Finite Group Databasebeta

← #7683574

Subgroups — #7683574

Order 512.

4812 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59791C214yesmaximal, complemented
2#59750C214yesmaximal, complemented
3#59730C214yesmaximal, complemented
4#59646C212yesmaximal, complemented
5#59533C214yesmaximal, complemented
6#59432C212yesmaximal, complemented
7#59228C212yesmaximal, complemented
8#59139C212yesmaximal, complemented
9#45423C211yesmaximal, characteristic, complemented
10#45400C211yesmaximal, characteristic, complemented
11#45398C212yesmaximal, complemented
12#44982C211yesmaximal, characteristic, complemented
13#44975C212yesmaximal, complemented
14#44965C211yesmaximal, characteristic, complemented
15#44120C214yesmaximal, complemented
16#44108C214yesmaximal, complemented
17#44076C214yesmaximal, complemented
18#44069C214yesmaximal, complemented
19#35603C212yesmaximal, complemented
20#35567C212yesmaximal, complemented
21#35551C212yesmaximal, complemented
22#34880C211yesmaximal, characteristic, complemented
23#34797C212yesmaximal, complemented
24#34301C212yesmaximal, complemented
25#34280C211yesmaximal, characteristic, complemented
26#34242C212yesmaximal, complemented
27#34217C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#540C2211yescharacteristic
30C2×#529C2212yes—
31C22×#125C2211yescharacteristic
32#2803C2214yes—
33#2803C2214yes—
34#2803C2214yes—
35#2803C2214yes—
36#2803C2214yes—
37#2802C2214yes—
38#2800C2214yes—
39#2786C2214yes—
40#2786C2214yes—
41#2758C2214yes—
42#2757C2214yes—
43#2756C2214yes—
44#2756C2214yes—
45#2756C2214yes—
46#2740C2214yes—
47#2726C2214yes—
48#2725C2214yes—
49#2715C2214yes—
50#2711C2214yes—
51#2705C2214yes—
52#2703C2214yes—
53#2701C2214yes—
54#2691C2214yes—
55#2673C2214yes—
56#2602C2214yes—
57#2602C2214yes—
58#2601C2214yes—
59#2601C2214yes—
60#2597C2214yes—
61#2596C2214yes—
62#2596C2214yes—
63#2596C2214yes—
64#2595C2214yes—
65#2593C2214yes—
66#2593C2214yes—
67#2593C2214yes—
68#2587C2214yes—
69#2584C2212yes—
70#2584C2214yes—
71#2578C2214yes—
72#2578C2214yes—
73#2577C2214yes—
74#2573C2214yes—
75#2566C2212yes—
76#2562C2212yes—
77#2562C2212yes—
78#2562C2214yes—
79#2559C2214yes—
80#2558C2214yes—
81#2558C2214yes—
82#2558C2214yes—
83#2558C2214yes—
84#2556C2212yes—
85#2555C2212yes—
86#2555C2214yes—
87#2554C2212yes—
88#2554C2214yes—
89#2553C2212yes—
90#2552C2212yes—
91#2548C2214yes—
92#2548C2212yes—
93#2541C2212yes—
94#2537C2212yes—
95#2531C2214yes—
96#2529C2214yes—
97#2525C2214yes—
98#2525C2214yes—
99#2525C2214yes—
100#2524C2214yes—
101#2521C2212yes—
102#2519C2212yes—
103#2518C2214yes—
104#2518C2214yes—
105#2513C2212yes—
106#2513C2214yes—
107#2512C2212yes—
108#2507C2212yes—
109#2506C2212yes—
110#2505C2214yes—
111#2500C2212yes—
112#2500C2212yes—
113#2497C2212yes—
114#2495C2212yes—
115#2495C2212yes—
116#2495C2212yes—
117#2490C2212yes—
118#2490C2212yes—
119#2490C2214yes—
120#2490C2214yes—
121#2490C2214yes—
122#2485C2212yes—
123#2485C2212yes—
124#2481C2214yes—
125#2476C2214yes—
126#2476C2214yes—
127#2475C2214yes—
128#2474C2214yes—
129#2474C2214yes—
130#2470C2214yes—
131#2467C2214yes—
132#2467C2214yes—
133#2464C2212yes—
134#2464C2214yes—
135#2462C2214yes—
136#2461C2212yes—
137#2461C2214yes—
138#2460C2214yes—
139#2460C2214yes—
140#2457C2214yes—
141#2445C2214yes—
142#2445C2214yes—
143#2443C2214yes—
144#2442C2212yes—
145#2441C2212yes—
146#2428C2214yes—
147#2428C2214yes—
148#2425C2214yes—
149#2422C2212yes—
150#2422C2212yes—
151#2416C2214yes—
152#2416C2212yes—
153#2416C2212yes—
154#2416C2212yes—
155#2414C2214yes—
156#2414C2212yes—
157#2414C2212yes—
158#2414C2212yes—
159#2414C2214yes—
160#2399C2211yescharacteristic
161#2397C2211yescharacteristic
162#2395C2214yes—
163#2392C2214yes—
164#2392C2211yescharacteristic
165#2392C2211yescharacteristic
166#2374C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2373C2214yes—
170#2370C2212yes—
171#2370C2214yes—
172#2370C2214yes—
173#2367C2214yes—
174#2364C2214yes—
175#2363C2214yes—
176#2363C2214yes—
177#2363C2214yes—
178#2363C2212yes—
179#2363C2212yes—
180#2362C2214yes—
181#2361C2214yes—
182#2359C2214yes—
183#2359C2214yes—
184#2355C2212yes—
185#2354C2212yes—
186#2354C2212yes—
187#2354C2212yes—
188#2354C2212yes—
189#2354C2212yes—
190#2353C2214yes—
191#2352C2212yes—
192#2352C2212yes—
193Q8×C4⋊C4C2212yes—
194D4×C4⋊C4C2212yes—
195#2347C2212yes—
196#2347C2214yes—
197#2347C2214yes—
198#2345C2214yes—
199#2345C2214yes—
200#2344C2212yes—
201#2335C2214yes—
202#2335C2214yes—
203#2335C2214yes—
204#2333C2214yes—
205#2330C2211yescharacteristic
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2330C2211yescharacteristic
209#2330C2211yescharacteristic
210#2328C2211yescharacteristic
211#2324C2212yes—
212#2324C2212yes—
213#2324C2212yes—
214#2316C2212yes—
215#2314C2212yes—
216#2314C2211yescharacteristic
217C4×#127C2211yescharacteristic
218C4×#125C2212yes—
219C4×#125C2211yescharacteristic
220C4×#125C2212yes—
221C4×#125C2214yes—
222C4×#126C2214yes—
223C4×#126C2214yes—
224C4×#124C2212yes—
225C4×#124C2214yes—
226C4×#121C2212yes—
227C4×#121C2212yes—
228C4×#121C2212yes—
229C4×#121C2212yes—
230#2293C2211yescharacteristic
231#2293C2212yes—
232#2293C2214yes—
233#2293C2214yes—
234#2290C2212yes—
235#2285C2211yescharacteristic
236#2285C2212yes—
237#2275C2212yes—
238#2274C2212yes—
239#2274C2212yes—
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243#553—216no—
244#540—28no—
245C2×#127C2311yescharacteristic
246C2×#127C2314yes—
247#529—216no—
248C2×#126C2314yes—
249C2×#126C2312yes—
250C2×#126C2312yes—
251C2×#126C2314yes—
252C2×#125—28no—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2311yescharacteristic
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2311yescharacteristic
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#399C2312yes—
327#399C2312yes—
328#399C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2311yescharacteristic
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2311yescharacteristic
338#398C2314yes—
339#398C2312yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2311yescharacteristic
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2311yescharacteristic
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2312yes—
360#396C2314yes—
361#396C2314yes—
362#396C2312yes—
363#396C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2312yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2312yes—
382#394C2314yes—
383#394C2311yescharacteristic
384#394C2314yes—
385#394C2311yescharacteristic
386#394C2312yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2311yescharacteristic
396#392C2314yes—
397#392C2311yescharacteristic
398#392C2312yes—
399#392C2312yes—
400#392C2314yes—
401#392C2314yes—
402#391C2314yes—
403#391C2312yes—
404#390C2314yes—
405#390C2312yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2314yes—
410#390C2314yes—
411#390C2312yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2312yes—
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#388C2312yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#387C2312yes—
519#387C2314yes—
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#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2312yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2312yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#384C2311yescharacteristic
579#384C2312yes—
580#384C2312yes—
581#384C2311yescharacteristic
582#384C2311yescharacteristic
583#384C2312yes—
584#383C2314yes—
585#383C2314yes—
586#383C2314yes—
587#383C2314yes—
588#382C2312yes—
589#382C2311yescharacteristic
590#382C2314yes—
591#382C2312yes—
592#382C2312yes—
593#381C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2312yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2312yes—
604#380C2312yes—
605#380C2312yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2311yescharacteristic
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671#376C2311yescharacteristic
672#376C2311yescharacteristic
673#376C2314yes—
674C2×#95C2314yes—
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8C2412yes—
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2411yescharacteristic
689C22×D4C2411yescharacteristic
690C22×D4C2414yes—
691C22×D4C2414yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2414yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2412yes—
702C23×C4C2414yes—
703#127—24no—
704#127—84no—
705#126—28no—
706#126—216no—
707#126—28no—
708#126—48no—
709#125—28no—
710#125—216no—
711#125—28no—
712#125—24no—
713#125—24no—
714#125—84no—
715#125—84no—
716#125#4118yes—
717#124—28no—
718#124—44no—
719#124—48no—
720#123—28no—
721#123—216no—
722#123—216no—
723#123—28no—
724#123—84no—
725#123—84no—
726C22⋊Q8—28no—
727#121—28no—
728#121—216no—
729#121—28no—
730#121—28no—
731#121—28no—
732#121—216no—
733#121—44no—
734#121—48no—
735#121—44no—
736#121—44no—
737#121—84no—
738#121—84no—
739#121—84no—
740C4×Q8—28no—
741C4×Q8—84no—
742C4×D4—28no—
743C4×D4—28no—
744C4×D4—216no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—44no—
750C4×D4—42no—
751C4×D4—42no—
752C4×D4—48no—
753C4×D4—44no—
754C4×D4—84no—
755C4×D4—84no—
756C4×D4—84no—
757C4×D4—84no—
758#117—28no—
759#117—28no—
760#117—42no—
761#117—48no—
762#117—48no—
763#117—44no—
764#117—44no—
765#117—44no—
766#117—84no—
767#117—84no—
768#117#4118yes—
769C2×C4⋊C4—28no—
770C2×C4⋊C4—216no—
771C2×C4⋊C4—28no—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2411yescharacteristic
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⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C42—24no—
880C2×C42—28no—
881C2×C42C2414yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2414yes—
963#95C2414yes—
964C24C2512yes—
965C24C2512yes—
966C24C2514yes—
967C24C2511yescharacteristic
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—42no—
971C2×D4—24no—
972C2×D4—24no—
973C2×D4—28no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—41no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4—41no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—28no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4C2×#4114yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4C2×#4118yes—
1113C4⋊C4C2×#41116yes—
1114C4⋊C4C2×#4118yes—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—41no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—41no—
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—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4C2×#4118yes—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—22no—
1175C42—24no—
1176C42—24no—
1177C42—28no—
1178C42—28no—
1179C42—22no—
1180C42—22no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—42no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—42no—
1198C42C2×#4114yes—
1199C42C2×#4114yes—
1200C42C2×#4114yes—
1201C23—21no—
1202C23—21no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—22no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—24no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—24no—
1223C23—24no—
1224C23—22no—
1225C23—22no—
1226C23C22×#4112yes—
1227C23C2611yescharacteristic
1228Q8—48no—
1229D4—48no—
1230D4—44no—
1231D4—48no—
1232D4—84no—
1233D4—88no—
1234D4—88no—
1235D4—84no—
1236D4—88no—
1237D4—88no—
1238D4—84no—
1239D4—82no—
1240D4—88no—
1241D4—164no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—28no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—21no—
1268C2×C4—24no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—84no—
1303C2×C4—88no—
1304C2×C4—88no—
1305C2×C4—88no—
1306C2×C4—84no—
1307C2×C4—88no—
1308C2×C4—164no—
1309C2×C4C22×#4114yes—
1310C2×C4C22×#4114yes—
1311C2×C4C22×#4118yes—
1312C2×C4C22×#4114yes—
1313C2×C4C22×#4112yes—
1314C2×C4C22×#4112yes—
1315C2×C4C22×#4112yes—
1316C2×C4#58514yes—
1317C2×C4#58512yes—
1318C22—24no—
1319C22—22no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—44no—
1325C22—42no—
1326C22—42no—
1327C22—44no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—44no—
1332C22—42no—
1333C22—44no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—44no—
1338C22—44no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22C23×#4111yescharacteristic
1345C22C23×#4111yescharacteristic
1346C22C2×#58512yes—
1347C22C2×#58511yescharacteristic
1348C22H(7,𝔽2)12yes—
1349C4—24no—
1350C4—28no—
1351C4—24no—
1352C4—24no—
1353C4—24no—
1354C4—22no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—42no—
1362C4—41no—
1363C4—44no—
1364C4—41no—
1365C4—44no—
1366C4—41no—
1367C4—41no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4#348014yes—
1372C2—42no—
1373C2—82no—
1374C2—84no—
1375C2—82no—
1376C2C2×#348011yescharacteristic
1377C2#6284011yescharacteristic
1378C2#6288311yescharacteristic
1379C2#6299412yes—
1380C2#6300812yes—
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. #59791C2semidirect
2. #59750C2semidirect
3. #59730C2semidirect
4. #59646C2semidirect
5. #59533C2semidirect
6. #59432C2semidirect
7. #59228C2semidirect
8. #59139C2semidirect
9. #45423C2semidirect
10. #45400C2semidirect
11. #45398C2semidirect
12. #44982C2semidirect
13. #44975C2semidirect
14. #44965C2semidirect
15. #44120C2semidirect
16. #44108C2semidirect
17. #44076C2semidirect
18. #44069C2semidirect
19. #35603C2semidirect
20. #35567C2semidirect
21. #35551C2semidirect
22. #34880C2semidirect
23. #34797C2semidirect
24. #34301C2semidirect
25. #34280C2semidirect
26. #34242C2semidirect
27. #34217C2semidirect

Maximal subgroups

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

subgroupindex
#597912
#597502
#597302
#596462
#595332
#594322
#592282
#591392
#454232
#454002
#453982
#449822
#449752
#449652
#441202
#441082
#440762
#440692
#356032
#355672
#355512
#348802
#347972
#343012
#342802
#342422
#342172