Finite Group Databasebeta

← #7658577

Subgroups — #7658577

Order 512.

5285 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42617C213yesmaximal, complemented
2#42608C213yesmaximal, complemented
3#42584C213yesmaximal, complemented
4#42578C213yesmaximal, complemented
5#42570C213yesmaximal, complemented
6#42565C213yesmaximal, complemented
7#42541C213yesmaximal, complemented
8#42533C213yesmaximal, complemented
9#42529C213yesmaximal, complemented
10#42508C213yesmaximal, complemented
11#42468C213yesmaximal, complemented
12#42454C213yesmaximal, complemented
13#37626C213yesmaximal, complemented
14#37587C213yesmaximal, complemented
15#37570C213yesmaximal, complemented
16#36692C213yesmaximal, complemented
17#36076C211yesmaximal, characteristic, complemented
18#36066C211yesmaximal, characteristic, complemented
19#36029C211yesmaximal, characteristic, complemented
20#36029C211yesmaximal, characteristic, complemented
21#36029C211yesmaximal, characteristic, complemented
22#36018C211yesmaximal, characteristic, complemented
23#36005C211yesmaximal, characteristic, complemented
24#35983C211yesmaximal, characteristic, complemented
25#35971C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35831C211yesmaximal, characteristic, complemented
28#35801C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34312C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×#520C2211yescharacteristic
46C2×#519C2211yescharacteristic
47#2837C2213yes—
48#2837C2213yes—
49#2837C2213yes—
50#2837C2213yes—
51#2836C2213yes—
52#2836C2213yes—
53#2836C2211yescharacteristic
54#2836C2213yes—
55#2829C2213yes—
56#2829C2213yes—
57#2829C2213yes—
58#2829C2213yes—
59#2828C2213yes—
60#2828C2213yes—
61#2828C2213yes—
62#2828C2213yes—
63#2828C2216yes—
64#2780C2216yes—
65#2761C2216yes—
66#2753C2216yes—
67#2752C2216yes—
68#2748C2216yes—
69#2743C2216yes—
70#2740C2216yes—
71#2709C2216yes—
72#2703C2216yes—
73#2701C2216yes—
74#2699C2216yes—
75#2688C2216yes—
76#2688C2216yes—
77#2673C2216yes—
78#2671C2216yes—
79#2671C2216yes—
80#2661C2216yes—
81#2661C2216yes—
82#2657C2213yes—
83#2649C2216yes—
84#2648C2216yes—
85#2648C2216yes—
86#2648C2216yes—
87#2647C2213yes—
88#2635C2216yes—
89#2635C2216yes—
90#2635C2216yes—
91#2630C2216yes—
92#2625C2213yes—
93#2624C2213yes—
94#2624C2216yes—
95#2624C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2620C2213yes—
99#2619C2213yes—
100#2619C2216yes—
101#2619C2213yes—
102#2619C2213yes—
103#2619C2213yes—
104#2571C2213yes—
105#2570C2213yes—
106#2548C2213yes—
107#2544C2213yes—
108#2544C2213yes—
109#2541C2213yes—
110#2541C2213yes—
111#2541C2213yes—
112#2541C2213yes—
113#2541C2213yes—
114#2541C2213yes—
115#2540C2213yes—
116#2540C2213yes—
117#2540C2213yes—
118#2537C2213yes—
119#2537C2213yes—
120#2536C2213yes—
121#2535C2213yes—
122#2535C2213yes—
123#2535C2213yes—
124#2509C2213yes—
125#2508C2213yes—
126#2508C2213yes—
127#2507C2213yes—
128#2504C2213yes—
129#2503C2213yes—
130#2501C2213yes—
131#2500C2213yes—
132#2487C2213yes—
133#2487C2213yes—
134#2486C2213yes—
135#2485C2213yes—
136#2476C2216yes—
137#2471C2216yes—
138#2464C2216yes—
139#2457C2216yes—
140#2448C2213yes—
141#2448C2213yes—
142#2447C2213yes—
143#2447C2213yes—
144#2445C2213yes—
145#2445C2213yes—
146#2445C2213yes—
147#2445C2213yes—
148#2428C2213yes—
149#2428C2213yes—
150#2428C2213yes—
151#2428C2213yes—
152#2428C2213yes—
153#2428C2213yes—
154#2428C2216yes—
155#2428C2213yes—
156#2428C2213yes—
157#2427C2213yes—
158#2427C2213yes—
159#2426C2213yes—
160#2426C2213yes—
161#2423C2213yes—
162#2422C2213yes—
163#2422C2213yes—
164#2421C2213yes—
165#2420C2216yes—
166#2420C2213yes—
167#2420C2213yes—
168#2420C2213yes—
169#2420C2213yes—
170#2417C2213yes—
171#2417C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2416C2213yes—
177#2416C2213yes—
178#2416C2213yes—
179#2416C2213yes—
180#2414C2213yes—
181#2414C2213yes—
182#2402C2213yes—
183#2397C2213yes—
184#2395C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2395C2213yes—
188#2392C2213yes—
189#2392C2213yes—
190#2392C2213yes—
191#2392C2213yes—
192#2392C2213yes—
193#2392C2213yes—
194#2367C2213yes—
195#2366C2213yes—
196#2363C2213yes—
197#2361C2213yes—
198#2361C2213yes—
199#2360C2213yes—
200#2357C2213yes—
201#2354C2213yes—
202#2352C2213yes—
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211D4×C4⋊C4C2213yes—
212#2345C2213yes—
213#2344C2213yes—
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2324C2213yes—
225#2324C2213yes—
226#2324C2213yes—
227#2323C2213yes—
228#2319C2213yes—
229#2314C2213yes—
230C4×#127C2213yes—
231C4×#124C2213yes—
232#2298C2213yes—
233#2293C2213yes—
234#2293C2213yes—
235#2293C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#550—28no—
244#550—44no—
245#550—44no—
246#550—44no—
247#550—44no—
248#550—44no—
249#548—28no—
250#548—44no—
251#548—44no—
252#548—44no—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#127C2313yes—
259C2×#127C2316yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#123C2316yes—
265C2×#123C2316yes—
266C2×#123C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2316yes—
288C2×#121C2316yes—
289C2×#121C2316yes—
290C2×#121C2316yes—
291C2×#121C2316yes—
292C2×#121C2316yes—
293C2×#121C2316yes—
294C2×#121C2316yes—
295#520—28no—
296#520—44no—
297#520—44no—
298#520—44no—
299#519—44no—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2316yes—
331C2×C4×D4C2316yes—
332C2×#117C2313yes—
333C2×#117C2313yes—
334C2×#117C2313yes—
335C2×#117C2313yes—
336C2×#117C2313yes—
337C2×#117C2313yes—
338C2×#117C2316yes—
339C22×C4⋊C4C2313yes—
340C22×C4⋊C4C2313yes—
341C22×C4⋊C4C2313yes—
342C22×C4⋊C4C2313yes—
343#400C2316yes—
344#400C2313yes—
345#400C2311yescharacteristic
346#400C2313yes—
347#400C2313yes—
348#400C2311yescharacteristic
349#400C2313yes—
350#400C2313yes—
351#400C2313yes—
352#400C2316yes—
353#400C2316yes—
354#399C2313yes—
355#399C2313yes—
356#399C2313yes—
357#399C2313yes—
358#399C2311yescharacteristic
359#399C2313yes—
360#399C2313yes—
361#399C2313yes—
362#399C2316yes—
363#399C2316yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2311yescharacteristic
369#398C2311yescharacteristic
370#398C2311yescharacteristic
371#398C2313yes—
372#398C2313yes—
373#398C2313yes—
374#398C2311yescharacteristic
375#398C2313yes—
376#398C2313yes—
377#398C2313yes—
378#398C2316yes—
379#397C2311yescharacteristic
380#397C2311yescharacteristic
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2316yes—
388#397C2316yes—
389#397C2311yescharacteristic
390#397C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2313yes—
395#397C2313yes—
396#397C2313yes—
397#397C2313yes—
398#397C2313yes—
399#397C2316yes—
400#397C2316yes—
401#396C2311yescharacteristic
402#396C2311yescharacteristic
403#396C2313yes—
404#396C2313yes—
405#396C2313yes—
406#396C2313yes—
407#396C2313yes—
408#396C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#396C2313yes—
413#396C2316yes—
414#396C2316yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2316yes—
436#394C2316yes—
437#394C2316yes—
438#394C2316yes—
439#394C2316yes—
440#394C2313yes—
441#394C2313yes—
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2313yes—
446#394C2316yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2316yes—
454#394C2316yes—
455#392C2313yes—
456#392C2313yes—
457#392C2313yes—
458#392C2313yes—
459#392C2313yes—
460#392C2313yes—
461#392C2313yes—
462#392C2313yes—
463#392C2313yes—
464#392C2313yes—
465#392C2316yes—
466#392C2316yes—
467#392C2316yes—
468#392C2316yes—
469#392C2316yes—
470#392C2316yes—
471#392C2316yes—
472#392C2316yes—
473#392C2316yes—
474#392C2316yes—
475#391C2313yes—
476#391C2313yes—
477#391C2313yes—
478#391C2313yes—
479#390C2313yes—
480#390C2316yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2316yes—
501#390C2316yes—
502#390C2316yes—
503#390C2316yes—
504#390C2316yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2316yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2311yescharacteristic
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#388C2316yes—
527#388C2316yes—
528#388C2311yescharacteristic
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2316yes—
541#388C2316yes—
542#388C2316yes—
543#388C2316yes—
544#388C2316yes—
545#388C2316yes—
546#388C2316yes—
547#387C2313yes—
548#387C2316yes—
549#387C2316yes—
550#387C2316yes—
551#387C2311yescharacteristic
552#387C2313yes—
553#387C2313yes—
554#387C2316yes—
555#387C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#386C2316yes—
563#386C2316yes—
564#386C2316yes—
565#386C2316yes—
566#386C2316yes—
567#386C2316yes—
568#386C2316yes—
569#386C2316yes—
570#386C2316yes—
571#386C2316yes—
572#386C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2316yes—
577#385C2316yes—
578#384C2313yes—
579#384C2313yes—
580#384C2313yes—
581#382C2313yes—
582#382C2313yes—
583#382C2313yes—
584#382C2313yes—
585#382C2313yes—
586#382C2316yes—
587#381C2316yes—
588#381C2316yes—
589#381C2316yes—
590#381C2316yes—
591#380C2313yes—
592#380C2313yes—
593#380C2316yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2313yes—
602#380C2316yes—
603#380C2316yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2316yes—
629C4×C22⋊C4C2316yes—
630C4×C22⋊C4C2316yes—
631#376C2313yes—
632C43C2313yes—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—24no—
643C2×#41—24no—
644C2×#41—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8C2413yes—
649C22×Q8C2411yescharacteristic
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C22×D4C2413yes—
658C22×D4C2413yes—
659C22×D4C2413yes—
660C22×D4C2413yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C22×D4C2413yes—
665C22×D4C2416yes—
666C22×D4C2416yes—
667C22×D4C2416yes—
668C22×D4C2416yes—
669C22×D4C2416yes—
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2416yes—
676C23×C4C2416yes—
677C23×C4C2416yes—
678C23×C4C2416yes—
679#127—212no—
680#127—46no—
681#127—46no—
682#127—46no—
683#127—46no—
684#127—46no—
685#127—86no—
686#124—212no—
687#124—46no—
688#124—46no—
689#124—46no—
690#123—86no—
691#123—86no—
692#123—86no—
693C22⋊Q8—212no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697#121—212no—
698#121—212no—
699#121—212no—
700#121—46no—
701#121—46no—
702#121—46no—
703#121—46no—
704#121—46no—
705#121—46no—
706#121—46no—
707#121—46no—
708#121—46no—
709#121—46no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—86no—
714#121—86no—
715#121—86no—
716#121—86no—
717#121—86no—
718#121—86no—
719#121—86no—
720#121—86no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8#4118yes—
733C4×D4—212no—
734C4×D4—212no—
735C4×D4—212no—
736C4×D4—212no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—46no—
750C4×D4—46no—
751C4×D4—86no—
752C4×D4—86no—
753#117—212no—
754#117—46no—
755#117—46no—
756#117—46no—
757#117—46no—
758#117—46no—
759#117—86no—
760C2×C4⋊C4—212no—
761C2×C4⋊C4—46no—
762C2×C4⋊C4—46no—
763C2×C4⋊C4—46no—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2416yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2416yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2416yes—
860C2×C22⋊C4C2416yes—
861C2×C22⋊C4C2416yes—
862C2×C22⋊C4C2416yes—
863C2×C22⋊C4C2416yes—
864C2×C22⋊C4C2416yes—
865C2×C22⋊C4C2416yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2416yes—
886C2×C42C2416yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2411yescharacteristic
890C2×C42C2413yes—
891#95C2411yescharacteristic
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2413yes—
901#95C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2416yes—
916#95C2413yes—
917#95C2413yes—
918#95C2416yes—
919#95C2413yes—
920#95C2416yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2411yescharacteristic
924#95C2411yescharacteristic
925#95C2411yescharacteristic
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2416yes—
936#95C2416yes—
937#95C2416yes—
938#95C2416yes—
939C24C2513yes—
940C24C2513yes—
941C24C2511yescharacteristic
942C24C2513yes—
943C24C2513yes—
944#41—416no—
945#41—416no—
946#41—416no—
947#41—416no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—416no—
952C2×Q8C2×#4114yes—
953C2×Q8H(5,𝔽2)14yes—
954C2×Q8H(5,𝔽2)14yes—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—212no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—46no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—43no—
984C2×D4—43no—
985C2×D4—43no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—46no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—46no—
1001C2×D4—46no—
1002C2×D4—46no—
1003C2×D4—46no—
1004C2×D4—46no—
1005C2×D4—46no—
1006C2×D4—46no—
1007C2×D4—46no—
1008C2×D4—46no—
1009C2×D4—46no—
1010C2×D4—46no—
1011C2×D4—46no—
1012C2×D4—46no—
1013C2×D4—46no—
1014C2×D4—46no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—26no—
1030C22×C4—212no—
1031C22×C4—46no—
1032C22×C4—46no—
1033C22×C4—46no—
1034C22×C4—46no—
1035C22×C4—46no—
1036C22×C4—46no—
1037C22×C4—46no—
1038C22×C4—46no—
1039C22×C4—46no—
1040C22×C4—46no—
1041C22×C4—46no—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2513yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2513yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2513yes—
1067C22×C4C2513yes—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—26no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—43no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—46no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—46no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—46no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C4⋊C4C2×#41112yes—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—22no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—26no—
1123C22⋊C4—212no—
1124C22⋊C4—43no—
1125C22⋊C4—41no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—46no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—46no—
1161C22⋊C4—46no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—46no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—46no—
1172C22⋊C4—46no—
1173C22⋊C4—46no—
1174C22⋊C4—46no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C42—26no—
1180C42—26no—
1181C42—26no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—26no—
1186C42—26no—
1187C42—26no—
1188C42—41no—
1189C42—46no—
1190C42—43no—
1191C42—46no—
1192C42—43no—
1193C42—43no—
1194C42C2×#41112yes—
1195C23—23no—
1196C23—23no—
1197C23—21no—
1198C23—23no—
1199C23—23no—
1200C23—21no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23—21no—
1207C23—23no—
1208C23—23no—
1209C23—23no—
1210C23—23no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—23no—
1215C23—21no—
1216C23—21no—
1217C23—23no—
1218C23—23no—
1219C23—23no—
1220C23—23no—
1221C23—23no—
1222C23—23no—
1223C23—23no—
1224C23—21no—
1225C23—21no—
1226C23—23no—
1227C23—23no—
1228C23—23no—
1229C23—23no—
1230C23C2611yescharacteristic
1231Q8—412no—
1232Q8#540116yes—
1233D4—412no—
1234D4—412no—
1235D4—412no—
1236D4—412no—
1237D4—412no—
1238D4—86no—
1239D4—812no—
1240D4—86no—
1241D4—86no—
1242D4—86no—
1243D4—86no—
1244D4—86no—
1245D4—86no—
1246D4—86no—
1247D4—86no—
1248D4—166no—
1249D4—166no—
1250D4—166no—
1251D4—166no—
1252D4—166no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—23no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—412no—
1327C2×C4—412no—
1328C2×C4—412no—
1329C2×C4—412no—
1330C2×C4—412no—
1331C2×C4—812no—
1332C2×C4—166no—
1333C2×C4—166no—
1334C2×C4—166no—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4116yes—
1337C2×C4C22×#4116yes—
1338C2×C4C2×H(5,𝔽2)16yes—
1339C2×C4C2×H(5,𝔽2)16yes—
1340C22—41no—
1341C22—43no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22—43no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—41no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—41no—
1354C22—41no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—43no—
1364C22—41no—
1365C22—43no—
1366C22—41no—
1367C22—43no—
1368C22—43no—
1369C22—43no—
1370C22—41no—
1371C22—43no—
1372C22—43no—
1373C22—43no—
1374C22—43no—
1375C22C23×#4111yescharacteristic
1376C22C22×H(5,𝔽2)11yescharacteristic
1377C22C22×H(5,𝔽2)11yescharacteristic
1378C22H(7,𝔽2)11yescharacteristic
1379C22H(7,𝔽2)11yescharacteristic
1380C22H(7,𝔽2)11yescharacteristic
1381C222−1+611yescharacteristic
1382C4—22no—
1383C4—26no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—43no—
1391C4—43no—
1392C4—43no—
1393C4—43no—
1394C4—43no—
1395C4—43no—
1396C4—43no—
1397C4—41no—
1398C4—41no—
1399C4—43no—
1400C4—41no—
1401C4—43no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—43no—
1407C4C2×#540112yes—
1408C2—81no—
1409C2—83no—
1410C2—83no—
1411C2—83no—
1412C2—83no—
1413C2C22×#54011yescharacteristic
1414C2#6285111yescharacteristic
1415C2#6285811yescharacteristic
1416C2#6305211yescharacteristic
1417C2#6305211yescharacteristic
1418C2#6306611yescharacteristic
1419C2#6306611yescharacteristic
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. #42617C2semidirect
2. #42608C2semidirect
3. #42584C2semidirect
4. #42578C2semidirect
5. #42570C2semidirect
6. #42565C2semidirect
7. #42541C2semidirect
8. #42533C2semidirect
9. #42529C2semidirect
10. #42508C2semidirect
11. #42468C2semidirect
12. #42454C2semidirect
13. #37626C2semidirect
14. #37587C2semidirect
15. #37570C2semidirect
16. #36692C2semidirect
17. #36076C2semidirect
18. #36066C2semidirect
19. #36029C2semidirect
20. #36029C2semidirect
21. #36029C2semidirect
22. #36018C2semidirect
23. #36005C2semidirect
24. #35983C2semidirect
25. #35971C2semidirect
26. #35831C2semidirect
27. #35831C2semidirect
28. #35801C2semidirect
29. #34313C2semidirect
30. #34312C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#426172
#426082
#425842
#425782
#425702
#425652
#425412
#425332
#425292
#425082
#424682
#424542
#376262
#375872
#375702
#366922
#360762
#360662
#360292
#360182
#360052
#359832
#359712
#358312
#358012
#343132
#343122
#342632