Finite Group Databasebeta

← #7642209

Subgroups — #7642209

Order 512.

4194 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37430C212yesmaximal, complemented
2#37393C212yesmaximal, complemented
3#37385C212yesmaximal, complemented
4#37384C212yesmaximal, complemented
5#37325C212yesmaximal
6#37323C212yesmaximal, complemented
7#37294C212yesmaximal, complemented
8#37291C212yesmaximal, complemented
9#37030C212yesmaximal, complemented
10#37028C212yesmaximal, complemented
11#37012C214yesmaximal, complemented
12#37009C214yesmaximal, complemented
13#37006C214yesmaximal, complemented
14#37005C214yesmaximal, complemented
15#36992C214yesmaximal, complemented
16#36836C212yesmaximal, complemented
17#36834C212yesmaximal, complemented
18#36786C214yesmaximal, complemented
19#35342C211yesmaximal, characteristic
20#35326C211yesmaximal, characteristic, complemented
21#35304C211yesmaximal, characteristic, complemented
22#35297C211yesmaximal, characteristic, complemented
23#35217C212yesmaximal, complemented
24#35204C212yesmaximal, complemented
25#35203C212yesmaximal, complemented
26#35194C212yesmaximal, complemented
27#34085C211yesmaximal, characteristic, complemented
28#34084C211yesmaximal, characteristic, complemented
29#34056C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2866C2214yes—
34#2865C2214yes—
35#2865C2214yes—
36#2864C2214yes—
37#2863C2214yes—
38#2861C2214yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2857C2212yes—
43#2853C2214yes—
44#2851C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2850C2212yes—
48#2850C2212yes—
49#2810C2214yes—
50#2809C2214yes—
51#2805C2214yes—
52#2803C2214yes—
53#2800C2214yes—
54#2800C2214yes—
55#2796C2214yes—
56#2788C2214yes—
57#2787C2214yes—
58#2782C2214yes—
59#2781C2214yes—
60#2781C2214yes—
61#2779C2214yes—
62#2779C2214yes—
63#2778C2214yes—
64#2777C2214yes—
65#2777C2214yes—
66#2775C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2773C2214yes—
71#2773C2214yes—
72#2771C2214yes—
73#2770C2214yes—
74#2768C2214yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2763C2214yes—
79#2762C2214yes—
80#2759C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2757C2214yes—
84#2756C2214yes—
85#2754C2214yes—
86#2748C2214yes—
87#2747C2214yes—
88#2747C2214yes—
89#2747C2214yes—
90#2746C2214yes—
91#2745C2214yes—
92#2744C2214yes—
93#2743C2214yes—
94#2742C2214yes—
95#2741C2214yes—
96#2741C2214yes—
97#2740C2214yes—
98#2739C2214yes—
99#2738C2214yes—
100#2738C2214yes—
101#2730C2214yes—
102#2726C2214yes—
103#2719C2214yes—
104#2717C2214yes—
105#2710C2214yes—
106#2704C2214yes—
107#2700C2214yes—
108#2696C2214yes—
109#2690C2214yes—
110#2690C2214yes—
111#2690C2214yes—
112#2687C2214yes—
113#2660C2212yes—
114#2660C2211yescharacteristic
115#2658C2211yescharacteristic
116#2655C2214yes—
117#2655C2214yes—
118#2654C2214yes—
119#2652C2214yes—
120#2651C2214yes—
121#2650C2214yes—
122#2650C2214yes—
123#2649C2214yes—
124#2647C2212yes—
125#2642C2211yescharacteristic
126#2640C2211yescharacteristic
127#2625C2211yescharacteristic
128#2625C2212yes—
129#2624C2211yescharacteristic
130#2616C2211yescharacteristic
131#2616C2212yes—
132#2615C2211yescharacteristic
133#2612C2214yes—
134#2611C2212yes—
135#2611C2212yes—
136#2606C2212yes—
137#2605C2212yes—
138#2604C2212yes—
139#2604C2214yes—
140#2603C2212yes—
141#2602C2214yes—
142#2600C2214yes—
143#2599C2212yes—
144#2598C2212yes—
145#2597C2214yes—
146#2596C2214yes—
147#2594C2214yes—
148#2590C2214yes—
149#2589C2214yes—
150#2588C2214yes—
151#2584C2212yes—
152#2581C2212yes—
153#2575C2214yes—
154#2569C2212yes—
155#2564C2214yes—
156#2562C2212yes—
157#2558C2214yes—
158#2549C2212yes—
159#2536C2212yes—
160#2533C2214yes—
161#2532C2214yes—
162#2531C2214yes—
163#2530C2214yes—
164#2529C2214yes—
165#2528C2214yes—
166#2514C2212yes—
167#2513C2212yes—
168#2511C2212yes—
169#2511C2212yes—
170#2509C2212yes—
171#2508C2212yes—
172#2506C2212yes—
173#2506C2212yes—
174#2498C2212yes—
175#2498C2212yes—
176#2497C2212yes—
177#2497C2212yes—
178#2495C2212yes—
179#2494C2212yes—
180#2492C2212yes—
181#2491C2212yes—
182#2489C2212yes—
183#2489C2212yes—
184#2485C2214yes—
185#2475C2214yes—
186#2474C2214yes—
187#2454C2212yes—
188#2453C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2448C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2438C2214yes—
196#2429C2212yes—
197#2429C2212yes—
198#2427C2212yes—
199#2426C2212yes—
200#2423C2212yes—
201#2422C2212yes—
202#2421C2212yes—
203#2421C2212yes—
204#2415C2214yes—
205#2336C2212yes—
206#2336C2212yes—
207#2335C2214yes—
208#2334C2214yes—
209#2332C2212yes—
210#2332C2212yes—
211#2331C2212yes—
212#2331C2212yes—
213#2330C2212yes—
214#2330C2212yes—
215#2327C2212yes—
216#2327C2212yes—
217#2326C2212yes—
218#2326C2212yes—
219#2324C2212yes—
220#2324C2212yes—
221#2323C2212yes—
222#2323C2212yes—
223#2323C2212yes—
224#2323C2212yes—
225#2323C2212yes—
226#2323C2212yes—
227#2320C2212yes—
228#2320C2211yescharacteristic
229#2320C2211yescharacteristic
230#2319C2212yes—
231#2319C2211yescharacteristic
232#2319C2211yescharacteristic
233#2318C2212yes—
234#2318C2212yes—
235#2318C2212yes—
236#2318C2212yes—
237#2298C2212yes—
238#2298C2212yes—
239#2298C2212yes—
240#2298C2214yes—
241#2297C2212yes—
242#2296C2212yes—
243#2296C2212yes—
244#2295C2211yescharacteristic
245#2295C2212yes—
246#2295C2214yes—
247#2293C2211yescharacteristic
248#2293C2212yes—
249#2290C2212yes—
250#2285C2211yescharacteristic
251#2283C2212yes—
252#2283C2212yes—
253#2283C2211yescharacteristic
254C42×Q8C2211yescharacteristic
255C42×Q8C2212yes—
256C42×D4C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2311yescharacteristic
260#533—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265#529—28no—
266C2×#126C2312yes—
267C2×#125C2312yes—
268C2×#125C2311yescharacteristic
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2311yescharacteristic
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#123C2312yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2311yescharacteristic
286C2×#121C2312yes—
287C4×#41—28no—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2312yes—
313C22×C42C2311yescharacteristic
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2312yes—
349#399C2312yes—
350#399C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2314yes—
377#397C2312yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2312yes—
415#393C2314yes—
416#392C2312yes—
417#392C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#390C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2312yes—
486#388C2312yes—
487#388C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
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#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2312yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2312yes—
606#385C2312yes—
607#385C2312yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2312yes—
619#384C2312yes—
620#384C2312yes—
621#383C2312yes—
622#383C2312yes—
623#383C2312yes—
624#383C2312yes—
625#383C2312yes—
626#383C2314yes—
627#383C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2314yes—
638#382C2314yes—
639#381C2312yes—
640#381C2312yes—
641#381C2312yes—
642#381C2312yes—
643#381C2314yes—
644#381C2312yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#380C2314yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698#376C2312yes—
699#376C2311yescharacteristic
700#376C2311yescharacteristic
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2312yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2311yescharacteristic
710C2×#95C2311yescharacteristic
711C43C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C43C2311yescharacteristic
715C2×#41—24no—
716C2×#41—44no—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×D4C2411yescharacteristic
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2414yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C4⋊Q8—24no—
738C4⋊Q8—24no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741#126—28no—
742#125—24no—
743#125—28no—
744#125—44no—
745#125—84no—
746#125—84no—
747#124—24no—
748#124—44no—
749#124—84no—
750#123—28no—
751#123—84no—
752C22⋊Q8—24no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8—44no—
756C22⋊Q8—44no—
757C22⋊Q8—44no—
758C22⋊Q8—84no—
759C22⋊Q8—84no—
760#121—24no—
761#121—44no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—24no—
774C4×D4—24no—
775C4×D4—24no—
776C4×D4—44no—
777#117—24no—
778#117—28no—
779#117—28no—
780#117—28no—
781#117—44no—
782#117—82no—
783#117—82no—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C42—28no—
883C2×C42—44no—
884C2×C42—82no—
885C2×C42#4118yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2412yes—
919#95C2411yescharacteristic
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24C2512yes—
998C24C2512yes—
999C24C2511yescharacteristic
1000#41—416no—
1001C2×Q8—22no—
1002C2×Q8—22no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—22no—
1017C2×D4—22no—
1018C2×D4—24no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—42no—
1034C22×C4—41no—
1035C22×C4—42no—
1036C22×C4—41no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4C2×#4114yes—
1052C22×C4C2×#4114yes—
1053C22×C4C2×#4114yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—42no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—28no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—42no—
1188C42—42no—
1189C42—41no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42—42no—
1194C42—44no—
1195C42—41no—
1196C42—41no—
1197C42—44no—
1198C42—44no—
1199C42—41no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42C2×#4114yes—
1206C42C2×#4114yes—
1207C42C2×#4114yes—
1208C42C2×#4114yes—
1209C23—22no—
1210C23—21no—
1211C23—21no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—24no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—24no—
1225C23C22×#4112yes—
1226C23C2611yescharacteristic
1227Q8—44no—
1228Q8—44no—
1229Q8—48no—
1230Q8—84no—
1231Q8—164no—
1232D4—44no—
1233D4—48no—
1234D4—44no—
1235D4—84no—
1236D4—164no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—28no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—48no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—88no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4C22×#4112yes—
1313C2×C4C22×#4112yes—
1314C2×C4C22×#4112yes—
1315C2×C4C22×#4112yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4112yes—
1318C2×C4#58514yes—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—44no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22C23×#4111yescharacteristic
1337C22C2×#58512yes—
1338C22H(7,𝔽2)11yescharacteristic
1339C222−1+611yescharacteristic
1340C222−1+612yes—
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—22no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4#345514yes—
1367C2—42no—
1368C2—82no—
1369C2—82no—
1370C2C2×#345511yescharacteristic
1371C2#6285611yescharacteristic
1372C2#6286011yescharacteristic
1373C2#6288212yes—
1374C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2615C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37430C2semidirect
2. #37393C2semidirect
3. #37385C2semidirect
4. #37384C2semidirect
6. #37323C2semidirect
7. #37294C2semidirect
8. #37291C2semidirect
9. #37030C2semidirect
10. #37028C2semidirect
11. #37012C2semidirect
12. #37009C2semidirect
13. #37006C2semidirect
14. #37005C2semidirect
15. #36992C2semidirect
16. #36836C2semidirect
17. #36834C2semidirect
18. #36786C2semidirect
20. #35326C2semidirect
21. #35304C2semidirect
22. #35297C2semidirect
23. #35217C2semidirect
24. #35204C2semidirect
25. #35203C2semidirect
26. #35194C2semidirect
27. #34085C2semidirect
28. #34084C2semidirect
29. #34056C2semidirect

Maximal subgroups

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

subgroupindex
#374302
#373932
#373852
#373842
#373252
#373232
#372942
#372912
#370302
#370282
#370122
#370092
#370062
#370052
#369922
#368362
#368342
#367862
#353422
#353262
#353042
#352972
#352172
#352042
#352032
#351942
#340852
#340842
#340562