Finite Group Databasebeta

← #7110823

Subgroups — #7110823

Order 512.

1532 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#59290C211yesmaximal, characteristic, complemented
2#59119C211yesmaximal, characteristic
3#32133C211yesmaximal, characteristic, complemented
4#31990C211yesmaximal, characteristic, complemented
5#31868C211yesmaximal, characteristic, complemented
6#31693C211yesmaximal, characteristic, complemented
7#31622C211yesmaximal, characteristic, complemented
8#31506C211yesmaximal, characteristic, complemented
9#31456C211yesmaximal, characteristic, complemented
10#31376C211yesmaximal, characteristic, complemented
11#27706C211yesmaximal, characteristic, complemented
12#27615C211yesmaximal, characteristic, complemented
13#27395C211yesmaximal, characteristic, complemented
14#27294C211yesmaximal, characteristic, complemented
15#27118C211yesmaximal, characteristic, complemented
16#26689C211yesmaximal, characteristic, complemented
17#26455C211yesmaximal, characteristic, complemented
18#26431C211yesmaximal, characteristic, complemented
19#26427C211yesmaximal, characteristic, complemented
20#26220C211yesmaximal, characteristic, complemented
21#26106C211yesmaximal, characteristic, complemented
22#26012C211yesmaximal, characteristic, complemented
23#25256C211yesmaximal, characteristic, complemented
24#24588C211yesmaximal, characteristic, complemented
25#24104C211yesmaximal, characteristic
26#24067C211yesmaximal, characteristic, complemented
27#23670C211yesmaximal, characteristic, complemented
28#22929C211yesmaximal, characteristic, complemented
29#22503C211yesmaximal, characteristic
30#22073C211yesmaximal, characteristic, complemented
31#21890C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552—21no—
34C2×#529C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#423C2211yescharacteristic
40#2719—21no—
41#2717—21no—
42#2701—21no—
43#2698—21no—
44#2552C2211yescharacteristic
45#2550C2211yescharacteristic
46#2521—21no—
47#2506C2211yescharacteristic
48#2506C2211yescharacteristic
49#2499C2211yescharacteristic
50#2496C2211yescharacteristic
51#2496C2211yescharacteristic
52#2486C2211yescharacteristic
53#2484—21no—
54#2478—21no—
55#2478—21no—
56#2474—21no—
57#2462—21no—
58#2451C2211yescharacteristic
59#2447—21no—
60#2447C2211yescharacteristic
61#2443—21no—
62#2441C2211yescharacteristic
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2438—21no—
66#2427C2211yescharacteristic
67#2420C2211yescharacteristic
68#2419—21no—
69#2415C2211yescharacteristic
70#2365C2211yescharacteristic
71#2363C2211yescharacteristic
72#2362C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75#2344—21no—
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78C4×#123C2211yescharacteristic
79#2296C2211yescharacteristic
80C2×#389C2211yescharacteristic
81#2285C2211yescharacteristic
82#2101C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2024C2211yescharacteristic
121#2023C2211yescharacteristic
122#1993C2211yescharacteristic
123#1990C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1987C2211yescharacteristic
127#1987C2211yescharacteristic
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1949C2211yescharacteristic
131#1947C2211yescharacteristic
132#1942C2211yescharacteristic
133#1941C2211yescharacteristic
134#1940C2211yescharacteristic
135#1939C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1926C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1916C2211yescharacteristic
155#1916C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1872C2211yescharacteristic
165#1872C2211yescharacteristic
166#1870C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1851C2211yescharacteristic
180#1851C2211yescharacteristic
181#1851C2211yescharacteristic
182#1834C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic
186#1824C2211yescharacteristic
187#1817C2211yescharacteristic
188#1809C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206#555—24no—
207#555—42no—
208#552—48no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211#529—24no—
212#529—42no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123D411yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117—21no—
244C2×#117—21no—
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C42C2311yescharacteristic
255#484—42no—
256#481—24no—
257#436—42no—
258#428—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271#423—42no—
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#390—21no—
342#390C2311yescharacteristic
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388D411yescharacteristic
371#388D411yescharacteristic
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#386—21no—
392#386D411yescharacteristic
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385D411yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#382—21no—
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#381—21no—
414#381—21no—
415#381D411yescharacteristic
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C2×#95—21no—
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—41no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526#126—44no—
527#126—44no—
528#126—44no—
529#125—22no—
530#125—41no—
531#125—44no—
532#125—44no—
533#125—44no—
534#124—22no—
535#124—41no—
536#124—44no—
537#124—44no—
538#123—24no—
539#123—44no—
540#123—44no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—41no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121—44no—
551#121#4114yes—
552C4×Q8—22no—
553C4×Q8—41no—
554C4×Q8—44no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—44no—
564C4×D4—44no—
565#117—22no—
566#117—22no—
567#117—22no—
568#117—22no—
569#117—44no—
570#117—44no—
571#117—44no—
572#117—44no—
573#117—41no—
574#117—41no—
575#117—44no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#107—22no—
687#107—22no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#106—22no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721C22⋊C8—22no—
722C22⋊C8—22no—
723C22⋊C8—41no—
724C22⋊C8—41no—
725C22⋊C8—41no—
726#97—41no—
727C4×C8—41no—
728C4×C8—41no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775C24—21no—
776C24C22×D411yescharacteristic
777C24C22×D411yescharacteristic
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×D4—22no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—41no—
799C2×D4—42no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4C2×#4112yes—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C2×#4112yes—
867C22×C4H(5,𝔽2)12yes—
868C22×C4C2511yescharacteristic
869M16—44no—
870M16—82no—
871M16—82no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4AGL(1,ℤ/8)14yes—
962C4⋊C4C2×#4112yes—
963C4⋊C42−1+412yes—
964C4⋊C42−1+412yes—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C42—22no—
994C42—22no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—22no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23#54612yes—
1036C23C23×D411yescharacteristic
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—84no—
1042Q8—162no—
1043D4—22no—
1044D4—22no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—84no—
1049D4—162no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—44no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—84no—
1139C2×C4—82no—
1140C2×C4—84no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4#54612yes—
1144C2×C4C2×AGL(1,ℤ/8)12yes—
1145C2×C4C2×AGL(1,ℤ/8)12yes—
1146C2×C4C2×AGL(1,ℤ/8)12yes—
1147C2×C4C22×#4111yescharacteristic
1148C2×C4C2×H(5,𝔽2)11yescharacteristic
1149C2×C4C2×2−1+411yescharacteristic
1150C2×C4C2×2−1+411yescharacteristic
1151C2×C4#58511yescharacteristic
1152C2×C4#58511yescharacteristic
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—42no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—42no—
1175C22—42no—
1176C22—41no—
1177C22—41no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22C2×#54611yescharacteristic
1183C22#348911yescharacteristic
1184C22#348911yescharacteristic
1185C22C22×AGL(1,ℤ/8)11yescharacteristic
1186C22#358411yescharacteristic
1187C22#358611yescharacteristic
1188C22#358611yescharacteristic
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—41no—
1200C4—42no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4#351511yescharacteristic
1217C4#351511yescharacteristic
1218C4#353311yescharacteristic
1219C4#354411yescharacteristic
1220C2—42no—
1221C2—81no—
1222C2—82no—
1223C2#4449411yescharacteristic
1224C2#6116111yescharacteristic
1225C2#6118811yescharacteristic
1226C2#6210711yescharacteristic
1227C2#6215111yescharacteristic
1228C2#6219811yescharacteristic
1229C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#555C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59290C2semidirect
3. #32133C2semidirect
4. #31990C2semidirect
5. #31868C2semidirect
6. #31693C2semidirect
7. #31622C2semidirect
8. #31506C2semidirect
9. #31456C2semidirect
10. #31376C2semidirect
11. #27706C2semidirect
12. #27615C2semidirect
13. #27395C2semidirect
14. #27294C2semidirect
15. #27118C2semidirect
16. #26689C2semidirect
17. #26455C2semidirect
18. #26431C2semidirect
19. #26427C2semidirect
20. #26220C2semidirect
21. #26106C2semidirect
22. #26012C2semidirect
23. #25256C2semidirect
24. #24588C2semidirect
26. #24067C2semidirect
27. #23670C2semidirect
28. #22929C2semidirect
30. #22073C2semidirect
31. #21890C2semidirect

Maximal subgroups

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

subgroupindex
#592902
#591192
#321332
#319902
#318682
#316932
#316222
#315062
#314562
#313762
#277062
#276152
#273952
#272942
#271182
#266892
#264552
#264312
#264272
#262202
#261062
#260122
#252562
#245882
#241042
#240672
#236702
#229292
#225032
#220732
#218902