Finite Group Databasebeta

← #7898114

Subgroups — #7898114

Order 512.

5221 conjugacy classes of subgroups.

The subgroup lattice has 1557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic, complemented
2#59097C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#51059C214yesmaximal, complemented
5#50278C214yesmaximal, complemented
6#49998C214yesmaximal, complemented
7#47505C214yesmaximal, complemented
8#46016C212yesmaximal, complemented
9#45319C212yesmaximal, complemented
10#45289C212yesmaximal, complemented
11#44986C212yesmaximal, complemented
12#44016C214yesmaximal, complemented
13#42890C212yesmaximal, complemented
14#42578C212yesmaximal, complemented
15#41750C214yesmaximal, complemented
16#39765C211yesmaximal, characteristic, complemented
17#39739C211yesmaximal, characteristic, complemented
18#39572C212yesmaximal, complemented
19#39500C212yesmaximal, complemented
20#39023C212yesmaximal, complemented
21#38095C212yesmaximal, complemented
22#37772C212yesmaximal, complemented
23#37202C212yesmaximal, complemented
24#36465C211yesmaximal, characteristic, complemented
25#36051C212yesmaximal, complemented
26#35607C212yesmaximal, complemented
27#35199C211yesmaximal, characteristic, complemented
28#34474C212yesmaximal, complemented
29#34331C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#559C2212yes—
32C2×#555C2212yes—
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#548C2212yes—
37C2×#542C2212yes—
38C2×#532C2212yes—
39#2863C2212yes—
40#2862C2212yes—
41#2858C2211yescharacteristic
42#2858C2212yes—
43#2850C2212yes—
44#2828C2214yes—
45#2819C2214yes—
46#2808C2212yes—
47#2808C2211yescharacteristic
48#2808C2211yescharacteristic
49#2808C2212yes—
50#2808C2214yes—
51#2804C2211yescharacteristic
52#2804C2212yes—
53#2803C2214yes—
54#2796C2212yes—
55#2796C2212yes—
56#2796C2214yes—
57#2794C2212yes—
58#2793C2214yes—
59#2753C2214yes—
60#2753C2214yes—
61#2751C2212yes—
62#2751C2212yes—
63#2748C2214yes—
64#2741C2214yes—
65#2733C2214yes—
66#2733C2212yes—
67#2733C2212yes—
68#2733C2212yes—
69#2733C2212yes—
70#2730C2214yes—
71#2724C2211yescharacteristic
72#2724C2212yes—
73#2716C2214yes—
74#2714C2214yes—
75#2712C2214yes—
76#2712C2214yes—
77#2712C2214yes—
78#2710C2214yes—
79#2710C2214yes—
80#2709C2212yes—
81#2703C2214yes—
82#2700C2214yes—
83#2699C2214yes—
84#2696C2214yes—
85#2696C2214yes—
86#2692C2214yes—
87#2688C2214yes—
88#2688C2214yes—
89#2687C2214yes—
90#2687C2214yes—
91#2682C2212yes—
92#2682C2212yes—
93#2673C2214yes—
94#2673C2214yes—
95#2673C2214yes—
96#2673C2214yes—
97#2673C2214yes—
98#2671C2214yes—
99#2671C2214yes—
100#2666C2214yes—
101#2661C2214yes—
102#2661C2214yes—
103#2657C2212yes—
104#2651C2214yes—
105#2640C2212yes—
106#2631C2214yes—
107#2631C2214yes—
108#2619C2214yes—
109#2619C2212yes—
110#2602C2214yes—
111#2597C2214yes—
112#2596C2214yes—
113#2592C2214yes—
114#2592C2212yes—
115#2589C2214yes—
116#2582C2211yescharacteristic
117#2568C2211yescharacteristic
118#2564C2214yes—
119#2560C2214yes—
120#2559C2214yes—
121#2557C2214yes—
122#2557C2214yes—
123#2555C2214yes—
124#2555C2214yes—
125#2551C2211yescharacteristic
126#2548C2214yes—
127#2546C2211yescharacteristic
128#2545C2212yes—
129#2544C2212yes—
130#2543C2214yes—
131#2542C2211yescharacteristic
132#2542C2212yes—
133#2541C2212yes—
134#2541C2212yes—
135#2541C2212yes—
136#2541C2211yescharacteristic
137#2541C2212yes—
138#2540C2214yes—
139#2540C2212yes—
140#2540C2214yes—
141#2540C2212yes—
142#2537C2212yes—
143#2535C2214yes—
144#2521C2214yes—
145#2520C2214yes—
146#2516C2214yes—
147#2508C2212yes—
148#2500C2212yes—
149#2499C2212yes—
150#2498C2214yes—
151#2492C2212yes—
152#2492C2214yes—
153#2491C2214yes—
154#2491C2212yes—
155#2491C2214yes—
156#2491C2214yes—
157#2477C2214yes—
158#2477C2214yes—
159#2476C2214yes—
160#2471C2214yes—
161#2467C2214yes—
162#2464C2214yes—
163#2464C2214yes—
164#2459C2214yes—
165#2459C2214yes—
166#2459C2214yes—
167#2459C2214yes—
168#2459C2214yes—
169#2458C2214yes—
170#2458C2214yes—
171#2457C2214yes—
172#2456C2214yes—
173#2456C2214yes—
174#2456C2214yes—
175#2451C2212yes—
176#2451C2212yes—
177#2450C2214yes—
178#2446C2212yes—
179#2446C2212yes—
180#2445C2212yes—
181#2436C2212yes—
182#2436C2212yes—
183#2432C2214yes—
184#2431C2212yes—
185#2431C2214yes—
186#2431C2214yes—
187#2431C2212yes—
188#2430C2214yes—
189#2430C2214yes—
190#2428C2212yes—
191#2428C2212yes—
192#2428C2212yes—
193#2428C2212yes—
194#2427C2212yes—
195#2427C2212yes—
196#2427C2212yes—
197#2426C2212yes—
198#2425C2214yes—
199#2423C2212yes—
200#2422C2212yes—
201#2414C2214yes—
202#2414C2212yes—
203#2414C2212yes—
204#2407C2214yes—
205#2398C2212yes—
206#2398C2212yes—
207#2395C2214yes—
208#2395C2212yes—
209#2379C2214yes—
210#2377C2214yes—
211#2368C2214yes—
212#2367C2212yes—
213#2367C2212yes—
214#2367C2212yes—
215#2366C2211yescharacteristic
216#2364C2214yes—
217#2363C2212yes—
218#2363C2212yes—
219#2362C2212yes—
220#2362C2212yes—
221#2359C2214yes—
222#2357C2214yes—
223#2355C2211yescharacteristic
224#2354C2212yes—
225#2354C2212yes—
226#2354C2212yes—
227Q8×C4⋊C4C2211yescharacteristic
228#2349C2212yes—
229Q8×C22⋊C4C2212yes—
230#2339C2212yes—
231#2337C2214yes—
232#2335C2214yes—
233#2333C2214yes—
234#2332C2214yes—
235#2331C2212yes—
236#2326C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2324C2212yes—
240#2320C2212yes—
241#2318C2214yes—
242#2314C2214yes—
243#2310C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#127C2212yes—
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#123C2212yes—
251#2297C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254#2293C2212yes—
255#2290C2212yes—
256#2290C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2314yes—
261C23×Q8C2312yes—
262#559—28no—
263#559—48no—
264#555—48no—
265#550—44no—
266D4×Q8—44no—
267#548—216no—
268#548—48no—
269#542—48no—
270#532—48no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#127C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282C2×#127C2312yes—
283C2×#127C2312yes—
284C2×#127C2314yes—
285C2×#126C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2314yes—
364C2×#117C2312yes—
365C2×#117C2314yes—
366C22×C42C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#393C2314yes—
438#393C2312yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2312yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2312yes—
448#393C2312yes—
449#393C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2314yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#391C2311yescharacteristic
497#390C2314yes—
498#390C2311yescharacteristic
499#390C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2312yes—
508#390C2314yes—
509#390C2312yes—
510#390C2314yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2312yes—
516#390C2314yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2312yes—
525#390C2312yes—
526#390C2314yes—
527#390C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
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#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2312yes—
636#386C2314yes—
637#386C2314yes—
638#386C2312yes—
639#386C2314yes—
640#386C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2312yes—
652#385C2314yes—
653#385C2312yes—
654#385C2312yes—
655#385C2312yes—
656#385C2312yes—
657#384C2312yes—
658#384C2311yescharacteristic
659#384C2311yescharacteristic
660#384C2311yescharacteristic
661#384C2312yes—
662#383C2314yes—
663#382C2314yes—
664#382C2312yes—
665#382C2314yes—
666#382C2312yes—
667#381C2314yes—
668#381C2314yes—
669#381C2314yes—
670#381C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716#376C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C43C2312yes—
721C2×#41—28no—
722C2×#41—48no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—84no—
726C2×#41—84no—
727C22×Q8—28no—
728C22×Q8—44no—
729C22×Q8—44no—
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2411yescharacteristic
733C22×Q8C2411yescharacteristic
734C22×Q8C2412yes—
735C22×Q8C2414yes—
736C22×Q8C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2411yescharacteristic
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2412yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C22×D4C2414yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C4⋊Q8—28no—
771C4⋊Q8—24no—
772C4⋊Q8—44no—
773C4⋊Q8—42no—
774C4⋊Q8—82no—
775C4⋊Q8—82no—
776#127—24no—
777#127—44no—
778#127—42no—
779#127—44no—
780#127—42no—
781#127—44no—
782#127—44no—
783#127—84no—
784#126—48no—
785#124—28no—
786#124—216no—
787#124—28no—
788#124—28no—
789#124—28no—
790#124—48no—
791#124—44no—
792#124—44no—
793#124—48no—
794#124—48no—
795#124—48no—
796#124—48no—
797#124—48no—
798#124—84no—
799#123—216no—
800#123—48no—
801#123—48no—
802#123—48no—
803#123—44no—
804#123—84no—
805#123—84no—
806C22⋊Q8—28no—
807C22⋊Q8—216no—
808C22⋊Q8—28no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—44no—
813#121—28no—
814#121—216no—
815#121—28no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—48no—
820#121—44no—
821#121—44no—
822#121—44no—
823#121—44no—
824#121—44no—
825#121—48no—
826#121—84no—
827#121—84no—
828#121—84no—
829#121—84no—
830#121—84no—
831#121—84no—
832C4×Q8—24no—
833C4×Q8—24no—
834C4×Q8—24no—
835C4×Q8—24no—
836C4×Q8—44no—
837C4×Q8—44no—
838C4×Q8—82no—
839C4×Q8—82no—
840C4×Q8#4118yescomplemented
841C4×D4—28no—
842C4×D4—28no—
843C4×D4—216no—
844C4×D4—28no—
845C4×D4—28no—
846C4×D4—28no—
847C4×D4—28no—
848C4×D4—44no—
849C4×D4—48no—
850C4×D4—44no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—42no—
855C4×D4—42no—
856C4×D4—48no—
857C4×D4—48no—
858C4×D4—82no—
859C4×D4—82no—
860#117—44no—
861#117—48no—
862#117—44no—
863#117—44no—
864#117—48no—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2411yescharacteristic
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2411yescharacteristic
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C42—44no—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055C24C2514yes—
1056C24C2514yes—
1057C24C2512yes—
1058C24C2512yes—
1059#41—816no—
1060#41—832no—
1061C2×Q8—22no—
1062C2×Q8—24no—
1063C2×Q8—28no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—22no—
1069C2×Q8—28no—
1070C2×Q8—24no—
1071C2×Q8—41no—
1072C2×Q8—41no—
1073C2×Q8—42no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—44no—
1077C2×Q8—41no—
1078C2×Q8—44no—
1079C2×Q8—41no—
1080C2×Q8—42no—
1081C2×Q8—816no—
1082C2×Q8C2×#4114yes—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—24no—
1088C2×D4—28no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—28no—
1096C2×D4—22no—
1097C2×D4—24no—
1098C2×D4—22no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—41no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—42no—
1107C2×D4—41no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—42no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—42no—
1126C2×D4—44no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—44no—
1130C2×D4—42no—
1131C2×D4—41no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—42no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—42no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—42no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—24no—
1155C22×C4—28no—
1156C22×C4—28no—
1157C22×C4—28no—
1158C22×C4—28no—
1159C22×C4—28no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—42no—
1163C22×C4—42no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—42no—
1177C22×C4—44no—
1178C22×C4—42no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2514yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2514yes—
1192C22×C4C2514yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2511yescharacteristic
1198C22×C4C2512yes—
1199C22×C4C2511yescharacteristic
1200C22×C4C2511yescharacteristic
1201C22×C4C2512yes—
1202C22×C4C2511yescharacteristic
1203C22×C4C2512yes—
1204C22×C4C2511yescharacteristic
1205C22×C4C2511yescharacteristic
1206C22×C4C2511yescharacteristic
1207C4⋊C4—22no—
1208C4⋊C4—28no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—28no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—28no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—41no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—41no—
1251C4⋊C4C2×#4114yes—
1252C4⋊C4C2×#4118yes—
1253C4⋊C4H(5,𝔽2)14yes—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
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—28no—
1265C22⋊C4—28no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—28no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—42no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—22no—
1324C42—42no—
1325C42—42no—
1326C42—41no—
1327C42—44no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—41no—
1332C42—42no—
1333C42—44no—
1334C42—41no—
1335C42—44no—
1336C42—44no—
1337C42—42no—
1338C42C2×#4118yes—
1339C42C2×#4114yes—
1340C42H(5,𝔽2)14yes—
1341C23—24no—
1342C23—22no—
1343C23—24no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—24no—
1348C23—22no—
1349C23—24no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—24no—
1354C23—22no—
1355C23—24no—
1356C23—22no—
1357C23—22no—
1358C23—24no—
1359C23—22no—
1360C23—24no—
1361C23—24no—
1362C23—22no—
1363C23—22no—
1364C23—24no—
1365C23—24no—
1366C23—22no—
1367C23—22no—
1368C23—24no—
1369C23C2611yescharacteristic
1370Q8—28no—
1371Q8—44no—
1372Q8—48no—
1373Q8—82no—
1374Q8—84no—
1375Q8—88no—
1376Q8—88no—
1377D4—48no—
1378D4—44no—
1379D4—48no—
1380D4—48no—
1381D4—88no—
1382D4—84no—
1383D4—84no—
1384D4—82no—
1385D4—84no—
1386D4—84no—
1387D4—88no—
1388D4—88no—
1389D4—88no—
1390D4—88no—
1391D4—88no—
1392D4—88no—
1393D4—88no—
1394D4—164no—
1395D4—162no—
1396D4—164no—
1397D4—164no—
1398D4—164no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—24no—
1449C2×C4—21no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—22no—
1461C2×C4—24no—
1462C2×C4—22no—
1463C2×C4—48no—
1464C2×C4—48no—
1465C2×C4—48no—
1466C2×C4—88no—
1467C2×C4—88no—
1468C2×C4—88no—
1469C2×C4—88no—
1470C2×C4—88no—
1471C2×C4—84no—
1472C2×C4—88no—
1473C2×C4—164no—
1474C2×C4C22×#4112yes—
1475C2×C4C22×#4114yes—
1476C2×C4C22×#4112yes—
1477C2×C4C22×#4114yes—
1478C2×C4C22×#4112yes—
1479C2×C4C2×H(5,𝔽2)12yes—
1480C2×C4C2×H(5,𝔽2)14yes—
1481C2×C4C2×H(5,𝔽2)12yes—
1482C2×C4C2×H(5,𝔽2)12yes—
1483C2×C4C2×H(5,𝔽2)12yes—
1484C2×C4#58512yes—
1485C22—44no—
1486C22—42no—
1487C22—42no—
1488C22—44no—
1489C22—42no—
1490C22—44no—
1491C22—44no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—44no—
1496C22—44no—
1497C22—44no—
1498C22—42no—
1499C22—44no—
1500C22—42no—
1501C22—44no—
1502C22—44no—
1503C22—42no—
1504C22—42no—
1505C22—42no—
1506C22—42no—
1507C22—44no—
1508C22—44no—
1509C22—44no—
1510C22—44no—
1511C22—42no—
1512C22—42no—
1513C22C23×#4111yescharacteristic
1514C22C22×H(5,𝔽2)11yescharacteristic
1515C22C22×H(5,𝔽2)11yescharacteristic
1516C22C2×#58511yescharacteristic
1517C22H(7,𝔽2)11yescharacteristic
1518C22H(7,𝔽2)11yescharacteristic
1519C222−1+611yescharacteristic
1520C4—24no—
1521C4—22no—
1522C4—24no—
1523C4—24no—
1524C4—22no—
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—42no—
1529C4—42no—
1530C4—42no—
1531C4—44no—
1532C4—41no—
1533C4—42no—
1534C4—42no—
1535C4—44no—
1536C4—42no—
1537C4—42no—
1538C4—44no—
1539C4—42no—
1540C4—42no—
1541C4—44no—
1542C4—42no—
1543C4—42no—
1544C4#350814yes—
1545C2—84no—
1546C2—82no—
1547C2—82no—
1548C2—84no—
1549C2C2×#350811yescharacteristic
1550C2#6285111yescharacteristic
1551C2#6287811yescharacteristic
1552C2#6289711yescharacteristic
1553C2#6295511yescharacteristic
1554C2#6299411yescharacteristic
1555C2#6304511yescharacteristic
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. #59822C2semidirect
2. #59097C2semidirect
3. #52273C2semidirect
4. #51059C2semidirect
5. #50278C2semidirect
6. #49998C2semidirect
7. #47505C2semidirect
8. #46016C2semidirect
9. #45319C2semidirect
10. #45289C2semidirect
11. #44986C2semidirect
12. #44016C2semidirect
13. #42890C2semidirect
14. #42578C2semidirect
15. #41750C2semidirect
16. #39765C2semidirect
17. #39739C2semidirect
18. #39572C2semidirect
19. #39500C2semidirect
20. #39023C2semidirect
21. #38095C2semidirect
22. #37772C2semidirect
23. #37202C2semidirect
24. #36465C2semidirect
25. #36051C2semidirect
26. #35607C2semidirect
27. #35199C2semidirect
28. #34474C2semidirect
29. #34331C2semidirect
840. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598222
#590972
#522732
#510592
#502782
#499982
#475052
#460162
#453192
#452892
#449862
#440162
#428902
#425782
#417502
#397652
#397392
#395722
#395002
#390232
#380952
#377722
#372022
#364652
#360512
#356072
#351992
#344742
#343312