Finite Group Databasebeta

← #8747883

Subgroups — #8747883

Order 512.

4620 conjugacy classes of subgroups.

The subgroup lattice has 1478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59198C211yesmaximal, characteristic, complemented
2#59014C212yesmaximal, complemented
3#58207C214yesmaximal, complemented
4#58200C214yesmaximal, complemented
5#56501C214yesmaximal, complemented
6#53886C212yesmaximal, complemented
7#53873C214yesmaximal, complemented
8#53019C212yesmaximal, complemented
9#52961C211yesmaximal, characteristic, complemented
10#52750C212yesmaximal, complemented
11#52496C214yesmaximal, complemented
12#46829C212yesmaximal, complemented
13#45433C211yesmaximal, characteristic, complemented
14#45351C212yesmaximal, complemented
15#45120C212yesmaximal, complemented
16#45055C212yesmaximal, complemented
17#44921C212yesmaximal, complemented
18#42949C212yesmaximal, complemented
19#42839C212yesmaximal, complemented
20#42810C211yesmaximal, characteristic, complemented
21#42620C212yesmaximal, complemented
22#42596C212yesmaximal, complemented
23#41604C212yesmaximal, complemented
24#40520C214yesmaximal, complemented
25#39723C211yesmaximal, characteristic, complemented
26#39349C212yesmaximal, complemented
27#36676C211yesmaximal, characteristic, complemented
28#35996C211yesmaximal, characteristic, complemented
29#35772C212yesmaximal, complemented
30C2×#554C2211yescharacteristic, complemented
31C2×#552C2212yes—
32C2×#551C2212yes—
33C2×#548C2211yescharacteristic
34C2×#538C2214yes—
35C22×C22⋊Q8C2211yescharacteristic
36C2×#520C2211yescharacteristic, complemented
37#2847C2211yescharacteristic
38#2845C2214yescomplemented
39#2842C2211yescharacteristic
40#2841C2214yescomplemented
41#2836C2214yescomplemented
42#2836C2214yescomplemented
43#2834C2212yes—
44#2834C2211yescharacteristic
45#2833C2212yescomplemented
46#2831C2214yescomplemented
47#2831C2214yescomplemented
48#2830C2214yescomplemented
49#2829C2214yescomplemented
50#2827C2212yes—
51#2827C2212yes—
52#2827C2212yes—
53#2826C2211yescharacteristic
54#2826C2212yes—
55#2825C2212yes—
56#2820C2212yescomplemented
57#2814C2214yes—
58#2812C2212yes—
59#2812C2211yescharacteristic
60#2809C2212yescomplemented
61#2803C2214yescomplemented
62#2802C2214yescomplemented
63#2800C2214yescomplemented
64#2799C2214yescomplemented
65#2794C2214yescomplemented
66#2787C2214yescomplemented
67#2786C2214yescomplemented
68#2786C2214yescomplemented
69#2782C2214yescomplemented
70#2782C2214yescomplemented
71#2774C2214yescomplemented
72#2768C2214yescomplemented
73#2766C2214yescomplemented
74#2765C2214yes—
75#2765C2214yescomplemented
76#2763C2214yescomplemented
77#2761C2214yes—
78#2761C2214yescomplemented
79#2754C2214yescomplemented
80#2754C2214yescomplemented
81#2754C2214yescomplemented
82#2752C2212yescomplemented
83#2744C2214yes—
84#2740C2214yes—
85#2730C2214yes—
86#2728C2214yes—
87#2726C2214yescomplemented
88#2722C2212yes—
89#2722C2214yes—
90#2722C2212yes—
91#2720C2214yescomplemented
92#2717C2212yes—
93#2715C2214yes—
94#2715C2214yes—
95#2712C2212yes—
96#2710C2214yes—
97#2708C2214yes—
98#2708C2214yes—
99#2706C2214yes—
100#2702C2214yes—
101#2700C2214yes—
102#2699C2214yes—
103#2698C2214yes—
104#2695C2214yes—
105#2692C2214yescomplemented
106#2691C2214yes—
107#2690C2214yes—
108#2689C2214yescomplemented
109#2687C2214yes—
110#2686C2214yes—
111#2686C2214yes—
112#2680C2214yes—
113#2676C2214yes—
114#2667C2214yescomplemented
115#2661C2214yes—
116#2653C2214yescomplemented
117#2652C2214yescomplemented
118#2650C2214yescomplemented
119#2649C2214yes—
120#2640C2211yescharacteristic, complemented
121#2638C2214yes—
122#2636C2214yescomplemented
123#2633C2212yes—
124#2631C2212yescomplemented
125#2629C2212yescomplemented
126#2625C2211yescharacteristic, complemented
127#2625C2212yescomplemented
128#2624C2214yes—
129#2624C2212yescomplemented
130#2622C2214yes—
131#2617C2212yes—
132#2609C2214yes—
133#2607C2212yescomplemented
134#2601C2214yescomplemented
135#2600C2214yes—
136#2591C2212yes—
137#2587C2214yescomplemented
138#2586C2214yescomplemented
139#2579C2212yes—
140#2576C2214yes—
141#2570C2212yescomplemented
142#2566C2212yescomplemented
143#2563C2212yescomplemented
144#2557C2214yes—
145#2553C2214yes—
146#2550C2212yescomplemented
147#2547C2212yes—
148#2547C2211yescharacteristic
149#2540C2211yescharacteristic, complemented
150#2537C2212yes—
151#2536C2212yes—
152#2536C2212yes—
153#2535C2212yes—
154#2521C2214yes—
155#2521C2214yes—
156#2520C2214yescomplemented
157#2517C2214yes—
158#2517C2212yes—
159#2515C2214yes—
160#2513C2212yescomplemented
161#2508C2212yescomplemented
162#2507C2212yescomplemented
163#2504C2211yescharacteristic
164#2503C2212yes—
165#2502C2211yescharacteristic, complemented
166#2502C2212yescomplemented
167#2499C2214yes—
168#2496C2212yes—
169#2496C2212yes—
170#2496C2212yes—
171#2494C2212yescomplemented
172#2491C2212yes—
173#2489C2212yes—
174#2488C2214yes—
175#2487C2211yescharacteristic
176#2486C2212yes—
177#2486C2212yes—
178#2486C2211yescharacteristic
179#2486C2212yes—
180#2485C2212yescomplemented
181#2483C2212yes—
182#2481C2214yes—
183#2478C2214yes—
184#2476C2214yes—
185#2475C2214yes—
186#2473C2214yescomplemented
187#2468C2214yes—
188#2468C2214yescomplemented
189#2466C2214yes—
190#2460C2214yescomplemented
191#2456C2214yes—
192#2455C2214yes—
193#2451C2212yescomplemented
194#2451C2212yescomplemented
195#2450C2214yes—
196#2447C2214yes—
197#2447C2214yescomplemented
198#2447C2212yescomplemented
199#2444C2214yes—
200#2443C2214yes—
201#2442C2214yes—
202#2442C2212yes—
203#2442C2212yescomplemented
204#2440C2212yes—
205#2440C2212yes—
206#2438C2214yes—
207#2438C2214yes—
208#2426C2212yes—
209#2423C2212yescomplemented
210#2423C2212yescomplemented
211#2422C2214yes—
212#2422C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2419C2214yes—
216#2417C2212yes—
217#2417C2212yescomplemented
218#2416C2212yes—
219#2416C2212yes—
220#2415C2212yes—
221#2415C2214yes—
222#2412C2214yes—
223#2409C2212yes—
224#2407C2212yes—
225#2407C2212yescomplemented
226#2401C2212yes—
227#2397C2211yescharacteristic
228#2395C2212yes—
229#2395C2212yes—
230#2395C2211yescharacteristic
231#2392C2214yes—
232#2392C2212yes—
233#2392C2212yes—
234#2392C2212yes—
235#2363C2212yescomplemented
236#2361C2212yes—
237#2360C2212yes—
238#2355C2212yescomplemented
239#2355C2212yescomplemented
240#2352C2212yes—
241#2352C2212yescomplemented
242Q8×C4⋊C4C2212yescomplemented
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245#2344C2212yes—
246#2342C2214yes—
247#2341C2211yescharacteristic, complemented
248Q8×C22⋊C4C2211yescharacteristic
249Q8×C22⋊C4C2212yes—
250#2331C2212yescomplemented
251#2323C2212yescomplemented
252#2323C2212yescomplemented
253#2321C2212yes—
254#2320C2211yescharacteristic, complemented
255#2317C2212yescomplemented
256C4×#120C2211yescharacteristic
257C4×#120C2212yes—
258C2×#380C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262#554—44no—
263#552—48no—
264#551—48no—
265#548—44no—
266#538—416no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×C22⋊Q8—44no—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#120C2312yes—
305C2×#120C2311yescharacteristic
306C2×#120C2312yes—
307#520—44no—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2312yes—
331C2×#117C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2312yes—
339C22×C22⋊C4C2314yes—
340C22×C22⋊C4C2312yes—
341#401C2312yes—
342#401C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2311yescharacteristic
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#399C2311yescharacteristic
363#399C2312yes—
364#399C2311yescharacteristic
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2311yescharacteristic
369#399C2312yes—
370#399C2314yes—
371#399C2314yes—
372#398C2314yes—
373#398C2311yescharacteristic
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2314yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2311yescharacteristic
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2312yes—
438#397C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2312yes—
444#396C2312yes—
445#396C2312yes—
446#396C2312yes—
447#396C2312yes—
448#396C2312yes—
449#396C2312yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2314yes—
492#393C2314yes—
493#392C2311yescharacteristic
494#392C2312yes—
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#392C2311yescharacteristic
499#392C2312yes—
500#392C2314yes—
501#392C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2312yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#390C2314yes—
518#390C2312yes—
519#390C2312yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2312yes—
524#390C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
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#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#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#386C2312yes—
601#386C2312yes—
602#386C2312yes—
603#386C2311yescharacteristic
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2311yescharacteristic
624#385C2312yes—
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#384C2312yes—
648#384C2312yes—
649#384C2314yes—
650#384C2312yes—
651#383C2312yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2314yes—
659#382C2314yes—
660#382C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2312yes—
666#381C2314yes—
667#381C2314yes—
668#380C2311yescharacteristic
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2311yescharacteristic
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2312yes—
690#379C2311yescharacteristic
691#379C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717#376C2311yescharacteristic
718C2×#95C2314yes—
719C25C2411yescharacteristic
720C2×#41—24no—
721C2×#41—44no—
722C22×Q8—24no—
723C22×Q8—44no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2414yes—
741C23×C4—42no—
742C23×C4—44no—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C4⋊Q8—44no—
758C4⋊Q8—42no—
759#126—48no—
760#126—48no—
761#126—48no—
762#126—48no—
763#125—44no—
764#125—44no—
765#125—48no—
766#124—44no—
767#124—42no—
768#124—48no—
769#124—48no—
770#124—44no—
771#123—48no—
772#123—48no—
773#123—48no—
774#123—44no—
775#123—48no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—42no—
785C22⋊Q8—44no—
786#121—48no—
787#121—48no—
788#121—44no—
789#121—44no—
790#121—42no—
791#121—44no—
792#121—48no—
793#120—28no—
794#120—28no—
795#120—24no—
796C4×Q8—28no—
797C4×Q8—24no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×D4—44no—
801C4×D4—48no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—44no—
810C4×D4—42no—
811C4×D4—48no—
812C4×D4—48no—
813C4×D4—48no—
814#117—44no—
815#117—44no—
816#117—42no—
817#117—48no—
818#117—48no—
819#117—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—42no—
822C2×C4⋊C4—44no—
823C2×C4⋊C4—42no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—44no—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C22⋊C4—216no—
886C2×C22⋊C4—44no—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2411yescharacteristic
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2412yes—
968#95C2412yes—
969#95C2411yescharacteristic
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2411yescharacteristic
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24—41no—
1027C24—42no—
1028C24—41no—
1029C24—42no—
1030C24H(5,𝔽2)14yes—
1031C24C2512yes—
1032C24C2511yescharacteristic
1033C24C2512yes—
1034C24C2512yes—
1035C24C2511yescharacteristic
1036#41—416no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—88no—
1049C2×Q8H(5,𝔽2)14yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—28no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—22no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—41no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—41no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—42no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—88no—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C4⋊C4—24no—
1145C4⋊C4—22no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—22no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—41no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—41no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—41no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C42—28no—
1262C42—24no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—44no—
1269C42—42no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C23—22no—
1277C23—21no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—21no—
1285C23—22no—
1286C23—22no—
1287C23—21no—
1288C23—22no—
1289C23—21no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23—22no—
1298C23—24no—
1299C23—22no—
1300C23—22no—
1301C23—21no—
1302C23—22no—
1303C23—44no—
1304C23—48no—
1305C23—82no—
1306C23—82no—
1307C23—84no—
1308C23C2×H(5,𝔽2)12yes—
1309C23C2×H(5,𝔽2)14yes—
1310C23C2611yescharacteristic
1311Q8—28no—
1312Q8—44no—
1313Q8—84no—
1314Q8—162no—
1315Q8—164no—
1316D4—48no—
1317D4—48no—
1318D4—48no—
1319D4—44no—
1320D4—44no—
1321D4—84no—
1322D4—84no—
1323D4—82no—
1324D4—88no—
1325D4—84no—
1326D4—84no—
1327D4—164no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—24no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—48no—
1392C2×C4—48no—
1393C2×C4—48no—
1394C2×C4—44no—
1395C2×C4—44no—
1396C2×C4—84no—
1397C2×C4—88no—
1398C2×C4—88no—
1399C2×C4—84no—
1400C2×C4—82no—
1401C2×C4—84no—
1402C2×C4—162no—
1403C2×C4—164no—
1404C2×C4—164no—
1405C2×C4C2×H(5,𝔽2)14yes—
1406C2×C4C2×H(5,𝔽2)12yes—
1407C2×C4#58514yes—
1408C22—24no—
1409C22—22no—
1410C22—24no—
1411C22—24no—
1412C22—24no—
1413C22—41no—
1414C22—42no—
1415C22—41no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—41no—
1422C22—42no—
1423C22—42no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—44no—
1430C22—42no—
1431C22—41no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—44no—
1437C22—88no—
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C22×H(5,𝔽2)11yescharacteristic
1440C22C2×#58512yes—
1441C222−1+612yes—
1442C222−1+611yescharacteristic
1443C4—24no—
1444C4—42no—
1445C4—41no—
1446C4—42no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—41no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—44no—
1456C4—44no—
1457C4—42no—
1458C4—42no—
1459C4—41no—
1460C4—44no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4—44no—
1465C4—42no—
1466C4#353314yes—
1467C2—44no—
1468C2—42no—
1469C2—81no—
1470C2—82no—
1471C2—82no—
1472C2C2×#353311yescharacteristic
1473C2#6289511yescharacteristic
1474C2#6290112yes—
1475C2#6304411yescharacteristic
1476C2#6305312yes—
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. #59198C2semidirect
2. #59014C2semidirect
3. #58207C2semidirect
4. #58200C2semidirect
5. #56501C2semidirect
6. #53886C2semidirect
7. #53873C2semidirect
8. #53019C2semidirect
9. #52961C2semidirect
10. #52750C2semidirect
11. #52496C2semidirect
12. #46829C2semidirect
13. #45433C2semidirect
14. #45351C2semidirect
15. #45120C2semidirect
16. #45055C2semidirect
17. #44921C2semidirect
18. #42949C2semidirect
19. #42839C2semidirect
20. #42810C2semidirect
21. #42620C2semidirect
22. #42596C2semidirect
23. #41604C2semidirect
24. #40520C2semidirect
25. #39723C2semidirect
26. #39349C2semidirect
27. #36676C2semidirect
28. #35996C2semidirect
29. #35772C2semidirect
30. C2×#554C22semidirect
36. C2×#520C22semidirect
38. #2845C22semidirect
40. #2841C22semidirect
41. #2836C22semidirect
42. #2836C22semidirect
45. #2833C22semidirect
46. #2831C22semidirect
47. #2831C22semidirect
48. #2830C22semidirect
49. #2829C22semidirect
56. #2820C22semidirect
60. #2809C22semidirect
61. #2803C22semidirect
62. #2802C22semidirect
63. #2800C22semidirect
64. #2799C22semidirect
65. #2794C22semidirect
66. #2787C22semidirect
67. #2786C22semidirect
68. #2786C22semidirect
69. #2782C22semidirect
70. #2782C22semidirect
71. #2774C22semidirect
72. #2768C22semidirect
73. #2766C22semidirect
75. #2765C22semidirect
76. #2763C22semidirect
78. #2761C22semidirect
79. #2754C22semidirect
80. #2754C22semidirect
81. #2754C22semidirect
82. #2752C22semidirect
87. #2726C22semidirect
91. #2720C22semidirect
105. #2692C22semidirect
108. #2689C22semidirect
114. #2667C22semidirect
116. #2653C22semidirect
117. #2652C22semidirect
118. #2650C22semidirect
120. #2640C22semidirect
122. #2636C22semidirect
124. #2631C22semidirect
125. #2629C22semidirect
126. #2625C22semidirect
127. #2625C22semidirect
129. #2624C22semidirect
133. #2607C22semidirect
134. #2601C22semidirect
137. #2587C22semidirect
138. #2586C22semidirect
141. #2570C22semidirect
142. #2566C22semidirect
143. #2563C22semidirect
146. #2550C22semidirect
149. #2540C22semidirect
156. #2520C22semidirect
160. #2513C22semidirect
161. #2508C22semidirect
162. #2507C22semidirect
165. #2502C22semidirect
166. #2502C22semidirect
171. #2494C22semidirect
180. #2485C22semidirect
186. #2473C22semidirect
188. #2468C22semidirect
190. #2460C22semidirect
193. #2451C22semidirect
194. #2451C22semidirect
197. #2447C22semidirect
198. #2447C22semidirect
203. #2442C22semidirect
209. #2423C22semidirect
210. #2423C22semidirect
217. #2417C22semidirect
225. #2407C22semidirect
235. #2363C22semidirect
238. #2355C22semidirect
239. #2355C22semidirect
241. #2352C22semidirect
242. Q8×C4⋊C4C22semidirect
247. #2341C22semidirect
250. #2331C22semidirect
251. #2323C22semidirect
252. #2323C22semidirect
254. #2320C22semidirect
255. #2317C22semidirect

Maximal subgroups

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

subgroupindex
#591982
#590142
#582072
#582002
#565012
#538862
#538732
#530192
#529612
#527502
#524962
#468292
#454332
#453512
#451202
#450552
#449212
#429492
#428392
#428102
#426202
#425962
#416042
#405202
#397232
#393492
#366762
#359962
#357722