Finite Group Databasebeta

← #8701625

Subgroups — #8701625

Order 512.

4509 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C212yesmaximal, complemented
2#59871C212yesmaximal, complemented
3#59114C212yesmaximal, complemented
4#59055C212yesmaximal, complemented
5#58710C214yesmaximal, complemented
6#55487C214yesmaximal, complemented
7#54880C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic
9#51878C214yesmaximal, complemented
10#50058C214yesmaximal, complemented
11#49734C214yesmaximal, complemented
12#46023C211yesmaximal, characteristic, complemented
13#46007C211yesmaximal, characteristic, complemented
14#46005C211yesmaximal, characteristic, complemented
15#45238C212yesmaximal, complemented
16#45217C212yesmaximal, complemented
17#44997C212yesmaximal, complemented
18#42929C212yesmaximal, complemented
19#42791C212yesmaximal, complemented
20#42708C212yesmaximal, complemented
21#39959C212yesmaximal, complemented
22#39656C212yesmaximal, complemented
23#39599C212yesmaximal, complemented
24#37265C212yesmaximal, complemented
25#37265C212yesmaximal, complemented
26#37251C212yesmaximal
27#36508C211yesmaximal, characteristic, complemented
28#36508C211yesmaximal, characteristic, complemented
29#36497C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#556C2212yes—
35C2×#552C2212yes—
36C2×#541C2212yes—
37C2×#533C2212yes—
38#2864C2212yes—
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2861C2212yes—
42#2861C2212yes—
43#2859C2211yescharacteristic
44#2857C2212yes—
45#2845C2212yes—
46#2845C2212yes—
47#2836C2214yes—
48#2823C2214yes—
49#2822C2214yes—
50#2820C2212yes—
51#2808C2211yescharacteristic
52#2808C2212yes—
53#2806C2211yescharacteristic
54#2806C2212yes—
55#2806C2212yes—
56#2806C2212yes—
57#2806C2212yes—
58#2800C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2791C2214yes—
62#2790C2214yes—
63#2783C2212yes—
64#2781C2212yes—
65#2780C2214yes—
66#2773C2214yes—
67#2773C2214yes—
68#2772C2214yes—
69#2768C2214yes—
70#2768C2214yes—
71#2768C2214yes—
72#2768C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2754C2214yes—
77#2744C2212yes—
78#2732C2211yescharacteristic
79#2732C2212yes—
80#2730C2212yes—
81#2729C2214yes—
82#2729C2214yes—
83#2727C2214yes—
84#2726C2214yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2725C2214yes—
89#2725C2214yes—
90#2722C2214yes—
91#2722C2214yes—
92#2721C2214yes—
93#2721C2214yes—
94#2721C2214yes—
95#2721C2214yes—
96#2721C2214yes—
97#2719C2214yes—
98#2718C2214yes—
99#2718C2214yes—
100#2715C2214yes—
101#2715C2214yes—
102#2715C2214yes—
103#2712C2214yes—
104#2704C2214yes—
105#2704C2214yes—
106#2704C2214yes—
107#2698C2214yes—
108#2695C2214yes—
109#2694C2212yes—
110#2694C2214yes—
111#2686C2212yes—
112#2682C2211yescharacteristic
113#2674C2214yes—
114#2672C2214yes—
115#2667C2214yes—
116#2664C2214yes—
117#2664C2214yes—
118#2654C2214yes—
119#2651C2214yes—
120#2637C2214yes—
121#2637C2214yes—
122#2637C2214yes—
123#2629C2214yes—
124#2621C2212yes—
125#2601C2214yes—
126#2590C2214yes—
127#2589C2214yes—
128#2589C2214yes—
129#2587C2214yes—
130#2585C2214yes—
131#2584C2214yes—
132#2584C2214yes—
133#2584C2214yes—
134#2582C2212yes—
135#2582C2214yes—
136#2582C2214yes—
137#2581C2212yes—
138#2570C2212yes—
139#2567C2214yes—
140#2565C2212yes—
141#2565C2212yes—
142#2554C2214yes—
143#2552C2214yes—
144#2552C2211yescharacteristic
145#2552C2214yes—
146#2551C2211yescharacteristic
147#2550C2212yes—
148#2546C2211yescharacteristic
149#2546C2212yes—
150#2546C2212yes—
151#2546C2212yes—
152#2546C2211yescharacteristic
153#2546C2212yes—
154#2545C2212yes—
155#2545C2212yes—
156#2542C2211yescharacteristic
157#2542C2211yescharacteristic
158#2542C2212yes—
159#2542C2212yes—
160#2522C2214yes—
161#2520C2214yes—
162#2520C2214yes—
163#2520C2214yes—
164#2519C2214yes—
165#2519C2214yes—
166#2519C2214yes—
167#2519C2214yes—
168#2519C2214yes—
169#2519C2214yes—
170#2509C2212yes—
171#2507C2212yes—
172#2507C2214yes—
173#2507C2214yes—
174#2502C2212yes—
175#2499C2212yes—
176#2479C2214yes—
177#2479C2214yes—
178#2479C2214yes—
179#2478C2214yes—
180#2478C2214yes—
181#2478C2214yes—
182#2474C2214yes—
183#2469C2214yes—
184#2465C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2453C2212yes—
188#2453C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2212yes—
192#2451C2212yes—
193#2448C2214yes—
194#2446C2212yes—
195#2446C2212yes—
196#2441C2212yes—
197#2441C2214yes—
198#2440C2212yes—
199#2439C2212yes—
200#2439C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2429C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2426C2214yes—
212#2423C2214yes—
213#2423C2212yes—
214#2423C2212yes—
215#2417C2212yes—
216#2417C2212yes—
217#2415C2212yes—
218#2415C2212yes—
219#2415C2212yes—
220#2415C2212yes—
221#2396C2212yes—
222#2395C2212yes—
223#2392C2212yes—
224#2382C2212yes—
225#2382C2212yes—
226#2379C2212yes—
227#2370C2212yes—
228#2369C2214yes—
229#2365C2214yes—
230#2365C2212yes—
231#2362C2212yes—
232#2362C2212yes—
233#2362C2212yes—
234#2362C2212yes—
235#2362C2212yes—
236#2360C2212yes—
237#2355C2211yescharacteristic
238#2355C2211yescharacteristic
239#2351C2212yes—
240Q8×C4⋊C4C2214yes—
241Q8×C4⋊C4C2212yes—
242#2335C2214yes—
243#2323C2214yes—
244#2323C2214yes—
245#2323C2212yes—
246#2317C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×#125C2211yescharacteristic
251C4×#124C2211yescharacteristic
252C4×#124C2211yescharacteristic
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256C4×#121C2212yes—
257#2296C2212yes—
258C42×Q8C2211yescharacteristic
259#557—44no—
260#557—44no—
261#556—44no—
262#556—44no—
263#556—48no—
264#552—48no—
265#541—48no—
266#533—48no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#125C2311yescharacteristic
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×#121C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2314yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2314yes—
333C2×C4×Q8C2314yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C42C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2312yes—
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2312yes—
439#396C2312yes—
440#396C2314yes—
441#396C2312yes—
442#396C2312yes—
443#396C2314yes—
444#396C2314yes—
445#395C2314yes—
446#395C2312yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#393C2314yes—
463#393C2314yes—
464#393C2312yes—
465#392C2312yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2311yescharacteristic
497#390C2312yes—
498#390C2312yes—
499#390C2314yes—
500#389C2311yescharacteristic
501#389C2311yescharacteristic
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2314yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2312yes—
651#384C2312yes—
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#384C2314yes—
656#384C2312yes—
657#384C2311yescharacteristic
658#384C2311yescharacteristic
659#384C2314yes—
660#384C2314yes—
661#382C2311yescharacteristic
662#382C2312yes—
663#382C2311yescharacteristic
664#382C2311yescharacteristic
665#382C2314yes—
666#382C2312yes—
667#382C2314yes—
668#382C2312yes—
669#382C2312yes—
670#382C2312yes—
671#382C2312yes—
672#382C2312yes—
673#382C2312yes—
674#381C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681#380C2314yes—
682#380C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C43C2311yescharacteristic
719C43C2312yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—42no—
741C4⋊Q8—42no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749#126—48no—
750#126—48no—
751#126—48no—
752#126—48no—
753#126—48no—
754#126—48no—
755#126—48no—
756#125—28no—
757#125—24no—
758#125—44no—
759#125—48no—
760#125—48no—
761#125—48no—
762#125—44no—
763#125—44no—
764#125—48no—
765#125—48no—
766#125—48no—
767#124—24no—
768#124—44no—
769#124—44no—
770#124—42no—
771#124—48no—
772#123—28no—
773#123—48no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—28no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787#121—44no—
788C4×Q8—28no—
789C4×Q8—28no—
790C4×Q8—24no—
791C4×Q8—24no—
792C4×Q8—24no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—42no—
796C4×Q8—44no—
797C4×Q8—42no—
798C4×Q8—44no—
799C4×Q8—48no—
800C4×Q8—44no—
801C4×Q8—48no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—48no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—42no—
810#117—28no—
811#117—28no—
812#117—44no—
813#117—48no—
814#117—48no—
815#117—44no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C42—44no—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2512yes—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—28no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—28no—
1043C2×Q8—24no—
1044C2×Q8—22no—
1045C2×Q8—24no—
1046C2×Q8—41no—
1047C2×Q8—41no—
1048C2×Q8—44no—
1049C2×Q8—41no—
1050C2×Q8—41no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q82−1+414yes—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—41no—
1067C2×D4—42no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—44no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4H(5,𝔽2)14yes—
1191C4⋊C4H(5,𝔽2)14yes—
1192C4⋊C42−1+414yes—
1193C4⋊C42−1+414yes—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C42—24no—
1230C42—24no—
1231C42—28no—
1232C42—28no—
1233C42—24no—
1234C42—28no—
1235C42—24no—
1236C42—22no—
1237C42—22no—
1238C42—24no—
1239C42—24no—
1240C42—28no—
1241C42—22no—
1242C42—24no—
1243C42—22no—
1244C42—22no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—22no—
1249C42—42no—
1250C42—42no—
1251C42—41no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23C2611yescharacteristic
1274Q8—44no—
1275Q8—416no—
1276Q8—44no—
1277Q8—44no—
1278Q8—48no—
1279Q8—48no—
1280Q8—84no—
1281Q8—84no—
1282D4—84no—
1283D4—82no—
1284D4—82no—
1285D4—84no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—48no—
1357C2×C4—48no—
1358C2×C4—48no—
1359C2×C4—84no—
1360C2×C4—88no—
1361C2×C4C2×H(5,𝔽2)14yes—
1362C2×C4C2×H(5,𝔽2)14yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4C2×2−1+412yes—
1367C2×C4C2×2−1+414yes—
1368C2×C4C2×2−1+414yes—
1369C2×C4C2×2−1+414yes—
1370C2×C4C2×2−1+412yes—
1371C2×C4#58512yes—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C22×H(5,𝔽2)11yescharacteristic
1388C22C22×2−1+411yescharacteristic
1389C22C22×2−1+411yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C2×#58511yescharacteristic
1392C222−1+611yescharacteristic
1393C4—24no—
1394C4—24no—
1395C4—24no—
1396C4—24no—
1397C4—24no—
1398C4—22no—
1399C4—22no—
1400C4—22no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—44no—
1406C4—41no—
1407C4—42no—
1408C4—44no—
1409C4—41no—
1410C4—42no—
1411C4—42no—
1412C4—41no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4#354814yes—
1420C2—82no—
1421C2—82no—
1422C2C2×#354811yescharacteristic
1423C2#6289311yescharacteristic
1424C2#6289711yescharacteristic
1425C2#6294711yescharacteristic
1426C2#6301311yescharacteristic
1427C2#6303211yescharacteristic
1428C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2682C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59922C2semidirect
2. #59871C2semidirect
3. #59114C2semidirect
4. #59055C2semidirect
5. #58710C2semidirect
6. #55487C2semidirect
7. #54880C2semidirect
9. #51878C2semidirect
10. #50058C2semidirect
11. #49734C2semidirect
12. #46023C2semidirect
13. #46007C2semidirect
14. #46005C2semidirect
15. #45238C2semidirect
16. #45217C2semidirect
17. #44997C2semidirect
18. #42929C2semidirect
19. #42791C2semidirect
20. #42708C2semidirect
21. #39959C2semidirect
22. #39656C2semidirect
23. #39599C2semidirect
24. #37265C2semidirect
25. #37265C2semidirect
27. #36508C2semidirect
28. #36508C2semidirect
29. #36497C2semidirect

Maximal subgroups

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

subgroupindex
#599222
#598712
#591142
#590552
#587102
#554872
#548802
#523032
#518782
#500582
#497342
#460232
#460072
#460052
#452382
#452172
#449972
#429292
#427912
#427082
#399592
#396562
#395992
#372652
#372512
#365082
#364972