Finite Group Databasebeta

← #7597833

Subgroups — #7597833

Order 512.

1683 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59654C211yesmaximal, characteristic
2#59431C211yesmaximal, characteristic, complemented
3#31688C211yesmaximal, characteristic, complemented
4#31686C211yesmaximal, characteristic, complemented
5#30632C211yesmaximal, characteristic, complemented
6#30631C211yesmaximal, characteristic, complemented
7#29273C211yesmaximal, characteristic, complemented
8#29068C211yesmaximal, characteristic, complemented
9#29039C211yesmaximal, characteristic, complemented
10#28784C211yesmaximal, characteristic, complemented
11#28771C211yesmaximal, characteristic, complemented
12#28207C211yesmaximal, characteristic, complemented
13#28091C211yesmaximal, characteristic, complemented
14#28080C211yesmaximal, characteristic, complemented
15#27350C211yesmaximal, characteristic, complemented
16#27343C211yesmaximal, characteristic, complemented
17#27113C211yesmaximal, characteristic, complemented
18#27110C211yesmaximal, characteristic, complemented
19#25844C211yesmaximal, characteristic, complemented
20#25709C211yesmaximal, characteristic, complemented
21#25486C211yesmaximal, characteristic, complemented
22#25355C211yesmaximal, characteristic, complemented
23#25073C211yesmaximal, characteristic, complemented
24#25026C211yesmaximal, characteristic, complemented
25#22936C211yesmaximal, characteristic, complemented
26#22924C211yesmaximal, characteristic, complemented
27#22523C211yesmaximal, characteristic, complemented
28#22495C211yesmaximal, characteristic, complemented
29#21731C211yesmaximal, characteristic, complemented
30#21646C211yesmaximal, characteristic, complemented
31#21632C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×#548—21no—
34C2×#547C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#435C2211yescharacteristic
43#2767—21no—
44#2715—21no—
45#2681—21no—
46#2681—21no—
47#2605—21no—
48#2584C2211yescharacteristic
49#2562C2211yescharacteristic
50#2560—21no—
51#2538C2211yescharacteristic
52#2537C2211yescharacteristic
53#2536—21no—
54#2525—21no—
55#2497C2211yescharacteristic
56#2496C2211yescharacteristic
57#2496C2211yescharacteristic
58#2495C2211yescharacteristic
59#2491C2211yescharacteristic
60#2491C2211yescharacteristic
61#2469—21no—
62#2461—21no—
63#2461—21no—
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2440C2211yescharacteristic
67#2439C2211yescharacteristic
68#2428C2211yescharacteristic
69#2428C2211yescharacteristic
70#2421—21no—
71#2409—21no—
72#2407—21no—
73#2373—21no—
74#2361C2211yescharacteristic
75#2361C2211yescharacteristic
76#2355C2211yescharacteristic
77#2352C2211yescharacteristic
78#2346C2211yescharacteristic
79#2345C2211yescharacteristic
80C4×C4⋊Q8C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic
101#2058C2211yescharacteristic
102#2058C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2057C2211yescharacteristic
106#2057C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#1993C2211yescharacteristic
118#1993C2211yescharacteristic
119#1992C2211yescharacteristic
120#1990C2211yescharacteristic
121#1990C2211yescharacteristic
122#1988C2211yescharacteristic
123#1987C2211yescharacteristic
124#1987C2211yescharacteristic
125#1987C2211yescharacteristic
126#1985C2211yescharacteristic
127#1957C2211yescharacteristic
128#1955C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1944C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1941C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1934C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1854C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1847C2211yescharacteristic
176#1834C2211yescharacteristic
177#1831C2211yescharacteristic
178#1824C2211yescharacteristic
179#1823C2211yescharacteristic
180#1809C2211yescharacteristic
181#1807C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×#41—21no—
204C23×Q8—21no—
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207D4×Q8—24no—
208D4×Q8—42no—
209#548—48no—
210#547—24no—
211#547—42no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#124D411yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×C4×Q8—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256#501—24no—
257#486—24no—
258#482—24no—
259#481—24no—
260#478—42no—
261#478—42no—
262#446—42no—
263#435—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#392—21no—
345#392—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391D411yescharacteristic
351#390—21no—
352#390—21no—
353#390D411yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388D411yescharacteristic
386#388D411yescharacteristic
387#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382—21no—
416#382D411yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#380—21no—
420#380—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#376—21no—
450C43C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—44no—
492C2×#41—44no—
493C2×#41—82no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—44no—
499C22×Q8—44no—
500C22×Q8—82no—
501C22×Q8C2×D411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×M16—22no—
521C2×M16—41no—
522C2×M16—41no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8#4114yes—
542#127—22no—
543#127—41no—
544#126—44no—
545#126—82no—
546#125—22no—
547#125—22no—
548#124—24no—
549#124—44no—
550#124—44no—
551#123—44no—
552#123—44no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C22⋊Q8—44no—
560C22⋊Q8—82no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—44no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—44no—
571#121—44no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—44no—
575C4×Q8—82no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—82no—
590#117—22no—
591#117—41no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
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—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—22no—
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102#4114yescomplemented
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740#97—22no—
741#97—22no—
742#97—22no—
743#97—22no—
744#97—41no—
745C4×C8—22no—
746C4×C8—41no—
747C4×C8—41no—
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#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792#41—816no—
793C2×Q8—22no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—41no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—816no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—41no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4C2×#4112yes—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C2511yescharacteristic
902M16—82no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—82no—
925C2×C8C2×#4112yes—
926C2×C82−1+412yes—
927C2×C82−1+412yes—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4C2×#4112yes—
987C4⋊C4C2×#4112yes—
988C4⋊C4C2×#4112yes—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4AGL(1,ℤ/8)14yes—
1024C42—22no—
1025C42—22no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—41no—
1035C42—41no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42C2×#4112yes—
1046C42H(5,𝔽2)12yes—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23C2×AGL(1,ℤ/8)12yes—
1075C23C23×D411yescharacteristic
1076Q8—44no—
1077Q8—48no—
1078Q8—84no—
1079Q8—84no—
1080Q8—84no—
1081D4—22no—
1082D4—22no—
1083D4—44no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—84no—
1091D4—84no—
1092D4—84no—
1093D4—84no—
1094D4—84no—
1095D4—84no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—162no—
1184C2×C4#54612yes—
1185C2×C4#54612yes—
1186C2×C4C2×AGL(1,ℤ/8)12yes—
1187C2×C4C2×AGL(1,ℤ/8)12yes—
1188C2×C4#57712yes—
1189C2×C4C22×#4111yescharacteristic
1190C2×C4C22×#4111yescharacteristic
1191C2×C4C2×H(5,𝔽2)11yescharacteristic
1192C2×C4C2×2−1+411yescharacteristic
1193C2×C4C2×2−1+411yescharacteristic
1194C2×C4#58511yescharacteristic
1195C8—22no—
1196C8—22no—
1197C8—22no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—42no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—41no—
1217C22—42no—
1218C22—41no—
1219C22—41no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22C2×#54611yescharacteristic
1232C22D4×#4111yescharacteristic
1233C22#349911yescharacteristic
1234C22C22×AGL(1,ℤ/8)11yescharacteristic
1235C22C2×#57711yescharacteristic
1236C22#358511yescharacteristic
1237C22#358611yescharacteristic
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—41no—
1251C4—42no—
1252C4—42no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4#348211yescharacteristic
1265C4#351111yescharacteristic
1266C4#351611yescharacteristic
1267C4#356111yescharacteristic
1268C2—42no—
1269C2—81no—
1270C2—82no—
1271C2—161no—
1272C2#5941511yescharacteristic
1273C2#6115511yescharacteristic
1274C2#6120211yescharacteristic
1275C2#6145211yescharacteristic
1276C2#6152211yescharacteristic
1277C2#6247711yescharacteristic
1278C2#6250011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59654C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59431C2semidirect
3. #31688C2semidirect
4. #31686C2semidirect
5. #30632C2semidirect
6. #30631C2semidirect
7. #29273C2semidirect
8. #29068C2semidirect
9. #29039C2semidirect
10. #28784C2semidirect
11. #28771C2semidirect
12. #28207C2semidirect
13. #28091C2semidirect
14. #28080C2semidirect
15. #27350C2semidirect
16. #27343C2semidirect
17. #27113C2semidirect
18. #27110C2semidirect
19. #25844C2semidirect
20. #25709C2semidirect
21. #25486C2semidirect
22. #25355C2semidirect
23. #25073C2semidirect
24. #25026C2semidirect
25. #22936C2semidirect
26. #22924C2semidirect
27. #22523C2semidirect
28. #22495C2semidirect
29. #21731C2semidirect
30. #21646C2semidirect
31. #21632C2semidirect
733. #102#41semidirect

Maximal subgroups

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

subgroupindex
#596542
#594312
#316882
#316862
#306322
#306312
#292732
#290682
#290392
#287842
#287712
#282072
#280912
#280802
#273502
#273432
#271132
#271102
#258442
#257092
#254862
#253552
#250732
#250262
#229362
#229242
#225232
#224952
#217312
#216462
#216322