Finite Group Databasebeta

← #8990780

Subgroups — #8990780

Order 512.

5640 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59220C211yesmaximal, characteristic, complemented
2#57725C212yesmaximal, complemented
3#57331C214yesmaximal, complemented
4#53558C214yesmaximal, complemented
5#53488C212yesmaximal, complemented
6#52410C212yesmaximal, complemented
7#52004C212yesmaximal, complemented
8#50958C214yesmaximal, complemented
9#49198C214yesmaximal, complemented
10#47177C212yesmaximal, complemented
11#46762C212yesmaximal, complemented
12#46350C214yesmaximal, complemented
13#46232C211yesmaximal, characteristic, complemented
14#44063C214yesmaximal, complemented
15#43023C214yesmaximal, complemented
16#43017C212yesmaximal, complemented
17#43013C214yesmaximal, complemented
18#41311C214yesmaximal, complemented
19#40783C214yesmaximal, complemented
20#39412C212yesmaximal, complemented
21#38760C212yesmaximal, complemented
22#35729C212yesmaximal, complemented
23#35531C211yesmaximal, characteristic, complemented
24C2×#546C2214yescomplemented
25C2×#546C2212yescomplemented
26C2×D42C2212yescomplemented
27C2×#538C2212yescomplemented
28C2×#535C2211yescharacteristic
29C2×#534C2214yescomplemented
30C2×#534C2212yescomplemented
31C2×#520C2211yescharacteristic, complemented
32#2850C2212yescomplemented
33#2844C2211yescharacteristic, complemented
34#2838C2214yescomplemented
35#2836C2214yescomplemented
36#2828C2212yescomplemented
37#2828C2214yescomplemented
38#2826C2212yescomplemented
39#2824C2214yescomplemented
40#2819C2211yescharacteristic, complemented
41#2812C2214yescomplemented
42#2808C2212yescomplemented
43#2807C2212yescomplemented
44#2804C2212yescomplemented
45#2803C2214yescomplemented
46#2800C2214yescomplemented
47#2796C2214yescomplemented
48#2795C2212yescomplemented
49#2790C2214yescomplemented
50#2784C2212yescomplemented
51#2782C2212yescomplemented
52#2782C2212yescomplemented
53#2779C2214yescomplemented
54#2778C2214yescomplemented
55#2778C2214yescomplemented
56#2777C2214yescomplemented
57#2770C2214yescomplemented
58#2756C2214yescomplemented
59#2753C2214yescomplemented
60#2750C2214yescomplemented
61#2732C2212yescomplemented
62#2723C2214yescomplemented
63#2717C2214yescomplemented
64#2714C2214yescomplemented
65#2708C2214yescomplemented
66#2708C2214yescomplemented
67#2706C2214yescomplemented
68#2706C2214yescomplemented
69#2706C2214yescomplemented
70#2705C2214yescomplemented
71#2703C2214yescomplemented
72#2703C2214yescomplemented
73#2702C2214yescomplemented
74#2697C2214yescomplemented
75#2697C2214yescomplemented
76#2693C2214yescomplemented
77#2692C2214yescomplemented
78#2688C2214yescomplemented
79#2688C2214yescomplemented
80#2685C2214yescomplemented
81#2684C2214yescomplemented
82#2684C2214yescomplemented
83#2684C2214yescomplemented
84#2682C2214yescomplemented
85#2681C2214yescomplemented
86#2680C2212yescomplemented
87#2679C2212yescomplemented
88#2679C2212yescomplemented
89#2678C2214yescomplemented
90#2675C2212yes—
91#2672C2214yescomplemented
92#2672C2214yescomplemented
93#2671C2214yescomplemented
94#2671C2214yescomplemented
95#2670C2214yescomplemented
96#2670C2214yescomplemented
97#2669C2214yes—
98#2668C2214yescomplemented
99#2668C2214yescomplemented
100#2668C2214yescomplemented
101#2668C2214yescomplemented
102#2653C2214yescomplemented
103#2653C2214yescomplemented
104#2649C2214yescomplemented
105#2648C2214yescomplemented
106#2643C2214yescomplemented
107#2639C2214yescomplemented
108#2635C2212yescomplemented
109#2632C2212yescomplemented
110#2631C2212yescomplemented
111#2631C2212yescomplemented
112#2627C2212yescomplemented
113#2626C2212yescomplemented
114#2617C2212yescomplemented
115#2610C2212yescomplemented
116#2603C2214yescomplemented
117#2602C2214yescomplemented
118#2598C2212yescomplemented
119#2598C2212yescomplemented
120#2598C2212yescomplemented
121#2591C2214yescomplemented
122#2591C2212yescomplemented
123#2576C2214yescomplemented
124#2571C2211yescharacteristic, complemented
125#2564C2212yescomplemented
126#2559C2214yescomplemented
127#2557C2214yescomplemented
128#2557C2214yescomplemented
129#2555C2212yescomplemented
130#2554C2214yescomplemented
131#2553C2214yescomplemented
132#2539C2214yescomplemented
133#2537C2211yescharacteristic, complemented
134#2535C2214yescomplemented
135#2532C2214yescomplemented
136#2516C2214yescomplemented
137#2505C2214yescomplemented
138#2504C2212yescomplemented
139#2501C2212yescomplemented
140#2500C2212yescomplemented
141#2500C2212yescomplemented
142#2495C2214yescomplemented
143#2487C2214yescomplemented
144#2481C2214yescomplemented
145#2480C2214yescomplemented
146#2480C2214yescomplemented
147#2476C2214yescomplemented
148#2476C2214yescomplemented
149#2472C2214yescomplemented
150#2472C2214yescomplemented
151#2467C2214yescomplemented
152#2464C2214yescomplemented
153#2464C2214yescomplemented
154#2463C2214yescomplemented
155#2461C2214yescomplemented
156#2458C2214yescomplemented
157#2455C2212yescomplemented
158#2455C2214yescomplemented
159#2448C2214yescomplemented
160#2445C2214yescomplemented
161#2443C2214yescomplemented
162#2430C2214yescomplemented
163#2427C2214yescomplemented
164#2425C2214yescomplemented
165#2425C2214yescomplemented
166#2424C2214yescomplemented
167#2424C2214yescomplemented
168#2424C2214yescomplemented
169#2424C2214yescomplemented
170#2424C2214yescomplemented
171#2424C2214yescomplemented
172#2422C2214yescomplemented
173#2418C2214yescomplemented
174#2418C2214yescomplemented
175#2418C2214yescomplemented
176#2418C2214yescomplemented
177#2418C2214yescomplemented
178#2416C2214yescomplemented
179#2412C2214yescomplemented
180#2410C2214yescomplemented
181#2410C2214yescomplemented
182#2410C2214yescomplemented
183#2410C2214yescomplemented
184#2410C2214yescomplemented
185#2408C2214yescomplemented
186#2408C2212yescomplemented
187#2408C2214yescomplemented
188#2406C2212yescomplemented
189#2405C2214yescomplemented
190#2404C2214yescomplemented
191#2403C2214yescomplemented
192#2403C2214yescomplemented
193#2403C2214yescomplemented
194#2403C2214yescomplemented
195#2398C2212yescomplemented
196#2388C2212yescomplemented
197C2×#394C2212yescomplemented
198C2×#394C2214yescomplemented
199#2380C2212yescomplemented
200#2379C2212yescomplemented
201#2364C2214yescomplemented
202#2361C2214yescomplemented
203#2358C2214yescomplemented
204#2358C2214yescomplemented
205#2353C2212yescomplemented
206D4×C4⋊C4C2212yescomplemented
207#2342C2214yescomplemented
208D4×C22⋊C4C2214yescomplemented
209#2325C2214yescomplemented
210#2321C2214yescomplemented
211#2321C2214yescomplemented
212#2321C2214yescomplemented
213#2317C2211yescharacteristic, complemented
214#2309C2211yescharacteristic, complemented
215C4×#121C2212yescomplemented
216#2297C2211yescharacteristic, complemented
217C2×#390C2211yescharacteristic, complemented
218#2285C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C22×#41C2312yes—
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223C23×D4C2314yes—
224C23×D4C2314yes—
225C23×D4C2314yes—
226#546—48no—
227#546—416no—
228D42—48no—
229#538—48no—
230#535—44no—
231#534—48no—
232#534—416no—
233C2×#127C2312yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#120C2314yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288#520—44no—
289C2×C4×Q8C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2314yes—
318C22×C42C2311yescharacteristic
319#401C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#399C2312yes—
333#399C2312yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2312yes—
374#395C2314yes—
375#395C2312yes—
376#395C2312yes—
377#394C2312yes—
378#394C2312yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2312yes—
392#394C2312yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2312yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#392C2312yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2312yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2314yes—
463#390C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
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#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2312yes—
558#385C2312yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#384C2311yescharacteristic
577#384C2312yes—
578#384C2311yescharacteristic
579#383C2312yes—
580#383C2312yes—
581#383C2312yes—
582#382C2311yescharacteristic
583#382C2314yes—
584#382C2312yes—
585#382C2312yes—
586#382C2311yescharacteristic
587#381C2314yes—
588#381C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#379C2314yes—
600#379C2314yes—
601#379C2314yes—
602#379C2314yes—
603#379C2314yes—
604#379C2314yes—
605#379C2314yes—
606#379C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C25C2414yes—
623C25C2412yes—
624C25C2414yes—
625C2×#41—24no—
626C2×#41—42no—
627C2×#41—42no—
628C2×#41—44no—
629C2×#41—48no—
630C22×Q8C2411yescharacteristic
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×D4—42no—
634C22×D4—42no—
635C22×D4—44no—
636C22×D4—42no—
637C22×D4—48no—
638C22×D4—48no—
639C22×D4—48no—
640C22×D4—48no—
641C22×D4—48no—
642C22×D4—48no—
643C22×D4—48no—
644C22×D4—84no—
645C22×D4—84no—
646C22×D4—84no—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2412yes—
662C22×D4C2412yes—
663C22×D4C2412yes—
664C22×D4C2414yes—
665C22×D4C2412yes—
666C22×D4C2414yes—
667C22×D4C2412yes—
668C22×D4C2414yes—
669C22×D4C2412yes—
670C22×D4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2414yes—
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2414yes—
677C23×C4C2412yes—
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2414yes—
684C23×C4C2414yes—
685C23×C4C2414yes—
686#127—28no—
687#126—48no—
688#126—84no—
689#124—44no—
690#124—44no—
691#124—44no—
692#124—48no—
693#124—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—48no—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—48no—
702#123—48no—
703#123—48no—
704C22⋊Q8—44no—
705C22⋊Q8—48no—
706C22⋊Q8—44no—
707C22⋊Q8—84no—
708#121—28no—
709#121—216no—
710#121—216no—
711#121—48no—
712#121—44no—
713#121—48no—
714#121—48no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—44no—
722#121—44no—
723#121—44no—
724#121—84no—
725#121—84no—
726#120—216no—
727#120—216no—
728#120—216no—
729#120—48no—
730#120—48no—
731#120—48no—
732#120—48no—
733#120—48no—
734#120—48no—
735#120—48no—
736#120—48no—
737#120—48no—
738#120—84no—
739#120—84no—
740#120—84no—
741C4×Q8—44no—
742C4×D4—28no—
743C4×D4—44no—
744C4×D4—44no—
745C4×D4—44no—
746C4×D4—44no—
747C4×D4—48no—
748C4×D4—44no—
749C4×D4—44no—
750C4×D4—48no—
751C4×D4—48no—
752C4×D4—84no—
753C4×D4—84no—
754C4×D4—84no—
755#117—42no—
756#117—42no—
757#117—42no—
758#117—44no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4—44no—
761C2×C4⋊C4—84no—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C22⋊C4—48no—
798C2×C22⋊C4—48no—
799C2×C22⋊C4—44no—
800C2×C22⋊C4—44no—
801C2×C22⋊C4—48no—
802C2×C22⋊C4—48no—
803C2×C22⋊C4—48no—
804C2×C22⋊C4—84no—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C42—42no—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
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#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921C24—28no—
922C24—28no—
923C24—24no—
924C24—28no—
925C24—44no—
926C24—42no—
927C24—42no—
928C24—44no—
929C24—44no—
930C24—44no—
931C24—44no—
932C24—44no—
933C24—44no—
934C24—44no—
935C24—44no—
936C24—44no—
937C24—42no—
938C24—42no—
939C24—44no—
940C24—42no—
941C24—42no—
942C24C2514yes—
943C24C2514yes—
944C24C2512yes—
945C24C2514yes—
946C24C2511yescharacteristic
947#41—416no—
948#41—816no—
949C2×Q8—22no—
950C2×Q8—41no—
951C2×Q8—41no—
952C2×Q8—42no—
953C2×Q8—44no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—28no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—41no—
985C2×D4—41no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—42no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—42no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—42no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—88no—
1024C2×D4—832no—
1025C2×D4—816no—
1026C2×D4—832no—
1027C2×D4—832no—
1028C2×D4H(5,𝔽2)14yes—
1029C2×D4H(5,𝔽2)18yes—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—24no—
1038C22×C4—28no—
1039C22×C4—24no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—41no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C42—24no—
1188C42—24no—
1189C42—22no—
1190C42—22no—
1191C42—42no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C23—24no—
1200C23—24no—
1201C23—21no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—22no—
1206C23—24no—
1207C23—21no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—416no—
1228C23—48no—
1229C23—88no—
1230C23—88no—
1231C23—84no—
1232C23—88no—
1233C23—88no—
1234C23—84no—
1235C23—88no—
1236C23—88no—
1237C23—88no—
1238C23—88no—
1239C23—88no—
1240C23—162no—
1241C23—162no—
1242C23—164no—
1243C23—164no—
1244C23—164no—
1245C23—162no—
1246C23—164no—
1247C23—162no—
1248C23C2×H(5,𝔽2)18yes—
1249C23C2×H(5,𝔽2)14yes—
1250C23#58512yes—
1251C23C2611yescharacteristic
1252Q8—44no—
1253Q8—84no—
1254Q8—162no—
1255D4—48no—
1256D4—44no—
1257D4—416no—
1258D4—48no—
1259D4—416no—
1260D4—48no—
1261D4—48no—
1262D4—48no—
1263D4—84no—
1264D4—84no—
1265D4—88no—
1266D4—88no—
1267D4—88no—
1268D4—88no—
1269D4—88no—
1270D4—88no—
1271D4—88no—
1272D4—88no—
1273D4—88no—
1274D4—84no—
1275D4—88no—
1276D4—88no—
1277D4—164no—
1278D4—162no—
1279C2×C4—28no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—48no—
1326C2×C4—88no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—84no—
1330C2×C4—88no—
1331C2×C4—88no—
1332C2×C4—88no—
1333C2×C4—88no—
1334C2×C4—161no—
1335C2×C4—161no—
1336C2×C4—164no—
1337C2×C4—164no—
1338C2×C4—164no—
1339C2×C4C2×H(5,𝔽2)12yes—
1340C2×C4C2×H(5,𝔽2)14yes—
1341C2×C4#58512yes—
1342C22—24no—
1343C22—28no—
1344C22—24no—
1345C22—22no—
1346C22—24no—
1347C22—24no—
1348C22—28no—
1349C22—28no—
1350C22—41no—
1351C22—44no—
1352C22—41no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—42no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—1616no—
1374C22—168no—
1375C22—1616no—
1376C22C22×H(5,𝔽2)11yescharacteristic
1377C22C22×H(5,𝔽2)12yes—
1378C22C2×#58511yescharacteristic
1379C22C2×#58511yescharacteristic
1380C22H(7,𝔽2)12yes—
1381C4—22no—
1382C4—22no—
1383C4—24no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—42no—
1393C4—44no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—42no—
1398C4—44no—
1399C2—44no—
1400C2—48no—
1401C2—42no—
1402C2—84no—
1403C2—84no—
1404C2#6282011yescharacteristic
1405C2#6289612yes—
1406C2#6290512yes—
1407C2#6301111yescharacteristic
1408C2#6304511yescharacteristic
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. #59220C2semidirect
2. #57725C2semidirect
3. #57331C2semidirect
4. #53558C2semidirect
5. #53488C2semidirect
6. #52410C2semidirect
7. #52004C2semidirect
8. #50958C2semidirect
9. #49198C2semidirect
10. #47177C2semidirect
11. #46762C2semidirect
12. #46350C2semidirect
13. #46232C2semidirect
14. #44063C2semidirect
15. #43023C2semidirect
16. #43017C2semidirect
17. #43013C2semidirect
18. #41311C2semidirect
19. #40783C2semidirect
20. #39412C2semidirect
21. #38760C2semidirect
22. #35729C2semidirect
23. #35531C2semidirect
24. C2×#546C22semidirect
25. C2×#546C22semidirect
26. C2×D42C22semidirect
27. C2×#538C22semidirect
29. C2×#534C22semidirect
30. C2×#534C22semidirect
31. C2×#520C22semidirect
32. #2850C22semidirect
33. #2844C22semidirect
34. #2838C22semidirect
35. #2836C22semidirect
36. #2828C22semidirect
37. #2828C22semidirect
38. #2826C22semidirect
39. #2824C22semidirect
40. #2819C22semidirect
41. #2812C22semidirect
42. #2808C22semidirect
43. #2807C22semidirect
44. #2804C22semidirect
45. #2803C22semidirect
46. #2800C22semidirect
47. #2796C22semidirect
48. #2795C22semidirect
49. #2790C22semidirect
50. #2784C22semidirect
51. #2782C22semidirect
52. #2782C22semidirect
53. #2779C22semidirect
54. #2778C22semidirect
55. #2778C22semidirect
56. #2777C22semidirect
57. #2770C22semidirect
58. #2756C22semidirect
59. #2753C22semidirect
60. #2750C22semidirect
61. #2732C22semidirect
62. #2723C22semidirect
63. #2717C22semidirect
64. #2714C22semidirect
65. #2708C22semidirect
66. #2708C22semidirect
67. #2706C22semidirect
68. #2706C22semidirect
69. #2706C22semidirect
70. #2705C22semidirect
71. #2703C22semidirect
72. #2703C22semidirect
73. #2702C22semidirect
74. #2697C22semidirect
75. #2697C22semidirect
76. #2693C22semidirect
77. #2692C22semidirect
78. #2688C22semidirect
79. #2688C22semidirect
80. #2685C22semidirect
81. #2684C22semidirect
82. #2684C22semidirect
83. #2684C22semidirect
84. #2682C22semidirect
85. #2681C22semidirect
86. #2680C22semidirect
87. #2679C22semidirect
88. #2679C22semidirect
89. #2678C22semidirect
91. #2672C22semidirect
92. #2672C22semidirect
93. #2671C22semidirect
94. #2671C22semidirect
95. #2670C22semidirect
96. #2670C22semidirect
98. #2668C22semidirect
99. #2668C22semidirect
100. #2668C22semidirect
101. #2668C22semidirect
102. #2653C22semidirect
103. #2653C22semidirect
104. #2649C22semidirect
105. #2648C22semidirect
106. #2643C22semidirect
107. #2639C22semidirect
108. #2635C22semidirect
109. #2632C22semidirect
110. #2631C22semidirect
111. #2631C22semidirect
112. #2627C22semidirect
113. #2626C22semidirect
114. #2617C22semidirect
115. #2610C22semidirect
116. #2603C22semidirect
117. #2602C22semidirect
118. #2598C22semidirect
119. #2598C22semidirect
120. #2598C22semidirect
121. #2591C22semidirect
122. #2591C22semidirect
123. #2576C22semidirect
124. #2571C22semidirect
125. #2564C22semidirect
126. #2559C22semidirect
127. #2557C22semidirect
128. #2557C22semidirect
129. #2555C22semidirect
130. #2554C22semidirect
131. #2553C22semidirect
132. #2539C22semidirect
133. #2537C22semidirect
134. #2535C22semidirect
135. #2532C22semidirect
136. #2516C22semidirect
137. #2505C22semidirect
138. #2504C22semidirect
139. #2501C22semidirect
140. #2500C22semidirect
141. #2500C22semidirect
142. #2495C22semidirect
143. #2487C22semidirect
144. #2481C22semidirect
145. #2480C22semidirect
146. #2480C22semidirect
147. #2476C22semidirect
148. #2476C22semidirect
149. #2472C22semidirect
150. #2472C22semidirect
151. #2467C22semidirect
152. #2464C22semidirect
153. #2464C22semidirect
154. #2463C22semidirect
155. #2461C22semidirect
156. #2458C22semidirect
157. #2455C22semidirect
158. #2455C22semidirect
159. #2448C22semidirect
160. #2445C22semidirect
161. #2443C22semidirect
162. #2430C22semidirect
163. #2427C22semidirect
164. #2425C22semidirect
165. #2425C22semidirect
166. #2424C22semidirect
167. #2424C22semidirect
168. #2424C22semidirect
169. #2424C22semidirect
170. #2424C22semidirect
171. #2424C22semidirect
172. #2422C22semidirect
173. #2418C22semidirect
174. #2418C22semidirect
175. #2418C22semidirect
176. #2418C22semidirect
177. #2418C22semidirect
178. #2416C22semidirect
179. #2412C22semidirect
180. #2410C22semidirect
181. #2410C22semidirect
182. #2410C22semidirect
183. #2410C22semidirect
184. #2410C22semidirect
185. #2408C22semidirect
186. #2408C22semidirect
187. #2408C22semidirect
188. #2406C22semidirect
189. #2405C22semidirect
190. #2404C22semidirect
191. #2403C22semidirect
192. #2403C22semidirect
193. #2403C22semidirect
194. #2403C22semidirect
195. #2398C22semidirect
196. #2388C22semidirect
197. C2×#394C22semidirect
198. C2×#394C22semidirect
199. #2380C22semidirect
200. #2379C22semidirect
201. #2364C22semidirect
202. #2361C22semidirect
203. #2358C22semidirect
204. #2358C22semidirect
205. #2353C22semidirect
206. D4×C4⋊C4C22semidirect
207. #2342C22semidirect
208. D4×C22⋊C4C22semidirect
209. #2325C22semidirect
210. #2321C22semidirect
211. #2321C22semidirect
212. #2321C22semidirect
213. #2317C22semidirect
214. #2309C22semidirect
215. C4×#121C22semidirect
216. #2297C22semidirect
217. C2×#390C22semidirect
218. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#592202
#577252
#573312
#535582
#534882
#524102
#520042
#509582
#491982
#471772
#467622
#463502
#462322
#440632
#430232
#430172
#430132
#413112
#407832
#394122
#387602
#357292
#355312