Finite Group Databasebeta

← #7699989

Subgroups — #7699989

Order 512.

7142 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60045C211yesmaximal, characteristic, complemented
2#60040C213yesmaximal, complemented
3#60037C211yesmaximal, characteristic, complemented
4#60034C213yesmaximal, complemented
5#59940C213yesmaximal, complemented
6#59915C213yesmaximal, complemented
7#59685C216yesmaximal, complemented
8#59623C213yesmaximal, complemented
9#59089C213yesmaximal, complemented
10#58990C211yesmaximal, characteristic, complemented
11#36362C213yesmaximal, complemented
12#36322C216yesmaximal, complemented
13#36316C213yesmaximal, complemented
14#36244C216yesmaximal, complemented
15#36221C216yesmaximal, complemented
16#36098C213yesmaximal, complemented
17C4×D42C213yesmaximal, complemented
18#34152C213yesmaximal, complemented
19C2×#2358C213yesmaximal, complemented
20C2×#553C2213yescomplemented
21C2×#546C2213yescomplemented
22C2×D42C2213yes—
23C2×#525C2213yes—
24C22×#120C2213yes—
25C22×C4×D4C2216yescomplemented
26C22×C4×D4C2213yescomplemented
27C23×C22⋊C4C2213yescomplemented
28#2861C2213yescomplemented
29#2856C2211yescharacteristic, complemented
30#2853C2213yescomplemented
31#2852C2216yescomplemented
32#2850C2213yescomplemented
33#2849C2213yescomplemented
34#2849C2213yescomplemented
35#2847C2213yescomplemented
36#2847C2211yescharacteristic, complemented
37#2846C2211yescharacteristic, complemented
38#2804C2213yescomplemented
39#2801C2212yescomplemented
40#2797C2216yescomplemented
41#2790C2216yescomplemented
42#2748C2213yescomplemented
43#2709C2213yescomplemented
44#2703C2216yescomplemented
45#2697C2213yescomplemented
46#2679C2211yescharacteristic
47#2669C2213yes—
48#2603C2216yescomplemented
49#2602C2216yescomplemented
50#2600C2216yescomplemented
51#2598C2216yescomplemented
52#2597C2216yescomplemented
53#2591C2213yescomplemented
54#2589C2216yescomplemented
55#2579C2216yescomplemented
56#2579C2213yescomplemented
57#2576C2216yescomplemented
58#2572C2216yescomplemented
59#2566C2213yescomplemented
60#2557C2216yescomplemented
61#2554C2216yescomplemented
62#2554C2216yescomplemented
63#2544C2213yescomplemented
64#2543C2216yescomplemented
65#2539C2213yescomplemented
66#2534C2213yescomplemented
67#2531C2216yescomplemented
68#2526C2216yescomplemented
69#2525C2216yescomplemented
70#2516C2216yescomplemented
71#2510C2216yescomplemented
72#2505C2216yescomplemented
73#2502C2213yescomplemented
74#2500C2213yescomplemented
75#2480C2216yescomplemented
76#2476C2216yescomplemented
77#2473C2216yescomplemented
78#2472C2216yescomplemented
79#2472C2216yescomplemented
80#2471C2216yescomplemented
81#2468C2216yescomplemented
82#2464C2216yescomplemented
83#2464C2216yescomplemented
84#2460C2216yescomplemented
85#2459C2216yescomplemented
86#2457C2216yescomplemented
87#2456C2216yescomplemented
88#2450C2216yescomplemented
89#2450C2216yescomplemented
90#2444C2216yescomplemented
91#2444C2216yescomplemented
92#2443C2216yescomplemented
93#2437C2216yescomplemented
94#2433C2213yes—
95#2431C2213yescomplemented
96#2424C2216yes—
97#2424C2216yescomplemented
98#2424C2216yescomplemented
99#2424C2216yescomplemented
100#2418C2216yescomplemented
101#2412C2213yescomplemented
102#2411C2213yescomplemented
103#2411C2213yescomplemented
104#2410C2216yes—
105#2410C2216yescomplemented
106#2410C2213yescomplemented
107#2405C2213yescomplemented
108#2404C2213yescomplemented
109#2404C2213yescomplemented
110#2403C2213yes—
111#2374C2213yescomplemented
112#2374C2216yescomplemented
113#2374C2213yescomplemented
114#2368C2216yescomplemented
115#2368C2216yescomplemented
116#2366C2213yescomplemented
117#2364C2216yescomplemented
118#2364C2216yescomplemented
119#2361C2216yescomplemented
120#2361C2216yescomplemented
121#2358C2213yes—
122#2358C2213yes—
123#2358C2213yes—
124#2358C2216yescomplemented
125#2358C2216yescomplemented
126#2358C2216yescomplemented
127#2358C2216yescomplemented
128#2358C2216yescomplemented
129#2358C2213yescomplemented
130#2358C2216yescomplemented
131#2358C2213yescomplemented
132#2358C2216yescomplemented
133#2358C2216yescomplemented
134#2358C2213yescomplemented
135#2353C2216yescomplemented
136D4×C4⋊C4C2216yescomplemented
137#2342C2213yescomplemented
138#2342C2213yescomplemented
139D4×C22⋊C4C2216yescomplemented
140D4×C22⋊C4C2216yescomplemented
141C4×#127C2213yescomplemented
142C4×#121C2216yescomplemented
143C4×#121C2216yescomplemented
144C4×#120C2213yes—
145C4×#120C2213yescomplemented
146C4×#120C2216yescomplemented
147#2298C2216yescomplemented
148#2297C2213yescomplemented
149#2297C2213yescomplemented
150C2×#390C2213yescomplemented
151#2290C2216yescomplemented
152#2290C2216yescomplemented
153C2×#388C2216yescomplemented
154C2×#386C2216yescomplemented
155C2×#386C2213yescomplemented
156C2×#385C2216yescomplemented
157C42×D4C2213yescomplemented
158C42×D4C2216yescomplemented
159C2×C4×C22⋊C4C2216yescomplemented
160C26C2311yescharacteristic
161C22×#41C2313yes—
162C23×D4C2313yes—
163C23×D4C2316yes—
164C23×D4C2313yes—
165C24×C4C2313yes—
166C24×C4C2313yes—
167C24×C4C2313yes—
168C24×C4C2311yescharacteristic, complemented
169#553—412no—
170#546—412no—
171D42—224no—
172C2×#127C2313yes—
173C2×#127C2311yescharacteristic
174C2×#126C2316yescomplemented
175C2×#125C2313yescomplemented
176C2×#124C2313yes—
177C2×#124C2313yescomplemented
178#525—224no—
179C2×#123C2313yes—
180C2×#123C2313yes—
181C2×#123C2313yes—
182C2×#123C2313yes—
183C2×#123C2313yes—
184C2×#123C2316yescomplemented
185C2×C22⋊Q8C2316yes—
186C2×C22⋊Q8C2313yes—
187C2×#121C2316yes—
188C2×#121C2316yes—
189C2×#121C2316yes—
190C2×#121C2313yes—
191C2×#121C2316yes—
192C2×#121C2313yes—
193C2×#121C2313yes—
194C2×#121C2313yes—
195C2×#121C2313yescomplemented
196C2×#120—224no—
197C2×#120C2313yes—
198C2×#120C2313yes—
199C2×#120C2316yes—
200C2×#120C2313yes—
201C2×#120C2313yes—
202C2×#120C2316yes—
203C2×#120C2313yes—
204C2×#120C2316yes—
205C2×#120C2313yes—
206C2×#120C2313yes—
207C2×#120C2311yescharacteristic
208C2×#120C2311yescharacteristic
209C2×#120C2313yes—
210C2×#120C2311yescharacteristic, complemented
211C2×C4×D4—424no—
212C2×C4×D4—412no—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2316yes—
223C2×C4×D4C2316yes—
224C2×C4×D4C2316yes—
225C2×C4×D4C2316yes—
226C2×C4×D4C2316yes—
227C2×C4×D4C2313yescomplemented
228C2×C4×D4C2316yescomplemented
229C2×C4×D4C2316yescomplemented
230C2×#117C2313yes—
231C2×#117C2313yescomplemented
232C2×#117C2313yescomplemented
233C22×C4⋊C4C2313yes—
234C22×C4⋊C4C2316yes—
235C22×C4⋊C4C2313yescomplemented
236C22×C22⋊C4—412no—
237C22×C22⋊C4C2313yes—
238C22×C22⋊C4C2316yes—
239C22×C22⋊C4C2313yes—
240C22×C22⋊C4C2313yes—
241C22×C22⋊C4C2316yes—
242C22×C22⋊C4C2316yes—
243C22×C22⋊C4C2316yes—
244C22×C22⋊C4C2313yes—
245C22×C22⋊C4C2313yes—
246C22×C22⋊C4C2313yes—
247C22×C22⋊C4C2316yes—
248C22×C22⋊C4C2316yes—
249C22×C22⋊C4C2313yes—
250C22×C22⋊C4C2313yescomplemented
251C22×C42C2316yes—
252C22×C42C2313yes—
253C22×C42C2313yescomplemented
254C22×C42C2311yescharacteristic, complemented
255#401C2312yescomplemented
256#400C2316yescomplemented
257#400C2316yescomplemented
258#400C2316yescomplemented
259#399C2316yes—
260#399C2312yescomplemented
261#398C2316yescomplemented
262#398C2316yescomplemented
263#398C2316yescomplemented
264#398C2316yescomplemented
265#397C2316yes—
266#397C2316yescomplemented
267#397C2316yescomplemented
268#397C2316yescomplemented
269#397C2316yescomplemented
270#396C2316yes—
271#396C2316yes—
272#396C2312yes—
273#396C2316yescomplemented
274#396C2316yescomplemented
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2316yes—
279#394C2316yes—
280#394C2316yes—
281#394C2316yes—
282#394C2316yescomplemented
283#394C2316yescomplemented
284#394C2316yescomplemented
285#393C2316yes—
286#393C2316yescomplemented
287#392C2316yes—
288#392C2316yes—
289#392C2316yes—
290#392C2316yes—
291#392C2316yes—
292#392C2316yescomplemented
293#391C2313yescomplemented
294#391C2313yescomplemented
295#391C2316yescomplemented
296#391C2313yescomplemented
297#390C2316yes—
298#390C2313yes—
299#390C2313yes—
300#390C2313yes—
301#390C2316yes—
302#390C2313yes—
303#390C2313yes—
304#390C2316yes—
305#390C2316yes—
306#390C2316yes—
307#390C2313yes—
308#390C2316yescomplemented
309#390C2313yescomplemented
310#390C2316yescomplemented
311#389C2316yescomplemented
312#389C2316yescomplemented
313#388C2316yes—
314#388C2316yes—
315#388C2316yes—
316#388C2316yes—
317#388C2316yes—
318#388C2316yes—
319#388C2316yes—
320#388C2316yes—
321#388C2316yes—
322#388C2316yes—
323#388C2316yes—
324#388C2316yes—
325#388C2316yes—
326#388C2316yescomplemented
327#388C2316yescomplemented
328#388C2316yescomplemented
329#388C2316yescomplemented
330#388C2316yescomplemented
331#388C2316yescomplemented
332#388C2316yescomplemented
333#388C2316yescomplemented
334#388C2316yescomplemented
335#388C2316yescomplemented
336#388C2316yescomplemented
337#388C2316yescomplemented
338#387C2316yescomplemented
339#387C2316yescomplemented
340#387C2316yescomplemented
341#387C2316yescomplemented
342#387C2316yescomplemented
343#387C2316yescomplemented
344#387C2316yescomplemented
345#387C2316yescomplemented
346#387C2316yescomplemented
347#387C2316yescomplemented
348#387C2316yescomplemented
349#386C2316yes—
350#386C2316yes—
351#386C2316yes—
352#386C2316yes—
353#386C2316yes—
354#386C2313yes—
355#386C2316yes—
356#386C2313yes—
357#386C2313yes—
358#386C2313yes—
359#386C2316yes—
360#386C2316yes—
361#386C2313yes—
362#386C2313yes—
363#386C2313yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2316yes—
372#386C2313yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#386C2316yes—
377#386C2316yes—
378#386C2313yes—
379#386C2313yescomplemented
380#386C2313yescomplemented
381#386C2313yescomplemented
382#386C2316yescomplemented
383#386C2316yescomplemented
384#386C2316yescomplemented
385#386C2316yescomplemented
386#385C2316yes—
387#385C2316yes—
388#385C2316yes—
389#385C2316yes—
390#385C2316yes—
391#385C2316yes—
392#385C2316yes—
393#385C2316yes—
394#385C2316yes—
395#385C2316yes—
396#385C2316yes—
397#385C2316yes—
398#385C2316yes—
399#385C2316yes—
400#385C2313yes—
401#385C2316yescomplemented
402#385C2313yescomplemented
403#385C2313yescomplemented
404#385C2316yescomplemented
405#385C2313yescomplemented
406#385C2316yescomplemented
407#384C2313yescomplemented
408#384C2311yescharacteristic, complemented
409#383C2316yescomplemented
410#382C2313yescomplemented
411#381C2313yes—
412#381C2313yes—
413#381C2313yescomplemented
414#381C2316yescomplemented
415#380C2316yes—
416#380C2313yes—
417#380C2316yes—
418#380C2313yescomplemented
419#380C2316yescomplemented
420#379C2313yes—
421#379C2313yes—
422#379C2311yescharacteristic
423#379C2313yes—
424#379C2316yes—
425#379C2313yescomplemented
426C4×C4⋊C4C2313yescomplemented
427C4×C4⋊C4C2316yescomplemented
428C4×C4⋊C4C2316yescomplemented
429C4×C4⋊C4C2316yescomplemented
430C4×C4⋊C4C2316yescomplemented
431C4×C22⋊C4C2316yes—
432C4×C22⋊C4C2316yes—
433C4×C22⋊C4C2313yes—
434C4×C22⋊C4C2316yes—
435C4×C22⋊C4C2316yes—
436C4×C22⋊C4C2313yes—
437C4×C22⋊C4C2316yes—
438C4×C22⋊C4C2316yes—
439C4×C22⋊C4C2316yes—
440C4×C22⋊C4C2316yes—
441C4×C22⋊C4C2316yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2316yescomplemented
444C4×C22⋊C4C2313yescomplemented
445C4×C22⋊C4C2316yescomplemented
446C4×C22⋊C4C2316yescomplemented
447C4×C22⋊C4C2313yescomplemented
448C4×C22⋊C4C2316yescomplemented
449C4×C22⋊C4C2316yescomplemented
450#376C2316yescomplemented
451C2×#95C2316yes—
452C2×#95C2316yes—
453C2×#95C2316yes—
454C43C2313yescomplemented
455C25—212no—
456C25—46no—
457C25—81no—
458C25C2413yes—
459C25C2413yes—
460C25C2413yes—
461C25C2411yescharacteristic
462C25C2411yescharacteristic
463C2×#41—212no—
464C2×#41—46no—
465C2×#41—83no—
466C22×Q8C2413yes—
467C22×D4—224no—
468C22×D4—224no—
469C22×D4—224no—
470C22×D4—212no—
471C22×D4—46no—
472C22×D4—46no—
473C22×D4—412no—
474C22×D4—83no—
475C22×D4C2413yes—
476C22×D4C2416yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C2416yes—
481C22×D4C2413yes—
482C22×D4C2413yes—
483C22×D4C2413yes—
484C22×D4C2413yes—
485C22×D4C2413yes—
486C22×D4C2413yes—
487C22×D4C2411yescharacteristic
488C22×D4C2413yes—
489C22×D4C2413yes—
490C23×C4—212no—
491C23×C4—46no—
492C23×C4—46no—
493C23×C4—412no—
494C23×C4—46no—
495C23×C4—46no—
496C23×C4—412no—
497C23×C4—83no—
498C23×C4C2416yes—
499C23×C4C2416yes—
500C23×C4C2413yes—
501C23×C4C2416yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2413yes—
505C23×C4C2413yes—
506C23×C4C2413yes—
507C23×C4C2416yes—
508C23×C4C2416yes—
509C23×C4C2413yes—
510C23×C4C2413yes—
511C23×C4C2413yes—
512C23×C4C2416yes—
513C23×C4C2413yes—
514C23×C4C2413yes—
515#127—212no—
516#127—81no—
517#126—412no—
518#125—46no—
519#124—46no—
520#124—83no—
521#123—212no—
522#123—212no—
523#123—46no—
524#123—46no—
525#123—412no—
526#123—83no—
527C22⋊Q8—224no—
528C22⋊Q8—46no—
529#121—224no—
530#121—224no—
531#121—224no—
532#121—46no—
533#121—46no—
534#121—46no—
535#121—46no—
536#121—412no—
537#121—46no—
538#120—212no—
539#120—212no—
540#120—212no—
541#120—224no—
542#120—212no—
543#120—212no—
544#120—224no—
545#120—224no—
546#120—46no—
547#120—46no—
548#120—81no—
549#120—81no—
550#120—81no—
551#120#41124yescomplemented
552C4×D4—224no—
553C4×D4—224no—
554C4×D4—224no—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—212no—
558C4×D4—412no—
559C4×D4—412no—
560C4×D4—412no—
561C4×D4—46no—
562C4×D4—46no—
563C4×D4—412no—
564C4×D4—412no—
565C4×D4—412no—
566C4×D4—412no—
567C4×D4—412no—
568C4×D4—412no—
569#117—212no—
570#117—46no—
571#117—83no—
572C2×C4⋊C4—412no—
573C2×C4⋊C4—46no—
574C2×C4⋊C4—46no—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2413yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2416yes—
594C2×C22⋊C4—212no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—212no—
598C2×C22⋊C4—212no—
599C2×C22⋊C4—46no—
600C2×C22⋊C4—46no—
601C2×C22⋊C4—412no—
602C2×C22⋊C4—412no—
603C2×C22⋊C4—412no—
604C2×C22⋊C4—46no—
605C2×C22⋊C4—46no—
606C2×C22⋊C4—412no—
607C2×C22⋊C4—83no—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2413yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2413yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2413yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C2413yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2413yes—
644C2×C22⋊C4C2413yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2413yes—
647C2×C22⋊C4C2413yes—
648C2×C22⋊C4C2413yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2413yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C2413yes—
654C2×C42—412no—
655C2×C42—46no—
656C2×C42—83no—
657C2×C42—81no—
658C2×C42C2416yes—
659C2×C42C2416yes—
660C2×C42C2413yes—
661C2×C42C2416yes—
662C2×C42C2413yes—
663C2×C42C2416yes—
664C2×C42C2416yes—
665C2×C42C2416yes—
666C2×C42C2416yes—
667C2×C42C2413yes—
668C2×C42C2411yescharacteristic
669C2×C42C2413yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2416yes—
684#95C2416yes—
685#95C2416yes—
686#95C2416yes—
687#95C2416yes—
688#95C2416yes—
689#95C2416yes—
690#95C2416yes—
691#95C2416yes—
692#95C2416yes—
693#95C2416yes—
694#95C2412yes—
695C24—212no—
696C24—212no—
697C24—26no—
698C24—26no—
699C24—26no—
700C24—212no—
701C24—26no—
702C24—212no—
703C24—26no—
704C24—26no—
705C24—43no—
706C24—43no—
707C24—46no—
708C24—43no—
709C24—46no—
710C24—43no—
711C24—43no—
712C24—43no—
713C24—41no—
714C24—41no—
715C24—448no—
716C24—824no—
717C24—88no—
718C24C2×#41112yes—
719C24C2511yescharacteristic
720C24C2513yes—
721C24C2511yescharacteristic
722C24C2513yes—
723C24C2513yes—
724C24C2513yes—
725#41—824no—
726C2×Q8—26no—
727C2×Q8—43no—
728C2×Q8—43no—
729C2×D4—212no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—212no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—26no—
740C2×D4—26no—
741C2×D4—26no—
742C2×D4—26no—
743C2×D4—26no—
744C2×D4—212no—
745C2×D4—212no—
746C2×D4—26no—
747C2×D4—26no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—43no—
752C2×D4—43no—
753C2×D4—43no—
754C2×D4—43no—
755C2×D4—43no—
756C2×D4—43no—
757C2×D4—43no—
758C2×D4—43no—
759C2×D4—43no—
760C2×D4—43no—
761C2×D4—43no—
762C2×D4—43no—
763C2×D4—43no—
764C2×D4—43no—
765C2×D4—43no—
766C2×D4—43no—
767C2×D4—46no—
768C2×D4—448no—
769C2×D4—496no—
770C2×D4—824no—
771C2×D4C2×#41124yes—
772C2×D4C2×#41112yes—
773C22×C4—26no—
774C22×C4—212no—
775C22×C4—26no—
776C22×C4—212no—
777C22×C4—26no—
778C22×C4—212no—
779C22×C4—212no—
780C22×C4—26no—
781C22×C4—212no—
782C22×C4—212no—
783C22×C4—26no—
784C22×C4—26no—
785C22×C4—212no—
786C22×C4—212no—
787C22×C4—26no—
788C22×C4—212no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—212no—
792C22×C4—26no—
793C22×C4—26no—
794C22×C4—212no—
795C22×C4—43no—
796C22×C4—46no—
797C22×C4—43no—
798C22×C4—46no—
799C22×C4—46no—
800C22×C4—43no—
801C22×C4—43no—
802C22×C4—43no—
803C22×C4—43no—
804C22×C4—43no—
805C22×C4—46no—
806C22×C4—46no—
807C22×C4—43no—
808C22×C4—43no—
809C22×C4—46no—
810C22×C4—46no—
811C22×C4—46no—
812C22×C4—46no—
813C22×C4—46no—
814C22×C4—46no—
815C22×C4—46no—
816C22×C4—46no—
817C22×C4—43no—
818C22×C4—824no—
819C22×C4—88no—
820C22×C4—824no—
821C22×C4—824no—
822C22×C4C2513yes—
823C22×C4C2516yes—
824C22×C4C2516yes—
825C22×C4C2513yes—
826C22×C4C2513yes—
827C22×C4C2513yes—
828C22×C4C2516yes—
829C22×C4C2513yes—
830C22×C4C2511yescharacteristic
831C22×C4C2516yes—
832C22×C4C2513yes—
833C22×C4C2513yes—
834C22×C4C2513yes—
835C4⋊C4—212no—
836C4⋊C4—212no—
837C4⋊C4—212no—
838C4⋊C4—212no—
839C4⋊C4—212no—
840C4⋊C4—212no—
841C4⋊C4—26no—
842C4⋊C4—43no—
843C4⋊C4—46no—
844C4⋊C4—46no—
845C4⋊C4—46no—
846C4⋊C4—43no—
847C4⋊C4—46no—
848C4⋊C4—43no—
849C4⋊C4—46no—
850C4⋊C4—43no—
851C4⋊C4—43no—
852C4⋊C4—43no—
853C4⋊C4—46no—
854C22⋊C4—26no—
855C22⋊C4—212no—
856C22⋊C4—26no—
857C22⋊C4—212no—
858C22⋊C4—212no—
859C22⋊C4—26no—
860C22⋊C4—212no—
861C22⋊C4—26no—
862C22⋊C4—26no—
863C22⋊C4—212no—
864C22⋊C4—212no—
865C22⋊C4—212no—
866C22⋊C4—212no—
867C22⋊C4—212no—
868C22⋊C4—212no—
869C22⋊C4—212no—
870C22⋊C4—212no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—26no—
875C22⋊C4—212no—
876C22⋊C4—212no—
877C22⋊C4—26no—
878C22⋊C4—46no—
879C22⋊C4—46no—
880C22⋊C4—46no—
881C22⋊C4—46no—
882C22⋊C4—46no—
883C22⋊C4—46no—
884C22⋊C4—43no—
885C22⋊C4—43no—
886C22⋊C4—46no—
887C22⋊C4—46no—
888C22⋊C4—43no—
889C22⋊C4—43no—
890C22⋊C4—43no—
891C22⋊C4—46no—
892C22⋊C4—43no—
893C22⋊C4—43no—
894C22⋊C4—43no—
895C22⋊C4—46no—
896C22⋊C4—46no—
897C22⋊C4C2×#41112yes—
898C22⋊C4C2×#41124yes—
899C22⋊C4H(5,𝔽2)112yes—
900C42—212no—
901C42—26no—
902C42—212no—
903C42—212no—
904C42—26no—
905C42—46no—
906C42—46no—
907C42—46no—
908C42—43no—
909C42—46no—
910C42—43no—
911C42—41no—
912C23—23no—
913C23—26no—
914C23—23no—
915C23—26no—
916C23—26no—
917C23—26no—
918C23—26no—
919C23—23no—
920C23—23no—
921C23—23no—
922C23—23no—
923C23—248no—
924C23—23no—
925C23—23no—
926C23—26no—
927C23—23no—
928C23—23no—
929C23—23no—
930C23—26no—
931C23—23no—
932C23—23no—
933C23—21no—
934C23—21no—
935C23—412no—
936C23—412no—
937C23—412no—
938C23—424no—
939C23—424no—
940C23—412no—
941C23—412no—
942C23—412no—
943C23—424no—
944C23—412no—
945C23—412no—
946C23—412no—
947C23—86no—
948C23—812no—
949C23—86no—
950C23—812no—
951C23—86no—
952C23—86no—
953C23—82no—
954C23—864no—
955C23—82no—
956C23C22×#4116yes—
957C23C22×#4116yes—
958C23C22×#41112yes—
959C23C2×H(5,𝔽2)16yes—
960C23C2611yescharacteristic
961Q8—86no—
962D4—248no—
963D4—412no—
964D4—424no—
965D4—424no—
966D4—424no—
967D4—412no—
968D4—424no—
969D4—86no—
970D4—86no—
971D4—86no—
972D4—86no—
973D4—86no—
974D4—86no—
975D4—163no—
976D4—161no—
977C2×C4—23no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—26no—
981C2×C4—23no—
982C2×C4—23no—
983C2×C4—23no—
984C2×C4—26no—
985C2×C4—23no—
986C2×C4—26no—
987C2×C4—26no—
988C2×C4—26no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—26no—
992C2×C4—26no—
993C2×C4—23no—
994C2×C4—26no—
995C2×C4—23no—
996C2×C4—23no—
997C2×C4—23no—
998C2×C4—26no—
999C2×C4—23no—
1000C2×C4—23no—
1001C2×C4—26no—
1002C2×C4—26no—
1003C2×C4—26no—
1004C2×C4—23no—
1005C2×C4—23no—
1006C2×C4—23no—
1007C2×C4—412no—
1008C2×C4—412no—
1009C2×C4—412no—
1010C2×C4—424no—
1011C2×C4—424no—
1012C2×C4—412no—
1013C2×C4—424no—
1014C2×C4—412no—
1015C2×C4—412no—
1016C2×C4—812no—
1017C2×C4—86no—
1018C2×C4—86no—
1019C2×C4—86no—
1020C2×C4—812no—
1021C2×C4—812no—
1022C2×C4—86no—
1023C2×C4—86no—
1024C2×C4C22×#41112yes—
1025C2×C4C22×#4116yes—
1026C2×C4C2×H(5,𝔽2)16yes—
1027C2×C4C2×H(5,𝔽2)16yes—
1028C22—212no—
1029C22—26no—
1030C22—26no—
1031C22—212no—
1032C22—26no—
1033C22—26no—
1034C22—212no—
1035C22—212no—
1036C22—448no—
1037C22—46no—
1038C22—46no—
1039C22—43no—
1040C22—43no—
1041C22—43no—
1042C22—43no—
1043C22—43no—
1044C22—43no—
1045C22—43no—
1046C22—46no—
1047C22—43no—
1048C22—41no—
1049C22—41no—
1050C22—43no—
1051C22—46no—
1052C22—43no—
1053C22—43no—
1054C22—824no—
1055C22—824no—
1056C22—88no—
1057C22—88no—
1058C22#3481112yes—
1059C22C23×#4113yes—
1060C22C22×H(5,𝔽2)13yes—
1061C22H(7,𝔽2)11yescharacteristic
1062C4—26no—
1063C4—26no—
1064C4—26no—
1065C4—212no—
1066C4—46no—
1067C4—43no—
1068C4—43no—
1069C4—43no—
1070C4—46no—
1071C4—43no—
1072C4—41no—
1073C4—46no—
1074C4—43no—
1075C2—212no—
1076C2—46no—
1077C2—46no—
1078C2—81no—
1079C2—83no—
1080C2—81no—
1081C2C2×#348113yes—
1082C2#6298313yes—
1083C2#6301111yescharacteristic
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. #60045C2semidirect
2. #60040C2semidirect
3. #60037C2semidirect
4. #60034C2semidirect
5. #59940C2semidirect
6. #59915C2semidirect
7. #59685C2semidirect
8. #59623C2semidirect
9. #59089C2semidirect
10. #58990C2semidirect
11. #36362C2semidirect
12. #36322C2semidirect
13. #36316C2semidirect
14. #36244C2semidirect
15. #36221C2semidirect
16. #36098C2semidirect
17. C4×D42C2semidirect
18. #34152C2semidirect
19. C2×#2358C2semidirect
20. C2×#553C22semidirect
21. C2×#546C22semidirect
25. C22×C4×D4C22semidirect
26. C22×C4×D4C22semidirect
27. C23×C22⋊C4C22semidirect
28. #2861C22semidirect
29. #2856C22semidirect
30. #2853C22semidirect
31. #2852C22semidirect
32. #2850C22semidirect
33. #2849C22semidirect
34. #2849C22semidirect
35. #2847C22semidirect
36. #2847C22semidirect
37. #2846C22semidirect
38. #2804C22semidirect
39. #2801C22semidirect
40. #2797C22semidirect
41. #2790C22semidirect
42. #2748C22semidirect
43. #2709C22semidirect
44. #2703C22semidirect
45. #2697C22semidirect
48. #2603C22semidirect
49. #2602C22semidirect
50. #2600C22semidirect
51. #2598C22semidirect
52. #2597C22semidirect
53. #2591C22semidirect
54. #2589C22semidirect
55. #2579C22semidirect
56. #2579C22semidirect
57. #2576C22semidirect
58. #2572C22semidirect
59. #2566C22semidirect
60. #2557C22semidirect
61. #2554C22semidirect
62. #2554C22semidirect
63. #2544C22semidirect
64. #2543C22semidirect
65. #2539C22semidirect
66. #2534C22semidirect
67. #2531C22semidirect
68. #2526C22semidirect
69. #2525C22semidirect
70. #2516C22semidirect
71. #2510C22semidirect
72. #2505C22semidirect
73. #2502C22semidirect
74. #2500C22semidirect
75. #2480C22semidirect
76. #2476C22semidirect
77. #2473C22semidirect
78. #2472C22semidirect
79. #2472C22semidirect
80. #2471C22semidirect
81. #2468C22semidirect
82. #2464C22semidirect
83. #2464C22semidirect
84. #2460C22semidirect
85. #2459C22semidirect
86. #2457C22semidirect
87. #2456C22semidirect
88. #2450C22semidirect
89. #2450C22semidirect
90. #2444C22semidirect
91. #2444C22semidirect
92. #2443C22semidirect
93. #2437C22semidirect
95. #2431C22semidirect
97. #2424C22semidirect
98. #2424C22semidirect
99. #2424C22semidirect
100. #2418C22semidirect
101. #2412C22semidirect
102. #2411C22semidirect
103. #2411C22semidirect
105. #2410C22semidirect
106. #2410C22semidirect
107. #2405C22semidirect
108. #2404C22semidirect
109. #2404C22semidirect
111. #2374C22semidirect
112. #2374C22semidirect
113. #2374C22semidirect
114. #2368C22semidirect
115. #2368C22semidirect
116. #2366C22semidirect
117. #2364C22semidirect
118. #2364C22semidirect
119. #2361C22semidirect
120. #2361C22semidirect
124. #2358C22semidirect
125. #2358C22semidirect
126. #2358C22semidirect
127. #2358C22semidirect
128. #2358C22semidirect
129. #2358C22semidirect
130. #2358C22semidirect
131. #2358C22semidirect
132. #2358C22semidirect
133. #2358C22semidirect
134. #2358C22semidirect
135. #2353C22semidirect
136. D4×C4⋊C4C22semidirect
137. #2342C22semidirect
138. #2342C22semidirect
139. D4×C22⋊C4C22semidirect
140. D4×C22⋊C4C22semidirect
141. C4×#127C22semidirect
142. C4×#121C22semidirect
143. C4×#121C22semidirect
145. C4×#120C22semidirect
146. C4×#120C22semidirect
147. #2298C22semidirect
148. #2297C22semidirect
149. #2297C22semidirect
150. C2×#390C22semidirect
151. #2290C22semidirect
152. #2290C22semidirect
153. C2×#388C22semidirect
154. C2×#386C22semidirect
155. C2×#386C22semidirect
156. C2×#385C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect
159. C2×C4×C22⋊C4C22semidirect
168. C24×C4C23semidirect
174. C2×#126C23semidirect
175. C2×#125C23semidirect
177. C2×#124C23semidirect
184. C2×#123C23semidirect
195. C2×#121C23semidirect
210. C2×#120C23semidirect
227. C2×C4×D4C23semidirect
228. C2×C4×D4C23semidirect
229. C2×C4×D4C23semidirect
231. C2×#117C23semidirect
232. C2×#117C23semidirect
235. C22×C4⋊C4C23semidirect
250. C22×C22⋊C4C23semidirect
253. C22×C42C23semidirect
254. C22×C42C23semidirect
255. #401C23semidirect
256. #400C23semidirect
257. #400C23semidirect
258. #400C23semidirect
260. #399C23semidirect
261. #398C23semidirect
262. #398C23semidirect
263. #398C23semidirect
264. #398C23semidirect
266. #397C23semidirect
267. #397C23semidirect
268. #397C23semidirect
269. #397C23semidirect
273. #396C23semidirect
274. #396C23semidirect
282. #394C23semidirect
283. #394C23semidirect
284. #394C23semidirect
286. #393C23semidirect
292. #392C23semidirect
293. #391C23semidirect
294. #391C23semidirect
295. #391C23semidirect
296. #391C23semidirect
308. #390C23semidirect
309. #390C23semidirect
310. #390C23semidirect
311. #389C23semidirect
312. #389C23semidirect
326. #388C23semidirect
327. #388C23semidirect
328. #388C23semidirect
329. #388C23semidirect
330. #388C23semidirect
331. #388C23semidirect
332. #388C23semidirect
333. #388C23semidirect
334. #388C23semidirect
335. #388C23semidirect
336. #388C23semidirect
337. #388C23semidirect
338. #387C23semidirect
339. #387C23semidirect
340. #387C23semidirect
341. #387C23semidirect
342. #387C23semidirect
343. #387C23semidirect
344. #387C23semidirect
345. #387C23semidirect
346. #387C23semidirect
347. #387C23semidirect
348. #387C23semidirect
379. #386C23semidirect
380. #386C23semidirect
381. #386C23semidirect
382. #386C23semidirect
383. #386C23semidirect
384. #386C23semidirect
385. #386C23semidirect
401. #385C23semidirect
402. #385C23semidirect
403. #385C23semidirect
404. #385C23semidirect
405. #385C23semidirect
406. #385C23semidirect
407. #384C23semidirect
408. #384C23semidirect
409. #383C23semidirect
410. #382C23semidirect
413. #381C23semidirect
414. #381C23semidirect
418. #380C23semidirect
419. #380C23semidirect
425. #379C23semidirect
426. C4×C4⋊C4C23semidirect
427. C4×C4⋊C4C23semidirect
428. C4×C4⋊C4C23semidirect
429. C4×C4⋊C4C23semidirect
430. C4×C4⋊C4C23semidirect
443. C4×C22⋊C4C23semidirect
444. C4×C22⋊C4C23semidirect
445. C4×C22⋊C4C23semidirect
446. C4×C22⋊C4C23semidirect
447. C4×C22⋊C4C23semidirect
448. C4×C22⋊C4C23semidirect
449. C4×C22⋊C4C23semidirect
450. #376C23semidirect
454. C43C23semidirect
551. #120#41semidirect

Maximal subgroups

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

subgroupindex
#600452
#600402
#600372
#600342
#599402
#599152
#596852
#596232
#590892
#589902
#363622
#363222
#363162
#362442
#362212
#360982
C4×D422
#341522
C2×#23582