Finite Group Databasebeta

← #7337579

Subgroups — #7337579

Order 512.

1435 conjugacy classes of subgroups.

The subgroup lattice has 1235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59076C211yesmaximal, characteristic
2#45502C211yesmaximal, characteristic, complemented
3#32294C211yesmaximal, characteristic, complemented
4#32294C211yesmaximal, characteristic, complemented
5#32158C211yesmaximal, characteristic, complemented
6#31882C211yesmaximal, characteristic, complemented
7#31774C211yesmaximal, characteristic
8#31616C211yesmaximal, characteristic, complemented
9#31440C211yesmaximal, characteristic, complemented
10#31322C211yesmaximal, characteristic
11#31103C211yesmaximal, characteristic, complemented
12#30946C211yesmaximal, characteristic, complemented
13#30832C211yesmaximal, characteristic, complemented
14#30659C211yesmaximal, characteristic, complemented
15#29966C211yesmaximal, characteristic, complemented
16#29689C211yesmaximal, characteristic, complemented
17#29302C211yesmaximal, characteristic, complemented
18#29050C211yesmaximal, characteristic, complemented
19#29029C211yesmaximal, characteristic, complemented
20#28821C211yesmaximal, characteristic, complemented
21#27305C211yesmaximal, characteristic, complemented
22#27117C211yesmaximal, characteristic, complemented
23#27113C211yesmaximal, characteristic, complemented
24#27053C211yesmaximal, characteristic, complemented
25#26336C211yesmaximal, characteristic, complemented
26#26071C211yesmaximal, characteristic, complemented
27#26056C211yesmaximal, characteristic, complemented
28#25706C211yesmaximal, characteristic, complemented
29#25678C211yesmaximal, characteristic, complemented
30#24098C211yesmaximal, characteristic, complemented
31#22367C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C22×#107C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2841—21no—
45#2774—21no—
46#2774—21no—
47#2729—21no—
48#2729—21no—
49#2725—21no—
50#2723—21no—
51#2683—21no—
52#2677—21no—
53#2563C2211yescharacteristic
54#2551C2211yescharacteristic
55#2551C2211yescharacteristic
56#2550C2211yescharacteristic
57#2507C2211yescharacteristic
58#2507C2211yescharacteristic
59#2504C2211yescharacteristic
60#2497C2211yescharacteristic
61#2497C2211yescharacteristic
62#2497C2211yescharacteristic
63#2497C2211yescharacteristic
64#2488—21no—
65#2487C2211yescharacteristic
66#2475—21no—
67#2452C2211yescharacteristic
68#2449—21no—
69#2448C2211yescharacteristic
70#2442C2211yescharacteristic
71#2440C2211yescharacteristic
72#2440C2211yescharacteristic
73#2426C2211yescharacteristic
74#2425—21no—
75#2421C2211yescharacteristic
76#2416C2211yescharacteristic
77#2415—21no—
78#2376—21no—
79#2361—21no—
80#2361C2211yescharacteristic
81#2360C2211yescharacteristic
82#2351C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#389C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2072C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2034C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2023C2211yescharacteristic
133#1992C2211yescharacteristic
134#1987C2211yescharacteristic
135#1959C2211yescharacteristic
136#1954C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1947C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1944C2211yescharacteristic
143#1944C2211yescharacteristic
144#1943C2211yescharacteristic
145#1941C2211yescharacteristic
146#1940C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1934C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic
167#1874C2211yescharacteristic
168#1869C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1850C2211yescharacteristic
187#1847C2211yescharacteristic
188#1847C2211yescharacteristic
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic
191#1823C2211yescharacteristic
192#1807C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1776C2211yescharacteristic
198#1771C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1752C2211yescharacteristic
202#1749C2211yescharacteristic
203C23×C8C2311yescharacteristic
204#554—42no—
205#554—42no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212#529—42no—
213#529—42no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123D411yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#501—42no—
248#500—42no—
249#489—42no—
250#484—42no—
251#477—42no—
252#475—42no—
253#474—42no—
254C2×#107—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386D411yescharacteristic
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385D411yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381D411yescharacteristic
429#380—21no—
430#380—21no—
431#380—21no—
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C2×#95—21no—
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—82no—
528C4⋊Q8—82no—
529#126—44no—
530#125—22no—
531#125—41no—
532#125—44no—
533#124—22no—
534#124—41no—
535#123—24no—
536#123—44no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—44no—
541C22⋊Q8—41no—
542C22⋊Q8—44no—
543C22⋊Q8—82no—
544C22⋊Q8—82no—
545C22⋊Q8—82no—
546C22⋊Q8—82no—
547C22⋊Q8—82no—
548#121—22no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—44no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—44no—
564C4×D4—44no—
565C4×D4—82no—
566#117—44no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
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—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—82no—
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—41no—
671C2×C42—41no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#107—22no—
680#107—22no—
681#107—22no—
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#106—22no—
692#106—22no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—41no—
711#103—41no—
712#102—22no—
713#102—22no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722C22⋊C8—22no—
723C22⋊C8—41no—
724C22⋊C8—41no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727#97—22no—
728#97—41no—
729#97—41no—
730#97—41no—
731C4×C8—41no—
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#95—21no—
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
775#95C2×D411yescharacteristic
776C24—21no—
777C24C22×D411yescharacteristic
778C24C22×D411yescharacteristic
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×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8H(5,𝔽2)12yes—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—41no—
804C2×D4—41no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—81no—
811C2×D4#13714yes—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
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—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C2511yescharacteristic
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—44no—
896C2×C82−1+412yes—
897C2×C82−1+412yes—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
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—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—41no—
929C4⋊C4—41no—
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—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
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⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4H(5,𝔽2)12yes—
969C4⋊C42−1+412yes—
970C22⋊C4—24no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
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—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—41no—
1010C42—41no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23C2×#13712yes—
1038C23C2×#13712yes—
1039C23C23×D411yescharacteristic
1040Q8—22no—
1041Q8—22no—
1042Q8—41no—
1043Q8—41no—
1044Q8—162no—
1045Q8—162no—
1046Q8—162no—
1047Q8—162no—
1048D4—44no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—84no—
1054D4—84no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
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—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
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—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—82no—
1143C2×C4—84no—
1144C2×C4—82no—
1145C2×C4—84no—
1146C2×C4—162no—
1147C2×C4—162no—
1148C2×C4—162no—
1149C2×C4C2×#13712yes—
1150C2×C4#57612yes—
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×H(5,𝔽2)11yescharacteristic
1153C2×C4C2×2−1+411yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C2×C4C2×2−1+411yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—22no—
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22#348411yescharacteristic
1187C22#348911yescharacteristic
1188C22#349911yescharacteristic
1189C22C22×#13711yescharacteristic
1190C22C2×#57611yescharacteristic
1191C22#358511yescharacteristic
1192C22#358611yescharacteristic
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—42no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—41no—
1207C4—42no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4#354111yescharacteristic
1221C4#354411yescharacteristic
1222C4#355211yescharacteristic
1223C4#355911yescharacteristic
1224C2—42no—
1225C2—42no—
1226C2—161no—
1227C2#4795311yescharacteristic
1228C2#6157311yescharacteristic
1229C2#6161711yescharacteristic
1230C2#6212711yescharacteristic
1231C2#6223311yescharacteristic
1232C2#6250411yescharacteristic
1233C2#6252011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2416C22
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
2. #45502C2semidirect
3. #32294C2semidirect
4. #32294C2semidirect
5. #32158C2semidirect
6. #31882C2semidirect
8. #31616C2semidirect
9. #31440C2semidirect
11. #31103C2semidirect
12. #30946C2semidirect
13. #30832C2semidirect
14. #30659C2semidirect
15. #29966C2semidirect
16. #29689C2semidirect
17. #29302C2semidirect
18. #29050C2semidirect
19. #29029C2semidirect
20. #28821C2semidirect
21. #27305C2semidirect
22. #27117C2semidirect
23. #27113C2semidirect
24. #27053C2semidirect
25. #26336C2semidirect
26. #26071C2semidirect
27. #26056C2semidirect
28. #25706C2semidirect
29. #25678C2semidirect
30. #24098C2semidirect
31. #22367C2semidirect

Maximal subgroups

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

subgroupindex
#590762
#455022
#322942
#321582
#318822
#317742
#316162
#314402
#313222
#311032
#309462
#308322
#306592
#299662
#296892
#293022
#290502
#290292
#288212
#273052
#271172
#271132
#270532
#263362
#260712
#260562
#257062
#256782
#240982
#223672