Finite Group Databasebeta

← #8701620

Subgroups — #8701620

Order 512.

4359 conjugacy classes of subgroups.

The subgroup lattice has 1439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C212yesmaximal, complemented
2#59376C211yesmaximal, characteristic, complemented
3#59201C211yesmaximal, characteristic, complemented
4#59140C212yesmaximal, complemented
5#59027C212yesmaximal, complemented
6#57113C214yesmaximal, complemented
7#55323C214yesmaximal, complemented
8#55317C214yesmaximal, complemented
9#52293C211yesmaximal, characteristic
10#51214C212yesmaximal, complemented
11#50293C212yesmaximal, complemented
12#49882C214yesmaximal, complemented
13#49868C214yesmaximal, complemented
14#46342C211yesmaximal, characteristic, complemented
15#46011C212yesmaximal, complemented
16#45133C212yesmaximal, complemented
17#44977C212yesmaximal, complemented
18#44919C212yesmaximal, complemented
19#42866C212yesmaximal, complemented
20#42675C212yesmaximal, complemented
21#42669C212yesmaximal, complemented
22#40070C212yesmaximal, complemented
23#39932C212yesmaximal, complemented
24#39594C211yesmaximal, characteristic, complemented
25#39122C211yesmaximal, characteristic, complemented
26#37241C212yesmaximal
27#37073C214yesmaximal, complemented
28#36559C211yesmaximal, characteristic, complemented
29#36491C212yesmaximal, complemented
30C2×#554C2211yescharacteristic
31C2×#554C2211yescharacteristic, complemented
32C2×#552C2212yes—
33C22×#125C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2868C2211yescharacteristic, complemented
36#2866C2214yes—
37#2863C2212yescomplemented
38#2859C2212yescomplemented
39#2855C2211yescharacteristic, complemented
40#2848C2211yescharacteristic
41#2837C2214yes—
42#2831C2214yescomplemented
43#2830C2212yescomplemented
44#2821C2214yes—
45#2814C2214yes—
46#2808C2214yes—
47#2803C2214yes—
48#2797C2212yes—
49#2794C2214yescomplemented
50#2793C2214yes—
51#2793C2214yescomplemented
52#2793C2214yescomplemented
53#2792C2212yescomplemented
54#2791C2214yescomplemented
55#2791C2214yescomplemented
56#2790C2212yes—
57#2786C2214yes—
58#2786C2214yes—
59#2785C2214yes—
60#2779C2214yes—
61#2775C2214yescomplemented
62#2775C2214yescomplemented
63#2774C2214yescomplemented
64#2773C2214yes—
65#2771C2214yes—
66#2770C2214yescomplemented
67#2768C2214yes—
68#2768C2214yes—
69#2768C2214yescomplemented
70#2763C2212yescomplemented
71#2761C2214yes—
72#2757C2214yes—
73#2757C2212yes—
74#2752C2214yes—
75#2749C2212yes—
76#2748C2211yescharacteristic
77#2748C2212yes—
78#2747C2214yescomplemented
79#2747C2214yescomplemented
80#2740C2214yes—
81#2737C2214yescomplemented
82#2736C2212yes—
83#2735C2214yes—
84#2726C2214yescomplemented
85#2725C2214yes—
86#2725C2214yes—
87#2721C2214yes—
88#2720C2214yes—
89#2719C2214yescomplemented
90#2719C2214yescomplemented
91#2719C2214yescomplemented
92#2716C2214yes—
93#2713C2214yescomplemented
94#2711C2214yes—
95#2709C2212yes—
96#2709C2211yescharacteristic
97#2707C2214yes—
98#2704C2214yescomplemented
99#2702C2214yes—
100#2698C2214yes—
101#2697C2212yes—
102#2697C2211yescharacteristic
103#2692C2214yes—
104#2691C2212yes—
105#2690C2214yes—
106#2687C2214yes—
107#2685C2212yes—
108#2685C2214yes—
109#2669C2211yescharacteristic
110#2667C2214yescomplemented
111#2666C2214yescomplemented
112#2654C2214yes—
113#2652C2214yes—
114#2651C2214yes—
115#2649C2214yes—
116#2630C2214yes—
117#2627C2212yescomplemented
118#2626C2212yes—
119#2625C2214yescomplemented
120#2621C2212yescomplemented
121#2607C2212yescomplemented
122#2596C2214yes—
123#2595C2214yes—
124#2595C2214yes—
125#2593C2214yescomplemented
126#2590C2214yescomplemented
127#2590C2214yescomplemented
128#2587C2214yes—
129#2574C2214yes—
130#2572C2214yes—
131#2570C2212yescomplemented
132#2566C2212yes—
133#2566C2212yescomplemented
134#2565C2212yescomplemented
135#2563C2211yescharacteristic
136#2563C2211yescharacteristic, complemented
137#2562C2212yes—
138#2562C2214yes—
139#2562C2214yescomplemented
140#2556C2214yes—
141#2550C2212yescomplemented
142#2542C2212yes—
143#2538C2212yes—
144#2538C2212yescomplemented
145#2536C2212yes—
146#2533C2214yescomplemented
147#2532C2214yescomplemented
148#2530C2214yes—
149#2529C2214yes—
150#2526C2214yes—
151#2525C2214yes—
152#2524C2214yescomplemented
153#2524C2214yescomplemented
154#2523C2212yes—
155#2522C2214yescomplemented
156#2520C2214yescomplemented
157#2519C2214yes—
158#2519C2214yes—
159#2516C2214yescomplemented
160#2516C2214yescomplemented
161#2515C2214yes—
162#2511C2212yescomplemented
163#2508C2214yescomplemented
164#2506C2212yescomplemented
165#2506C2212yescomplemented
166#2503C2211yescharacteristic, complemented
167#2503C2212yescomplemented
168#2502C2212yes—
169#2499C2212yes—
170#2497C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2492C2212yes—
174#2489C2212yes—
175#2489C2212yes—
176#2489C2212yescomplemented
177#2487C2212yes—
178#2486C2211yescharacteristic
179#2486C2212yes—
180#2485C2212yes—
181#2485C2212yes—
182#2485C2214yescomplemented
183#2481C2214yes—
184#2480C2214yes—
185#2477C2214yes—
186#2475C2214yescomplemented
187#2473C2214yes—
188#2467C2214yes—
189#2460C2214yes—
190#2453C2212yescomplemented
191#2452C2214yes—
192#2452C2214yescomplemented
193#2451C2212yescomplemented
194#2446C2212yescomplemented
195#2443C2214yes—
196#2442C2212yes—
197#2442C2214yescomplemented
198#2442C2212yescomplemented
199#2441C2212yes—
200#2439C2212yes—
201#2434C2211yescharacteristic
202#2429C2212yes—
203#2429C2212yescomplemented
204#2423C2212yes—
205#2423C2212yes—
206#2423C2212yescomplemented
207#2418C2214yes—
208#2417C2212yes—
209#2417C2212yes—
210#2417C2212yescomplemented
211#2415C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2415C2212yescomplemented
215#2415C2212yescomplemented
216#2409C2212yes—
217#2409C2211yescharacteristic
218#2395C2212yes—
219#2392C2212yes—
220#2392C2212yes—
221#2381C2214yescomplemented
222#2376C2212yes—
223#2374C2212yes—
224#2374C2212yes—
225#2370C2212yescomplemented
226#2365C2212yescomplemented
227#2362C2212yes—
228#2362C2212yes—
229#2355C2212yescomplemented
230#2354C2212yes—
231#2352C2212yes—
232#2352C2214yes—
233#2352C2214yescomplemented
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2212yescomplemented
236#2347C2212yes—
237#2346C2212yescomplemented
238#2345C2211yescharacteristic
239#2345C2211yescharacteristic, complemented
240Q8×C22⋊C4C2212yes—
241#2334C2214yes—
242#2330C2214yescomplemented
243#2323C2212yescomplemented
244#2322C2212yes—
245#2321C2212yes—
246#2316C2212yescomplemented
247#2314C2212yescomplemented
248C4×#127C2211yescharacteristic
249C4×#127C2212yes—
250C4×#125C2214yescomplemented
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yescomplemented
253C4×#123C2211yescharacteristic
254C4×#121C2212yes—
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257#2280C2212yes—
258C42×Q8C2211yescharacteristic, complemented
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#554—44no—
262#554—44no—
263#552—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×#127C2311yescharacteristic
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125—44no—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#123C2312yes—
282C2×#123C2311yescharacteristic
283C2×#123C2314yes—
284C2×C22⋊Q8—44no—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#120C2311yescharacteristic
300C2×#120C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C22⋊C4C2312yes—
329C22×C42C2311yescharacteristic
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2312yes—
355#399C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2312yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2314yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#393C2312yes—
443#393C2312yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2312yes—
449#392C2312yes—
450#392C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2311yescharacteristic
468#390C2311yescharacteristic
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
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#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
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#388C2312yes—
548#388C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
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#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#386C2312yes—
596#386C2314yes—
597#386C2312yes—
598#386C2314yes—
599#386C2311yescharacteristic
600#386C2312yes—
601#386C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2311yescharacteristic
605#386C2314yes—
606#386C2312yes—
607#386C2312yes—
608#386C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2312yes—
618#385C2312yes—
619#385C2312yes—
620#385C2314yes—
621#385C2312yes—
622#385C2311yescharacteristic
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2312yes—
628#385C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2312yes—
635#384C2314yes—
636#383C2312yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#381C2312yes—
650#381C2314yes—
651#381C2312yes—
652#381C2312yes—
653#381C2311yescharacteristic
654#381C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2311yescharacteristic
672#380C2311yescharacteristic
673#380C2314yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#379C2312yes—
678#379C2311yescharacteristic
679#379C2314yes—
680#379C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714#376C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C25C2411yescharacteristic
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C23×C4—42no—
733C23×C4—44no—
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C4⋊Q8—48no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751#127—24no—
752#126—44no—
753#126—48no—
754#126—48no—
755#125—28no—
756#125—44no—
757#125—48no—
758#125—44no—
759#125—44no—
760#125—48no—
761#125—48no—
762#125—48no—
763#123—28no—
764#123—24no—
765#123—48no—
766C22⋊Q8—28no—
767C22⋊Q8—48no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—42no—
778C22⋊Q8—42no—
779#121—44no—
780#120—24no—
781#120—44no—
782C4×Q8—24no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×D4—48no—
787C4×D4—48no—
788C4×D4—44no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—42no—
796C4×D4—42no—
797#117—44no—
798#117—44no—
799#117—44no—
800#117—44no—
801#117—48no—
802C2×C4⋊C4—24no—
803C2×C4⋊C4—24no—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—44no—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C22⋊C4—44no—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2411yescharacteristic
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C42—42no—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2414yes—
948C2×C42C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24—22no—
1015C24—41no—
1016C24—41no—
1017C24—42no—
1018C24—42no—
1019C24C2512yes—
1020C24C2512yes—
1021C24C2511yescharacteristic
1022C24C2511yescharacteristic
1023C2×Q8—22no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—42no—
1029C2×Q8—44no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—88no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—41no—
1042C2×D4—41no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D42−1+414yes—
1056C22×C4—24no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—24no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—41no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—41no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—88no—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—22no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
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⋊C4H(5,𝔽2)14yes—
1178C22⋊C4—22no—
1179C22⋊C4—24no—
1180C22⋊C4—22no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—41no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—41no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—41no—
1215C22⋊C4—42no—
1216C22⋊C4—41no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C42—24no—
1231C42—24no—
1232C42—22no—
1233C42—22no—
1234C42—24no—
1235C42—24no—
1236C42—24no—
1237C42—28no—
1238C42—24no—
1239C42—42no—
1240C42—42no—
1241C42—41no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C23—21no—
1253C23—21no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—21no—
1259C23—21no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—44no—
1275C23—84no—
1276C23—82no—
1277C23—82no—
1278C23—84no—
1279C23C2×2−1+412yes—
1280C23C2×2−1+412yes—
1281C23C2611yescharacteristic
1282Q8—44no—
1283Q8—48no—
1284Q8—84no—
1285Q8—162no—
1286Q8—162no—
1287D4—44no—
1288D4—48no—
1289D4—48no—
1290D4—44no—
1291D4—84no—
1292D4—84no—
1293D4—84no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—44no—
1357C2×C4—48no—
1358C2×C4—48no—
1359C2×C4—44no—
1360C2×C4—84no—
1361C2×C4—84no—
1362C2×C4—88no—
1363C2×C4—82no—
1364C2×C4—84no—
1365C2×C4—82no—
1366C2×C4—82no—
1367C2×C4—84no—
1368C2×C4—84no—
1369C2×C4C2×H(5,𝔽2)14yes—
1370C2×C4C2×H(5,𝔽2)12yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4#58514yes—
1373C2×C4#58514yes—
1374C22—24no—
1375C22—24no—
1376C22—22no—
1377C22—22no—
1378C22—41no—
1379C22—41no—
1380C22—41no—
1381C22—41no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—88no—
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C22×2−1+411yescharacteristic
1401C22C2×#58512yes—
1402C22C2×#58512yes—
1403C222−1+611yescharacteristic
1404C4—24no—
1405C4—24no—
1406C4—22no—
1407C4—41no—
1408C4—42no—
1409C4—42no—
1410C4—41no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—41no—
1418C4—42no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—42no—
1424C4—44no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4#355114yes—
1429C2—42no—
1430C2—42no—
1431C2—82no—
1432C2—82no—
1433C2C2×#355111yescharacteristic
1434C2#6289311yescharacteristic
1435C2#6293912yes—
1436C2#6302111yescharacteristic
1437C2#6302312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2669C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59865C2semidirect
2. #59376C2semidirect
3. #59201C2semidirect
4. #59140C2semidirect
5. #59027C2semidirect
6. #57113C2semidirect
7. #55323C2semidirect
8. #55317C2semidirect
10. #51214C2semidirect
11. #50293C2semidirect
12. #49882C2semidirect
13. #49868C2semidirect
14. #46342C2semidirect
15. #46011C2semidirect
16. #45133C2semidirect
17. #44977C2semidirect
18. #44919C2semidirect
19. #42866C2semidirect
20. #42675C2semidirect
21. #42669C2semidirect
22. #40070C2semidirect
23. #39932C2semidirect
24. #39594C2semidirect
25. #39122C2semidirect
27. #37073C2semidirect
28. #36559C2semidirect
29. #36491C2semidirect
31. C2×#554C22semidirect
33. C22×#125C22semidirect
35. #2868C22semidirect
37. #2863C22semidirect
38. #2859C22semidirect
39. #2855C22semidirect
42. #2831C22semidirect
43. #2830C22semidirect
49. #2794C22semidirect
51. #2793C22semidirect
52. #2793C22semidirect
53. #2792C22semidirect
54. #2791C22semidirect
55. #2791C22semidirect
61. #2775C22semidirect
62. #2775C22semidirect
63. #2774C22semidirect
66. #2770C22semidirect
69. #2768C22semidirect
70. #2763C22semidirect
78. #2747C22semidirect
79. #2747C22semidirect
81. #2737C22semidirect
84. #2726C22semidirect
89. #2719C22semidirect
90. #2719C22semidirect
91. #2719C22semidirect
93. #2713C22semidirect
98. #2704C22semidirect
110. #2667C22semidirect
111. #2666C22semidirect
117. #2627C22semidirect
119. #2625C22semidirect
120. #2621C22semidirect
121. #2607C22semidirect
125. #2593C22semidirect
126. #2590C22semidirect
127. #2590C22semidirect
131. #2570C22semidirect
133. #2566C22semidirect
134. #2565C22semidirect
136. #2563C22semidirect
139. #2562C22semidirect
141. #2550C22semidirect
144. #2538C22semidirect
146. #2533C22semidirect
147. #2532C22semidirect
152. #2524C22semidirect
153. #2524C22semidirect
155. #2522C22semidirect
156. #2520C22semidirect
159. #2516C22semidirect
160. #2516C22semidirect
162. #2511C22semidirect
163. #2508C22semidirect
164. #2506C22semidirect
165. #2506C22semidirect
166. #2503C22semidirect
167. #2503C22semidirect
176. #2489C22semidirect
182. #2485C22semidirect
186. #2475C22semidirect
190. #2453C22semidirect
192. #2452C22semidirect
193. #2451C22semidirect
194. #2446C22semidirect
197. #2442C22semidirect
198. #2442C22semidirect
203. #2429C22semidirect
206. #2423C22semidirect
210. #2417C22semidirect
214. #2415C22semidirect
215. #2415C22semidirect
221. #2381C22semidirect
225. #2370C22semidirect
226. #2365C22semidirect
229. #2355C22semidirect
233. #2352C22semidirect
235. D4×C4⋊C4C22semidirect
237. #2346C22semidirect
239. #2345C22semidirect
242. #2330C22semidirect
243. #2323C22semidirect
246. #2316C22semidirect
247. #2314C22semidirect
250. C4×#125C22semidirect
252. C4×C22⋊Q8C22semidirect
258. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598652
#593762
#592012
#591402
#590272
#571132
#553232
#553172
#522932
#512142
#502932
#498822
#498682
#463422
#460112
#451332
#449772
#449192
#428662
#426752
#426692
#400702
#399322
#395942
#391222
#372412
#370732
#365592
#364912