Finite Group Databasebeta

← #9058481

Subgroups — #9058481

Order 512.

4514 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59596C211yesmaximal, characteristic, complemented
2#59591C213yesmaximal, complemented
3#58918C211yesmaximal, characteristic, complemented
4#58460C211yesmaximal, characteristic, complemented
5#54221C213yesmaximal, complemented
6#54159C213yesmaximal, complemented
7#47852C213yesmaximal, complemented
8#47849C213yesmaximal, complemented
9#47613C213yesmaximal, complemented
10#47578C213yesmaximal, complemented
11#46888C213yesmaximal, complemented
12#46684C213yesmaximal, complemented
13#45292C213yesmaximal, complemented
14#45232C213yesmaximal, complemented
15#44793C213yesmaximal, complemented
16#44733C213yesmaximal, complemented
17#44316C213yesmaximal, complemented
18#43687C213yesmaximal, complemented
19#43471C213yesmaximal, complemented
20#43062C213yesmaximal, complemented
21#35780C213yesmaximal, complemented
22#35706C213yesmaximal, complemented
23#35467C213yesmaximal, complemented
24C2×H(3,𝔽4)C2211yescharacteristic
25C2×#560C2211yescharacteristic, complemented
26C2×#538C2213yes—
27C22×#126C2211yescharacteristic, complemented
28#2838C2213yescomplemented
29#2833C2213yescomplemented
30#2827C2213yescomplemented
31#2824C2213yescomplemented
32#2803C2213yescomplemented
33#2802C2213yescomplemented
34#2801C2213yescomplemented
35#2798C2213yescomplemented
36#2798C2213yescomplemented
37#2798C2213yescomplemented
38#2796C2213yescomplemented
39#2793C2213yescomplemented
40#2793C2213yescomplemented
41#2793C2213yescomplemented
42#2788C2213yescomplemented
43#2787C2213yescomplemented
44#2780C2213yescomplemented
45#2779C2213yescomplemented
46#2775C2213yescomplemented
47#2774C2213yescomplemented
48#2765C2213yescomplemented
49#2763C2213yescomplemented
50#2763C2213yescomplemented
51#2759C2213yescomplemented
52#2759C2213yescomplemented
53#2759C2213yescomplemented
54#2758C2213yescomplemented
55#2758C2213yescomplemented
56#2753C2213yescomplemented
57#2752C2213yescomplemented
58#2743C2213yescomplemented
59#2742C2213yescomplemented
60#2738C2213yescomplemented
61#2738C2213yescomplemented
62#2736C2211yescharacteristic, complemented
63#2735C2213yescomplemented
64#2720C2213yescomplemented
65#2718C2213yescomplemented
66#2717C2213yes—
67#2717C2213yescomplemented
68#2715C2213yes—
69#2715C2213yes—
70#2715C2213yes—
71#2712C2213yes—
72#2710C2213yescomplemented
73#2708C2213yescomplemented
74#2707C2213yescomplemented
75#2700C2213yes—
76#2698C2213yescomplemented
77#2695C2213yescomplemented
78#2693C2213yes—
79#2691C2213yescomplemented
80#2688C2213yes—
81#2686C2213yes—
82#2686C2213yes—
83#2684C2213yes—
84#2682C2213yes—
85#2678C2213yes—
86#2674C2213yes—
87#2674C2213yescomplemented
88#2673C2213yes—
89#2672C2213yes—
90#2672C2213yescomplemented
91#2671C2213yes—
92#2670C2213yescomplemented
93#2668C2213yes—
94#2653C2213yes—
95#2653C2213yescomplemented
96#2652C2213yescomplemented
97#2648C2213yes—
98#2617C2213yes—
99#2617C2213yes—
100#2612C2213yescomplemented
101#2610C2213yescomplemented
102#2597C2213yescomplemented
103#2594C2213yescomplemented
104#2591C2213yes—
105#2591C2213yes—
106#2589C2213yescomplemented
107#2589C2213yescomplemented
108#2588C2213yescomplemented
109#2588C2213yescomplemented
110#2583C2213yescomplemented
111#2577C2213yescomplemented
112#2576C2213yescomplemented
113#2576C2213yescomplemented
114#2573C2213yescomplemented
115#2572C2213yes—
116#2572C2213yescomplemented
117#2572C2213yescomplemented
118#2569C2213yescomplemented
119#2567C2213yescomplemented
120#2560C2213yescomplemented
121#2559C2213yes—
122#2559C2213yes—
123#2559C2213yes—
124#2559C2213yes—
125#2558C2213yescomplemented
126#2557C2213yes—
127#2557C2213yes—
128#2557C2213yes—
129#2557C2213yescomplemented
130#2555C2213yes—
131#2554C2213yes—
132#2553C2213yes—
133#2553C2213yes—
134#2553C2213yescomplemented
135#2553C2213yescomplemented
136#2553C2213yescomplemented
137#2547C2213yes—
138#2544C2213yescomplemented
139#2535C2213yes—
140#2534C2213yes—
141#2529C2213yescomplemented
142#2529C2213yescomplemented
143#2527C2213yescomplemented
144#2527C2213yescomplemented
145#2526C2213yes—
146#2526C2213yescomplemented
147#2523C2213yescomplemented
148#2523C2213yescomplemented
149#2521C2213yes—
150#2521C2213yes—
151#2521C2213yes—
152#2521C2213yes—
153#2521C2213yescomplemented
154#2521C2213yescomplemented
155#2518C2213yes—
156#2518C2213yescomplemented
157#2518C2213yescomplemented
158#2515C2213yescomplemented
159#2510C2213yes—
160#2510C2213yes—
161#2510C2213yescomplemented
162#2503C2213yescomplemented
163#2501C2213yes—
164#2497C2213yescomplemented
165#2496C2213yescomplemented
166#2496C2213yescomplemented
167#2496C2213yescomplemented
168#2496C2213yescomplemented
169#2496C2213yescomplemented
170#2495C2213yescomplemented
171#2493C2213yescomplemented
172#2491C2213yes—
173#2481C2213yescomplemented
174#2470C2213yes—
175#2468C2213yes—
176#2467C2213yescomplemented
177#2466C2213yescomplemented
178#2461C2213yes—
179#2460C2213yes—
180#2459C2213yes—
181#2459C2213yes—
182#2459C2213yes—
183#2459C2213yescomplemented
184#2458C2213yes—
185#2458C2213yescomplemented
186#2457C2213yes—
187#2456C2213yes—
188#2451C2213yescomplemented
189#2448C2213yescomplemented
190#2448C2213yescomplemented
191#2447C2213yes—
192#2444C2213yescomplemented
193#2442C2213yescomplemented
194#2441C2213yescomplemented
195#2436C2213yes—
196#2427C2213yes—
197#2425C2213yes—
198#2425C2213yescomplemented
199#2424C2213yes—
200#2422C2213yes—
201#2422C2213yescomplemented
202#2418C2213yes—
203#2418C2213yescomplemented
204#2412C2213yes—
205#2412C2213yes—
206#2412C2213yescomplemented
207#2412C2213yescomplemented
208#2401C2213yescomplemented
209#2398C2213yes—
210#2398C2213yescomplemented
211#2392C2213yes—
212C2×#396C2211yescharacteristic, complemented
213C2×#393C2211yescharacteristic, complemented
214#2374C2213yescomplemented
215#2373C2213yescomplemented
216#2368C2213yescomplemented
217#2367C2213yescomplemented
218#2364C2213yes—
219#2361C2213yes—
220#2358C2213yes—
221#2358C2213yescomplemented
222#2355C2213yescomplemented
223#2353C2213yes—
224#2353C2213yescomplemented
225#2353C2213yescomplemented
226#2353C2213yescomplemented
227#2352C2213yes—
228#2347C2213yescomplemented
229#2345C2213yescomplemented
230#2342C2213yescomplemented
231Q8×C22⋊C4C2213yescomplemented
232#2337C2213yescomplemented
233#2335C2213yescomplemented
234#2331C2213yescomplemented
235#2330C2213yescomplemented
236#2326C2213yescomplemented
237#2322C2213yes—
238#2322C2213yescomplemented
239#2321C2213yescomplemented
240#2320C2213yescomplemented
241#2318C2213yescomplemented
242C4×#123C2213yes—
243C4×#123C2213yescomplemented
244#2273C2213yescomplemented
245C23×Q8C2311yescharacteristic
246H(3,𝔽4)—44no—
247#560—44no—
248#538—412no—
249C2×C4⋊Q8C2313yes—
250C2×#127C2311yescharacteristic
251C2×#126—44no—
252C2×#126C2313yes—
253C2×#126C2311yescharacteristic
254C2×#126C2313yes—
255C2×#126C2313yes—
256C2×#126C2311yescharacteristic
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2311yescharacteristic
260C2×#126C2311yescharacteristic
261C2×#125C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#123C2313yes—
271C2×#123C2313yes—
272C2×#123C2313yes—
273C2×#123C2313yes—
274C2×#123C2313yes—
275C2×#123C2313yes—
276C2×#123C2313yes—
277C2×#123C2313yes—
278C2×#123C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#120C2313yes—
289C2×#120C2313yes—
290C2×#120C2313yes—
291C2×#120C2311yescharacteristic
292C2×#120C2311yescharacteristic
293C2×#120C2311yescharacteristic
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×#117C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C4⋊C4C2313yes—
307C22×C22⋊C4C2313yes—
308C22×C22⋊C4C2313yes—
309C22×C22⋊C4C2313yes—
310C22×C22⋊C4C2313yes—
311C22×C42C2311yescharacteristic
312#401C2313yes—
313#401C2313yes—
314#401C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#399C2313yes—
336#399C2313yes—
337#399C2313yes—
338#399C2313yes—
339#399C2313yes—
340#399C2313yes—
341#399C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2311yescharacteristic
389#396C2311yescharacteristic
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#395C2313yes—
395#395C2313yes—
396#395C2313yes—
397#395C2313yes—
398#395C2313yes—
399#395C2313yes—
400#395C2313yes—
401#395C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#393C2313yes—
430#393C2313yes—
431#393C2313yes—
432#393C2311yescharacteristic
433#393C2313yes—
434#393C2313yes—
435#393C2313yes—
436#393C2311yescharacteristic
437#393C2313yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2313yes—
446#392C2313yes—
447#392C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2313yes—
564#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2313yes—
571#387C2313yes—
572#387C2313yes—
573#387C2313yes—
574#387C2313yes—
575#387C2313yes—
576#387C2313yes—
577#387C2313yes—
578#387C2313yes—
579#387C2313yes—
580#387C2313yes—
581#387C2313yes—
582#387C2313yes—
583#387C2313yes—
584#386C2313yes—
585#386C2313yes—
586#386C2313yes—
587#386C2313yes—
588#386C2313yes—
589#386C2313yes—
590#386C2313yes—
591#386C2313yes—
592#386C2313yes—
593#386C2313yes—
594#386C2313yes—
595#386C2313yes—
596#386C2313yes—
597#386C2313yes—
598#386C2313yes—
599#386C2313yes—
600#386C2313yes—
601#386C2313yes—
602#386C2313yes—
603#386C2313yes—
604#386C2313yes—
605#386C2313yes—
606#386C2313yes—
607#386C2313yes—
608#386C2313yes—
609#386C2313yes—
610#386C2313yes—
611#386C2313yes—
612#386C2313yes—
613#386C2313yes—
614#386C2313yes—
615#386C2313yes—
616#386C2313yes—
617#385C2313yes—
618#385C2313yes—
619#385C2313yes—
620#385C2313yes—
621#385C2313yes—
622#385C2313yes—
623#385C2313yes—
624#385C2313yes—
625#385C2313yes—
626#385C2313yes—
627#385C2313yes—
628#385C2313yes—
629#385C2313yes—
630#385C2313yes—
631#385C2313yes—
632#385C2313yes—
633#385C2313yes—
634#385C2313yes—
635#385C2313yes—
636#385C2313yes—
637#385C2313yes—
638#385C2313yes—
639#385C2313yes—
640#384C2313yes—
641#384C2313yes—
642#384C2313yes—
643#383C2313yes—
644#383C2313yes—
645#383C2313yes—
646#383C2313yes—
647#383C2313yes—
648#383C2313yes—
649#382C2313yes—
650#382C2313yes—
651#382C2313yes—
652#382C2313yes—
653#382C2313yes—
654#381C2313yes—
655#381C2313yes—
656#381C2313yes—
657#381C2313yes—
658#381C2313yes—
659#381C2313yes—
660#381C2313yes—
661#381C2313yes—
662#380C2313yes—
663#380C2313yes—
664#380C2313yes—
665#380C2313yes—
666#380C2313yes—
667#380C2313yes—
668#380C2313yes—
669#380C2313yes—
670#380C2313yes—
671#380C2313yes—
672#380C2313yes—
673#380C2313yes—
674#380C2313yes—
675#380C2313yes—
676#380C2313yes—
677#380C2313yes—
678#379C2313yes—
679#379C2313yes—
680C4×C4⋊C4C2313yes—
681C4×C4⋊C4C2313yes—
682C4×C4⋊C4C2313yes—
683C4×C4⋊C4C2313yes—
684C4×C4⋊C4C2313yes—
685C4×C4⋊C4C2313yes—
686C4×C4⋊C4C2313yes—
687C4×C4⋊C4C2313yes—
688C4×C4⋊C4C2313yes—
689C4×C4⋊C4C2313yes—
690C4×C4⋊C4C2313yes—
691C4×C22⋊C4C2313yes—
692C4×C22⋊C4C2313yes—
693C4×C22⋊C4C2313yes—
694C4×C22⋊C4C2313yes—
695C4×C22⋊C4C2313yes—
696C4×C22⋊C4C2313yes—
697C4×C22⋊C4C2313yes—
698C4×C22⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713C4×C22⋊C4C2313yes—
714C4×C22⋊C4C2313yes—
715C4×C22⋊C4C2313yes—
716C4×C22⋊C4C2313yes—
717C4×C22⋊C4C2313yes—
718#376C2313yes—
719#376C2313yes—
720#376C2313yes—
721C2×#95C2313yes—
722C2×#95C2313yes—
723C2×#95C2311yescharacteristic
724C25C2411yescharacteristic
725C25C2411yescharacteristic
726C22×Q8—46no—
727C22×Q8C2413yes—
728C22×Q8C2413yes—
729C22×Q8C2413yes—
730C22×Q8C2411yescharacteristic
731C22×D4C2413yes—
732C22×D4C2413yes—
733C22×D4C2413yes—
734C22×D4C2413yes—
735C22×D4C2413yes—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C23×C4C2413yes—
742C23×C4C2413yes—
743C23×C4C2413yes—
744C23×C4C2413yes—
745C23×C4C2413yes—
746C23×C4C2413yes—
747C23×C4C2413yes—
748C23×C4C2413yes—
749C23×C4C2413yes—
750C23×C4C2413yes—
751C23×C4C2413yes—
752C4⋊Q8—46no—
753#127—42no—
754#126—42no—
755#126—46no—
756#126—46no—
757#126—42no—
758#126—46no—
759#126—46no—
760#126—42no—
761#126—42no—
762#126—46no—
763#125—46no—
764#124—46no—
765#124—46no—
766#124—46no—
767#124—46no—
768#124—46no—
769#124—46no—
770#124—46no—
771#124—46no—
772#123—46no—
773#123—46no—
774#123—46no—
775#123—46no—
776#123—46no—
777#123—46no—
778#123—46no—
779#123—46no—
780#123—46no—
781C22⋊Q8—46no—
782C22⋊Q8—46no—
783#121—46no—
784#121—46no—
785#121—46no—
786#121—46no—
787#121—46no—
788#121—46no—
789#121—46no—
790#120—212no—
791#120—212no—
792#120—46no—
793#120—42no—
794#120—42no—
795#120—42no—
796C4×Q8—46no—
797C4×Q8—46no—
798C4×D4—46no—
799C4×D4—46no—
800C4×D4—46no—
801C4×D4—46no—
802C4×D4—46no—
803C4×D4—46no—
804C4×D4—46no—
805C4×D4—46no—
806#117—46no—
807C2×C4⋊C4—46no—
808C2×C4⋊C4—46no—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C22⋊C4—212no—
854C2×C22⋊C4—46no—
855C2×C22⋊C4—46no—
856C2×C22⋊C4—46no—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C42—42no—
918C2×C42C2413yes—
919C2×C42C2413yes—
920C2×C42C2413yes—
921C2×C42C2413yes—
922C2×C42C2413yes—
923C2×C42C2413yes—
924C2×C42C2413yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2413yes—
937C2×C42C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2411yescharacteristic
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2413yes—
1003#95C2413yes—
1004#95C2413yes—
1005#95C2413yes—
1006#95C2413yes—
1007#95C2413yes—
1008C24—43no—
1009C24—43no—
1010C24—43no—
1011C24—43no—
1012C24—41no—
1013C24H(5,𝔽2)14yes—
1014C24C2513yes—
1015C24C2513yes—
1016C24C2511yescharacteristic
1017C24C2511yescharacteristic
1018C24C2511yescharacteristic
1019C2×Q8—26no—
1020C2×Q8—26no—
1021C2×Q8—43no—
1022C2×Q8—43no—
1023C2×Q8—43no—
1024C2×Q8—43no—
1025C2×Q8—43no—
1026C2×Q8—43no—
1027C2×Q8—43no—
1028C2×Q8—43no—
1029C2×Q8—88no—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—26no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—43no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—43no—
1046C2×D4—43no—
1047C2×D4—43no—
1048C2×D4—43no—
1049C2×D4—43no—
1050C2×D4—43no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C22×C4—26no—
1061C22×C4—26no—
1062C22×C4—26no—
1063C22×C4—26no—
1064C22×C4—26no—
1065C22×C4—43no—
1066C22×C4—43no—
1067C22×C4—43no—
1068C22×C4—43no—
1069C22×C4—43no—
1070C22×C4—43no—
1071C22×C4—43no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4—43no—
1083C22×C4—43no—
1084C22×C4—43no—
1085C22×C4—43no—
1086C22×C4—43no—
1087C22×C4—43no—
1088C22×C4—43no—
1089C22×C4—43no—
1090C22×C4—43no—
1091C22×C4—43no—
1092C22×C4—43no—
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2513yes—
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2513yes—
1102C22×C4C2513yes—
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C22×C4C2513yes—
1106C22×C4C2513yes—
1107C22×C4C2513yes—
1108C22×C4C2513yes—
1109C22×C4C2513yes—
1110C22×C4C2513yes—
1111C4⋊C4—26no—
1112C4⋊C4—26no—
1113C4⋊C4—26no—
1114C4⋊C4—26no—
1115C4⋊C4—26no—
1116C4⋊C4—26no—
1117C4⋊C4—26no—
1118C4⋊C4—26no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—43no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C4—43no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—43no—
1148C4⋊C4—43no—
1149C4⋊C4—43no—
1150C4⋊C4—43no—
1151C4⋊C4—43no—
1152C4⋊C4—43no—
1153C4⋊C4—43no—
1154C4⋊C4—43no—
1155C22⋊C4—26no—
1156C22⋊C4—26no—
1157C22⋊C4—26no—
1158C22⋊C4—26no—
1159C22⋊C4—26no—
1160C22⋊C4—26no—
1161C22⋊C4—26no—
1162C22⋊C4—26no—
1163C22⋊C4—26no—
1164C22⋊C4—26no—
1165C22⋊C4—26no—
1166C22⋊C4—26no—
1167C22⋊C4—26no—
1168C22⋊C4—26no—
1169C22⋊C4—26no—
1170C22⋊C4—26no—
1171C22⋊C4—26no—
1172C22⋊C4—26no—
1173C22⋊C4—26no—
1174C22⋊C4—26no—
1175C22⋊C4—26no—
1176C22⋊C4—26no—
1177C22⋊C4—26no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—43no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—43no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—43no—
1197C22⋊C4—43no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C22⋊C4—43no—
1201C22⋊C4—43no—
1202C22⋊C4—43no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C22⋊C4—43no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4—43no—
1215C42—26no—
1216C42—26no—
1217C42—26no—
1218C42—41no—
1219C42—43no—
1220C42—43no—
1221C42—43no—
1222C42—43no—
1223C42—43no—
1224C42—43no—
1225C42—43no—
1226C42—43no—
1227C42—43no—
1228C42—43no—
1229C42—43no—
1230C42—43no—
1231C42—43no—
1232C42—43no—
1233C42—43no—
1234C42—41no—
1235C23—23no—
1236C23—23no—
1237C23—23no—
1238C23—23no—
1239C23—23no—
1240C23—23no—
1241C23—23no—
1242C23—23no—
1243C23—23no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23—23no—
1248C23—23no—
1249C23—23no—
1250C23—23no—
1251C23—23no—
1252C23—23no—
1253C23—23no—
1254C23—23no—
1255C23—412no—
1256C23—86no—
1257C23—161no—
1258C23—163no—
1259C23—161no—
1260C23—163no—
1261C23C2×H(5,𝔽2)12yes—
1262C23C2×H(5,𝔽2)12yes—
1263C23C2×H(5,𝔽2)12yes—
1264C23C2611yescharacteristic
1265Q8—412no—
1266Q8—82no—
1267Q8—163no—
1268Q8—163no—
1269D4—86no—
1270D4—86no—
1271D4—86no—
1272D4—86no—
1273D4—86no—
1274D4—86no—
1275D4—86no—
1276D4—86no—
1277D4—163no—
1278D4—163no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—86no—
1332C2×C4—86no—
1333C2×C4—86no—
1334C2×C4—86no—
1335C2×C4—86no—
1336C2×C4—163no—
1337C2×C4—163no—
1338C2×C4—163no—
1339C2×C4—163no—
1340C2×C4—163no—
1341C2×C4—163no—
1342C2×C4#58516yes—
1343C2×C4#58516yes—
1344C22—26no—
1345C22—26no—
1346C22—26no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—43no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—43no—
1364C22—43no—
1365C22—43no—
1366C22—43no—
1367C22—164no—
1368C22—164no—
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C2×#58513yes—
1371C22C2×#58513yes—
1372C4—26no—
1373C4—26no—
1374C4—43no—
1375C4—43no—
1376C4—43no—
1377C4—43no—
1378C4—43no—
1379C4—43no—
1380C4—43no—
1381C4—43no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4—43no—
1387C4—43no—
1388C4—43no—
1389C4—43no—
1390C2—42no—
1391C2—42no—
1392C2—42no—
1393C2—83no—
1394C2—83no—
1395C2#6282213yes—
1396C2#6302611yescharacteristic
1397C2#6302913yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59596C2semidirect
2. #59591C2semidirect
3. #58918C2semidirect
4. #58460C2semidirect
5. #54221C2semidirect
6. #54159C2semidirect
7. #47852C2semidirect
8. #47849C2semidirect
9. #47613C2semidirect
10. #47578C2semidirect
11. #46888C2semidirect
12. #46684C2semidirect
13. #45292C2semidirect
14. #45232C2semidirect
15. #44793C2semidirect
16. #44733C2semidirect
17. #44316C2semidirect
18. #43687C2semidirect
19. #43471C2semidirect
20. #43062C2semidirect
21. #35780C2semidirect
22. #35706C2semidirect
23. #35467C2semidirect
25. C2×#560C22semidirect
27. C22×#126C22semidirect
28. #2838C22semidirect
29. #2833C22semidirect
30. #2827C22semidirect
31. #2824C22semidirect
32. #2803C22semidirect
33. #2802C22semidirect
34. #2801C22semidirect
35. #2798C22semidirect
36. #2798C22semidirect
37. #2798C22semidirect
38. #2796C22semidirect
39. #2793C22semidirect
40. #2793C22semidirect
41. #2793C22semidirect
42. #2788C22semidirect
43. #2787C22semidirect
44. #2780C22semidirect
45. #2779C22semidirect
46. #2775C22semidirect
47. #2774C22semidirect
48. #2765C22semidirect
49. #2763C22semidirect
50. #2763C22semidirect
51. #2759C22semidirect
52. #2759C22semidirect
53. #2759C22semidirect
54. #2758C22semidirect
55. #2758C22semidirect
56. #2753C22semidirect
57. #2752C22semidirect
58. #2743C22semidirect
59. #2742C22semidirect
60. #2738C22semidirect
61. #2738C22semidirect
62. #2736C22semidirect
63. #2735C22semidirect
64. #2720C22semidirect
65. #2718C22semidirect
67. #2717C22semidirect
72. #2710C22semidirect
73. #2708C22semidirect
74. #2707C22semidirect
76. #2698C22semidirect
77. #2695C22semidirect
79. #2691C22semidirect
87. #2674C22semidirect
90. #2672C22semidirect
92. #2670C22semidirect
95. #2653C22semidirect
96. #2652C22semidirect
100. #2612C22semidirect
101. #2610C22semidirect
102. #2597C22semidirect
103. #2594C22semidirect
106. #2589C22semidirect
107. #2589C22semidirect
108. #2588C22semidirect
109. #2588C22semidirect
110. #2583C22semidirect
111. #2577C22semidirect
112. #2576C22semidirect
113. #2576C22semidirect
114. #2573C22semidirect
116. #2572C22semidirect
117. #2572C22semidirect
118. #2569C22semidirect
119. #2567C22semidirect
120. #2560C22semidirect
125. #2558C22semidirect
129. #2557C22semidirect
134. #2553C22semidirect
135. #2553C22semidirect
136. #2553C22semidirect
138. #2544C22semidirect
141. #2529C22semidirect
142. #2529C22semidirect
143. #2527C22semidirect
144. #2527C22semidirect
146. #2526C22semidirect
147. #2523C22semidirect
148. #2523C22semidirect
153. #2521C22semidirect
154. #2521C22semidirect
156. #2518C22semidirect
157. #2518C22semidirect
158. #2515C22semidirect
161. #2510C22semidirect
162. #2503C22semidirect
164. #2497C22semidirect
165. #2496C22semidirect
166. #2496C22semidirect
167. #2496C22semidirect
168. #2496C22semidirect
169. #2496C22semidirect
170. #2495C22semidirect
171. #2493C22semidirect
173. #2481C22semidirect
176. #2467C22semidirect
177. #2466C22semidirect
183. #2459C22semidirect
185. #2458C22semidirect
188. #2451C22semidirect
189. #2448C22semidirect
190. #2448C22semidirect
192. #2444C22semidirect
193. #2442C22semidirect
194. #2441C22semidirect
198. #2425C22semidirect
201. #2422C22semidirect
203. #2418C22semidirect
206. #2412C22semidirect
207. #2412C22semidirect
208. #2401C22semidirect
210. #2398C22semidirect
212. C2×#396C22semidirect
213. C2×#393C22semidirect
214. #2374C22semidirect
215. #2373C22semidirect
216. #2368C22semidirect
217. #2367C22semidirect
221. #2358C22semidirect
222. #2355C22semidirect
224. #2353C22semidirect
225. #2353C22semidirect
226. #2353C22semidirect
228. #2347C22semidirect
229. #2345C22semidirect
230. #2342C22semidirect
231. Q8×C22⋊C4C22semidirect
232. #2337C22semidirect
233. #2335C22semidirect
234. #2331C22semidirect
235. #2330C22semidirect
236. #2326C22semidirect
238. #2322C22semidirect
239. #2321C22semidirect
240. #2320C22semidirect
241. #2318C22semidirect
243. C4×#123C22semidirect
244. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#595962
#595912
#589182
#584602
#542212
#541592
#478522
#478492
#476132
#475782
#468882
#466842
#452922
#452322
#447932
#447332
#443162
#436872
#434712
#430622
#357802
#357062
#354672