Finite Group Databasebeta

← #9061100

Subgroups — #9061100

Order 512.

7061 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60032C211yesmaximal, characteristic, complemented
2#58997C213yesmaximal, complemented
3#58260C211yesmaximal, characteristic, complemented
4#57961C213yesmaximal, complemented
5#56344C211yesmaximal, characteristic, complemented
6#53613C213yesmaximal, complemented
7#48454C216yesmaximal, complemented
8#47621C213yesmaximal, complemented
9#47087C216yesmaximal, complemented
10#46350C213yesmaximal, complemented
11#45355C213yesmaximal, complemented
12#44328C216yesmaximal, complemented
13#43404C213yesmaximal, complemented
14#43098C213yesmaximal, complemented
15#43001C216yesmaximal, complemented
16#42996C213yesmaximal, complemented
17#35692C213yesmaximal, complemented
18#35691C213yesmaximal, complemented
19#35355C213yesmaximal, complemented
20C2×#546C2213yescomplemented
21C2×D42C2216yescomplemented
22C2×D42C2216yescomplemented
23C2×D42C2216yescomplemented
24C2×D42C2213yescomplemented
25C2×#534C2216yescomplemented
26C22×#121C2213yescomplemented
27C2×#518C2213yescomplemented
28#2829C2216yescomplemented
29#2824C2213yescomplemented
30#2812C2213yescomplemented
31#2797C2216yescomplemented
32#2780C2216yescomplemented
33#2768C2216yescomplemented
34#2757C2216yescomplemented
35#2756C2216yescomplemented
36#2756C2216yescomplemented
37#2753C2216yescomplemented
38#2749C2216yescomplemented
39#2736C2211yescharacteristic, complemented
40#2708C2216yescomplemented
41#2706C2216yescomplemented
42#2703C2216yescomplemented
43#2697C2216yescomplemented
44#2693C2213yescomplemented
45#2678C2216yescomplemented
46#2678C2216yescomplemented
47#2678C2216yescomplemented
48#2676C2216yescomplemented
49#2675C2213yescomplemented
50#2675C2213yescomplemented
51#2675C2213yescomplemented
52#2673C2216yescomplemented
53#2673C2216yescomplemented
54#2673C2216yescomplemented
55#2671C2216yescomplemented
56#2670C2213yescomplemented
57#2669C2216yescomplemented
58#2669C2216yescomplemented
59#2669C2216yescomplemented
60#2669C2216yescomplemented
61#2668C2213yescomplemented
62#2668C2216yescomplemented
63#2668C2216yescomplemented
64#2668C2216yescomplemented
65#2668C2213yescomplemented
66#2635C2213yescomplemented
67#2631C2213yescomplemented
68#2626C2213yescomplemented
69#2619C2213yescomplemented
70#2617C2213yescomplemented
71#2617C2213yescomplemented
72#2610C2213yescomplemented
73#2598C2213yescomplemented
74#2579C2213yescomplemented
75#2579C2213yescomplemented
76#2578C2216yescomplemented
77#2564C2213yescomplemented
78#2543C2216yescomplemented
79#2543C2213yescomplemented
80#2543C2213yescomplemented
81#2541C2213yescomplemented
82#2539C2213yescomplemented
83#2535C2213yescomplemented
84#2535C2216yescomplemented
85#2535C2216yescomplemented
86#2534C2216yescomplemented
87#2529C2216yescomplemented
88#2518C2216yescomplemented
89#2517C2213yescomplemented
90#2476C2216yescomplemented
91#2476C2216yescomplemented
92#2471C2216yescomplemented
93#2464C2216yescomplemented
94#2464C2216yescomplemented
95#2464C2216yescomplemented
96#2464C2216yescomplemented
97#2463C2213yescomplemented
98#2456C2216yescomplemented
99#2456C2216yescomplemented
100#2456C2216yescomplemented
101#2456C2216yescomplemented
102#2455C2213yescomplemented
103#2433C2216yescomplemented
104#2433C2216yescomplemented
105#2428C2216yescomplemented
106#2428C2216yescomplemented
107#2425C2216yescomplemented
108#2424C2216yescomplemented
109#2424C2216yescomplemented
110#2424C2216yescomplemented
111#2424C2216yescomplemented
112#2424C2216yescomplemented
113#2424C2216yescomplemented
114#2418C2216yescomplemented
115#2416C2216yescomplemented
116#2414C2216yescomplemented
117#2410C2216yescomplemented
118#2410C2216yescomplemented
119#2410C2216yescomplemented
120#2410C2216yescomplemented
121#2410C2216yescomplemented
122#2408C2213yescomplemented
123#2408C2213yescomplemented
124#2408C2213yescomplemented
125#2408C2213yescomplemented
126#2408C2216yescomplemented
127#2408C2213yescomplemented
128#2405C2213yescomplemented
129#2405C2213yescomplemented
130#2404C2213yescomplemented
131#2403C2213yescomplemented
132#2403C2216yescomplemented
133#2403C2213yescomplemented
134#2403C2213yescomplemented
135#2403C2213yescomplemented
136#2403C2216yescomplemented
137#2403C2216yescomplemented
138#2403C2213yescomplemented
139#2397C2213yescomplemented
140#2392C2213yescomplemented
141#2388C2211yescharacteristic, complemented
142C2×#392C2213yescomplemented
143C2×#392C2211yescharacteristic, complemented
144C2×#392C2213yescomplemented
145#2380C2212yescomplemented
146#2364C2216yescomplemented
147#2361C2216yescomplemented
148#2358C2216yescomplemented
149#2353C2213yescomplemented
150#2349C2213yescomplemented
151D4×C22⋊C4C2216yescomplemented
152#2328C2216yescomplemented
153#2325C2216yescomplemented
154#2321C2213yescomplemented
155#2321C2213yescomplemented
156#2321C2216yescomplemented
157#2312C2213yescomplemented
158C4×#120C2211yescharacteristic, complemented
159C4×#120C2213yescomplemented
160C22×#41C2311yescharacteristic
161C23×D4C2313yes—
162C23×D4C2316yes—
163C23×D4C2313yes—
164C23×D4C2313yes—
165C23×D4C2316yes—
166C23×D4C2313yes—
167C23×D4C2313yes—
168C23×D4C2313yes—
169C23×D4C2316yes—
170C23×D4C2313yes—
171C24×C4C2311yescharacteristic
172#546—412no—
173D42—412no—
174D42—424no—
175D42—424no—
176D42—424no—
177#534—424no—
178C2×#127C2316yes—
179C2×#127C2313yes—
180C2×#127C2312yes—
181C2×#127C2316yes—
182C2×#124C2313yes—
183C2×#123C2316yes—
184C2×#123C2316yes—
185C2×#123C2316yes—
186C2×#123C2316yes—
187C2×#123C2316yes—
188C2×C22⋊Q8C2313yes—
189C2×#121—412no—
190C2×#121C2316yes—
191C2×#121C2316yes—
192C2×#121C2316yes—
193C2×#121C2313yes—
194C2×#121C2313yes—
195C2×#121C2316yes—
196C2×#121C2313yes—
197C2×#121C2316yes—
198C2×#121C2316yes—
199C2×#121C2316yes—
200C2×#121C2316yes—
201C2×#121C2316yes—
202C2×#121C2316yes—
203C2×#121C2316yes—
204C2×#121C2316yes—
205C2×#121C2316yes—
206C2×#121C2316yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2316yes—
210C2×#121C2316yes—
211C2×#121C2316yes—
212C2×#120C2313yes—
213C2×#120C2316yes—
214C2×#120C2316yes—
215C2×#120C2313yes—
216C2×#120C2313yes—
217C2×#120C2316yes—
218C2×#120C2316yes—
219C2×#120C2311yescharacteristic
220C2×#120C2316yes—
221C2×#120C2316yes—
222C2×#120C2316yes—
223C2×#120C2316yes—
224C2×#120C2316yes—
225C2×#120C2316yes—
226C2×#120C2316yes—
227C2×#120C2316yes—
228C2×#120C2316yes—
229C2×#120C2316yes—
230C2×#120C2316yes—
231#518—412no—
232C2×C4×D4C2313yes—
233C2×C4×D4C2313yes—
234C2×C4×D4C2313yes—
235C2×C4×D4C2316yes—
236C2×C4×D4C2313yes—
237C2×C4×D4C2313yes—
238C2×C4×D4C2313yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2313yes—
248C2×#117C2313yes—
249C2×#117C2313yes—
250C22×C4⋊C4C2313yes—
251C22×C22⋊C4C2313yes—
252C22×C22⋊C4C2313yes—
253C22×C22⋊C4C2316yes—
254C22×C22⋊C4C2313yes—
255C22×C22⋊C4C2316yes—
256C22×C22⋊C4C2313yes—
257C22×C22⋊C4C2313yes—
258#400C2313yes—
259#400C2316yes—
260#399C2313yes—
261#399C2313yes—
262#399C2313yes—
263#399C2316yes—
264#398C2316yes—
265#398C2316yes—
266#398C2313yes—
267#398C2316yes—
268#397C2316yes—
269#397C2316yes—
270#397C2316yes—
271#397C2313yes—
272#397C2316yes—
273#397C2313yes—
274#397C2313yes—
275#397C2316yes—
276#397C2316yes—
277#396C2316yes—
278#396C2316yes—
279#396C2316yes—
280#396C2316yes—
281#396C2316yes—
282#396C2316yes—
283#395C2311yescharacteristic
284#394C2316yes—
285#394C2316yes—
286#394C2313yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yes—
290#394C2316yes—
291#394C2313yes—
292#394C2313yes—
293#394C2316yes—
294#394C2316yes—
295#394C2316yes—
296#394C2316yes—
297#394C2313yes—
298#394C2316yes—
299#394C2313yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C2316yes—
304#394C2316yes—
305#394C2316yes—
306#393C2313yes—
307#393C2313yes—
308#393C2311yescharacteristic
309#392C2313yes—
310#392C2316yes—
311#392C2313yes—
312#392C2313yes—
313#392C2311yescharacteristic
314#392C2313yes—
315#392C2313yes—
316#392C2313yes—
317#392C2316yes—
318#392C2313yes—
319#392C2316yes—
320#392C2313yes—
321#392C2313yes—
322#392C2313yes—
323#392C2313yes—
324#392C2316yes—
325#392C2311yescharacteristic
326#392C2316yes—
327#392C2313yes—
328#392C2316yes—
329#392C2316yes—
330#392C2316yes—
331#392C2313yes—
332#392C2316yes—
333#392C2316yes—
334#392C2316yes—
335#392C2316yes—
336#392C2316yes—
337#392C2316yes—
338#392C2316yes—
339#392C2316yes—
340#392C2316yes—
341#392C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C2316yes—
346#390C2316yes—
347#390C2316yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#390C2316yes—
352#389C2316yes—
353#389C2316yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#388C2316yes—
371#387C2316yes—
372#387C2316yes—
373#387C2316yes—
374#387C2316yes—
375#387C2316yes—
376#386C2316yes—
377#386C2316yes—
378#386C2313yes—
379#386C2313yes—
380#386C2316yes—
381#386C2316yes—
382#386C2316yes—
383#386C2316yes—
384#386C2316yes—
385#386C2316yes—
386#386C2316yes—
387#386C2313yes—
388#386C2313yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#386C2316yes—
396#386C2316yes—
397#386C2316yes—
398#386C2316yes—
399#386C2316yes—
400#386C2316yes—
401#386C2316yes—
402#386C2316yes—
403#386C2316yes—
404#386C2316yes—
405#386C2316yes—
406#386C2316yes—
407#386C2316yes—
408#386C2316yes—
409#386C2316yes—
410#385C2316yes—
411#385C2313yes—
412#385C2313yes—
413#385C2316yes—
414#385C2316yes—
415#385C2313yes—
416#385C2313yes—
417#385C2316yes—
418#385C2316yes—
419#385C2316yes—
420#385C2316yes—
421#385C2316yes—
422#383C2312yes—
423#383C2313yes—
424#383C2312yes—
425#382C2316yes—
426#382C2313yes—
427#381C2313yes—
428#380C2316yes—
429#380C2313yes—
430#380C2313yes—
431#380C2316yes—
432#380C2313yes—
433#380C2313yes—
434#380C2313yes—
435#379C2313yes—
436#379C2313yes—
437#379C2316yes—
438#379C2313yes—
439#379C2313yes—
440#379C2316yes—
441#379C2316yes—
442#379C2313yes—
443#379C2311yescharacteristic
444C4×C4⋊C4C2313yes—
445C4×C22⋊C4C2313yes—
446C4×C22⋊C4C2313yes—
447C4×C22⋊C4C2316yes—
448C4×C22⋊C4C2316yes—
449C4×C22⋊C4C2313yes—
450C4×C22⋊C4C2316yes—
451#376C2313yes—
452C2×#95C2313yes—
453C2×#95C2313yes—
454C2×#95C2311yescharacteristic
455C25C2411yescharacteristic
456C25C2413yes—
457C25C2416yes—
458C25C2413yes—
459C25C2413yes—
460C2×#41—46no—
461C22×Q8C2411yescharacteristic
462C22×D4—212no—
463C22×D4—46no—
464C22×D4—412no—
465C22×D4—46no—
466C22×D4—412no—
467C22×D4—412no—
468C22×D4—46no—
469C22×D4—46no—
470C22×D4—46no—
471C22×D4—46no—
472C22×D4—46no—
473C22×D4—46no—
474C22×D4—412no—
475C22×D4—412no—
476C22×D4—412no—
477C22×D4—412no—
478C22×D4—412no—
479C22×D4—412no—
480C22×D4—412no—
481C22×D4—412no—
482C22×D4—412no—
483C22×D4—412no—
484C22×D4—412no—
485C22×D4—412no—
486C22×D4C2413yes—
487C22×D4C2413yes—
488C22×D4C2413yes—
489C22×D4C2413yes—
490C22×D4C2416yes—
491C22×D4C2413yes—
492C22×D4C2416yes—
493C22×D4C2416yes—
494C22×D4C2416yes—
495C22×D4C2416yes—
496C22×D4C2416yes—
497C22×D4C2416yes—
498C22×D4C2416yes—
499C22×D4C2416yes—
500C22×D4C2416yes—
501C22×D4C2416yes—
502C22×D4C2416yes—
503C22×D4C2416yes—
504C22×D4C2416yes—
505C22×D4C2416yes—
506C22×D4C2413yes—
507C22×D4C2413yes—
508C22×D4C2416yes—
509C22×D4C2413yes—
510C22×D4C2413yes—
511C23×C4—46no—
512C23×C4C2413yes—
513C23×C4C2413yes—
514C23×C4C2413yes—
515C23×C4C2413yes—
516C23×C4C2413yes—
517C23×C4C2416yes—
518C23×C4C2413yes—
519C23×C4C2416yes—
520C23×C4C2413yes—
521C23×C4C2413yes—
522C23×C4C2411yescharacteristic
523C23×C4C2413yes—
524C23×C4C2413yes—
525C23×C4C2416yes—
526#127—224no—
527#127—46no—
528#127—44no—
529#127—412no—
530#124—46no—
531#123—412no—
532#123—412no—
533#123—412no—
534#123—412no—
535#123—412no—
536C22⋊Q8—46no—
537#121—224no—
538#121—224no—
539#121—224no—
540#121—412no—
541#121—412no—
542#121—46no—
543#121—412no—
544#121—412no—
545#121—412no—
546#121—412no—
547#121—412no—
548#121—412no—
549#121—412no—
550#121—412no—
551#121—412no—
552#121—412no—
553#121—412no—
554#121—412no—
555#121—412no—
556#121—412no—
557#121—46no—
558#121—46no—
559#120—212no—
560#120—224no—
561#120—212no—
562#120—224no—
563#120—412no—
564#120—412no—
565#120—412no—
566#120—412no—
567#120—412no—
568#120—412no—
569#120—412no—
570#120—412no—
571#120—412no—
572#120—42no—
573#120—46no—
574#120—412no—
575#120—412no—
576#120—412no—
577#120—412no—
578C4×D4—212no—
579C4×D4—212no—
580C4×D4—46no—
581C4×D4—412no—
582C4×D4—412no—
583C4×D4—412no—
584C4×D4—46no—
585C4×D4—46no—
586C4×D4—412no—
587C4×D4—46no—
588C4×D4—46no—
589C4×D4—46no—
590C4×D4—412no—
591C4×D4—412no—
592C4×D4—46no—
593C4×D4—46no—
594#117—46no—
595#117—46no—
596C2×C4⋊C4—46no—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2413yes—
599C2×C4⋊C4C2413yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2413yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2416yes—
607C2×C4⋊C4C2416yes—
608C2×C4⋊C4C2413yes—
609C2×C4⋊C4C2413yes—
610C2×C4⋊C4C2416yes—
611C2×C4⋊C4C2416yes—
612C2×C4⋊C4C2416yes—
613C2×C22⋊C4—212no—
614C2×C22⋊C4—46no—
615C2×C22⋊C4—46no—
616C2×C22⋊C4—46no—
617C2×C22⋊C4—412no—
618C2×C22⋊C4—412no—
619C2×C22⋊C4—46no—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2413yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2413yes—
638C2×C22⋊C4C2413yes—
639C2×C22⋊C4C2413yes—
640C2×C22⋊C4C2413yes—
641C2×C22⋊C4C2413yes—
642C2×C22⋊C4C2413yes—
643C2×C22⋊C4C2413yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C2416yes—
654C2×C22⋊C4C2416yes—
655C2×C22⋊C4C2416yes—
656C2×C22⋊C4C2416yes—
657C2×C22⋊C4C2416yes—
658C2×C22⋊C4C2416yes—
659C2×C22⋊C4C2416yes—
660C2×C22⋊C4C2416yes—
661C2×C22⋊C4C2416yes—
662C2×C22⋊C4C2416yes—
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C2416yes—
665C2×C22⋊C4C2413yes—
666C2×C22⋊C4C2413yes—
667C2×C22⋊C4C2416yes—
668C2×C22⋊C4C2413yes—
669C2×C42C2413yes—
670C2×C42C2413yes—
671C2×C42C2416yes—
672C2×C42C2413yes—
673C2×C42C2413yes—
674C2×C42C2416yes—
675C2×C42C2412yes—
676#95C2413yes—
677#95C2413yes—
678#95C2416yes—
679#95C2411yescharacteristic
680#95C2413yes—
681#95C2416yes—
682#95C2413yes—
683#95C2413yes—
684#95C2416yes—
685#95C2413yes—
686#95C2416yes—
687#95C2416yes—
688#95C2416yes—
689#95C2416yes—
690#95C2416yes—
691#95C2416yes—
692#95C2413yes—
693#95C2416yes—
694#95C2416yes—
695#95C2416yes—
696#95C2416yes—
697#95C2416yes—
698#95C2416yes—
699C24—26no—
700C24—26no—
701C24—212no—
702C24—212no—
703C24—26no—
704C24—26no—
705C24—26no—
706C24—26no—
707C24—43no—
708C24—43no—
709C24—46no—
710C24—43no—
711C24—43no—
712C24—41no—
713C24—46no—
714C24—46no—
715C24—46no—
716C24—46no—
717C24—46no—
718C24—46no—
719C24—46no—
720C24—46no—
721C24—46no—
722C24—46no—
723C24—43no—
724C24C2513yes—
725C24C2516yes—
726C24C2513yes—
727C24C2513yes—
728C24C2513yes—
729C24C2511yescharacteristic
730#41—88no—
731C2×Q8—43no—
732C2×D4—26no—
733C2×D4—26no—
734C2×D4—26no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—26no—
739C2×D4—26no—
740C2×D4—212no—
741C2×D4—212no—
742C2×D4—212no—
743C2×D4—212no—
744C2×D4—212no—
745C2×D4—212no—
746C2×D4—26no—
747C2×D4—212no—
748C2×D4—212no—
749C2×D4—212no—
750C2×D4—212no—
751C2×D4—212no—
752C2×D4—212no—
753C2×D4—212no—
754C2×D4—26no—
755C2×D4—212no—
756C2×D4—212no—
757C2×D4—212no—
758C2×D4—212no—
759C2×D4—212no—
760C2×D4—43no—
761C2×D4—43no—
762C2×D4—46no—
763C2×D4—46no—
764C2×D4—46no—
765C2×D4—46no—
766C2×D4—43no—
767C2×D4—46no—
768C2×D4—43no—
769C2×D4—43no—
770C2×D4—43no—
771C2×D4—46no—
772C2×D4—46no—
773C2×D4—46no—
774C2×D4—46no—
775C2×D4—46no—
776C2×D4—46no—
777C2×D4—46no—
778C2×D4—46no—
779C2×D4—46no—
780C2×D4—46no—
781C2×D4—46no—
782C2×D4—46no—
783C2×D4—46no—
784C2×D4—46no—
785C2×D4—46no—
786C2×D4—46no—
787C2×D4—46no—
788C2×D4—46no—
789C2×D4—46no—
790C2×D4—43no—
791C2×D4—46no—
792C2×D4—46no—
793C2×D4—43no—
794C2×D4—43no—
795C2×D4—46no—
796C2×D4—46no—
797C2×D4—46no—
798C2×D4—46no—
799C2×D4—46no—
800C2×D4—46no—
801C2×D4—448no—
802C2×D4—824no—
803C2×D4—848no—
804C2×D4—824no—
805C2×D4—848no—
806C2×D4—824no—
807C2×D4—824no—
808C2×D4—824no—
809C2×D4—848no—
810C2×D4—824no—
811C2×D4H(5,𝔽2)112yes—
812C22×C4—26no—
813C22×C4—26no—
814C22×C4—26no—
815C22×C4—212no—
816C22×C4—26no—
817C22×C4—26no—
818C22×C4—26no—
819C22×C4—26no—
820C22×C4—212no—
821C22×C4—212no—
822C22×C4—43no—
823C22×C4—43no—
824C22×C4—43no—
825C22×C4—43no—
826C22×C4—46no—
827C22×C4—46no—
828C22×C4—46no—
829C22×C4—46no—
830C22×C4—46no—
831C22×C4—46no—
832C22×C4—46no—
833C22×C4—46no—
834C22×C4—46no—
835C22×C4—46no—
836C22×C4—46no—
837C22×C4—46no—
838C22×C4—46no—
839C22×C4—46no—
840C22×C4—43no—
841C22×C4—43no—
842C22×C4—46no—
843C22×C4—88no—
844C22×C4C2516yes—
845C22×C4C2513yes—
846C22×C4C2513yes—
847C22×C4C2516yes—
848C22×C4C2513yes—
849C22×C4C2516yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2513yes—
853C22×C4C2513yes—
854C22×C4C2513yes—
855C22×C4C2513yes—
856C22×C4C2513yes—
857C4⋊C4—212no—
858C4⋊C4—26no—
859C4⋊C4—26no—
860C4⋊C4—212no—
861C4⋊C4—212no—
862C4⋊C4—46no—
863C4⋊C4—43no—
864C4⋊C4—43no—
865C4⋊C4—46no—
866C4⋊C4—46no—
867C4⋊C4—46no—
868C4⋊C4—43no—
869C4⋊C4—43no—
870C4⋊C4—46no—
871C4⋊C4—46no—
872C4⋊C4—46no—
873C22⋊C4—26no—
874C22⋊C4—26no—
875C22⋊C4—212no—
876C22⋊C4—26no—
877C22⋊C4—212no—
878C22⋊C4—212no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—26no—
882C22⋊C4—26no—
883C22⋊C4—212no—
884C22⋊C4—212no—
885C22⋊C4—212no—
886C22⋊C4—212no—
887C22⋊C4—212no—
888C22⋊C4—212no—
889C22⋊C4—212no—
890C22⋊C4—212no—
891C22⋊C4—43no—
892C22⋊C4—43no—
893C22⋊C4—43no—
894C22⋊C4—43no—
895C22⋊C4—43no—
896C22⋊C4—43no—
897C22⋊C4—46no—
898C22⋊C4—46no—
899C22⋊C4—46no—
900C22⋊C4—46no—
901C22⋊C4—46no—
902C22⋊C4—46no—
903C22⋊C4—46no—
904C22⋊C4—46no—
905C22⋊C4—46no—
906C22⋊C4—46no—
907C22⋊C4—46no—
908C22⋊C4—46no—
909C22⋊C4—43no—
910C22⋊C4—46no—
911C22⋊C4—43no—
912C22⋊C4—46no—
913C22⋊C4—46no—
914C22⋊C4—46no—
915C22⋊C4—46no—
916C22⋊C4—46no—
917C22⋊C4—46no—
918C22⋊C4—46no—
919C22⋊C4—46no—
920C22⋊C4—46no—
921C22⋊C4H(5,𝔽2)112yes—
922C42—26no—
923C42—26no—
924C42—212no—
925C42—43no—
926C42—43no—
927C42—46no—
928C42—42no—
929C23—23no—
930C23—23no—
931C23—26no—
932C23—26no—
933C23—26no—
934C23—23no—
935C23—26no—
936C23—23no—
937C23—23no—
938C23—26no—
939C23—26no—
940C23—23no—
941C23—23no—
942C23—23no—
943C23—23no—
944C23—26no—
945C23—26no—
946C23—26no—
947C23—26no—
948C23—26no—
949C23—23no—
950C23—26no—
951C23—26no—
952C23—26no—
953C23—26no—
954C23—23no—
955C23—412no—
956C23—412no—
957C23—412no—
958C23—424no—
959C23—86no—
960C23—86no—
961C23—812no—
962C23—86no—
963C23—812no—
964C23—812no—
965C23—812no—
966C23—812no—
967C23—812no—
968C23—812no—
969C23—812no—
970C23—86no—
971C23—82no—
972C23—86no—
973C23—86no—
974C23—163no—
975C23—163no—
976C23—166no—
977C23—166no—
978C23—166no—
979C23—166no—
980C23C2×H(5,𝔽2)16yes—
981C23C2×H(5,𝔽2)16yes—
982C23C2×H(5,𝔽2)16yes—
983C23#58512yes—
984C23C2611yescharacteristic
985Q8—82no—
986D4—224no—
987D4—412no—
988D4—424no—
989D4—424no—
990D4—424no—
991D4—412no—
992D4—412no—
993D4—424no—
994D4—424no—
995D4—412no—
996D4—412no—
997D4—812no—
998D4—812no—
999D4—812no—
1000D4—812no—
1001D4—812no—
1002D4—812no—
1003D4—812no—
1004D4—812no—
1005D4—812no—
1006D4—86no—
1007D4—86no—
1008D4—812no—
1009D4—86no—
1010D4—166no—
1011C2×C4—23no—
1012C2×C4—26no—
1013C2×C4—26no—
1014C2×C4—23no—
1015C2×C4—23no—
1016C2×C4—26no—
1017C2×C4—23no—
1018C2×C4—23no—
1019C2×C4—23no—
1020C2×C4—26no—
1021C2×C4—23no—
1022C2×C4—23no—
1023C2×C4—23no—
1024C2×C4—26no—
1025C2×C4—26no—
1026C2×C4—26no—
1027C2×C4—26no—
1028C2×C4—26no—
1029C2×C4—26no—
1030C2×C4—26no—
1031C2×C4—26no—
1032C2×C4—26no—
1033C2×C4—26no—
1034C2×C4—23no—
1035C2×C4—26no—
1036C2×C4—23no—
1037C2×C4—412no—
1038C2×C4—412no—
1039C2×C4—86no—
1040C2×C4—86no—
1041C2×C4—86no—
1042C2×C4—812no—
1043C2×C4—86no—
1044C2×C4—812no—
1045C2×C4—86no—
1046C2×C4—86no—
1047C2×C4—86no—
1048C2×C4—812no—
1049C2×C4—161no—
1050C2×C4—163no—
1051C2×C4C2×H(5,𝔽2)16yes—
1052C2×C4C2×H(5,𝔽2)16yes—
1053C2×C4C2×H(5,𝔽2)16yes—
1054C22—26no—
1055C22—26no—
1056C22—212no—
1057C22—212no—
1058C22—26no—
1059C22—26no—
1060C22—26no—
1061C22—26no—
1062C22—43no—
1063C22—43no—
1064C22—43no—
1065C22—43no—
1066C22—46no—
1067C22—41no—
1068C22—43no—
1069C22—46no—
1070C22—46no—
1071C22—46no—
1072C22—46no—
1073C22—46no—
1074C22—46no—
1075C22—46no—
1076C22—43no—
1077C22—43no—
1078C22—46no—
1079C22—43no—
1080C22—46no—
1081C22—46no—
1082C22—46no—
1083C22—46no—
1084C22—88no—
1085C22—1612no—
1086C22—1612no—
1087C22—1624no—
1088C22—1612no—
1089C22C22×H(5,𝔽2)13yes—
1090C22C22×H(5,𝔽2)13yes—
1091C22C2×#58511yescharacteristic
1092C4—26no—
1093C4—26no—
1094C4—26no—
1095C4—41no—
1096C4—41no—
1097C4—46no—
1098C4—43no—
1099C4—46no—
1100C4—43no—
1101C4—43no—
1102C4—43no—
1103C4—43no—
1104C4—46no—
1105C2—46no—
1106C2—46no—
1107C2—46no—
1108C2—42no—
1109C2—86no—
1110C2—83no—
1111C2#6281813yes—
1112C2#6301111yescharacteristic
1113C2#6301113yes—
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. #60032C2semidirect
2. #58997C2semidirect
3. #58260C2semidirect
4. #57961C2semidirect
5. #56344C2semidirect
6. #53613C2semidirect
7. #48454C2semidirect
8. #47621C2semidirect
9. #47087C2semidirect
10. #46350C2semidirect
11. #45355C2semidirect
12. #44328C2semidirect
13. #43404C2semidirect
14. #43098C2semidirect
15. #43001C2semidirect
16. #42996C2semidirect
17. #35692C2semidirect
18. #35691C2semidirect
19. #35355C2semidirect
20. C2×#546C22semidirect
21. C2×D42C22semidirect
22. C2×D42C22semidirect
23. C2×D42C22semidirect
24. C2×D42C22semidirect
25. C2×#534C22semidirect
26. C22×#121C22semidirect
27. C2×#518C22semidirect
28. #2829C22semidirect
29. #2824C22semidirect
30. #2812C22semidirect
31. #2797C22semidirect
32. #2780C22semidirect
33. #2768C22semidirect
34. #2757C22semidirect
35. #2756C22semidirect
36. #2756C22semidirect
37. #2753C22semidirect
38. #2749C22semidirect
39. #2736C22semidirect
40. #2708C22semidirect
41. #2706C22semidirect
42. #2703C22semidirect
43. #2697C22semidirect
44. #2693C22semidirect
45. #2678C22semidirect
46. #2678C22semidirect
47. #2678C22semidirect
48. #2676C22semidirect
49. #2675C22semidirect
50. #2675C22semidirect
51. #2675C22semidirect
52. #2673C22semidirect
53. #2673C22semidirect
54. #2673C22semidirect
55. #2671C22semidirect
56. #2670C22semidirect
57. #2669C22semidirect
58. #2669C22semidirect
59. #2669C22semidirect
60. #2669C22semidirect
61. #2668C22semidirect
62. #2668C22semidirect
63. #2668C22semidirect
64. #2668C22semidirect
65. #2668C22semidirect
66. #2635C22semidirect
67. #2631C22semidirect
68. #2626C22semidirect
69. #2619C22semidirect
70. #2617C22semidirect
71. #2617C22semidirect
72. #2610C22semidirect
73. #2598C22semidirect
74. #2579C22semidirect
75. #2579C22semidirect
76. #2578C22semidirect
77. #2564C22semidirect
78. #2543C22semidirect
79. #2543C22semidirect
80. #2543C22semidirect
81. #2541C22semidirect
82. #2539C22semidirect
83. #2535C22semidirect
84. #2535C22semidirect
85. #2535C22semidirect
86. #2534C22semidirect
87. #2529C22semidirect
88. #2518C22semidirect
89. #2517C22semidirect
90. #2476C22semidirect
91. #2476C22semidirect
92. #2471C22semidirect
93. #2464C22semidirect
94. #2464C22semidirect
95. #2464C22semidirect
96. #2464C22semidirect
97. #2463C22semidirect
98. #2456C22semidirect
99. #2456C22semidirect
100. #2456C22semidirect
101. #2456C22semidirect
102. #2455C22semidirect
103. #2433C22semidirect
104. #2433C22semidirect
105. #2428C22semidirect
106. #2428C22semidirect
107. #2425C22semidirect
108. #2424C22semidirect
109. #2424C22semidirect
110. #2424C22semidirect
111. #2424C22semidirect
112. #2424C22semidirect
113. #2424C22semidirect
114. #2418C22semidirect
115. #2416C22semidirect
116. #2414C22semidirect
117. #2410C22semidirect
118. #2410C22semidirect
119. #2410C22semidirect
120. #2410C22semidirect
121. #2410C22semidirect
122. #2408C22semidirect
123. #2408C22semidirect
124. #2408C22semidirect
125. #2408C22semidirect
126. #2408C22semidirect
127. #2408C22semidirect
128. #2405C22semidirect
129. #2405C22semidirect
130. #2404C22semidirect
131. #2403C22semidirect
132. #2403C22semidirect
133. #2403C22semidirect
134. #2403C22semidirect
135. #2403C22semidirect
136. #2403C22semidirect
137. #2403C22semidirect
138. #2403C22semidirect
139. #2397C22semidirect
140. #2392C22semidirect
141. #2388C22semidirect
142. C2×#392C22semidirect
143. C2×#392C22semidirect
144. C2×#392C22semidirect
145. #2380C22semidirect
146. #2364C22semidirect
147. #2361C22semidirect
148. #2358C22semidirect
149. #2353C22semidirect
150. #2349C22semidirect
151. D4×C22⋊C4C22semidirect
152. #2328C22semidirect
153. #2325C22semidirect
154. #2321C22semidirect
155. #2321C22semidirect
156. #2321C22semidirect
157. #2312C22semidirect
158. C4×#120C22semidirect
159. C4×#120C22semidirect

Maximal subgroups

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

subgroupindex
#600322
#589972
#582602
#579612
#563442
#536132
#484542
#476212
#470872
#463502
#453552
#443282
#434042
#430982
#430012
#429962
#356922
#356912
#353552