Finite Group Databasebeta

← #6831166

Subgroups — #6831166

Order 512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42511C211yesmaximal, characteristic, complemented
2#42481C211yesmaximal, characteristic
3#33283C211yesmaximal, characteristic, complemented
4#31990C211yesmaximal, characteristic, complemented
5#31978C211yesmaximal, characteristic
6#31922C211yesmaximal, characteristic, complemented
7#31918C211yesmaximal, characteristic
8#31891C211yesmaximal, characteristic, complemented
9#31888C211yesmaximal, characteristic, complemented
10#31827C211yesmaximal, characteristic, complemented
11#31824C211yesmaximal, characteristic, complemented
12#30002C211yesmaximal, characteristic, complemented
13#29840C211yesmaximal, characteristic, complemented
14#29075C211yesmaximal, characteristic, complemented
15#29073C211yesmaximal, characteristic, complemented
16#29008C211yesmaximal, characteristic, complemented
17#29007C211yesmaximal, characteristic
18#28945C211yesmaximal, characteristic, complemented
19#28943C211yesmaximal, characteristic, complemented
20#28877C211yesmaximal, characteristic
21#28874C211yesmaximal, characteristic, complemented
22#26330C211yesmaximal, characteristic, complemented
23#26295C211yesmaximal, characteristic, complemented
24#25471C211yesmaximal, characteristic, complemented
25#25297C211yesmaximal, characteristic, complemented
26#24342C211yesmaximal, characteristic, complemented
27#24206C211yesmaximal, characteristic
28#22543C211yesmaximal, characteristic
29Q8×#102C211yesmaximal, characteristic, complemented
30#21715C211yesmaximal, characteristic, complemented
31#21291C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×C8×Q8C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38C2×#440C2211yescharacteristic
39#2839—21no—
40#2814—21no—
41#2776—21no—
42#2758—21no—
43#2755—21no—
44#2719—21no—
45#2700—21no—
46#2700—21no—
47#2680—21no—
48#2680—21no—
49#2655—21no—
50#2647C2211yescharacteristic
51#2640C2211yescharacteristic
52#2638—21no—
53#2634—21no—
54#2614—21no—
55#2592C2211yescharacteristic
56#2582C2211yescharacteristic
57#2581C2211yescharacteristic
58#2567C2211yescharacteristic
59#2514C2211yescharacteristic
60#2511C2211yescharacteristic
61#2511C2211yescharacteristic
62#2511C2211yescharacteristic
63#2509C2211yescharacteristic
64#2507C2211yescharacteristic
65#2506C2211yescharacteristic
66#2506C2211yescharacteristic
67#2462—21no—
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic
70#2451C2211yescharacteristic
71#2451C2211yescharacteristic
72#2447C2211yescharacteristic
73#2447C2211yescharacteristic
74#2445C2211yescharacteristic
75#2445C2211yescharacteristic
76#2409—21no—
77#2399C2211yescharacteristic
78#2355C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80#2320C2211yescharacteristic
81#2319C2211yescharacteristic
82#2101C2211yescharacteristic
83#2099C2211yescharacteristic
84#2095C2211yescharacteristic
85#2093C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2087C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2065C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2056C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2041C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2015C2211yescharacteristic
121#2014C2211yescharacteristic
122#1993C2211yescharacteristic
123#1990C2211yescharacteristic
124#1990C2211yescharacteristic
125#1990C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1985C2211yescharacteristic
130#1985C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1982C2211yescharacteristic
134#1973C2211yescharacteristic
135#1969C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1957C2211yescharacteristic
142#1949C2211yescharacteristic
143#1947C2211yescharacteristic
144#1943C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1940C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1940C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1933C2211yescharacteristic
166#1933C2211yescharacteristic
167#1933C2211yescharacteristic
168#1928C2211yescharacteristic
169#1927C2211yescharacteristic
170#1926C2211yescharacteristic
171#1925C2211yescharacteristic
172#1921C2211yescharacteristic
173#1921C2211yescharacteristic
174#1919C2211yescharacteristic
175#1918C2211yescharacteristic
176#1878C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1863C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1843C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1776C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C23×Q8—21no—
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#559—24no—
208#559—42no—
209D4×Q8—24no—
210D4×Q8—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125—21no—
216C2×#125—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239#477—42no—
240#464—42no—
241C8×Q8—42no—
242C8×Q8—42no—
243#440—24no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#401—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398D411yescharacteristic
325#398D411yescharacteristic
326#398D411yescharacteristic
327#398D411yescharacteristic
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395D411yescharacteristic
343#395D411yescharacteristic
344#395D411yescharacteristic
345#395D411yescharacteristic
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#384—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#383—21no—
434#382—21no—
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381—21no—
440#380—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452#376C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—44no—
491C22×Q8—82no—
492C22×Q8—82no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—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—22no—
525C4⋊Q8—22no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528#127—22no—
529#127—41no—
530#125—82no—
531#125—82no—
532#124—22no—
533#124—22no—
534#124—22no—
535#124—41no—
536#124—44no—
537#123—44no—
538#123—44no—
539#123—82no—
540#123—82no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544C22⋊Q8—82no—
545C22⋊Q8—82no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—41no—
554C4×Q8—82no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—44no—
563C4×D4#4114yes—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654#107—22no—
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#106—41no—
662#106—41no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#97—22no—
700#97—41no—
701#97—41no—
702C4×C8—22no—
703C4×C8—22no—
704C4×C8—22no—
705C4×C8—41no—
706C4×C8—41no—
707C4×C8—41no—
708C4×C8—41no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
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#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C24—21no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—41no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—816no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4C2×#4112yes—
815C22×C4—21no—
816C22×C4—24no—
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—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C2511yescharacteristic
856Q16—82no—
857SD16—44no—
858SD16—82no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
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×C82−1+412yes—
882C2×C82−1+412yes—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
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—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4C2×#4112yes—
950C22⋊C4—24no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42C2×#4112yes—
991C42H(5,𝔽2)12yes—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23C23×D411yescharacteristic
1007Q8—28no—
1008Q8—44no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—84no—
1018Q8—84no—
1019Q8—84no—
1020D4—22no—
1021D4—22no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—84no—
1029D4—162no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
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—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
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—84no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—162no—
1113C2×C4#54612yes—
1114C2×C4#54612yes—
1115C2×C4#57612yes—
1116C2×C4#57712yes—
1117C2×C4#57812yes—
1118C2×C4C22×#4111yescharacteristic
1119C2×C4C2×H(5,𝔽2)11yescharacteristic
1120C2×C4C2×2−1+411yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C2×C4#58511yescharacteristic
1123C2×C4#58511yescharacteristic
1124C8—22no—
1125C8—22no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22C2×#54611yescharacteristic
1147C22#349711yescharacteristic
1148C22#349711yescharacteristic
1149C22C2×#57611yescharacteristic
1150C22C2×#57711yescharacteristic
1151C22C2×#57811yescharacteristic
1152C22#358411yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#346111yescharacteristic
1182C4#349511yescharacteristic
1183C4#355211yescharacteristic
1184C4#356211yescharacteristic
1185C2—82no—
1186C2—161no—
1187C2#3941711yescharacteristic
1188C2#6116711yescharacteristic
1189C2#6117311yescharacteristic
1190C2#6237511yescharacteristic
1191C2#6237811yescharacteristic
1192C2#6238211yescharacteristic
1193C2#6238411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42511C2semidirect
3. #33283C2semidirect
4. #31990C2semidirect
6. #31922C2semidirect
8. #31891C2semidirect
9. #31888C2semidirect
10. #31827C2semidirect
11. #31824C2semidirect
12. #30002C2semidirect
13. #29840C2semidirect
14. #29075C2semidirect
15. #29073C2semidirect
16. #29008C2semidirect
18. #28945C2semidirect
19. #28943C2semidirect
21. #28874C2semidirect
22. #26330C2semidirect
23. #26295C2semidirect
24. #25471C2semidirect
25. #25297C2semidirect
26. #24342C2semidirect
29. Q8×#102C2semidirect
30. #21715C2semidirect
31. #21291C2semidirect

Maximal subgroups

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

subgroupindex
#425112
#424812
#332832
#319902
#319782
#319222
#319182
#318912
#318882
#318272
#318242
#300022
#298402
#290752
#290732
#290082
#290072
#289452
#289432
#288772
#288742
#263302
#262952
#254712
#252972
#243422
#242062
#225432
Q8×#1022
#217152
#212912