Finite Group Databasebeta

← #8197123

Subgroups — #8197123

Order 512.

4746 conjugacy classes of subgroups.

The subgroup lattice has 1526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C211yesmaximal, characteristic, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59247C212yesmaximal, complemented
4#59153C212yesmaximal, complemented
5#59084C212yesmaximal, complemented
6#57278C214yesmaximal, complemented
7#53642C212yesmaximal, complemented
8#53492C212yesmaximal, complemented
9#53048C212yesmaximal, complemented
10#52714C212yesmaximal, complemented
11#52079C212yesmaximal, complemented
12#51882C212yesmaximal, complemented
13#47632C214yesmaximal, complemented
14#46345C211yesmaximal, characteristic, complemented
15#46329C211yesmaximal, characteristic, complemented
16#46228C212yesmaximal, complemented
17#45048C212yesmaximal, complemented
18#43462C212yesmaximal, complemented
19#42758C212yesmaximal, complemented
20#42618C212yesmaximal, complemented
21#41198C214yesmaximal, complemented
22#40188C212yesmaximal, complemented
23#39877C212yesmaximal, complemented
24#39590C212yesmaximal, complemented
25#39240C212yesmaximal, complemented
26#38870C214yesmaximal, complemented
27#36519C212yesmaximal, complemented
28#36503C212yesmaximal, complemented
29#35200C211yesmaximal, characteristic, complemented
30#34979C211yesmaximal, characteristic, complemented
31#34937C211yesmaximal, characteristic
32C2×#563C2212yes—
33C2×Q82C2212yes—
34C2×#554C2212yes—
35C2×#533C2211yescharacteristic
36C2×#533C2211yescharacteristic
37C2×#532C2212yes—
38C2×#532C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40#2860C2212yes—
41#2860C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2214yes—
45#2838C2214yes—
46#2836C2214yes—
47#2832C2212yes—
48#2831C2214yes—
49#2830C2214yes—
50#2830C2214yes—
51#2823C2212yes—
52#2820C2214yes—
53#2803C2214yes—
54#2797C2214yes—
55#2796C2214yes—
56#2792C2212yes—
57#2777C2214yes—
58#2772C2214yes—
59#2765C2214yes—
60#2762C2214yes—
61#2751C2214yes—
62#2741C2214yes—
63#2740C2214yes—
64#2734C2212yes—
65#2734C2212yes—
66#2734C2212yes—
67#2732C2214yes—
68#2731C2212yes—
69#2731C2214yes—
70#2731C2212yes—
71#2729C2214yes—
72#2729C2214yes—
73#2728C2212yes—
74#2723C2214yes—
75#2718C2214yes—
76#2717C2214yes—
77#2716C2214yes—
78#2715C2214yes—
79#2713C2214yes—
80#2710C2214yes—
81#2709C2214yes—
82#2707C2214yes—
83#2702C2214yes—
84#2702C2214yes—
85#2700C2214yes—
86#2700C2214yes—
87#2700C2214yes—
88#2692C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2691C2214yes—
92#2691C2214yes—
93#2683C2214yes—
94#2681C2214yes—
95#2680C2212yes—
96#2677C2214yes—
97#2674C2214yes—
98#2672C2214yes—
99#2672C2214yes—
100#2672C2214yes—
101#2653C2214yes—
102#2651C2214yes—
103#2651C2214yes—
104#2650C2214yes—
105#2649C2214yes—
106#2638C2212yes—
107#2638C2212yes—
108#2638C2214yes—
109#2637C2214yes—
110#2629C2212yes—
111#2628C2212yes—
112#2611C2212yes—
113#2611C2212yes—
114#2604C2214yes—
115#2601C2214yes—
116#2599C2212yes—
117#2599C2212yes—
118#2597C2214yes—
119#2594C2214yes—
120#2590C2214yes—
121#2588C2214yes—
122#2586C2212yes—
123#2586C2214yes—
124#2584C2212yes—
125#2584C2212yes—
126#2582C2212yes—
127#2580C2212yes—
128#2580C2212yes—
129#2573C2214yes—
130#2569C2214yes—
131#2568C2211yescharacteristic
132#2567C2211yescharacteristic
133#2566C2212yes—
134#2563C2211yescharacteristic
135#2557C2214yes—
136#2556C2214yes—
137#2551C2212yes—
138#2551C2212yes—
139#2550C2212yes—
140#2550C2212yes—
141#2550C2212yes—
142#2549C2214yes—
143#2548C2211yescharacteristic
144#2548C2214yes—
145#2547C2211yescharacteristic
146#2547C2211yescharacteristic
147#2547C2211yescharacteristic
148#2546C2211yescharacteristic
149#2546C2212yes—
150#2546C2211yescharacteristic
151#2546C2211yescharacteristic
152#2545C2212yes—
153#2544C2212yes—
154#2543C2212yes—
155#2543C2212yes—
156#2542C2211yescharacteristic
157#2541C2211yescharacteristic
158#2538C2212yes—
159#2532C2214yes—
160#2527C2214yes—
161#2523C2214yes—
162#2520C2214yes—
163#2515C2214yes—
164#2513C2212yes—
165#2512C2212yes—
166#2508C2212yes—
167#2507C2214yes—
168#2506C2212yes—
169#2499C2212yes—
170#2499C2211yescharacteristic
171#2499C2211yescharacteristic
172#2497C2212yes—
173#2497C2212yes—
174#2495C2212yes—
175#2494C2212yes—
176#2491C2214yes—
177#2491C2212yes—
178#2491C2214yes—
179#2491C2212yes—
180#2491C2212yes—
181#2490C2212yes—
182#2490C2212yes—
183#2490C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2474C2214yes—
187#2473C2214yes—
188#2469C2214yes—
189#2466C2214yes—
190#2466C2214yes—
191#2465C2214yes—
192#2465C2214yes—
193#2465C2214yes—
194#2462C2214yes—
195#2458C2214yes—
196#2452C2212yes—
197#2452C2212yes—
198#2452C2214yes—
199#2452C2214yes—
200#2451C2214yes—
201#2451C2214yes—
202#2449C2214yes—
203#2449C2214yes—
204#2445C2212yes—
205#2445C2212yes—
206#2442C2212yes—
207#2441C2212yes—
208#2440C2212yes—
209#2439C2212yes—
210#2432C2212yes—
211#2432C2211yescharacteristic
212#2432C2211yescharacteristic
213#2432C2214yes—
214#2429C2214yes—
215#2426C2214yes—
216#2426C2214yes—
217#2422C2212yes—
218#2420C2212yes—
219#2416C2212yes—
220#2416C2212yes—
221#2415C2212yes—
222#2415C2212yes—
223#2406C2214yes—
224#2395C2212yes—
225#2395C2212yes—
226#2392C2212yes—
227#2392C2212yes—
228#2379C2212yes—
229#2373C2214yes—
230#2370C2212yes—
231#2370C2212yes—
232#2370C2212yes—
233#2369C2212yes—
234#2367C2214yes—
235#2367C2214yes—
236#2365C2212yes—
237#2365C2212yes—
238#2363C2212yes—
239#2363C2212yes—
240#2360C2214yes—
241#2357C2212yes—
242#2355C2212yes—
243#2345C2212yes—
244#2345C2212yes—
245#2337C2214yes—
246#2335C2214yes—
247#2327C2212yes—
248#2326C2212yes—
249#2324C2212yes—
250#2324C2212yes—
251#2322C2214yes—
252C4×C4⋊Q8C2211yescharacteristic
253C4×C4⋊Q8C2211yescharacteristic
254C4×C4⋊Q8C2212yes—
255C4×#125C2212yes—
256C4×#124C2211yescharacteristic
257C4×#124C2211yescharacteristic
258C4×C22⋊Q8C2212yes—
259C4×C22⋊Q8C2212yes—
260C4×C22⋊Q8C2214yes—
261C4×#121C2212yes—
262C4×#121C2212yes—
263#2297C2212yes—
264#2283C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269#563—48no—
270Q82—48no—
271#554—48no—
272#533—44no—
273#533—44no—
274#532—44no—
275#532—48no—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2311yescharacteristic
287C2×C4⋊Q8C2311yescharacteristic
288C2×C4⋊Q8C2314yes—
289C2×C4⋊Q8C2314yes—
290C2×#127C2311yescharacteristic
291C2×#127C2312yes—
292C2×#126C2314yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#125C2312yes—
296C2×#125C2312yes—
297C2×#125C2314yes—
298C2×#125C2312yes—
299C2×#125C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2314yes—
305C2×#124C2314yes—
306C2×#124C2311yescharacteristic
307C2×#124C2312yes—
308C2×#124C2311yescharacteristic
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C4×#41—44no—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2314yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2314yes—
342C2×C4×Q8C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2311yescharacteristic
355C2×#117C2312yes—
356C2×#117C2311yescharacteristic
357C2×#117C2311yescharacteristic
358C2×#117C2312yes—
359C2×#117C2311yescharacteristic
360C2×#117C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2314yes—
363C22×C42C2311yescharacteristic
364C22×C42C2311yescharacteristic
365C22×C42C2311yescharacteristic
366C22×C42C2312yes—
367#401C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2312yes—
382#399C2312yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2312yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2312yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2312yes—
423#397C2314yes—
424#396C2314yes—
425#396C2314yes—
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#396C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#394C2312yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#392C2312yes—
486#392C2312yes—
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2312yes—
507#391C2311yescharacteristic
508#391C2311yescharacteristic
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2311yescharacteristic
527#390C2311yescharacteristic
528#390C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2314yes—
562#389C2312yes—
563#389C2314yes—
564#389C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2312yes—
592#388C2312yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2312yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2312yes—
661#385C2312yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#384C2312yes—
666#384C2311yescharacteristic
667#384C2311yescharacteristic
668#384C2312yes—
669#384C2312yes—
670#383C2312yes—
671#383C2314yes—
672#382C2312yes—
673#382C2312yes—
674#382C2314yes—
675#382C2311yescharacteristic
676#382C2311yescharacteristic
677#382C2312yes—
678#382C2312yes—
679#381C2314yes—
680#381C2314yes—
681#381C2312yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687#380C2312yes—
688#380C2314yes—
689#380C2312yes—
690#380C2314yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2314yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2311yescharacteristic
718C4×C4⋊C4C2314yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2311yescharacteristic
721C4×C4⋊C4C2311yescharacteristic
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2311yescharacteristic
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2311yescharacteristic
737#376C2312yes—
738#376C2312yes—
739C2×#95C2312yes—
740C43C2311yescharacteristic
741C43C2311yescharacteristic
742C2×#41—24no—
743C2×#41—42no—
744C2×#41—44no—
745C2×#41—42no—
746C2×#41—44no—
747C2×#41—44no—
748C22×Q8C2414yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2412yes—
754C22×Q8C2412yes—
755C22×Q8C2414yes—
756C22×Q8C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2411yescharacteristic
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C22×D4C2412yes—
765C22×D4C2412yes—
766C23×C4C2411yescharacteristic
767C23×C4C2411yescharacteristic
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2411yescharacteristic
775C23×C4C2411yescharacteristic
776C23×C4C2411yescharacteristic
777C23×C4C2414yes—
778C23×C4C2414yes—
779C4⋊Q8—28no—
780C4⋊Q8—24no—
781C4⋊Q8—28no—
782C4⋊Q8—24no—
783C4⋊Q8—28no—
784C4⋊Q8—42no—
785C4⋊Q8—42no—
786C4⋊Q8—42no—
787C4⋊Q8—42no—
788C4⋊Q8—44no—
789C4⋊Q8—42no—
790C4⋊Q8—48no—
791C4⋊Q8—48no—
792C4⋊Q8—48no—
793#127—42no—
794#127—44no—
795#126—48no—
796#126—48no—
797#126—48no—
798#125—28no—
799#125—28no—
800#125—44no—
801#125—44no—
802#125—48no—
803#124—28no—
804#124—44no—
805#124—44no—
806#124—42no—
807#124—44no—
808#124—48no—
809#124—42no—
810#124—48no—
811#124—48no—
812#123—48no—
813#123—48no—
814#123—48no—
815C22⋊Q8—44no—
816C22⋊Q8—48no—
817C22⋊Q8—44no—
818C22⋊Q8—48no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—42no—
824C22⋊Q8—44no—
825C22⋊Q8—42no—
826C22⋊Q8—44no—
827C22⋊Q8—48no—
828C22⋊Q8—44no—
829#121—28no—
830#121—28no—
831#121—44no—
832#121—48no—
833#121—48no—
834#121—44no—
835C4×Q8—28no—
836C4×Q8—42no—
837C4×Q8—42no—
838C4×Q8—42no—
839C4×Q8—42no—
840C4×Q8—44no—
841C4×Q8—44no—
842C4×Q8—48no—
843C4×Q8—48no—
844C4×Q8—48no—
845C4×D4—28no—
846C4×D4—44no—
847C4×D4—44no—
848C4×D4—42no—
849C4×D4—42no—
850C4×D4—42no—
851C4×D4—42no—
852C4×D4—42no—
853C4×D4—42no—
854C4×D4—44no—
855C4×D4—48no—
856C4×D4—48no—
857#117—42no—
858#117—42no—
859#117—42no—
860#117—44no—
861#117—44no—
862#117—44no—
863C2×C4⋊C4—28no—
864C2×C4⋊C4—48no—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2411yescharacteristic
943C2×C22⋊C4C2411yescharacteristic
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2411yescharacteristic
946C2×C22⋊C4C2411yescharacteristic
947C2×C22⋊C4C2411yescharacteristic
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C42—24no—
978C2×C42—24no—
979C2×C42—24no—
980C2×C42—44no—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2412yes—
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2411yescharacteristic
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073C24C2514yes—
1074C24C2511yescharacteristic
1075C24C2511yescharacteristic
1076C24C2511yescharacteristic
1077#41—416no—
1078#41—816no—
1079C2×Q8—24no—
1080C2×Q8—22no—
1081C2×Q8—24no—
1082C2×Q8—24no—
1083C2×Q8—22no—
1084C2×Q8—28no—
1085C2×Q8—28no—
1086C2×Q8—44no—
1087C2×Q8—41no—
1088C2×Q8—41no—
1089C2×Q8—41no—
1090C2×Q8—41no—
1091C2×Q8—42no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—42no—
1095C2×Q8—44no—
1096C2×Q8—42no—
1097C2×Q8—41no—
1098C2×Q8—42no—
1099C2×Q8—41no—
1100C2×Q8—42no—
1101C2×Q8—44no—
1102C2×Q8—44no—
1103C2×Q8—44no—
1104C2×Q8H(5,𝔽2)14yes—
1105C2×D4—22no—
1106C2×D4—22no—
1107C2×D4—28no—
1108C2×D4—24no—
1109C2×D4—22no—
1110C2×D4—22no—
1111C2×D4—22no—
1112C2×D4—24no—
1113C2×D4—24no—
1114C2×D4—24no—
1115C2×D4—28no—
1116C2×D4—28no—
1117C2×D4—41no—
1118C2×D4—41no—
1119C2×D4—41no—
1120C2×D4—41no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—42no—
1131C22×C4—22no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—28no—
1148C22×C4—28no—
1149C22×C4—42no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2514yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2514yes—
1177C22×C4C2514yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2514yes—
1189C22×C4C2512yes—
1190C22×C4C2511yescharacteristic
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—28no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—28no—
1217C4⋊C4—24no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C42−1+418yes—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—24no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—42no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—42no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C42—22no—
1304C42—22no—
1305C42—22no—
1306C42—22no—
1307C42—22no—
1308C42—22no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—24no—
1313C42—24no—
1314C42—24no—
1315C42—24no—
1316C42—22no—
1317C42—24no—
1318C42—22no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—44no—
1323C42—42no—
1324C42—44no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C42—44no—
1329C42—44no—
1330C42—41no—
1331C42—42no—
1332C42—41no—
1333C42—44no—
1334C42H(5,𝔽2)14yes—
1335C23—21no—
1336C23—21no—
1337C23—22no—
1338C23—22no—
1339C23—24no—
1340C23—24no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—24no—
1346C23—24no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—24no—
1351C23—24no—
1352C23—22no—
1353C23—21no—
1354C23—21no—
1355C23—24no—
1356C23#58512yes—
1357C23C2611yescharacteristic
1358Q8—44no—
1359Q8—416no—
1360Q8—84no—
1361Q8—82no—
1362Q8—84no—
1363Q8—82no—
1364Q8—84no—
1365Q8—84no—
1366Q8—164no—
1367D4—44no—
1368D4—44no—
1369D4—44no—
1370D4—48no—
1371D4—88no—
1372D4—88no—
1373D4—84no—
1374D4—88no—
1375D4—84no—
1376C2×C4—28no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—44no—
1442C2×C4—44no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—82no—
1448C2×C4—82no—
1449C2×C4—88no—
1450C2×C4—88no—
1451C2×C4—88no—
1452C2×C4—164no—
1453C2×C4C2×H(5,𝔽2)12yes—
1454C2×C4C2×H(5,𝔽2)12yes—
1455C2×C4C2×H(5,𝔽2)12yes—
1456C2×C4C2×H(5,𝔽2)12yes—
1457C2×C4C2×H(5,𝔽2)12yes—
1458C2×C4C2×H(5,𝔽2)12yes—
1459C2×C4C2×2−1+418yes—
1460C2×C4C2×2−1+414yes—
1461C2×C4#58514yes—
1462C22—24no—
1463C22—22no—
1464C22—41no—
1465C22—41no—
1466C22—42no—
1467C22—41no—
1468C22—41no—
1469C22—44no—
1470C22—41no—
1471C22—44no—
1472C22—41no—
1473C22—42no—
1474C22—42no—
1475C22—44no—
1476C22—44no—
1477C22—44no—
1478C22—44no—
1479C22—42no—
1480C22—42no—
1481C22—41no—
1482C22—41no—
1483C22—44no—
1484C22C22×H(5,𝔽2)11yescharacteristic
1485C22C22×H(5,𝔽2)11yescharacteristic
1486C22C22×2−1+412yes—
1487C22C2×#58512yes—
1488C22C2×#58511yescharacteristic
1489C4—22no—
1490C4—28no—
1491C4—24no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—22no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—41no—
1500C4—42no—
1501C4—41no—
1502C4—44no—
1503C4—41no—
1504C4—42no—
1505C4—42no—
1506C4—44no—
1507C4—44no—
1508C4—42no—
1509C4—42no—
1510C4—44no—
1511C4—44no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4#355014yes—
1516C2—42no—
1517C2—81no—
1518C2—81no—
1519C2—84no—
1520C2C2×#355011yescharacteristic
1521C2#6275911yescharacteristic
1522C2#6281811yescharacteristic
1523C2#6301512yes—
1524C2#6303312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59925C2semidirect
2. #59832C2semidirect
3. #59247C2semidirect
4. #59153C2semidirect
5. #59084C2semidirect
6. #57278C2semidirect
7. #53642C2semidirect
8. #53492C2semidirect
9. #53048C2semidirect
10. #52714C2semidirect
11. #52079C2semidirect
12. #51882C2semidirect
13. #47632C2semidirect
14. #46345C2semidirect
15. #46329C2semidirect
16. #46228C2semidirect
17. #45048C2semidirect
18. #43462C2semidirect
19. #42758C2semidirect
20. #42618C2semidirect
21. #41198C2semidirect
22. #40188C2semidirect
23. #39877C2semidirect
24. #39590C2semidirect
25. #39240C2semidirect
26. #38870C2semidirect
27. #36519C2semidirect
28. #36503C2semidirect
29. #35200C2semidirect
30. #34979C2semidirect

Maximal subgroups

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

subgroupindex
#599252
#598322
#592472
#591532
#590842
#572782
#536422
#534922
#530482
#527142
#520792
#518822
#476322
#463452
#463292
#462282
#450482
#434622
#427582
#426182
#411982
#401882
#398772
#395902
#392402
#388702
#365192
#365032
#352002
#349792
#349372