Finite Group Databasebeta

← #8121423

Subgroups — #8121423

Order 512.

4362 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58681C214yesmaximal, complemented
2#58617C214yesmaximal, complemented
3#57567C214yesmaximal, complemented
4#56995C214yesmaximal, complemented
5#52741C212yesmaximal, complemented
6#52414C212yesmaximal, complemented
7#47653C214yesmaximal, complemented
8#47321C214yesmaximal, complemented
9#47297C214yesmaximal, complemented
10#47230C214yesmaximal, complemented
11#43643C212yesmaximal, complemented
12#43621C212yesmaximal, complemented
13#38605C214yesmaximal, complemented
14#38146C214yesmaximal, complemented
15#37895C212yesmaximal, complemented
16#37886C212yesmaximal, complemented
17#37754C212yesmaximal, complemented
18#37747C212yesmaximal, complemented
19#36970C211yesmaximal, characteristic, complemented
20#36961C211yesmaximal, characteristic
21#35247C212yesmaximal, complemented
22#35099C212yesmaximal, complemented
23C2×#2604C211yesmaximal, characteristic, complemented
24C2×#543C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#529C2212yes—
27C22×#126C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2855C2212yes—
30#2855C2212yes—
31#2854C2212yes—
32#2854C2212yes—
33#2853C2214yes—
34#2844C2212yescomplemented
35#2841C2212yes—
36#2838C2214yes—
37#2838C2214yescomplemented
38#2831C2214yescomplemented
39#2830C2212yescomplemented
40#2829C2214yes—
41#2827C2214yes—
42#2826C2212yes—
43#2817C2214yescomplemented
44#2805C2214yescomplemented
45#2800C2214yes—
46#2796C2214yes—
47#2795C2214yes—
48#2794C2214yescomplemented
49#2791C2214yescomplemented
50#2789C2212yescomplemented
51#2788C2214yescomplemented
52#2787C2214yescomplemented
53#2786C2214yes—
54#2784C2212yescomplemented
55#2783C2214yescomplemented
56#2780C2214yes—
57#2779C2214yescomplemented
58#2775C2214yescomplemented
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2773C2214yes—
62#2772C2214yes—
63#2771C2214yescomplemented
64#2769C2212yescomplemented
65#2767C2214yescomplemented
66#2765C2214yescomplemented
67#2763C2212yes—
68#2762C2214yescomplemented
69#2761C2214yes—
70#2760C2212yes—
71#2759C2214yes—
72#2756C2214yes—
73#2753C2214yes—
74#2753C2214yes—
75#2752C2212yes—
76#2746C2214yes—
77#2744C2214yescomplemented
78#2742C2212yes—
79#2740C2214yes—
80#2738C2214yes—
81#2737C2214yes—
82#2730C2214yes—
83#2723C2214yes—
84#2723C2214yes—
85#2723C2214yes—
86#2723C2214yescomplemented
87#2718C2214yes—
88#2714C2214yes—
89#2714C2214yes—
90#2702C2214yes—
91#2702C2214yescomplemented
92#2698C2214yes—
93#2698C2214yes—
94#2696C2214yes—
95#2691C2214yescomplemented
96#2690C2214yes—
97#2690C2214yescomplemented
98#2689C2214yes—
99#2689C2214yes—
100#2689C2214yescomplemented
101#2689C2214yescomplemented
102#2686C2214yescomplemented
103#2683C2212yescomplemented
104#2666C2214yescomplemented
105#2654C2214yes—
106#2649C2214yescomplemented
107#2648C2214yes—
108#2646C2212yes—
109#2643C2214yes—
110#2639C2212yes—
111#2637C2214yescomplemented
112#2637C2214yescomplemented
113#2627C2212yes—
114#2617C2212yes—
115#2612C2212yescomplemented
116#2607C2212yes—
117#2604C2214yes—
118#2604C2214yes—
119#2604C2214yes—
120#2604C2214yes—
121#2596C2214yes—
122#2595C2214yes—
123#2593C2214yes—
124#2593C2212yescomplemented
125#2592C2212yescomplemented
126#2592C2212yescomplemented
127#2587C2214yescomplemented
128#2586C2214yescomplemented
129#2584C2212yescomplemented
130#2584C2212yescomplemented
131#2583C2212yes—
132#2582C2212yescomplemented
133#2582C2212yescomplemented
134#2572C2214yes—
135#2564C2214yes—
136#2554C2214yes—
137#2539C2212yes—
138#2538C2212yescomplemented
139#2538C2212yescomplemented
140#2533C2214yescomplemented
141#2533C2214yescomplemented
142#2532C2214yescomplemented
143#2531C2214yes—
144#2531C2214yescomplemented
145#2530C2214yescomplemented
146#2529C2214yescomplemented
147#2528C2214yescomplemented
148#2528C2214yescomplemented
149#2527C2214yescomplemented
150#2526C2214yescomplemented
151#2526C2214yescomplemented
152#2524C2214yescomplemented
153#2522C2214yes—
154#2520C2214yescomplemented
155#2518C2214yescomplemented
156#2513C2214yes—
157#2508C2214yescomplemented
158#2505C2214yes—
159#2505C2214yescomplemented
160#2504C2212yes—
161#2503C2212yes—
162#2495C2214yescomplemented
163#2493C2214yes—
164#2488C2214yes—
165#2488C2214yes—
166#2486C2214yes—
167#2484C2214yes—
168#2483C2212yes—
169#2483C2212yes—
170#2481C2214yes—
171#2477C2214yes—
172#2476C2214yescomplemented
173#2465C2214yescomplemented
174#2463C2214yes—
175#2463C2212yes—
176#2457C2214yes—
177#2449C2214yes—
178#2444C2214yes—
179#2444C2214yescomplemented
180#2438C2214yescomplemented
181#2425C2214yes—
182#2421C2214yes—
183#2418C2214yes—
184#2415C2214yes—
185#2413C2214yes—
186#2413C2214yes—
187#2412C2214yes—
188#2411C2214yes—
189#2409C2214yes—
190#2406C2214yes—
191#2406C2212yes—
192#2404C2212yes—
193C2×#400C2211yescharacteristic
194C2×#399C2211yescharacteristic
195C2×#395C2211yescharacteristic
196C2×#393C2211yescharacteristic
197#2359C2214yes—
198#2358C2214yes—
199#2343C2214yes—
200#2339C2214yes—
201#2335C2214yes—
202#2334C2214yescomplemented
203#2329C2212yes—
204#2329C2214yescomplemented
205#2325C2212yes—
206#2323C2214yescomplemented
207#2323C2214yescomplemented
208#2319C2214yes—
209#2318C2214yes—
210#2313C2211yescharacteristic
211#2312C2211yescharacteristic
212C4×#123C2214yes—
213C2×#389C2212yes—
214C2×#388C2212yes—
215C2×#388C2212yes—
216C2×#387C2212yes—
217#2285C2212yes—
218C2×#376C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221#543—44no—
222#537—44no—
223#529—48no—
224C2×#126—44no—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#124C2312yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2314yes—
246C2×#120C2314yes—
247C2×C4×Q8—44no—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4C2311yescharacteristic
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275#401C2314yes—
276#401C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2312yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2312yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#399C2314yes—
303#399C2312yes—
304#399C2314yes—
305#399C2314yes—
306#399C2312yes—
307#399C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2312yes—
312#398C2312yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2312yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2312yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2312yes—
367#395C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2312yes—
386#393C2312yes—
387#393C2312yes—
388#393C2312yes—
389#393C2314yes—
390#393C2314yes—
391#392C2312yes—
392#392C2312yes—
393#392C2314yes—
394#392C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#390C2314yes—
407#390C2312yes—
408#390C2314yes—
409#390C2314yes—
410#390C2312yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2314yes—
415#390C2312yes—
416#390C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#385C2312yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2312yes—
558#385C2314yes—
559#384C2312yes—
560#384C2312yes—
561#383C2314yes—
562#383C2314yes—
563#383C2314yes—
564#382C2314yes—
565#382C2312yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#382C2312yes—
570#382C2314yes—
571#382C2314yes—
572#381C2314yes—
573#381C2312yes—
574#381C2312yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2312yes—
582#380C2314yes—
583#380C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#379C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608#376C2314yes—
609#376C2314yes—
610#376C2314yes—
611C2×#95C2314yes—
612C2×#95C2311yescharacteristic
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2311yescharacteristic
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C2×#41—44no—
621C2×#41—48no—
622C22×Q8—42no—
623C22×Q8—44no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C23×C4C2411yescharacteristic
637C23×C4C2412yes—
638C23×C4C2411yescharacteristic
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2414yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2411yescharacteristic
651#126—48no—
652#126—48no—
653#126—48no—
654#126—48no—
655#125—44no—
656#124—44no—
657#123—48no—
658#123—48no—
659#123—48no—
660#123—48no—
661C22⋊Q8—28no—
662C22⋊Q8—44no—
663C22⋊Q8—48no—
664C22⋊Q8—48no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668C22⋊Q8—48no—
669#121—28no—
670#121—48no—
671#121—44no—
672#120—48no—
673C4×Q8—44no—
674C4×Q8—44no—
675C4×Q8—44no—
676C4×Q8—44no—
677C4×Q8—44no—
678C4×D4—44no—
679C4×D4—48no—
680C4×D4—48no—
681C4×D4—48no—
682#117—48no—
683#117—48no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—44no—
686C2×C4⋊C4—44no—
687C2×C4⋊C4—44no—
688C2×C4⋊C4—42no—
689C2×C4⋊C4—42no—
690C2×C4⋊C4—42no—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C22⋊C4—24no—
741C2×C22⋊C4—44no—
742C2×C22⋊C4—44no—
743C2×C22⋊C4—44no—
744C2×C22⋊C4—42no—
745C2×C22⋊C4—42no—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C42—24no—
786C2×C42—28no—
787C2×C42—44no—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2412yes—
805#95C2414yes—
806#95C2412yes—
807#95C2412yes—
808#95C2414yes—
809#95C2414yes—
810#95C2412yes—
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2412yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867C24—22no—
868C24—24no—
869C24—42no—
870C24—41no—
871C24—41no—
872C24C2512yes—
873C24C2514yes—
874C24C2511yescharacteristic
875#41—816no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—41no—
880C2×Q8—42no—
881C2×Q8—41no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—416no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—24no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—42no—
907C2×D4—42no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—42no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—42no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4H(5,𝔽2)14yes—
948C22×C4C2514yes—
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—41no—
985C4⋊C4—44no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—44no—
1032C22⋊C4—42no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—42no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C42—24no—
1057C42—24no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—24no—
1062C42—44no—
1063C42—44no—
1064C42—42no—
1065C42—44no—
1066C42—42no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—44no—
1073C23—22no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—22no—
1087C23—22no—
1088C23—44no—
1089C23—82no—
1090C23—82no—
1091C23—84no—
1092C23—84no—
1093C23C2×H(5,𝔽2)12yes—
1094C23#58514yes—
1095C23C2611yescharacteristic
1096Q8—44no—
1097Q8—48no—
1098Q8—44no—
1099Q8—84no—
1100Q8—84no—
1101Q8—162no—
1102D4—416no—
1103D4—84no—
1104D4—88no—
1105D4—84no—
1106D4—162no—
1107D4—164no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—44no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—44no—
1169C2×C4—88no—
1170C2×C4—82no—
1171C2×C4—82no—
1172C2×C4—84no—
1173C2×C4—88no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4—164no—
1177C2×C4C2×H(5,𝔽2)14yes—
1178C2×C4#58514yes—
1179C22—22no—
1180C22—22no—
1181C22—24no—
1182C22—24no—
1183C22—44no—
1184C22—42no—
1185C22—44no—
1186C22—42no—
1187C22—42no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—164no—
1196C22#355114yes—
1197C22C22×H(5,𝔽2)11yescharacteristic
1198C22C2×#58512yes—
1199C22C2×#58512yes—
1200C222−1+611yescharacteristic
1201C222−1+611yescharacteristic
1202C4—24no—
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—41no—
1211C4—41no—
1212C4—44no—
1213C4—42no—
1214C4—42no—
1215C4—44no—
1216C4—44no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C2—24no—
1223C2—84no—
1224C2—82no—
1225C2C2×#355111yescharacteristic
1226C2#6282111yescharacteristic
1227C2#6287111yescharacteristic
1228C2#6290712yes—
1229C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36961C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58681C2semidirect
2. #58617C2semidirect
3. #57567C2semidirect
4. #56995C2semidirect
5. #52741C2semidirect
6. #52414C2semidirect
7. #47653C2semidirect
8. #47321C2semidirect
9. #47297C2semidirect
10. #47230C2semidirect
11. #43643C2semidirect
12. #43621C2semidirect
13. #38605C2semidirect
14. #38146C2semidirect
15. #37895C2semidirect
16. #37886C2semidirect
17. #37754C2semidirect
18. #37747C2semidirect
19. #36970C2semidirect
21. #35247C2semidirect
22. #35099C2semidirect
23. C2×#2604C2semidirect
34. #2844C22semidirect
37. #2838C22semidirect
38. #2831C22semidirect
39. #2830C22semidirect
43. #2817C22semidirect
44. #2805C22semidirect
48. #2794C22semidirect
49. #2791C22semidirect
50. #2789C22semidirect
51. #2788C22semidirect
52. #2787C22semidirect
54. #2784C22semidirect
55. #2783C22semidirect
57. #2779C22semidirect
58. #2775C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
63. #2771C22semidirect
64. #2769C22semidirect
65. #2767C22semidirect
66. #2765C22semidirect
68. #2762C22semidirect
77. #2744C22semidirect
86. #2723C22semidirect
91. #2702C22semidirect
95. #2691C22semidirect
97. #2690C22semidirect
100. #2689C22semidirect
101. #2689C22semidirect
102. #2686C22semidirect
103. #2683C22semidirect
104. #2666C22semidirect
106. #2649C22semidirect
111. #2637C22semidirect
112. #2637C22semidirect
115. #2612C22semidirect
124. #2593C22semidirect
125. #2592C22semidirect
126. #2592C22semidirect
127. #2587C22semidirect
128. #2586C22semidirect
129. #2584C22semidirect
130. #2584C22semidirect
132. #2582C22semidirect
133. #2582C22semidirect
138. #2538C22semidirect
139. #2538C22semidirect
140. #2533C22semidirect
141. #2533C22semidirect
142. #2532C22semidirect
144. #2531C22semidirect
145. #2530C22semidirect
146. #2529C22semidirect
147. #2528C22semidirect
148. #2528C22semidirect
149. #2527C22semidirect
150. #2526C22semidirect
151. #2526C22semidirect
152. #2524C22semidirect
154. #2520C22semidirect
155. #2518C22semidirect
157. #2508C22semidirect
159. #2505C22semidirect
162. #2495C22semidirect
172. #2476C22semidirect
173. #2465C22semidirect
179. #2444C22semidirect
180. #2438C22semidirect
202. #2334C22semidirect
204. #2329C22semidirect
206. #2323C22semidirect
207. #2323C22semidirect

Maximal subgroups

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

subgroupindex
#586812
#586172
#575672
#569952
#527412
#524142
#476532
#473212
#472972
#472302
#436432
#436212
#386052
#381462
#378952
#378862
#377542
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