Finite Group Databasebeta

← #8757400

Subgroups — #8757400

Order 512.

4341 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58988C212yesmaximal, complemented
2#58943C212yesmaximal, complemented
3#58267C212yesmaximal, complemented
4#56713C212yesmaximal, complemented
5#56152C214yesmaximal, complemented
6#54558C214yesmaximal, complemented
7#54214C214yesmaximal, complemented
8#53448C214yesmaximal, complemented
9#51860C212yesmaximal, complemented
10#51605C212yesmaximal, complemented
11#50329C212yesmaximal, complemented
12#50255C212yesmaximal, complemented
13#49660C212yesmaximal, complemented
14#48839C212yesmaximal, complemented
15#47806C212yesmaximal, complemented
16#47752C212yesmaximal, complemented
17#47599C214yesmaximal, complemented
18#47411C214yesmaximal, complemented
19#46233C212yesmaximal, complemented
20#46227C212yesmaximal, complemented
21#46142C212yesmaximal, complemented
22#46140C212yesmaximal, complemented
23#46136C212yesmaximal, complemented
24#45979C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic, complemented
26#35200C211yesmaximal, characteristic, complemented
27#35129C211yesmaximal, characteristic
28C2×#563C2212yes—
29C2×#533C2211yescharacteristic, complemented
30C22×#125C2211yescharacteristic, complemented
31C22×#124C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yescomplemented
36#2851C2212yescomplemented
37#2850C2212yes—
38#2850C2212yes—
39#2845C2212yescomplemented
40#2844C2212yescomplemented
41#2838C2214yescomplemented
42#2836C2214yescomplemented
43#2836C2214yescomplemented
44#2830C2214yescomplemented
45#2829C2214yes—
46#2823C2212yes—
47#2822C2212yescomplemented
48#2821C2214yescomplemented
49#2820C2212yes—
50#2820C2212yes—
51#2806C2214yescomplemented
52#2793C2214yescomplemented
53#2792C2212yescomplemented
54#2790C2214yes—
55#2790C2214yescomplemented
56#2789C2212yescomplemented
57#2787C2214yes—
58#2786C2214yescomplemented
59#2785C2212yes—
60#2784C2214yescomplemented
61#2778C2214yes—
62#2777C2214yescomplemented
63#2775C2214yescomplemented
64#2770C2214yescomplemented
65#2769C2214yescomplemented
66#2768C2214yes—
67#2768C2214yescomplemented
68#2768C2214yescomplemented
69#2766C2214yescomplemented
70#2763C2214yescomplemented
71#2757C2214yescomplemented
72#2757C2214yescomplemented
73#2756C2214yescomplemented
74#2754C2214yescomplemented
75#2754C2214yescomplemented
76#2748C2212yes—
77#2748C2214yescomplemented
78#2747C2214yescomplemented
79#2744C2214yes—
80#2741C2214yescomplemented
81#2738C2214yes—
82#2735C2214yes—
83#2735C2214yes—
84#2731C2214yes—
85#2729C2214yes—
86#2729C2214yescomplemented
87#2725C2214yescomplemented
88#2723C2214yes—
89#2721C2214yescomplemented
90#2721C2214yescomplemented
91#2720C2214yescomplemented
92#2720C2214yescomplemented
93#2718C2214yes—
94#2717C2214yes—
95#2716C2214yescomplemented
96#2716C2214yescomplemented
97#2716C2214yescomplemented
98#2715C2214yes—
99#2715C2214yes—
100#2713C2214yescomplemented
101#2707C2214yes—
102#2706C2214yes—
103#2704C2214yescomplemented
104#2702C2214yescomplemented
105#2701C2214yes—
106#2696C2214yescomplemented
107#2695C2214yescomplemented
108#2694C2214yescomplemented
109#2692C2214yescomplemented
110#2691C2214yes—
111#2690C2214yescomplemented
112#2689C2214yescomplemented
113#2685C2214yes—
114#2684C2212yes—
115#2684C2212yes—
116#2683C2212yes—
117#2681C2214yes—
118#2680C2212yes—
119#2677C2214yescomplemented
120#2677C2214yescomplemented
121#2674C2214yes—
122#2674C2214yes—
123#2660C2214yescomplemented
124#2653C2214yes—
125#2652C2214yes—
126#2648C2214yescomplemented
127#2638C2212yes—
128#2638C2212yescomplemented
129#2636C2214yescomplemented
130#2632C2212yes—
131#2631C2212yes—
132#2629C2212yes—
133#2629C2212yescomplemented
134#2626C2214yes—
135#2612C2214yescomplemented
136#2610C2212yes—
137#2610C2212yes—
138#2609C2212yes—
139#2609C2214yescomplemented
140#2606C2214yescomplemented
141#2602C2214yes—
142#2601C2214yescomplemented
143#2599C2212yes—
144#2599C2212yescomplemented
145#2597C2214yes—
146#2595C2214yescomplemented
147#2592C2212yes—
148#2587C2214yescomplemented
149#2585C2214yescomplemented
150#2579C2212yes—
151#2579C2212yes—
152#2579C2212yescomplemented
153#2579C2212yescomplemented
154#2577C2214yes—
155#2577C2214yescomplemented
156#2574C2214yescomplemented
157#2574C2214yescomplemented
158#2567C2211yescharacteristic, complemented
159#2566C2212yes—
160#2566C2212yes—
161#2565C2212yescomplemented
162#2565C2212yescomplemented
163#2563C2211yescharacteristic
164#2556C2214yes—
165#2553C2214yescomplemented
166#2551C2212yescomplemented
167#2547C2211yescharacteristic
168#2546C2211yescharacteristic, complemented
169#2540C2212yes—
170#2532C2214yescomplemented
171#2532C2214yescomplemented
172#2531C2214yes—
173#2531C2214yescomplemented
174#2529C2214yescomplemented
175#2528C2214yescomplemented
176#2524C2214yescomplemented
177#2522C2214yes—
178#2520C2214yescomplemented
179#2519C2214yescomplemented
180#2512C2214yescomplemented
181#2499C2212yescomplemented
182#2485C2212yes—
183#2485C2212yescomplemented
184#2482C2212yes—
185#2481C2214yescomplemented
186#2481C2214yescomplemented
187#2480C2214yes—
188#2480C2214yes—
189#2480C2214yes—
190#2479C2214yes—
191#2479C2214yescomplemented
192#2478C2214yescomplemented
193#2477C2214yescomplemented
194#2469C2214yescomplemented
195#2458C2214yes—
196#2452C2214yescomplemented
197#2451C2214yescomplemented
198#2449C2214yescomplemented
199#2443C2214yes—
200#2440C2214yescomplemented
201#2439C2214yescomplemented
202#2437C2214yes—
203#2437C2214yes—
204#2434C2214yes—
205#2432C2212yes—
206#2429C2214yescomplemented
207#2417C2214yescomplemented
208#2411C2214yes—
209#2409C2211yescharacteristic
210#2409C2211yescharacteristic
211#2408C2211yescharacteristic
212#2408C2211yescharacteristic
213#2405C2214yes—
214#2404C2212yes—
215#2382C2212yescomplemented
216#2382C2212yescomplemented
217#2379C2212yes—
218#2379C2212yes—
219#2375C2212yes—
220#2372C2212yes—
221#2358C2212yes—
222#2334C2214yescomplemented
223#2327C2212yescomplemented
224#2326C2212yes—
225#2321C2212yes—
226#2321C2212yes—
227#2317C2211yescharacteristic, complemented
228#2317C2211yescharacteristic, complemented
229#2314C2214yescomplemented
230#2311C2211yescharacteristic
231#2311C2211yescharacteristic
232#2285C2211yescharacteristic, complemented
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic, complemented
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×D4C2311yescharacteristic
238#563—48no—
239#533—44no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125—44no—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#124—44no—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#120C2312yes—
279C2×#120C2312yes—
280C4×#41—44no—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2314yes—
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2312yes—
377#397C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2312yes—
400#395C2314yes—
401#395C2312yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#395C2314yes—
407#395C2312yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#393C2312yes—
424#393C2312yes—
425#393C2314yes—
426#393C2314yes—
427#393C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#392C2312yes—
435#392C2312yes—
436#392C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#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#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
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#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2312yes—
561#386C2314yes—
562#386C2314yes—
563#386C2312yes—
564#386C2312yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2312yes—
579#385C2312yes—
580#385C2312yes—
581#385C2312yes—
582#385C2314yes—
583#385C2312yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2312yes—
602#384C2312yes—
603#384C2312yes—
604#384C2312yes—
605#384C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2312yes—
609#383C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#381C2312yes—
621#381C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2311yescharacteristic
637#380C2311yescharacteristic
638#380C2314yes—
639#380C2312yes—
640#379C2312yes—
641#379C2312yes—
642#379C2314yes—
643#379C2314yes—
644#379C2314yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660#376C2312yes—
661#376C2312yes—
662#376C2314yes—
663C25C2412yes—
664C2×#41—24no—
665C2×#41—42no—
666C2×#41—42no—
667C22×Q8—42no—
668C22×Q8—82no—
669C22×Q8C2411yescharacteristic
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2414yes—
674C22×Q8C2412yes—
675C22×D4—42no—
676C22×D4—82no—
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2414yes—
680C22×D4C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C4⋊Q8—42no—
699C4⋊Q8—42no—
700C4⋊Q8—44no—
701C4⋊Q8—48no—
702C4⋊Q8—84no—
703C4⋊Q8—84no—
704#126—48no—
705#126—48no—
706#126—48no—
707#126—84no—
708#126—84no—
709#125—28no—
710#125—28no—
711#125—44no—
712#125—44no—
713#125—44no—
714#125—84no—
715#124—28no—
716#124—28no—
717#124—44no—
718#124—44no—
719#124—44no—
720#123—48no—
721#123—84no—
722#123—84no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—44no—
726C22⋊Q8—44no—
727C22⋊Q8—84no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C22⋊Q8—82no—
731C22⋊Q8—82no—
732#121—82no—
733#121—82no—
734#120—28no—
735#120—44no—
736C4×Q8—42no—
737C4×Q8—42no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×D4—42no—
741C4×D4—42no—
742C4×D4—42no—
743C4×D4—42no—
744C4×D4—42no—
745C4×D4—42no—
746C4×D4—84no—
747#117—42no—
748#117—42no—
749#117—42no—
750#117—42no—
751#117—42no—
752#117—48no—
753#117—44no—
754C2×C4⋊C4—42no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—42no—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C22⋊C4—44no—
816C2×C22⋊C4—44no—
817C2×C22⋊C4—84no—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C42—24no—
865C2×C42—24no—
866C2×C42—24no—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2411yescharacteristic
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24—24no—
944C24—42no—
945C24—44no—
946C24—44no—
947C24—42no—
948C24C2514yes—
949C24C2511yescharacteristic
950C24C2511yescharacteristic
951C24C2511yescharacteristic
952#41—416no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—22no—
957C2×Q8—41no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—44no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—88no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—28no—
973C2×D4—24no—
974C2×D4—22no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—41no—
979C2×D4—41no—
980C2×D4—44no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—88no—
990C2×D42−1+414yes—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2514yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C22⋊C4—24no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—42no—
1125C22⋊C4—44no—
1126C22⋊C4—42no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—42no—
1171C42H(5,𝔽2)14yes—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—24no—
1181C23—21no—
1182C23—24no—
1183C23—21no—
1184C23—24no—
1185C23—21no—
1186C23—22no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—22no—
1191C23—24no—
1192C23—88no—
1193C23—84no—
1194C23—84no—
1195C23—84no—
1196C23—164no—
1197C23C2×2−1+412yes—
1198C23C2×2−1+412yes—
1199C23C2611yescharacteristic
1200Q8—44no—
1201Q8—84no—
1202Q8—84no—
1203Q8—84no—
1204Q8—84no—
1205Q8—164no—
1206D4—44no—
1207D4—44no—
1208D4—44no—
1209D4—84no—
1210D4—88no—
1211D4—84no—
1212D4—164no—
1213C2×C4—28no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—21no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—82no—
1275C2×C4—82no—
1276C2×C4—82no—
1277C2×C4—82no—
1278C2×C4—88no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—164no—
1283C2×C4C2×H(5,𝔽2)12yes—
1284C2×C4C2×H(5,𝔽2)12yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×2−1+412yes—
1287C2×C4#58512yes—
1288C22—24no—
1289C22—24no—
1290C22—22no—
1291C22—22no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—44no—
1299C22—42no—
1300C22—44no—
1301C22—44no—
1302C22—42no—
1303C22—44no—
1304C22—41no—
1305C22—44no—
1306C22—41no—
1307C22—44no—
1308C22—41no—
1309C22—44no—
1310C22—168no—
1311C22C22×H(5,𝔽2)11yescharacteristic
1312C22C22×2−1+411yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22H(7,𝔽2)12yes—
1315C222−1+612yes—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—44no—
1327C4—41no—
1328C4—44no—
1329C4—41no—
1330C4—41no—
1331C4—44no—
1332C4—41no—
1333C4—44no—
1334C4—44no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—44no—
1339C2—42no—
1340C2—42no—
1341C2—81no—
1342C2—84no—
1343C2#6281911yescharacteristic
1344C2#6287411yescharacteristic
1345C2#6288611yescharacteristic
1346C2#6305812yes—
1347C2#6306512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35129C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58988C2semidirect
2. #58943C2semidirect
3. #58267C2semidirect
4. #56713C2semidirect
5. #56152C2semidirect
6. #54558C2semidirect
7. #54214C2semidirect
8. #53448C2semidirect
9. #51860C2semidirect
10. #51605C2semidirect
11. #50329C2semidirect
12. #50255C2semidirect
13. #49660C2semidirect
14. #48839C2semidirect
15. #47806C2semidirect
16. #47752C2semidirect
17. #47599C2semidirect
18. #47411C2semidirect
19. #46233C2semidirect
20. #46227C2semidirect
21. #46142C2semidirect
22. #46140C2semidirect
23. #46136C2semidirect
24. #45979C2semidirect
25. #35333C2semidirect
26. #35200C2semidirect
29. C2×#533C22semidirect
30. C22×#125C22semidirect
35. #2851C22semidirect
36. #2851C22semidirect
39. #2845C22semidirect
40. #2844C22semidirect
41. #2838C22semidirect
42. #2836C22semidirect
43. #2836C22semidirect
44. #2830C22semidirect
47. #2822C22semidirect
48. #2821C22semidirect
51. #2806C22semidirect
52. #2793C22semidirect
53. #2792C22semidirect
55. #2790C22semidirect
56. #2789C22semidirect
58. #2786C22semidirect
60. #2784C22semidirect
62. #2777C22semidirect
63. #2775C22semidirect
64. #2770C22semidirect
65. #2769C22semidirect
67. #2768C22semidirect
68. #2768C22semidirect
69. #2766C22semidirect
70. #2763C22semidirect
71. #2757C22semidirect
72. #2757C22semidirect
73. #2756C22semidirect
74. #2754C22semidirect
75. #2754C22semidirect
77. #2748C22semidirect
78. #2747C22semidirect
80. #2741C22semidirect
86. #2729C22semidirect
87. #2725C22semidirect
89. #2721C22semidirect
90. #2721C22semidirect
91. #2720C22semidirect
92. #2720C22semidirect
95. #2716C22semidirect
96. #2716C22semidirect
97. #2716C22semidirect
100. #2713C22semidirect
103. #2704C22semidirect
104. #2702C22semidirect
106. #2696C22semidirect
107. #2695C22semidirect
108. #2694C22semidirect
109. #2692C22semidirect
111. #2690C22semidirect
112. #2689C22semidirect
119. #2677C22semidirect
120. #2677C22semidirect
123. #2660C22semidirect
126. #2648C22semidirect
128. #2638C22semidirect
129. #2636C22semidirect
133. #2629C22semidirect
135. #2612C22semidirect
139. #2609C22semidirect
140. #2606C22semidirect
142. #2601C22semidirect
144. #2599C22semidirect
146. #2595C22semidirect
148. #2587C22semidirect
149. #2585C22semidirect
152. #2579C22semidirect
153. #2579C22semidirect
155. #2577C22semidirect
156. #2574C22semidirect
157. #2574C22semidirect
158. #2567C22semidirect
161. #2565C22semidirect
162. #2565C22semidirect
165. #2553C22semidirect
166. #2551C22semidirect
168. #2546C22semidirect
170. #2532C22semidirect
171. #2532C22semidirect
173. #2531C22semidirect
174. #2529C22semidirect
175. #2528C22semidirect
176. #2524C22semidirect
178. #2520C22semidirect
179. #2519C22semidirect
180. #2512C22semidirect
181. #2499C22semidirect
183. #2485C22semidirect
185. #2481C22semidirect
186. #2481C22semidirect
191. #2479C22semidirect
192. #2478C22semidirect
193. #2477C22semidirect
194. #2469C22semidirect
196. #2452C22semidirect
197. #2451C22semidirect
198. #2449C22semidirect
200. #2440C22semidirect
201. #2439C22semidirect
206. #2429C22semidirect
207. #2417C22semidirect
215. #2382C22semidirect
216. #2382C22semidirect
222. #2334C22semidirect
223. #2327C22semidirect
227. #2317C22semidirect
228. #2317C22semidirect
229. #2314C22semidirect
232. #2285C22semidirect
234. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589882
#589432
#582672
#567132
#561522
#545582
#542142
#534482
#518602
#516052
#503292
#502552
#496602
#488392
#478062
#477522
#475992
#474112
#462332
#462272
#461422
#461402
#461362
#459792
#353332
#352002
#351292