Finite Group Databasebeta

← #6883500

Subgroups — #6883500

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1165 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36503C211yesmaximal, characteristic
2#36287C211yesmaximal, characteristic, complemented
3#33217C211yesmaximal, characteristic, complemented
4#32415C211yesmaximal, characteristic, complemented
5#32410C211yesmaximal, characteristic, complemented
6#32209C211yesmaximal, characteristic
7#32196C211yesmaximal, characteristic
8#31615C211yesmaximal, characteristic, complemented
9#31608C211yesmaximal, characteristic, complemented
10#30674C211yesmaximal, characteristic
11#30664C211yesmaximal, characteristic
12#30384C211yesmaximal, characteristic, complemented
13#30383C211yesmaximal, characteristic, complemented
14#29451C211yesmaximal, characteristic, complemented
15#29450C211yesmaximal, characteristic, complemented
16#29321C211yesmaximal, characteristic, complemented
17#29320C211yesmaximal, characteristic, complemented
18#26522C211yesmaximal, characteristic, complemented
19#26454C211yesmaximal, characteristic, complemented
20#26102C211yesmaximal, characteristic, complemented
21#26054C211yesmaximal, characteristic, complemented
22#25467C211yesmaximal, characteristic, complemented
23#25462C211yesmaximal, characteristic, complemented
24#24824C211yesmaximal, characteristic, complemented
25#24709C211yesmaximal, characteristic
26#24707C211yesmaximal, characteristic, complemented
27#24696C211yesmaximal, characteristic, complemented
28#22121C211yesmaximal, characteristic, complemented
29#22118C211yesmaximal, characteristic, complemented
30#21528C211yesmaximal, characteristic
31#21355C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#432C2211yescharacteristic
40C22×#97C2211yescharacteristic
41#2860C2211yescharacteristic
42#2860C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2857C2211yescharacteristic
46#2851C2211yescharacteristic
47#2612—21no—
48#2612—21no—
49#2601—21no—
50#2594—21no—
51#2567C2211yescharacteristic
52#2566C2211yescharacteristic
53#2556—21no—
54#2556—21no—
55#2552C2211yescharacteristic
56#2550C2211yescharacteristic
57#2527—21no—
58#2506—21no—
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2497C2211yescharacteristic
62#2494C2211yescharacteristic
63#2491C2211yescharacteristic
64#2490C2211yescharacteristic
65#2474—21no—
66#2469—21no—
67#2466—21no—
68#2441—21no—
69#2423C2211yescharacteristic
70#2423C2211yescharacteristic
71#2373—21no—
72#2370—21no—
73#2370C2211yescharacteristic
74#2369C2211yescharacteristic
75#2367—21no—
76#2357C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic
78#2346—21no—
79C4×C4⋊Q8C2211yescharacteristic
80C4×#125C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×#121C2211yescharacteristic
83#2295C2211yescharacteristic
84#2295C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2093C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2036C2211yescharacteristic
123#2035C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#1993C2211yescharacteristic
127#1992C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1988C2211yescharacteristic
131#1988C2211yescharacteristic
132#1973C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1947C2211yescharacteristic
143#1947C2211yescharacteristic
144#1947C2211yescharacteristic
145#1944C2211yescharacteristic
146#1944C2211yescharacteristic
147#1944C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1944C2211yescharacteristic
151#1943C2211yescharacteristic
152#1943C2211yescharacteristic
153#1943C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1940C2211yescharacteristic
157#1940C2211yescharacteristic
158#1936C2211yescharacteristic
159#1936C2211yescharacteristic
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic
162#1935C2211yescharacteristic
163#1935C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1927C2211yescharacteristic
168#1926C2211yescharacteristic
169#1925C2211yescharacteristic
170#1921C2211yescharacteristic
171#1921C2211yescharacteristic
172#1920C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1918C2211yescharacteristic
176#1893C2211yescharacteristic
177#1892C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1865C2211yescharacteristic
181#1863C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1776C2211yescharacteristic
197#1767C2211yescharacteristic
198#1767C2211yescharacteristic
199#1767C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×#117D411yescharacteristic
226C2×#117D411yescharacteristic
227C22×C42C2311yescharacteristic
228#501—42no—
229#479—24no—
230#479—42no—
231#475—24no—
232#474—42no—
233#465—24no—
234#440—42no—
235#432—42no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×#97—42no—
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288#401—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#394—21no—
310#394—21no—
311#393—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390—21no—
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—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#387—21no—
388#387—21no—
389#387—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#384—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4D411yescharacteristic
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
444#376—21no—
445#376D411yescharacteristic
446#376D411yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
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#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2411yescharacteristic
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—41no—
517#126—44no—
518#126—82no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—41no—
523#125—44no—
524#125—82no—
525#125—82no—
526#124—44no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529C22⋊Q8—82no—
530#121—22no—
531#121—41no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—82no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—82no—
542#117—24no—
543#117—42no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103#4114yes—
688#102—22no—
689#102—22no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697#97—22no—
698#97—22no—
699#97—41no—
700#97—41no—
701#97—41no—
702#97—41no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
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#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751C24—21no—
752C24C22×D411yescharacteristic
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×Q8C2×#4112yes—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—81no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—42no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C2511yescharacteristic
818SD16—44no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—44no—
841C2×C8—44no—
842C2×C8C2×#4112yes—
843C2×C82−1+412yes—
844C2×C82−1+412yes—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4C2×#4112yes—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—41no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4#13714yes—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—41no—
957C42—41no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42H(5,𝔽2)12yes—
970C422−1+412yes—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23C2×#13712yes—
985C23C23×D411yescharacteristic
986Q8—22no—
987Q8—22no—
988Q8—41no—
989Q8—41no—
990Q8—84no—
991Q8—162no—
992D4—41no—
993D4—41no—
994D4—41no—
995D4—41no—
996D4—84no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—44no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
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—82no—
1082C2×C4—162no—
1083C2×C4#53712yes—
1084C2×C4#53712yes—
1085C2×C4C2×#13712yes—
1086C2×C4C2×#13712yes—
1087C2×C4#57512yes—
1088C2×C4C22×#4111yescharacteristic
1089C2×C4C2×H(5,𝔽2)11yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C2×C4#58511yescharacteristic
1094C8—22no—
1095C8—22no—
1096C8—22no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22C2×#53711yescharacteristic
1117C22D4×#4111yescharacteristic
1118C22#349911yescharacteristic
1119C22C22×#13711yescharacteristic
1120C22C2×#57511yescharacteristic
1121C22#358511yescharacteristic
1122C22#358511yescharacteristic
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4#350911yescharacteristic
1152C4#352011yescharacteristic
1153C4#354111yescharacteristic
1154C4#355511yescharacteristic
1155C2—42no—
1156C2—161no—
1157C2#3995911yescharacteristic
1158C2#6091811yescharacteristic
1159C2#6093711yescharacteristic
1160C2#6145311yescharacteristic
1161C2#6146211yescharacteristic
1162C2#6250411yescharacteristic
1163C2#6250611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36287C2semidirect
3. #33217C2semidirect
4. #32415C2semidirect
5. #32410C2semidirect
8. #31615C2semidirect
9. #31608C2semidirect
12. #30384C2semidirect
13. #30383C2semidirect
14. #29451C2semidirect
15. #29450C2semidirect
16. #29321C2semidirect
17. #29320C2semidirect
18. #26522C2semidirect
19. #26454C2semidirect
20. #26102C2semidirect
21. #26054C2semidirect
22. #25467C2semidirect
23. #25462C2semidirect
24. #24824C2semidirect
26. #24707C2semidirect
27. #24696C2semidirect
28. #22121C2semidirect
29. #22118C2semidirect
31. #21355C2semidirect

Maximal subgroups

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

subgroupindex
#365032
#362872
#332172
#324152
#324102
#322092
#321962
#316152
#316082
#306742
#306642
#303842
#303832
#294512
#294502
#293212
#293202
#265222
#264542
#261022
#260542
#254672
#254622
#248242
#247092
#247072
#246962
#221212
#221182
#215282
#213552