Finite Group Databasebeta

← #8657055

Subgroups — #8657055

Order 512.

4472 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59119C212yesmaximal, complemented
2#56738C214yesmaximal, complemented
3#56603C212yesmaximal, complemented
4#56206C214yesmaximal, complemented
5#53137C211yesmaximal, characteristic, complemented
6#51163C214yesmaximal, complemented
7#48499C214yesmaximal, complemented
8#48315C214yesmaximal, complemented
9#47444C214yesmaximal, complemented
10#47151C212yesmaximal, complemented
11#46104C212yesmaximal, complemented
12#45684C211yesmaximal, characteristic, complemented
13#45351C211yesmaximal, characteristic, complemented
14#45006C212yesmaximal, complemented
15#43598C212yesmaximal, complemented
16#42851C212yesmaximal, complemented
17#42677C211yesmaximal, characteristic
18#40663C212yesmaximal, complemented
19#40193C212yesmaximal, complemented
20#40081C212yesmaximal, complemented
21#38977C212yesmaximal, complemented
22#38918C211yesmaximal, characteristic, complemented
23#38131C212yesmaximal, complemented
24#37405C212yesmaximal, complemented
25#36111C212yesmaximal, complemented
26#35987C211yesmaximal, characteristic, complemented
27#35654C212yesmaximal, complemented
28#35045C212yesmaximal, complemented
29#34921C211yesmaximal, characteristic, complemented
30C2×#555C2211yescharacteristic
31C2×#546C2211yescharacteristic
32C2×#529C2212yes—
33C22×#124C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2863C2212yescomplemented
36#2861C2212yes—
37#2859C2212yescomplemented
38#2855C2211yescharacteristic
39#2851C2212yes—
40#2850C2212yes—
41#2838C2214yescomplemented
42#2837C2214yescomplemented
43#2834C2212yes—
44#2831C2214yescomplemented
45#2826C2212yes—
46#2824C2212yescomplemented
47#2815C2212yes—
48#2807C2212yes—
49#2805C2214yescomplemented
50#2799C2212yescomplemented
51#2798C2214yescomplemented
52#2796C2214yescomplemented
53#2787C2214yes—
54#2786C2214yescomplemented
55#2781C2214yes—
56#2778C2214yes—
57#2778C2214yescomplemented
58#2773C2214yescomplemented
59#2773C2214yescomplemented
60#2771C2212yes—
61#2770C2214yescomplemented
62#2768C2214yescomplemented
63#2765C2214yescomplemented
64#2765C2214yescomplemented
65#2765C2214yescomplemented
66#2762C2214yescomplemented
67#2761C2214yescomplemented
68#2761C2214yescomplemented
69#2759C2214yescomplemented
70#2759C2214yescomplemented
71#2754C2214yescomplemented
72#2754C2214yescomplemented
73#2754C2214yescomplemented
74#2753C2214yescomplemented
75#2749C2214yes—
76#2747C2214yescomplemented
77#2746C2214yescomplemented
78#2745C2214yescomplemented
79#2743C2214yes—
80#2742C2214yescomplemented
81#2742C2212yescomplemented
82#2741C2214yescomplemented
83#2739C2214yescomplemented
84#2739C2214yescomplemented
85#2738C2214yescomplemented
86#2730C2214yescomplemented
87#2722C2212yes—
88#2717C2214yes—
89#2717C2212yes—
90#2717C2214yescomplemented
91#2710C2214yes—
92#2710C2214yescomplemented
93#2706C2214yescomplemented
94#2706C2214yescomplemented
95#2701C2214yescomplemented
96#2696C2214yes—
97#2694C2214yescomplemented
98#2694C2214yescomplemented
99#2686C2214yes—
100#2685C2214yes—
101#2670C2214yes—
102#2666C2214yescomplemented
103#2652C2214yescomplemented
104#2649C2214yes—
105#2648C2214yescomplemented
106#2648C2214yescomplemented
107#2645C2212yescomplemented
108#2645C2212yescomplemented
109#2640C2211yescharacteristic
110#2633C2214yes—
111#2624C2212yes—
112#2624C2211yescharacteristic
113#2623C2212yes—
114#2622C2212yes—
115#2617C2212yes—
116#2607C2211yescharacteristic
117#2602C2212yes—
118#2600C2211yescharacteristic
119#2600C2214yescomplemented
120#2596C2214yescomplemented
121#2596C2212yescomplemented
122#2593C2214yescomplemented
123#2590C2214yescomplemented
124#2589C2214yes—
125#2589C2212yescomplemented
126#2586C2212yescomplemented
127#2582C2212yescomplemented
128#2580C2212yes—
129#2579C2214yescomplemented
130#2578C2214yes—
131#2575C2214yes—
132#2575C2212yescomplemented
133#2568C2212yescomplemented
134#2561C2214yes—
135#2557C2214yes—
136#2557C2212yescomplemented
137#2550C2212yescomplemented
138#2547C2212yes—
139#2547C2211yescharacteristic
140#2540C2211yescharacteristic
141#2538C2212yes—
142#2522C2214yescomplemented
143#2521C2214yes—
144#2521C2214yes—
145#2521C2214yescomplemented
146#2518C2214yescomplemented
147#2517C2212yes—
148#2517C2211yescharacteristic
149#2517C2214yescomplemented
150#2516C2214yescomplemented
151#2513C2214yescomplemented
152#2510C2214yescomplemented
153#2508C2212yescomplemented
154#2508C2212yescomplemented
155#2503C2214yescomplemented
156#2501C2211yescharacteristic
157#2499C2212yescomplemented
158#2499C2212yescomplemented
159#2498C2212yes—
160#2496C2212yes—
161#2495C2212yes—
162#2494C2214yescomplemented
163#2494C2214yescomplemented
164#2494C2212yescomplemented
165#2489C2214yescomplemented
166#2487C2211yescharacteristic
167#2485C2212yes—
168#2485C2214yescomplemented
169#2484C2214yescomplemented
170#2483C2212yes—
171#2482C2212yes—
172#2482C2212yes—
173#2480C2214yes—
174#2480C2214yes—
175#2478C2214yescomplemented
176#2478C2214yescomplemented
177#2474C2214yes—
178#2474C2214yescomplemented
179#2470C2214yescomplemented
180#2468C2214yescomplemented
181#2466C2214yes—
182#2459C2214yes—
183#2459C2212yes—
184#2457C2214yescomplemented
185#2455C2211yescharacteristic
186#2453C2212yescomplemented
187#2451C2212yescomplemented
188#2448C2212yes—
189#2448C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2447C2214yescomplemented
193#2443C2214yes—
194#2443C2214yescomplemented
195#2442C2212yescomplemented
196#2442C2214yescomplemented
197#2441C2212yescomplemented
198#2434C2211yescharacteristic
199#2432C2212yes—
200#2429C2212yescomplemented
201#2429C2212yescomplemented
202#2427C2212yes—
203#2427C2212yes—
204#2426C2212yes—
205#2423C2212yes—
206#2423C2212yescomplemented
207#2422C2212yes—
208#2420C2212yes—
209#2418C2214yes—
210#2418C2214yes—
211#2417C2212yescomplemented
212#2415C2212yes—
213#2415C2212yescomplemented
214#2415C2212yescomplemented
215#2414C2212yes—
216#2412C2212yes—
217#2412C2214yes—
218#2409C2211yescharacteristic
219#2409C2212yes—
220#2408C2212yes—
221#2407C2212yes—
222#2398C2212yes—
223#2397C2211yescharacteristic
224#2395C2211yescharacteristic
225C2×#399C2212yes—
226#2379C2212yes—
227#2376C2214yescomplemented
228#2363C2212yes—
229#2363C2212yes—
230#2362C2212yescomplemented
231#2358C2214yes—
232#2355C2212yescomplemented
233D4×C4⋊C4C2212yes—
234#2344C2214yescomplemented
235#2342C2214yes—
236Q8×C22⋊C4C2212yes—
237#2339C2211yescharacteristic
238D4×C22⋊C4C2211yescharacteristic
239D4×C22⋊C4C2212yes—
240#2336C2214yescomplemented
241#2335C2214yescomplemented
242#2334C2214yes—
243#2329C2214yescomplemented
244#2327C2212yescomplemented
245#2323C2212yescomplemented
246#2319C2212yes—
247#2319C2211yescharacteristic
248#2319C2212yes—
249#2315C2212yes—
250C4×#124C2212yes—
251C4×#124C2212yescomplemented
252C4×C22⋊Q8C2212yescomplemented
253C4×#123C2211yescharacteristic
254C4×#123C2212yescomplemented
255#2296C2212yescomplemented
256#2295C2212yescomplemented
257#2290C2212yescomplemented
258C42×D4C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×D4C2311yescharacteristic
262#555—44no—
263#546—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266#529—48no—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#124—44no—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2311yescharacteristic
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#124C2312yes—
279C2×#123C2314yes—
280C2×#123C2311yescharacteristic
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2311yescharacteristic
295C2×#121C2312yes—
296C2×#120C2314yes—
297C2×#120C2312yes—
298#520—44no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2314yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C22⋊C4C2314yes—
325C22×C22⋊C4C2312yes—
326C22×C22⋊C4C2312yes—
327C22×C22⋊C4C2312yes—
328C22×C22⋊C4C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2311yescharacteristic
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2312yes—
353#399C2314yes—
354#399C2312yes—
355#399C2314yes—
356#399C2312yes—
357#399C2312yes—
358#399C2311yescharacteristic
359#399C2311yescharacteristic
360#399C2311yescharacteristic
361#399C2312yes—
362#399C2314yes—
363#399C2312yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2311yescharacteristic
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2311yescharacteristic
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2312yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#393C2312yes—
444#393C2314yes—
445#393C2314yes—
446#393C2312yes—
447#393C2312yes—
448#393C2314yes—
449#392C2311yescharacteristic
450#392C2311yescharacteristic
451#392C2314yes—
452#392C2312yes—
453#392C2312yes—
454#392C2314yes—
455#392C2314yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2314yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2311yescharacteristic
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#385C2312yes—
615#385C2312yes—
616#385C2311yescharacteristic
617#385C2314yes—
618#385C2312yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#385C2314yes—
632#385C2312yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#384C2312yes—
641#384C2312yes—
642#383C2314yes—
643#383C2314yes—
644#382C2314yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2312yes—
656#381C2312yes—
657#381C2312yes—
658#381C2312yes—
659#381C2314yes—
660#381C2314yes—
661#381C2311yescharacteristic
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#379C2312yes—
681#379C2314yes—
682#379C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2312yes—
717C25C2412yes—
718C2×#41—24no—
719C2×#41—44no—
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4—24no—
728C22×D4—44no—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756#126—48no—
757#126—48no—
758#125—48no—
759#125—44no—
760#124—28no—
761#124—44no—
762#124—42no—
763#124—48no—
764#124—44no—
765#124—48no—
766#124—44no—
767#123—48no—
768#123—48no—
769#123—44no—
770#123—48no—
771#123—42no—
772#123—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C22⋊Q8—42no—
779#121—28no—
780#121—44no—
781#121—42no—
782#121—44no—
783#121—44no—
784#120—48no—
785#120—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×D4—28no—
791C4×D4—24no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—42no—
798C4×D4—42no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—48no—
802#117—42no—
803#117—44no—
804#117—48no—
805#117—44no—
806#117—44no—
807#117—44no—
808C2×C4⋊C4—48no—
809C2×C4⋊C4—42no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C22⋊C4—48no—
863C2×C22⋊C4—44no—
864C2×C22⋊C4—44no—
865C2×C22⋊C4—44no—
866C2×C22⋊C4—44no—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C42—42no—
925C2×C42—44no—
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2411yescharacteristic
953#95C2412yes—
954#95C2411yescharacteristic
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2411yescharacteristic
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—24no—
1017C24—24no—
1018C24—42no—
1019C24—44no—
1020C24—44no—
1021C24C2512yes—
1022C24C2512yes—
1023C24C2511yescharacteristic
1024C24C2512yes—
1025C24C2511yescharacteristic
1026#41—416no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—88no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—28no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—41no—
1053C2×D4—41no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—88no—
1068C2×D4H(5,𝔽2)14yes—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—28no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—28no—
1081C22×C4—44no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—41no—
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—22no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—41no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—41no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—41no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C42—24no—
1237C42—24no—
1238C42—22no—
1239C42—24no—
1240C42—24no—
1241C42—24no—
1242C42—24no—
1243C42—42no—
1244C42—42no—
1245C42—42no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—42no—
1253C42—44no—
1254C42—42no—
1255C42—42no—
1256C42—44no—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—24no—
1261C23—22no—
1262C23—24no—
1263C23—21no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—22no—
1269C23—22no—
1270C23—24no—
1271C23—22no—
1272C23—21no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—22no—
1280C23—21no—
1281C23—22no—
1282C23—48no—
1283C23—84no—
1284C23—84no—
1285C23—88no—
1286C23—164no—
1287C23C2×H(5,𝔽2)14yes—
1288C23#58512yes—
1289C23C2611yescharacteristic
1290Q8—48no—
1291Q8—44no—
1292Q8—84no—
1293Q8—84no—
1294Q8—162no—
1295D4—28no—
1296D4—48no—
1297D4—48no—
1298D4—44no—
1299D4—88no—
1300D4—82no—
1301D4—84no—
1302D4—82no—
1303D4—84no—
1304D4—162no—
1305D4—164no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—44no—
1372C2×C4—44no—
1373C2×C4—88no—
1374C2×C4—88no—
1375C2×C4—84no—
1376C2×C4—82no—
1377C2×C4—82no—
1378C2×C4—84no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—162no—
1382C2×C4—164no—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4#58514yes—
1385C2×C4#58514yes—
1386C22—24no—
1387C22—24no—
1388C22—24no—
1389C22—22no—
1390C22—24no—
1391C22—41no—
1392C22—41no—
1393C22—44no—
1394C22—44no—
1395C22—42no—
1396C22—41no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—41no—
1401C22—42no—
1402C22—44no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—41no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—44no—
1413C22—168no—
1414C22C22×H(5,𝔽2)11yescharacteristic
1415C22C2×#58512yes—
1416C22C2×#58512yes—
1417C22C2×#58511yescharacteristic
1418C222−1+611yescharacteristic
1419C4—24no—
1420C4—42no—
1421C4—41no—
1422C4—42no—
1423C4—41no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—41no—
1428C4—44no—
1429C4—42no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—41no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4#353314yes—
1443C2—44no—
1444C2—42no—
1445C2—81no—
1446C2—82no—
1447C2—82no—
1448C2C2×#353311yescharacteristic
1449C2#6282712yes—
1450C2#6289811yescharacteristic
1451C2#6294012yes—
1452C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42677C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59119C2semidirect
2. #56738C2semidirect
3. #56603C2semidirect
4. #56206C2semidirect
5. #53137C2semidirect
6. #51163C2semidirect
7. #48499C2semidirect
8. #48315C2semidirect
9. #47444C2semidirect
10. #47151C2semidirect
11. #46104C2semidirect
12. #45684C2semidirect
13. #45351C2semidirect
14. #45006C2semidirect
15. #43598C2semidirect
16. #42851C2semidirect
18. #40663C2semidirect
19. #40193C2semidirect
20. #40081C2semidirect
21. #38977C2semidirect
22. #38918C2semidirect
23. #38131C2semidirect
24. #37405C2semidirect
25. #36111C2semidirect
26. #35987C2semidirect
27. #35654C2semidirect
28. #35045C2semidirect
29. #34921C2semidirect
35. #2863C22semidirect
37. #2859C22semidirect
41. #2838C22semidirect
42. #2837C22semidirect
44. #2831C22semidirect
46. #2824C22semidirect
49. #2805C22semidirect
50. #2799C22semidirect
51. #2798C22semidirect
52. #2796C22semidirect
54. #2786C22semidirect
57. #2778C22semidirect
58. #2773C22semidirect
59. #2773C22semidirect
61. #2770C22semidirect
62. #2768C22semidirect
63. #2765C22semidirect
64. #2765C22semidirect
65. #2765C22semidirect
66. #2762C22semidirect
67. #2761C22semidirect
68. #2761C22semidirect
69. #2759C22semidirect
70. #2759C22semidirect
71. #2754C22semidirect
72. #2754C22semidirect
73. #2754C22semidirect
74. #2753C22semidirect
76. #2747C22semidirect
77. #2746C22semidirect
78. #2745C22semidirect
80. #2742C22semidirect
81. #2742C22semidirect
82. #2741C22semidirect
83. #2739C22semidirect
84. #2739C22semidirect
85. #2738C22semidirect
86. #2730C22semidirect
90. #2717C22semidirect
92. #2710C22semidirect
93. #2706C22semidirect
94. #2706C22semidirect
95. #2701C22semidirect
97. #2694C22semidirect
98. #2694C22semidirect
102. #2666C22semidirect
103. #2652C22semidirect
105. #2648C22semidirect
106. #2648C22semidirect
107. #2645C22semidirect
108. #2645C22semidirect
119. #2600C22semidirect
120. #2596C22semidirect
121. #2596C22semidirect
122. #2593C22semidirect
123. #2590C22semidirect
125. #2589C22semidirect
126. #2586C22semidirect
127. #2582C22semidirect
129. #2579C22semidirect
132. #2575C22semidirect
133. #2568C22semidirect
136. #2557C22semidirect
137. #2550C22semidirect
142. #2522C22semidirect
145. #2521C22semidirect
146. #2518C22semidirect
149. #2517C22semidirect
150. #2516C22semidirect
151. #2513C22semidirect
152. #2510C22semidirect
153. #2508C22semidirect
154. #2508C22semidirect
155. #2503C22semidirect
157. #2499C22semidirect
158. #2499C22semidirect
162. #2494C22semidirect
163. #2494C22semidirect
164. #2494C22semidirect
165. #2489C22semidirect
168. #2485C22semidirect
169. #2484C22semidirect
175. #2478C22semidirect
176. #2478C22semidirect
178. #2474C22semidirect
179. #2470C22semidirect
180. #2468C22semidirect
184. #2457C22semidirect
186. #2453C22semidirect
187. #2451C22semidirect
192. #2447C22semidirect
194. #2443C22semidirect
195. #2442C22semidirect
196. #2442C22semidirect
197. #2441C22semidirect
200. #2429C22semidirect
201. #2429C22semidirect
206. #2423C22semidirect
211. #2417C22semidirect
213. #2415C22semidirect
214. #2415C22semidirect
227. #2376C22semidirect
230. #2362C22semidirect
232. #2355C22semidirect
234. #2344C22semidirect
240. #2336C22semidirect
241. #2335C22semidirect
243. #2329C22semidirect
244. #2327C22semidirect
245. #2323C22semidirect
251. C4×#124C22semidirect
252. C4×C22⋊Q8C22semidirect
254. C4×#123C22semidirect
255. #2296C22semidirect
256. #2295C22semidirect
257. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#591192
#567382
#566032
#562062
#531372
#511632
#484992
#483152
#474442
#471512
#461042
#456842
#453512
#450062
#435982
#428512
#426772
#406632
#401932
#400812
#389772
#389182
#381312
#374052
#361112
#359872
#356542
#350452
#349212