Finite Group Databasebeta

← #8701494

Subgroups — #8701494

Order 512.

4400 conjugacy classes of subgroups.

The subgroup lattice has 1435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59989C212yesmaximal, complemented
2#59651C212yesmaximal, complemented
3#59274C212yesmaximal, complemented
4#59227C212yesmaximal, complemented
5#58797C212yesmaximal, complemented
6#57422C214yesmaximal, complemented
7#54333C212yesmaximal, complemented
8#54263C214yesmaximal, complemented
9#52292C211yesmaximal, characteristic
10#50266C214yesmaximal, complemented
11#49195C214yesmaximal, complemented
12#48087C214yesmaximal, complemented
13#45667C212yesmaximal, complemented
14#45493C211yesmaximal, characteristic, complemented
15#45375C211yesmaximal, characteristic, complemented
16#45226C211yesmaximal, characteristic, complemented
17#45219C212yesmaximal, complemented
18#44971C212yesmaximal, complemented
19#42978C211yesmaximal, characteristic, complemented
20#42852C212yesmaximal, complemented
21#42808C211yesmaximal, characteristic, complemented
22#42717C212yesmaximal, complemented
23#39924C212yesmaximal, complemented
24#39022C212yesmaximal, complemented
25#38974C212yesmaximal, complemented
26#37428C212yesmaximal, complemented
27#36786C214yesmaximal, complemented
28#36427C211yesmaximal, characteristic, complemented
29#36234C212yesmaximal, complemented
30C2×#552C2212yes—
31C2×#552C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic, complemented
33C2×#544C2211yescharacteristic, complemented
34C22×#117C2211yescharacteristic
35#2853C2212yes—
36#2851C2214yes—
37#2851C2212yescomplemented
38#2848C2211yescharacteristic
39#2848C2212yes—
40#2842C2212yes—
41#2838C2214yes—
42#2835C2214yes—
43#2831C2214yes—
44#2822C2212yescomplemented
45#2821C2212yescomplemented
46#2808C2214yes—
47#2807C2211yescharacteristic
48#2807C2212yes—
49#2807C2212yes—
50#2807C2212yes—
51#2807C2212yescomplemented
52#2796C2212yes—
53#2794C2212yescomplemented
54#2793C2214yes—
55#2790C2214yes—
56#2790C2214yescomplemented
57#2783C2214yes—
58#2782C2214yes—
59#2782C2214yes—
60#2781C2214yes—
61#2781C2214yescomplemented
62#2781C2214yescomplemented
63#2780C2212yes—
64#2780C2214yes—
65#2779C2214yes—
66#2778C2212yes—
67#2777C2214yes—
68#2777C2214yes—
69#2775C2214yes—
70#2774C2214yescomplemented
71#2774C2214yescomplemented
72#2774C2214yescomplemented
73#2774C2214yescomplemented
74#2773C2214yescomplemented
75#2772C2214yes—
76#2771C2214yescomplemented
77#2767C2214yescomplemented
78#2767C2214yescomplemented
79#2763C2214yes—
80#2763C2214yes—
81#2763C2214yes—
82#2762C2214yescomplemented
83#2761C2214yes—
84#2755C2214yescomplemented
85#2751C2214yes—
86#2748C2212yes—
87#2747C2214yescomplemented
88#2746C2212yes—
89#2746C2214yes—
90#2745C2214yescomplemented
91#2738C2214yes—
92#2736C2214yes—
93#2735C2211yescharacteristic
94#2725C2214yes—
95#2723C2214yes—
96#2720C2214yescomplemented
97#2716C2214yes—
98#2696C2214yes—
99#2693C2211yescharacteristic
100#2690C2214yescomplemented
101#2690C2214yescomplemented
102#2689C2214yescomplemented
103#2688C2212yes—
104#2687C2214yes—
105#2684C2214yes—
106#2678C2212yes—
107#2674C2214yes—
108#2672C2214yes—
109#2668C2211yescharacteristic
110#2655C2214yescomplemented
111#2655C2214yescomplemented
112#2654C2214yes—
113#2650C2214yes—
114#2650C2214yescomplemented
115#2648C2214yes—
116#2643C2214yes—
117#2642C2212yescomplemented
118#2642C2211yescharacteristic, complemented
119#2636C2212yescomplemented
120#2628C2212yes—
121#2628C2212yes—
122#2625C2211yescharacteristic, complemented
123#2611C2214yes—
124#2611C2212yes—
125#2609C2214yes—
126#2600C2214yes—
127#2598C2212yes—
128#2597C2214yes—
129#2596C2214yes—
130#2589C2214yes—
131#2587C2214yescomplemented
132#2586C2214yescomplemented
133#2571C2212yescomplemented
134#2571C2214yescomplemented
135#2571C2214yescomplemented
136#2567C2212yescomplemented
137#2564C2214yes—
138#2562C2212yes—
139#2562C2212yes—
140#2562C2211yescharacteristic, complemented
141#2562C2212yescomplemented
142#2560C2214yes—
143#2552C2212yescomplemented
144#2550C2214yescomplemented
145#2550C2214yescomplemented
146#2550C2212yescomplemented
147#2547C2212yes—
148#2542C2211yescharacteristic
149#2538C2212yes—
150#2533C2214yescomplemented
151#2529C2214yes—
152#2529C2214yescomplemented
153#2528C2214yescomplemented
154#2517C2212yes—
155#2515C2214yescomplemented
156#2514C2212yescomplemented
157#2513C2214yes—
158#2511C2212yescomplemented
159#2511C2212yescomplemented
160#2509C2214yescomplemented
161#2505C2214yescomplemented
162#2505C2214yescomplemented
163#2503C2211yescharacteristic, complemented
164#2502C2211yescharacteristic
165#2500C2214yes—
166#2499C2212yes—
167#2497C2212yes—
168#2497C2212yescomplemented
169#2492C2212yes—
170#2492C2212yes—
171#2489C2212yes—
172#2489C2212yes—
173#2489C2212yes—
174#2489C2212yes—
175#2489C2212yescomplemented
176#2489C2212yescomplemented
177#2488C2214yes—
178#2487C2211yescharacteristic
179#2487C2211yescharacteristic
180#2486C2212yescomplemented
181#2485C2212yes—
182#2482C2212yes—
183#2480C2214yes—
184#2479C2214yes—
185#2478C2214yes—
186#2475C2214yes—
187#2475C2214yescomplemented
188#2474C2214yes—
189#2470C2214yes—
190#2470C2214yes—
191#2470C2214yescomplemented
192#2461C2214yes—
193#2455C2212yes—
194#2455C2212yescomplemented
195#2453C2212yescomplemented
196#2453C2212yescomplemented
197#2446C2212yescomplemented
198#2444C2214yes—
199#2442C2212yes—
200#2441C2212yes—
201#2441C2212yes—
202#2440C2212yescomplemented
203#2438C2214yescomplemented
204#2438C2214yescomplemented
205#2429C2212yes—
206#2425C2214yes—
207#2423C2212yes—
208#2418C2214yes—
209#2417C2212yes—
210#2417C2212yes—
211#2415C2212yes—
212#2415C2212yes—
213#2415C2212yescomplemented
214#2415C2214yescomplemented
215#2411C2212yes—
216#2409C2212yes—
217#2409C2212yes—
218#2409C2212yes—
219#2409C2212yescomplemented
220#2401C2212yes—
221#2397C2211yescharacteristic
222#2395C2211yescharacteristic
223#2392C2212yes—
224#2379C2214yes—
225#2375C2212yes—
226#2370C2212yescomplemented
227#2370C2212yescomplemented
228#2362C2212yes—
229#2362C2212yes—
230#2360C2212yes—
231#2359C2214yes—
232#2359C2214yescomplemented
233#2355C2212yescomplemented
234#2354C2212yes—
235#2352C2212yes—
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2212yescomplemented
238#2346C2212yes—
239#2346C2214yescomplemented
240#2346C2211yescharacteristic, complemented
241#2344C2211yescharacteristic
242Q8×C22⋊C4C2212yescomplemented
243#2332C2214yescomplemented
244#2330C2212yescomplemented
245#2323C2212yescomplemented
246#2320C2211yescharacteristic, complemented
247#2318C2214yescomplemented
248#2314C2214yes—
249C4×C22⋊Q8C2212yescomplemented
250C4×#123C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253C4×#120C2211yescharacteristic
254C4×#120C2212yes—
255#2296C2212yes—
256C2×#391C2212yescomplemented
257#2290C2214yes—
258#2285C2212yescomplemented
259C23×Q8C2312yes—
260C24×C4C2311yescharacteristic
261#552—44no—
262#552—48no—
263D4×Q8—44no—
264#544—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2314yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#120C2311yescharacteristic
297C2×#120C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×#117—44no—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C2×#117C2314yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2311yescharacteristic
325C22×C22⋊C4C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328#401C2314yes—
329#401C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2311yescharacteristic
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#399C2314yes—
366#399C2311yescharacteristic
367#399C2312yes—
368#399C2314yes—
369#399C2312yes—
370#399C2312yes—
371#399C2314yes—
372#399C2311yescharacteristic
373#399C2311yescharacteristic
374#399C2312yes—
375#399C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2311yescharacteristic
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#396C2312yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2312yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#392C2311yescharacteristic
454#392C2312yes—
455#392C2311yescharacteristic
456#392C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#386C2314yes—
590#386C2312yes—
591#386C2314yes—
592#386C2312yes—
593#386C2314yes—
594#386C2312yes—
595#386C2311yescharacteristic
596#386C2314yes—
597#386C2312yes—
598#386C2314yes—
599#386C2312yes—
600#386C2312yes—
601#386C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2312yes—
605#386C2312yes—
606#386C2312yes—
607#386C2312yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2314yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2312yes—
634#385C2311yescharacteristic
635#385C2312yes—
636#385C2312yes—
637#384C2312yes—
638#384C2312yes—
639#384C2314yes—
640#384C2312yes—
641#384C2312yes—
642#383C2312yes—
643#383C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2312yes—
655#382C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2312yes—
659#381C2312yes—
660#380C2312yes—
661#380C2311yescharacteristic
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2311yescharacteristic
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#379C2311yescharacteristic
680#379C2314yes—
681#379C2312yes—
682#379C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2311yescharacteristic
713#376C2314yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C25C2411yescharacteristic
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C23×C4—42no—
733C23×C4—44no—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—44no—
750C4⋊Q8—42no—
751#126—44no—
752#126—48no—
753#125—28no—
754#125—44no—
755#125—44no—
756#125—44no—
757#125—48no—
758#125—44no—
759#125—42no—
760#124—48no—
761#123—28no—
762#123—48no—
763#123—48no—
764#123—44no—
765C22⋊Q8—28no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—42no—
774C22⋊Q8—42no—
775C22⋊Q8—44no—
776#121—44no—
777#121—44no—
778#120—24no—
779#120—44no—
780C4×Q8—24no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—44no—
786C4×D4—44no—
787C4×D4—44no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—42no—
791C4×D4—48no—
792C4×D4—48no—
793#117—28no—
794#117—24no—
795#117—28no—
796#117—42no—
797#117—44no—
798#117—48no—
799#117—48no—
800#117—48no—
801#117—44no—
802C2×C4⋊C4—24no—
803C2×C4⋊C4—42no—
804C2×C4⋊C4—42no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4—44no—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2411yescharacteristic
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C42—44no—
921C2×C42—44no—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2411yescharacteristic
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24—22no—
1014C24—41no—
1015C24—42no—
1016C24—42no—
1017C24—41no—
1018C24C2512yes—
1019C24C2511yescharacteristic
1020C24C2511yescharacteristic
1021C24C2512yes—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—816no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—41no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—41no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—42no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—416no—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—41no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4H(5,𝔽2)14yes—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—28no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—41no—
1194C22⋊C4—41no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—41no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C42−1+414yes—
1227C42—28no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—22no—
1232C42—28no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—42no—
1237C42—42no—
1238C42—44no—
1239C42—42no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C23—22no—
1248C23—21no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—21no—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—21no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—21no—
1269C23—44no—
1270C23—84no—
1271C23—82no—
1272C23—82no—
1273C23—84no—
1274C23C2×2−1+412yes—
1275C23#58514yes—
1276C23C2611yescharacteristic
1277Q8—48no—
1278Q8—44no—
1279Q8—88no—
1280Q8—164no—
1281D4—44no—
1282D4—48no—
1283D4—48no—
1284D4—84no—
1285D4—84no—
1286D4—84no—
1287D4—82no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—21no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—21no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—48no—
1354C2×C4—48no—
1355C2×C4—44no—
1356C2×C4—48no—
1357C2×C4—44no—
1358C2×C4—44no—
1359C2×C4—48no—
1360C2×C4—48no—
1361C2×C4—88no—
1362C2×C4—84no—
1363C2×C4—84no—
1364C2×C4—88no—
1365C2×C4—162no—
1366C2×C4C2×H(5,𝔽2)14yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×2−1+414yes—
1369C2×C4#58514yes—
1370C22—24no—
1371C22—24no—
1372C22—24no—
1373C22—24no—
1374C22—22no—
1375C22—41no—
1376C22—42no—
1377C22—41no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—41no—
1384C22—41no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—41no—
1393C22—42no—
1394C22—88no—
1395C22C22×H(5,𝔽2)11yescharacteristic
1396C22C22×2−1+411yescharacteristic
1397C22C2×#58512yes—
1398C22C2×#58512yes—
1399C222−1+611yescharacteristic
1400C4—24no—
1401C4—24no—
1402C4—41no—
1403C4—42no—
1404C4—41no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—44no—
1409C4—44no—
1410C4—41no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—41no—
1424C4#354014yes—
1425C2—44no—
1426C2—42no—
1427C2—81no—
1428C2—82no—
1429C2C2×#354011yescharacteristic
1430C2#6290712yes—
1431C2#6291511yescharacteristic
1432C2#6302011yescharacteristic
1433C2#6302312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52292C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59989C2semidirect
2. #59651C2semidirect
3. #59274C2semidirect
4. #59227C2semidirect
5. #58797C2semidirect
6. #57422C2semidirect
7. #54333C2semidirect
8. #54263C2semidirect
10. #50266C2semidirect
11. #49195C2semidirect
12. #48087C2semidirect
13. #45667C2semidirect
14. #45493C2semidirect
15. #45375C2semidirect
16. #45226C2semidirect
17. #45219C2semidirect
18. #44971C2semidirect
19. #42978C2semidirect
20. #42852C2semidirect
21. #42808C2semidirect
22. #42717C2semidirect
23. #39924C2semidirect
24. #39022C2semidirect
25. #38974C2semidirect
26. #37428C2semidirect
27. #36786C2semidirect
28. #36427C2semidirect
29. #36234C2semidirect
32. C2×D4×Q8C22semidirect
33. C2×#544C22semidirect
37. #2851C22semidirect
44. #2822C22semidirect
45. #2821C22semidirect
51. #2807C22semidirect
53. #2794C22semidirect
56. #2790C22semidirect
61. #2781C22semidirect
62. #2781C22semidirect
70. #2774C22semidirect
71. #2774C22semidirect
72. #2774C22semidirect
73. #2774C22semidirect
74. #2773C22semidirect
76. #2771C22semidirect
77. #2767C22semidirect
78. #2767C22semidirect
82. #2762C22semidirect
84. #2755C22semidirect
87. #2747C22semidirect
90. #2745C22semidirect
96. #2720C22semidirect
100. #2690C22semidirect
101. #2690C22semidirect
102. #2689C22semidirect
110. #2655C22semidirect
111. #2655C22semidirect
114. #2650C22semidirect
117. #2642C22semidirect
118. #2642C22semidirect
119. #2636C22semidirect
122. #2625C22semidirect
131. #2587C22semidirect
132. #2586C22semidirect
133. #2571C22semidirect
134. #2571C22semidirect
135. #2571C22semidirect
136. #2567C22semidirect
140. #2562C22semidirect
141. #2562C22semidirect
143. #2552C22semidirect
144. #2550C22semidirect
145. #2550C22semidirect
146. #2550C22semidirect
150. #2533C22semidirect
152. #2529C22semidirect
153. #2528C22semidirect
155. #2515C22semidirect
156. #2514C22semidirect
158. #2511C22semidirect
159. #2511C22semidirect
160. #2509C22semidirect
161. #2505C22semidirect
162. #2505C22semidirect
163. #2503C22semidirect
168. #2497C22semidirect
175. #2489C22semidirect
176. #2489C22semidirect
180. #2486C22semidirect
187. #2475C22semidirect
191. #2470C22semidirect
194. #2455C22semidirect
195. #2453C22semidirect
196. #2453C22semidirect
197. #2446C22semidirect
202. #2440C22semidirect
203. #2438C22semidirect
204. #2438C22semidirect
213. #2415C22semidirect
214. #2415C22semidirect
219. #2409C22semidirect
226. #2370C22semidirect
227. #2370C22semidirect
232. #2359C22semidirect
233. #2355C22semidirect
237. D4×C4⋊C4C22semidirect
239. #2346C22semidirect
240. #2346C22semidirect
242. Q8×C22⋊C4C22semidirect
243. #2332C22semidirect
244. #2330C22semidirect
245. #2323C22semidirect
246. #2320C22semidirect
247. #2318C22semidirect
249. C4×C22⋊Q8C22semidirect
256. C2×#391C22semidirect
258. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#599892
#596512
#592742
#592272
#587972
#574222
#543332
#542632
#522922
#502662
#491952
#480872
#456672
#454932
#453752
#452262
#452192
#449712
#429782
#428522
#428082
#427172
#399242
#390222
#389742
#374282
#367862
#364272
#362342