Finite Group Databasebeta

← #8176041

Subgroups — #8176041

Order 512.

4578 conjugacy classes of subgroups.

The subgroup lattice has 1411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59657C212yesmaximal, complemented
2#59432C212yesmaximal, complemented
3#57199C214yesmaximal, complemented
4#56197C214yesmaximal, complemented
5#56185C214yesmaximal, complemented
6#55631C214yesmaximal, complemented
7#53119C212yesmaximal, complemented
8#53115C212yesmaximal, complemented
9#52474C214yesmaximal, complemented
10#43428C214yesmaximal, complemented
11#42625C212yesmaximal, complemented
12#42554C212yesmaximal, complemented
13#41708C214yesmaximal, complemented
14#41144C214yesmaximal, complemented
15#40003C212yesmaximal, complemented
16#39952C212yesmaximal, complemented
17#39590C212yesmaximal, complemented
18#37858C212yesmaximal, complemented
19#37851C212yesmaximal, complemented
20#37481C211yesmaximal, characteristic, complemented
21#37477C211yesmaximal, characteristic, complemented
22#37283C211yesmaximal, characteristic, complemented
23#37283C211yesmaximal, characteristic, complemented
24#36157C212yesmaximal, complemented
25#35336C211yesmaximal, characteristic, complemented
26#34946C211yesmaximal, characteristic, complemented
27#34621C211yesmaximal, characteristic, complemented
28C2×#554C2212yescomplemented
29C2×#553C2212yes—
30C2×#533C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32#2859C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2851C2212yes—
35#2847C2212yes—
36#2847C2212yes—
37#2842C2214yes—
38#2841C2214yes—
39#2839C2214yescomplemented
40#2837C2214yescomplemented
41#2837C2214yescomplemented
42#2836C2214yescomplemented
43#2830C2214yescomplemented
44#2827C2214yes—
45#2826C2214yescomplemented
46#2821C2214yescomplemented
47#2816C2214yescomplemented
48#2813C2214yes—
49#2798C2214yescomplemented
50#2796C2214yescomplemented
51#2777C2214yescomplemented
52#2773C2214yescomplemented
53#2770C2214yescomplemented
54#2770C2214yescomplemented
55#2758C2214yescomplemented
56#2758C2214yescomplemented
57#2757C2214yescomplemented
58#2756C2214yescomplemented
59#2756C2214yescomplemented
60#2749C2214yes—
61#2749C2214yes—
62#2748C2214yescomplemented
63#2743C2214yes—
64#2743C2214yescomplemented
65#2743C2214yescomplemented
66#2741C2214yescomplemented
67#2740C2214yes—
68#2740C2214yes—
69#2737C2214yescomplemented
70#2737C2214yescomplemented
71#2732C2214yes—
72#2730C2214yes—
73#2729C2214yescomplemented
74#2729C2214yescomplemented
75#2723C2214yescomplemented
76#2710C2214yes—
77#2708C2214yescomplemented
78#2708C2214yescomplemented
79#2705C2214yes—
80#2702C2214yes—
81#2701C2214yes—
82#2701C2214yescomplemented
83#2698C2214yescomplemented
84#2696C2214yescomplemented
85#2692C2214yes—
86#2689C2214yescomplemented
87#2685C2214yes—
88#2684C2214yes—
89#2681C2214yes—
90#2678C2214yes—
91#2678C2214yes—
92#2677C2214yescomplemented
93#2676C2214yes—
94#2674C2214yescomplemented
95#2672C2214yes—
96#2671C2214yes—
97#2667C2214yescomplemented
98#2667C2214yescomplemented
99#2663C2214yescomplemented
100#2659C2214yescomplemented
101#2652C2214yescomplemented
102#2651C2214yescomplemented
103#2650C2214yescomplemented
104#2649C2214yescomplemented
105#2648C2214yes—
106#2647C2212yescomplemented
107#2647C2211yescharacteristic, complemented
108#2646C2214yescomplemented
109#2644C2212yescomplemented
110#2641C2211yescharacteristic, complemented
111#2630C2214yes—
112#2629C2211yescharacteristic
113#2629C2211yescharacteristic
114#2629C2211yescharacteristic
115#2629C2212yes—
116#2628C2212yes—
117#2624C2212yes—
118#2624C2214yes—
119#2619C2211yescharacteristic
120#2608C2214yes—
121#2596C2214yescomplemented
122#2590C2214yescomplemented
123#2590C2214yescomplemented
124#2587C2214yes—
125#2587C2214yes—
126#2584C2212yescomplemented
127#2584C2212yescomplemented
128#2580C2212yescomplemented
129#2580C2212yescomplemented
130#2578C2214yescomplemented
131#2573C2214yescomplemented
132#2572C2214yes—
133#2563C2212yes—
134#2562C2212yes—
135#2562C2212yes—
136#2562C2212yes—
137#2561C2212yes—
138#2561C2212yes—
139#2560C2214yescomplemented
140#2556C2214yescomplemented
141#2547C2212yes—
142#2546C2212yescomplemented
143#2540C2214yes—
144#2538C2212yescomplemented
145#2535C2212yes—
146#2534C2214yes—
147#2525C2214yescomplemented
148#2524C2214yescomplemented
149#2521C2214yescomplemented
150#2516C2214yes—
151#2503C2212yes—
152#2501C2212yescomplemented
153#2500C2212yescomplemented
154#2498C2214yescomplemented
155#2497C2212yescomplemented
156#2497C2212yescomplemented
157#2496C2212yescomplemented
158#2495C2212yescomplemented
159#2495C2212yescomplemented
160#2495C2212yescomplemented
161#2491C2212yescomplemented
162#2490C2212yescomplemented
163#2490C2212yescomplemented
164#2490C2212yescomplemented
165#2487C2212yes—
166#2485C2212yes—
167#2481C2214yes—
168#2479C2214yescomplemented
169#2474C2214yes—
170#2473C2214yescomplemented
171#2470C2214yescomplemented
172#2470C2214yescomplemented
173#2467C2214yes—
174#2463C2214yescomplemented
175#2461C2214yescomplemented
176#2457C2214yes—
177#2452C2214yes—
178#2452C2214yescomplemented
179#2449C2214yes—
180#2444C2214yes—
181#2443C2214yescomplemented
182#2442C2212yescomplemented
183#2442C2212yescomplemented
184#2442C2212yescomplemented
185#2441C2212yescomplemented
186#2441C2212yescomplemented
187#2441C2212yescomplemented
188#2441C2212yescomplemented
189#2440C2212yescomplemented
190#2440C2212yescomplemented
191#2439C2212yescomplemented
192#2437C2214yes—
193#2435C2212yes—
194#2428C2212yescomplemented
195#2428C2212yescomplemented
196#2422C2212yescomplemented
197#2422C2212yescomplemented
198#2420C2212yescomplemented
199#2420C2212yescomplemented
200#2419C2214yescomplemented
201#2418C2214yes—
202#2416C2212yes—
203#2415C2214yescomplemented
204#2414C2212yes—
205#2413C2214yescomplemented
206#2411C2214yes—
207#2410C2214yes—
208#2398C2212yes—
209#2398C2212yes—
210#2395C2214yescomplemented
211#2392C2214yes—
212#2364C2214yes—
213#2363C2212yescomplemented
214#2361C2212yescomplemented
215#2361C2214yescomplemented
216#2358C2214yes—
217#2355C2212yescomplemented
218#2352C2212yes—
219#2347C2212yescomplemented
220#2347C2214yescomplemented
221#2344C2212yescomplemented
222#2335C2214yescomplemented
223#2330C2211yescharacteristic, complemented
224#2330C2211yescharacteristic, complemented
225#2324C2212yes—
226#2324C2212yes—
227#2322C2214yescomplemented
228#2314C2212yes—
229C4×#127C2211yescharacteristic, complemented
230C4×#125C2212yescomplemented
231C4×#125C2211yescharacteristic, complemented
232C4×#124C2212yes—
233C4×#124C2212yes—
234C4×#121C2212yes—
235#2293C2212yescomplemented
236#2280C2212yes—
237#2280C2211yescharacteristic
238#2280C2211yescharacteristic
239#2280C2211yescharacteristic
240#2280C2211yescharacteristic
241C2×#380C2212yes—
242C4×#117C2211yescharacteristic
243C23×D4C2311yescharacteristic
244C24×C4C2311yescharacteristic
245C24×C4C2311yescharacteristic
246#554—48no—
247#553—48no—
248#533—44no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2314yes—
253C2×#127C2311yescharacteristic
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2312yes—
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#125C2312yes—
261C2×#125C2311yescharacteristic
262C2×#125C2311yescharacteristic
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2314yes—
289C2×#120C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×D4—44no—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2314yes—
319C22×C42C2311yescharacteristic
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2312yes—
369#397C2312yes—
370#397C2312yes—
371#397C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2312yes—
417#394C2312yes—
418#394C2312yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#393C2314yes—
435#393C2312yes—
436#393C2314yes—
437#393C2312yes—
438#393C2312yes—
439#393C2312yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
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#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
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#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#384C2311yescharacteristic
593#384C2312yes—
594#384C2311yescharacteristic
595#384C2311yescharacteristic
596#384C2312yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#382C2312yes—
602#382C2311yescharacteristic
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#381C2314yes—
608#381C2312yes—
609#381C2312yes—
610#381C2312yes—
611#381C2312yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2312yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#379C2312yes—
641#379C2312yes—
642#379C2312yes—
643#379C2312yes—
644#379C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673#376C2311yescharacteristic
674#376C2311yescharacteristic
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C25C2411yescharacteristic
679C25C2411yescharacteristic
680C22×Q8C2412yes—
681C22×Q8C2412yes—
682C22×Q8C2414yes—
683C22×D4—42no—
684C22×D4—44no—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C23×C4—24no—
695C23×C4—24no—
696C23×C4—42no—
697C23×C4—42no—
698C23×C4—42no—
699C23×C4—42no—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2414yes—
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2414yes—
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C4⋊Q8—42no—
715C4⋊Q8—44no—
716C4⋊Q8—42no—
717C4⋊Q8—84no—
718#127—42no—
719#126—48no—
720#126—84no—
721#125—28no—
722#125—42no—
723#125—42no—
724#125—42no—
725#125—42no—
726#125—42no—
727#125—44no—
728#124—44no—
729#124—44no—
730#124—84no—
731#123—48no—
732#123—48no—
733#123—48no—
734#123—84no—
735#123—84no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—44no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—84no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744#121—28no—
745#121—48no—
746#121—48no—
747#121—44no—
748#121—44no—
749#121—44no—
750#121—44no—
751#121—48no—
752#121—84no—
753#120—48no—
754#120—84no—
755C4×Q8—28no—
756C4×Q8—44no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—44no—
760C4×D4—44no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—48no—
765C4×D4—84no—
766C4×D4—84no—
767C4×D4—84no—
768#117—24no—
769#117—42no—
770#117—42no—
771#117—42no—
772#117—48no—
773#117—44no—
774#117—44no—
775#117—84no—
776C2×C4⋊C4—44no—
777C2×C4⋊C4—42no—
778C2×C4⋊C4—44no—
779C2×C4⋊C4—48no—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C22⋊C4—42no—
833C2×C22⋊C4—42no—
834C2×C22⋊C4—84no—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C42—24no—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971C24—22no—
972C24—24no—
973C24—22no—
974C24—41no—
975C24—41no—
976C24—42no—
977C24—42no—
978C24—42no—
979C24—41no—
980C24—41no—
981C24C2512yes—
982C24C2514yes—
983C24C2511yescharacteristic
984C24C2512yes—
985C2×Q8—24no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—42no—
991C2×Q8—44no—
992C2×Q8—44no—
993C2×Q8—44no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—416no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—28no—
1027C22×C4—22no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—22no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—88no—
1062C22×C4—88no—
1063C22×C42−1+414yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
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—42no—
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—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—22no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—42no—
1210C42—44no—
1211C42—42no—
1212C42—44no—
1213C42—42no—
1214C42—42no—
1215C42—44no—
1216C42H(5,𝔽2)14yes—
1217C23—22no—
1218C23—21no—
1219C23—22no—
1220C23—21no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—24no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23—24no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—24no—
1241C23—44no—
1242C23—48no—
1243C23—44no—
1244C23—82no—
1245C23—82no—
1246C23—84no—
1247C23—84no—
1248C23—82no—
1249C23—82no—
1250C23—84no—
1251C23C2×2−1+412yes—
1252C23#58514yes—
1253C23C2611yescharacteristic
1254Q8—84no—
1255Q8—84no—
1256Q8—164no—
1257D4—48no—
1258D4—48no—
1259D4—48no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—164no—
1265D4—164no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—28no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—44no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—88no—
1330C2×C4—82no—
1331C2×C4—84no—
1332C2×C4—84no—
1333C2×C4—88no—
1334C2×C4—82no—
1335C2×C4—82no—
1336C2×C4—88no—
1337C2×C4—164no—
1338C2×C4—164no—
1339C2×C4C2×H(5,𝔽2)12yes—
1340C2×C4C2×H(5,𝔽2)12yes—
1341C2×C4C2×H(5,𝔽2)12yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4C2×2−1+412yes—
1344C2×C4#58512yes—
1345C22—24no—
1346C22—22no—
1347C22—24no—
1348C22—24no—
1349C22—24no—
1350C22—41no—
1351C22—42no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—44no—
1358C22—42no—
1359C22—42no—
1360C22—44no—
1361C22—44no—
1362C22—42no—
1363C22—44no—
1364C22—44no—
1365C22—42no—
1366C22—42no—
1367C22—44no—
1368C22—44no—
1369C22—42no—
1370C22—42no—
1371C22—88no—
1372C22—88no—
1373C22C22×H(5,𝔽2)11yescharacteristic
1374C22C22×2−1+411yescharacteristic
1375C22C2×#58512yes—
1376C22C2×#58511yescharacteristic
1377C22H(7,𝔽2)12yes—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—41no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—41no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—44no—
1394C4—44no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4#356114yes—
1401C2—44no—
1402C2—42no—
1403C2—84no—
1404C2—82no—
1405C2#6272911yescharacteristic
1406C2C2×#356111yescharacteristic
1407C2#6288011yescharacteristic
1408C2#6294112yes—
1409C2#6295812yes—
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. #59657C2semidirect
2. #59432C2semidirect
3. #57199C2semidirect
4. #56197C2semidirect
5. #56185C2semidirect
6. #55631C2semidirect
7. #53119C2semidirect
8. #53115C2semidirect
9. #52474C2semidirect
10. #43428C2semidirect
11. #42625C2semidirect
12. #42554C2semidirect
13. #41708C2semidirect
14. #41144C2semidirect
15. #40003C2semidirect
16. #39952C2semidirect
17. #39590C2semidirect
18. #37858C2semidirect
19. #37851C2semidirect
20. #37481C2semidirect
21. #37477C2semidirect
22. #37283C2semidirect
23. #37283C2semidirect
24. #36157C2semidirect
25. #35336C2semidirect
26. #34946C2semidirect
27. #34621C2semidirect
28. C2×#554C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
39. #2839C22semidirect
40. #2837C22semidirect
41. #2837C22semidirect
42. #2836C22semidirect
43. #2830C22semidirect
45. #2826C22semidirect
46. #2821C22semidirect
47. #2816C22semidirect
49. #2798C22semidirect
50. #2796C22semidirect
51. #2777C22semidirect
52. #2773C22semidirect
53. #2770C22semidirect
54. #2770C22semidirect
55. #2758C22semidirect
56. #2758C22semidirect
57. #2757C22semidirect
58. #2756C22semidirect
59. #2756C22semidirect
62. #2748C22semidirect
64. #2743C22semidirect
65. #2743C22semidirect
66. #2741C22semidirect
69. #2737C22semidirect
70. #2737C22semidirect
73. #2729C22semidirect
74. #2729C22semidirect
75. #2723C22semidirect
77. #2708C22semidirect
78. #2708C22semidirect
82. #2701C22semidirect
83. #2698C22semidirect
84. #2696C22semidirect
86. #2689C22semidirect
92. #2677C22semidirect
94. #2674C22semidirect
97. #2667C22semidirect
98. #2667C22semidirect
99. #2663C22semidirect
100. #2659C22semidirect
101. #2652C22semidirect
102. #2651C22semidirect
103. #2650C22semidirect
104. #2649C22semidirect
106. #2647C22semidirect
107. #2647C22semidirect
108. #2646C22semidirect
109. #2644C22semidirect
110. #2641C22semidirect
121. #2596C22semidirect
122. #2590C22semidirect
123. #2590C22semidirect
126. #2584C22semidirect
127. #2584C22semidirect
128. #2580C22semidirect
129. #2580C22semidirect
130. #2578C22semidirect
131. #2573C22semidirect
139. #2560C22semidirect
140. #2556C22semidirect
142. #2546C22semidirect
144. #2538C22semidirect
147. #2525C22semidirect
148. #2524C22semidirect
149. #2521C22semidirect
152. #2501C22semidirect
153. #2500C22semidirect
154. #2498C22semidirect
155. #2497C22semidirect
156. #2497C22semidirect
157. #2496C22semidirect
158. #2495C22semidirect
159. #2495C22semidirect
160. #2495C22semidirect
161. #2491C22semidirect
162. #2490C22semidirect
163. #2490C22semidirect
164. #2490C22semidirect
168. #2479C22semidirect
170. #2473C22semidirect
171. #2470C22semidirect
172. #2470C22semidirect
174. #2463C22semidirect
175. #2461C22semidirect
178. #2452C22semidirect
181. #2443C22semidirect
182. #2442C22semidirect
183. #2442C22semidirect
184. #2442C22semidirect
185. #2441C22semidirect
186. #2441C22semidirect
187. #2441C22semidirect
188. #2441C22semidirect
189. #2440C22semidirect
190. #2440C22semidirect
191. #2439C22semidirect
194. #2428C22semidirect
195. #2428C22semidirect
196. #2422C22semidirect
197. #2422C22semidirect
198. #2420C22semidirect
199. #2420C22semidirect
200. #2419C22semidirect
203. #2415C22semidirect
205. #2413C22semidirect
210. #2395C22semidirect
213. #2363C22semidirect
214. #2361C22semidirect
215. #2361C22semidirect
217. #2355C22semidirect
219. #2347C22semidirect
220. #2347C22semidirect
221. #2344C22semidirect
222. #2335C22semidirect
223. #2330C22semidirect
224. #2330C22semidirect
227. #2322C22semidirect
229. C4×#127C22semidirect
230. C4×#125C22semidirect
231. C4×#125C22semidirect
235. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#596572
#594322
#571992
#561972
#561852
#556312
#531192
#531152
#524742
#434282
#426252
#425542
#417082
#411442
#400032
#399522
#395902
#378582
#378512
#374812
#374772
#372832
#361572
#353362
#349462
#346212