complemented
8#45123C212yesmaximal, complemented
9#45122C212yesmaximal, complemented
10#44926C212yesmaximal, complemented
11#40251C214yesmaximal, complemented
12#39935C212yesmaximal, complemented
13#39908C212yesmaximal, complemented
14#38635C214yesmaximal, complemented
15#37963C212yesmaximal, complemented
16#37955C212yesmaximal, complemented
17#37894C212yesmaximal, complemented
18#37884C212yesmaximal, complemented
19#37567C211yesmaximal, characteristic, complemented
20#37028C212yesmaximal, complemented
21#37023C212yesmaximal, complemented
22#36451C212yesmaximal, complemented
23#36409C212yesmaximal, complemented
24#35502C212yesmaximal, complemented
25#35485C212yesmaximal, complemented
26#35325C211yesmaximal, characteristic, complemented
27#35297C211yesmaximal, characteristic, complemented
28#34875C211yesmaximal, characteristic
29#34373C211yesmaximal, characteristic, complemented
30#34191C211yesmaximal, characteristic, complemented
31#34048C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2864C2214yescomplemented
36#2863C2214yescomplemented
37#2857C2212yescomplemented
38#2857C2212yescomplemented
39#2855C2212yes—
40#2848C2212yes—
41#2841C2214yes—
42#2809C2214yescomplemented
43#2805C2214yescomplemented
44#2802C2214yescomplemented
45#2794C2214yescomplemented
46#2793C2214yes—
47#2790C2214yescomplemented
48#2789C2214yescomplemented
49#2783C2214yes—
50#2781C2214yes—
51#2777C2214yes—
52#2777C2214yes—
53#2775C2214yes—
54#2775C2214yes—
55#2775C2214yes—
56#2774C2214yescomplemented
57#2773C2214yes—
58#2772C2214yes—
59#2772C2214yes—
60#2769C2214yescomplemented
61#2767C2214yescomplemented
62#2766C2214yescomplemented
63#2766C2214yescomplemented
64#2765C2214yes—
65#2764C2214yes—
66#2762C2214yescomplemented
67#2759C2214yes—
68#2758C2214yescomplemented
69#2754C2214yes—
70#2750C2214yes—
71#2744C2214yescomplemented
72#2744C2214yescomplemented
73#2743C2214yes—
74#2737C2214yes—
75#2735C2214yes—
76#2735C2214yes—
77#2718C2214yes—
78#2700C2214yes—
79#2697C2214yes—
80#2689C2214yescomplemented
81#2684C2214yes—
82#2667C2212yes—
83#2666C2214yescomplemented
84#2665C2212yes—
85#2660C2212yescomplemented
86#2652C2214yes—
87#2652C2214yes—
88#2647C2212yescomplemented
89#2628C2211yescharacteristic
90#2628C2211yescharacteristic
91#2625C2212yes—
92#2621C2211yescharacteristic
93#2621C2211yescharacteristic
94#2616C2212yes—
95#2612C2214yescomplemented
96#2611C2212yes—
97#2611C2212yes—
98#2609C2212yes—
99#2609C2212yes—
100#2606C2212yescomplemented
101#2605C2214yescomplemented
102#2605C2212yescomplemented
103#2602C2214yes—
104#2599C2211yescharacteristic
105#2599C2211yescharacteristic
106#2599C2212yes—
107#2599C2212yes—
108#2598C2211yescharacteristic
109#2598C2211yescharacteristic
110#2596C2214yes—
111#2596C2214yes—
112#2595C2214yes—
113#2594C2214yes—
114#2589C2214yes—
115#2587C2214yes—
116#2584C2212yescomplemented
117#2583C2212yes—
118#2581C2212yescomplemented
119#2579C2212yes—
120#2578C2214yes—
121#2577C2214yescomplemented
122#2576C2214yes—
123#2576C2214yes—
124#2575C2214yes—
125#2574C2214yescomplemented
126#2574C2214yescomplemented
127#2573C2214yes—
128#2573C2214yes—
129#2573C2214yescomplemented
130#2572C2214yes—
131#2570C2212yescomplemented
132#2569C2214yescomplemented
133#2569C2214yescomplemented
134#2562C2212yes—
135#2562C2212yescomplemented
136#2561C2212yes—
137#2553C2214yes—
138#2550C2212yescomplemented
139#2547C2212yes—
140#2538C2212yes—
141#2536C2212yes—
142#2536C2212yescomplemented
143#2534C2212yes—
144#2533C2214yescomplemented
145#2533C2214yescomplemented
146#2532C2214yes—
147#2531C2214yes—
148#2530C2214yescomplemented
149#2529C2214yes—
150#2529C2214yes—
151#2528C2214yescomplemented
152#2527C2214yes—
153#2527C2214yescomplemented
154#2524C2214yescomplemented
155#2524C2214yescomplemented
156#2521C2214yes—
157#2514C2212yescomplemented
158#2514C2212yescomplemented
159#2514C2214yescomplemented
160#2510C2214yes—
161#2510C2214yes—
162#2509C2212yescomplemented
163#2508C2212yescomplemented
164#2498C2214yes—
165#2497C2212yes—
166#2496C2212yescomplemented
167#2495C2212yes—
168#2495C2212yes—
169#2495C2212yescomplemented
170#2494C2212yes—
171#2493C2214yescomplemented
172#2492C2212yes—
173#2492C2212yescomplemented
174#2489C2212yes—
175#2489C2212yescomplemented
176#2488C2214yes—
177#2487C2212yes—
178#2486C2212yes—
179#2485C2214yes—
180#2485C2214yescomplemented
181#2484C2211yescharacteristic
182#2484C2212yes—
183#2482C2211yescharacteristic
184#2482C2212yes—
185#2474C2214yes—
186#2470C2214yes—
187#2466C2214yescomplemented
188#2459C2214yes—
189#2441C2212yes—
190#2439C2212yes—
191#2438C2214yescomplemented
192#2421C2212yes—
193#2421C2212yes—
194#2417C2212yes—
195#2417C2212yes—
196#2415C2212yes—
197#2415C2212yes—
198#2406C2211yescharacteristic
199#2404C2211yescharacteristic
200#2396C2211yescharacteristic
201#2396C2211yescharacteristic
202#2392C2211yescharacteristic
203#2392C2211yescharacteristic
204#2378C2212yes—
205#2378C2212yes—
206#2370C2212yescomplemented
207#2369C2212yescomplemented
208#2362C2212yes—
209#2362C2212yes—
210#2360C2212yescomplemented
211#2360C2212yescomplemented
212#2356C2212yescomplemented
213#2355C2214yescomplemented
214#2355C2212yescomplemented
215#2355C2212yescomplemented
216#2355C2212yescomplemented
217#2352C2212yes—
218#2352C2212yes—
219Q8×C4⋊C4C2212yescomplemented
220D4×C4⋊C4C2212yescomplemented
221#2346C2212yes—
222#2345C2212yescomplemented
223#2344C2212yescomplemented
224#2343C2214yescomplemented
225#2339C2212yes—
226#2337C2214yes—
227#2336C2212yescomplemented
228#2336C2212yescomplemented
229#2335C2214yes—
230#2331C2212yescomplemented
231#2327C2212yescomplemented
232#2323C2212yes—
233#2323C2212yes—
234#2323C2214yescomplemented
235#2320C2212yescomplemented
236#2318C2214yes—
237#2314C2212yes—
238#2314C2212yes—
239#2314C2212yes—
240#2314C2212yes—
241#2314C2214yes—
242#2313C2212yes—
243#2313C2212yes—
244#2312C2212yes—
245#2312C2212yes—
246C4×#126C2214yescomplemented
247C4×#123C2212yes—
248C4×#120C2212yes—
249#2298C2212yes—
250#2298C2212yes—
251#2298C2212yes—
252#2298C2212yes—
253#2298C2214yescomplemented
254#2290C2212yes—
255#2290C2212yes—
256#2285C2211yescharacteristic
257#2285C2211yescharacteristic
258#2283C2211yescharacteristic
259#2283C2211yescharacteristic
260#2283C2212yescomplemented
261C2×#382C2212yescomplemented
262#2280C2211yescharacteristic
263#2280C2211yescharacteristic
264#2275C2212yescomplemented
265C4×#117C2211yescharacteristic
266C4×#117C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C24×C4C2311yescharacteristic
269#533—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#124C2314yes—
277C2×#123C2314yes—
278C2×#123C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×#120C2312yes—
287C4×#41—28no—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×#117—28no—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2314yes—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C22⋊C4C2311yescharacteristic
323C22×C22⋊C4C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327#401C2314yes—
328#401C2314yes—
329#401C2314yes—
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#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2311yescharacteristic
349#400C2311yescharacteristic
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2311yescharacteristic
359#399C2311yescharacteristic
360#399C2312yes—
361#399C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2311yescharacteristic
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2312yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2311yescharacteristic
394#397C2311yescharacteristic
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2312yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#396C2312yes—
411#396C2314yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2312yes—
417#395C2312yes—
418#395C2311yescharacteristic
419#395C2311yescharacteristic
420#395C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2311yescharacteristic
428#394C2311yescharacteristic
429#394C2312yes—
430#393C2312yes—
431#393C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2311yescharacteristic
436#393C2311yescharacteristic
437#392C2311yescharacteristic
438#392C2311yescharacteristic
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#390C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#386C2312yes—
588#386C2314yes—
589#386C2314yes—
590#386C2312yes—
591#386C2314yes—
592#386C2312yes—
593#386C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2312yes—
599#386C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2312yes—
617#384C2312yes—
618#384C2312yes—
619#384C2314yes—
620#384C2312yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2311yescharacteristic
628#383C2311yescharacteristic
629#383C2314yes—
630#383C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2312yes—
635#382C2314yes—
636#382C2314yes—
637#382C2314yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#381C2314yes—
647#381C2312yes—
648#381C2312yes—
649#381C2314yes—
650#381C2312yes—
651#381C2314yes—
652#381C2312yes—
653#381C2314yes—
654#381C2311yescharacteristic
655#381C2311yescharacteristic
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#379C2314yes—
679#379C2312yes—
680#379C2312yes—
681#379C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727#376C2312yes—
728#376C2312yes—
729#376C2314yes—
730#376C2314yes—
731#376C2312yes—
732#376C2312yes—
733C2×#95C2314yes—
734C2×#95C2314yes—
735C43C2312yes—
736C43C2312yes—
737C25C2411yescharacteristic
738C2×#41—24no—
739C2×#41—44no—
740C22×Q8C2412yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C23×C4—24no—
749C23×C4—42no—
750C23×C4—42no—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2414yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C4⋊Q8—24no—
767C4⋊Q8—24no—
768C4⋊Q8—44no—
769#126—48no—
770#125—28no—
771#125—44no—
772#124—48no—
773#123—44no—
774#123—48no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782#120—44no—
783C4×Q8—24no—
784C4×Q8—24no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—24no—
792C4×D4—24no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—48no—
796#117—24no—
797#117—28no—
798#117—24no—
799#117—24no—
800#117—24no—
801#117—24no—
802#117—24no—
803#117—24no—
804#117—24no—
805#117—24no—
806#117—28no—
807#117—48no—
808#117—42no—
809#117—42no—
810#117—42no—
811#117—42no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—24no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C22⋊C4—24no—
876C2×C22⋊C4—24no—
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C42—24no—
923C2×C42—28no—
924C2×C42#4118yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2411yescharacteristic
1017#95C2411yescharacteristic
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032C24—22no—
1033C24—41no—
1034C24—41no—
1035C24—42no—
1036C24—42no—
1037C24C2511yescharacteristic
1038C24C2511yescharacteristic
1039C24C2511yescharacteristic
1040C24C2512yes—
1041#41—416no—
1042C2×Q8—22no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—24no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—28no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—24no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—416no—
1102C22×C4C2×#4114yes—
1103C22×C4C2×#4114yes—
1104C22×C4C2×#4114yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—22no—
1139C4⋊C4—22no—
1140C4⋊C4—22no—
1141C4⋊C4—22no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—22no—
1202C22⋊C4—22no—
1203C22⋊C4—22no—
1204C22⋊C4—22no—
1205C22⋊C4—22no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C42—22no—
1237C42—22no—
1238C42—24no—
1239C42—22no—
1240C42—22no—
1241C42—24no—
1242C42—24no—
1243C42—28no—
1244C42—24no—
1245C42—24no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—42no—
1251C42—42no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42C2×#4114yes—
1262C42C2×#4114yes—
1263C42C2×#4114yes—
1264C42C2×#4114yes—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—21no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—21no—
1276C23—21no—
1277C23—22no—
1278C23—22no—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—22no—
1284C23—22no—
1285C23—44no—
1286C23—82no—
1287C23—82no—
1288C23—84no—
1289C23—84no—
1290C23C22×#4112yes—
1291C23#58514yes—
1292C23C2611yescharacteristic
1293Q8—44no—
1294Q8—48no—
1295Q8—84no—
1296Q8—164no—
1297D4—28no—
1298D4—48no—
1299D4—84no—
1300D4—84no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—28no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—44no—
1368C2×C4—44no—
1369C2×C4—48no—
1370C2×C4—44no—
1371C2×C4—44no—
1372C2×C4—44no—
1373C2×C4—48no—
1374C2×C4—44no—
1375C2×C4—44no—
1376C2×C4—84no—
1377C2×C4—82no—
1378C2×C4—82no—
1379C2×C4—88no—
1380C2×C4—164no—
1381C2×C4C22×#4112yes—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4C22×#4112yes—
1385C2×C4C22×#4112yes—
1386C2×C4C22×#4112yes—
1387C2×C4#58512yes—
1388C2×C4#58512yes—
1389C22—22no—
1390C22—22no—
1391C22—24no—
1392C22—22no—
1393C22—24no—
1394C22—24no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—41no—
1402C22—41no—
1403C22—41no—
1404C22—41no—
1405C22—41no—
1406C22—41no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—88no—
1412C22C23×#4111yescharacteristic
1413C22C2×#58511yescharacteristic
1414C22C2×#58511yescharacteristic
1415C22C2×#58512yes—
1416C222−1+612yes—
1417C4—22no—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—42no—
1423C4—41no—
1424C4—41no—
1425C4—44no—
1426C4—42no—
1427C4—41no—
1428C4—41no—
1429C4—44no—
1430C4—42no—
1431C4—41no—
1432C4—41no—
1433C4—42no—
1434C4—44no—
1435C4—44no—
1436C4—44no—
1437C4—42no—
1438C4—42no—
1439C4—44no—
1440C4—42no—
1441C4—44no—
1442C4—44no—
1443C4#349314yes—
1444C2—44no—
1445C2—42no—
1446C2—81no—
1447C2—81no—
1448C2C2×#349311yescharacteristic
1449C2#6281411yescharacteristic
1450C2#6286011yescharacteristic
1451C2#6294012yes—
1452C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2404C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50189C2semidirect
3. #48799C2semidirect
4. #47885C2semidirect
5. #47202C2semidirect
6. #46840C2semidirect
7. #45124C2semidirect
8. #45123C2semidirect
9. #45122C2semidirect
10. #44926C2semidirect
11. #40251C2semidirect
12. #39935C2semidirect
13. #39908C2semidirect
14. #38635C2semidirect
15. #37963C2semidirect
16. #37955C2semidirect
17. #37894C2semidirect
18. #37884C2semidirect
19. #37567C2semidirect
20. #37028C2semidirect
21. #37023C2semidirect
22. #36451C2semidirect
23. #36409C2semidirect
24. #35502C2semidirect
25. #35485C2semidirect
26. #35325C2semidirect
27. #35297C2semidirect
29. #34373C2semidirect
30. #34191C2semidirect
31. #34048C2semidirect
35. #2864C22semidirect
36. #2863C22semidirect
37. #2857C22semidirect
38. #2857C22semidirect
42. #2809C22semidirect
43. #2805C22semidirect
44. #2802C22semidirect
45. #2794C22semidirect
47. #2790C22semidirect
48. #2789C22semidirect
56. #2774C22semidirect
60. #2769C22semidirect
61. #2767C22semidirect
62. #2766C22semidirect
63. #2766C22semidirect
66. #2762C22semidirect
68. #2758C22semidirect
71. #2744C22semidirect
72. #2744C22semidirect
80. #2689C22semidirect
83. #2666C22semidirect
85. #2660C22semidirect
88. #2647C22semidirect
95. #2612C22semidirect
100. #2606C22semidirect
101. #2605C22semidirect
102. #2605C22semidirect
116. #2584C22semidirect
118. #2581C22semidirect
121. #2577C22semidirect
125. #2574C22semidirect
126. #2574C22semidirect
129. #2573C22semidirect
131. #2570C22semidirect
132. #2569C22semidirect
133. #2569C22semidirect
135. #2562C22semidirect
138. #2550C22semidirect
142. #2536C22semidirect
144. #2533C22semidirect
145. #2533C22semidirect
148. #2530C22semidirect
151. #2528C22semidirect
153. #2527C22semidirect
154. #2524C22semidirect
155. #2524C22semidirect
157. #2514C22semidirect
158. #2514C22semidirect
159. #2514C22semidirect
162. #2509C22semidirect
163. #2508C22semidirect
166. #2496C22semidirect
169. #2495C22semidirect
171. #2493C22semidirect
173. #2492C22semidirect
175. #2489C22semidirect
180. #2485C22semidirect
187. #2466C22semidirect
191. #2438C22semidirect
206. #2370C22semidirect
207. #2369C22semidirect
210. #2360C22semidirect
211. #2360C22semidirect
212. #2356C22semidirect
213. #2355C22semidirect
214. #2355C22semidirect
215. #2355C22semidirect
216. #2355C22semidirect
219. Q8×C4⋊C4C22semidirect
220. D4×C4⋊C4C22semidirect
222. #2345C22semidirect
223. #2344C22semidirect
224. #2343C22semidirect
227. #2336C22semidirect
228. #2336C22semidirect
230. #2331C22semidirect
231. #2327C22semidirect
234. #2323C22semidirect
235. #2320C22semidirect
246. C4×#126C22semidirect
253. #2298C22semidirect
260. #2283C22semidirect
261. C2×#382C22semidirect
264. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#501892
#495972
#487992
#478852
#472022
#468402
#451242
#451232
#451222
#449262
#402512
#399352
#399082
#386352
#379632
#379552
#378942
#378842
#375672
#370282
#370232
#364512
#364092
#355022
#354852
#353252
#352972
#348752
#343732
#341912
#340482