Finite Group Databasebeta

← #7041305

Subgroups — #7041305

Order 512.

1803 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59206C211yesmaximal, characteristic, complemented
2#59015C211yesmaximal, characteristic
3#32003C211yesmaximal, characteristic, complemented
4#31786C211yesmaximal, characteristic, complemented
5#31739C211yesmaximal, characteristic, complemented
6#31708C211yesmaximal, characteristic, complemented
7#31680C211yesmaximal, characteristic, complemented
8#31428C211yesmaximal, characteristic, complemented
9#31367C211yesmaximal, characteristic, complemented
10#31266C211yesmaximal, characteristic, complemented
11#27717C211yesmaximal, characteristic, complemented
12#27602C211yesmaximal, characteristic, complemented
13#27541C211yesmaximal, characteristic, complemented
14#27525C211yesmaximal, characteristic, complemented
15#27354C211yesmaximal, characteristic, complemented
16#27167C211yesmaximal, characteristic, complemented
17#26420C211yesmaximal, characteristic, complemented
18#26308C211yesmaximal, characteristic, complemented
19#26208C211yesmaximal, characteristic, complemented
20#26202C211yesmaximal, characteristic, complemented
21#25232C211yesmaximal, characteristic, complemented
22#24981C211yesmaximal, characteristic, complemented
23#24939C211yesmaximal, characteristic, complemented
24#24576C211yesmaximal, characteristic, complemented
25#24088C211yesmaximal, characteristic, complemented
26#24002C211yesmaximal, characteristic, complemented
27C2×#2076C211yesmaximal, characteristic, complemented
28#22938C211yesmaximal, characteristic, complemented
29#22485C211yesmaximal, characteristic, complemented
30#22030C211yesmaximal, characteristic, complemented
31#21761C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546—21no—
34C22×#121C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic, complemented
38C22×#107C2211yescharacteristic, complemented
39C22×C22⋊C8C2211yescharacteristic
40#2746—21no—
41#2739—21no—
42#2672—21no—
43#2671—21no—
44#2578—21no—
45#2562C2211yescharacteristic
46#2537C2211yescharacteristic
47#2534—21no—
48#2522—21no—
49#2501C2211yescharacteristic
50#2497C2211yescharacteristic
51#2494C2211yescharacteristic
52#2493—21no—
53#2491C2211yescharacteristic
54#2487C2211yescharacteristic
55#2486C2211yescharacteristic, complemented
56#2485C2211yescharacteristic, complemented
57#2482—21no—
58#2442C2211yescharacteristic, complemented
59#2441C2211yescharacteristic, complemented
60#2440C2211yescharacteristic
61#2437—21no—
62#2430—21no—
63#2425—21no—
64#2422C2211yescharacteristic
65#2418—21no—
66#2416C2211yescharacteristic
67#2416C2211yescharacteristic
68#2408C2211yescharacteristic
69#2405—21no—
70#2361C2211yescharacteristic
71#2359—21no—
72#2352C2211yescharacteristic, complemented
73D4×C4⋊C4C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic, complemented
75#2347C2211yescharacteristic, complemented
76#2344C2211yescharacteristic, complemented
77D4×C22⋊C4C2211yescharacteristic
78C4×#120C2211yescharacteristic
79#2280C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82#2101C2211yescharacteristic, complemented
83#2100C2211yescharacteristic, complemented
84#2100C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2087C2211yescharacteristic, complemented
87#2086C2211yescharacteristic, complemented
88#2083C2211yescharacteristic, complemented
89#2083C2211yescharacteristic, complemented
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic, complemented
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2073C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2057C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2034C2211yescharacteristic, complemented
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic, complemented
118#2033C2211yescharacteristic, complemented
119#2033C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#2025C2211yescharacteristic, complemented
122#1992C2211yescharacteristic, complemented
123#1990C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1988C2211yescharacteristic, complemented
126#1955C2211yescharacteristic
127#1955C2211yescharacteristic, complemented
128#1947C2211yescharacteristic, complemented
129#1947C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1942C2211yescharacteristic, complemented
132#1936C2211yescharacteristic, complemented
133#1936C2211yescharacteristic, complemented
134#1936C2211yescharacteristic, complemented
135#1934C2211yescharacteristic, complemented
136#1926C2211yescharacteristic, complemented
137#1926C2211yescharacteristic, complemented
138#1925C2211yescharacteristic, complemented
139#1925C2211yescharacteristic, complemented
140#1924C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1893C2211yescharacteristic
151#1893C2211yescharacteristic
152#1893C2211yescharacteristic, complemented
153#1893C2211yescharacteristic, complemented
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1875C2211yescharacteristic
157#1875C2211yescharacteristic
158#1874C2211yescharacteristic
159#1874C2211yescharacteristic
160#1874C2211yescharacteristic, complemented
161#1874C2211yescharacteristic, complemented
162#1869C2211yescharacteristic
163#1869C2211yescharacteristic, complemented
164#1869C2211yescharacteristic, complemented
165#1864C2211yescharacteristic, complemented
166#1862C2211yescharacteristic, complemented
167#1862C2211yescharacteristic, complemented
168#1862C2211yescharacteristic, complemented
169#1854C2211yescharacteristic, complemented
170#1854C2211yescharacteristic, complemented
171#1853C2211yescharacteristic, complemented
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic, complemented
175#1852C2211yescharacteristic, complemented
176#1852C2211yescharacteristic, complemented
177#1850C2211yescharacteristic, complemented
178#1836C2211yescharacteristic, complemented
179#1825C2211yescharacteristic, complemented
180#1825C2211yescharacteristic, complemented
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic, complemented
184#1823C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1808C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1779C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199C2×#340C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#547—24no—
211#547—42no—
212#546—48no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—24no—
230C2×#121—42no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120D411yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261#480—24no—
262#480—42no—
263C8×D4—42no—
264C2×#107—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
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×C22⋊C8—42no—
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#401—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#399—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#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#392—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#389—21no—
350#389—21no—
351#389—21no—
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
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#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386D411yescharacteristic
385#386D411yescharacteristic
386#386D411yescharacteristic
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385D411yescharacteristic
397#385D411yescharacteristic
398#385D411yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#383—21no—
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#379—21no—
430#379—21no—
431#379—21no—
432#379D411yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444C2×#95—21no—
445C2×#95—21no—
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C25C2×D411yescharacteristic
490C2×#41—44no—
491C2×#41—44no—
492C2×#41—82no—
493C22×Q8—21no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—44no—
508C22×D4—44no—
509C22×D4—82no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—41no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556#125—41no—
557#125—41no—
558#124—44no—
559#123—44no—
560#123—44no—
561#123—44no—
562#123—44no—
563#123—44no—
564#123—82no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—44no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—44no—
578#121—44no—
579#121—44no—
580#121—44no—
581#121—41no—
582#121—41no—
583#121#4114yes—
584#120—24no—
585#120—44no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—44no—
597C4×D4—44no—
598C4×D4—82no—
599#117—41no—
600#117—41no—
601#117—41no—
602#117—41no—
603#117—82no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
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—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—44no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762#97—41no—
763#97—41no—
764C4×C8—41no—
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#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—22no—
802C24—21no—
803C24—22no—
804C24—22no—
805C24—22no—
806C24—21no—
807C24—41no—
808C24—41no—
809C24—41no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821#41—816no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—81no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—24no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—81no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—816no—
870C2×D4AGL(1,ℤ/8)14yes—
871C2×D4C2×#4112yes—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
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—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—82no—
933C22×C4—82no—
934C22×C4—82no—
935C22×C4—82no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C2×#4112yes—
959C22×C4H(5,𝔽2)12yes—
960C22×C4C2511yescharacteristic
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—44no—
986C2×C8—82no—
987C2×C8—82no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4C2×#4112yes—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—24no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—42no—
1096C42—42no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—44no—
1126C23—44no—
1127C23—44no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—44no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—82no—
1143C23—82no—
1144C23—82no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#54612yes—
1153C23C2×AGL(1,ℤ/8)12yes—
1154C23C2×AGL(1,ℤ/8)12yes—
1155C23#57612yes—
1156C23#57812yes—
1157C23C23×D411yescharacteristic
1158Q8—84no—
1159D4—28no—
1160D4—22no—
1161D4—22no—
1162D4—44no—
1163D4—48no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—82no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—84no—
1176D4—162no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—82no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4#54612yes—
1276C2×C4C2×AGL(1,ℤ/8)12yes—
1277C2×C4C22×#4111yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—88no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—168no—
1334C22#331814yes—
1335C22C2×#54611yescharacteristic
1336C22#348511yescharacteristic
1337C22#348511yescharacteristic
1338C22C22×AGL(1,ℤ/8)11yescharacteristic
1339C22C2×#57611yescharacteristic
1340C22C2×#57811yescharacteristic
1341C22#358411yescharacteristic
1342C4—22no—
1343C4—22no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—42no—
1352C4—41no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4#352111yescharacteristic
1367C4#352111yescharacteristic
1368C4#353311yescharacteristic
1369C4#354511yescharacteristic
1370C2—24no—
1371C2—42no—
1372C2—42no—
1373C2—81no—
1374C2—82no—
1375C2—161no—
1376C2#4352511yescharacteristic
1377C2C2×#331811yescharacteristic
1378C2#6117311yescharacteristic
1379C2#6173311yescharacteristic
1380C2#6173711yescharacteristic
1381C2#6176411yescharacteristic
1382C2#6177211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59015C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59206C2semidirect
3. #32003C2semidirect
4. #31786C2semidirect
5. #31739C2semidirect
6. #31708C2semidirect
7. #31680C2semidirect
8. #31428C2semidirect
9. #31367C2semidirect
10. #31266C2semidirect
11. #27717C2semidirect
12. #27602C2semidirect
13. #27541C2semidirect
14. #27525C2semidirect
15. #27354C2semidirect
16. #27167C2semidirect
17. #26420C2semidirect
18. #26308C2semidirect
19. #26208C2semidirect
20. #26202C2semidirect
21. #25232C2semidirect
22. #24981C2semidirect
23. #24939C2semidirect
24. #24576C2semidirect
25. #24088C2semidirect
26. #24002C2semidirect
27. C2×#2076C2semidirect
28. #22938C2semidirect
29. #22485C2semidirect
30. #22030C2semidirect
31. #21761C2semidirect
37. C2×C8×D4C22semidirect
38. C22×#107C22semidirect
55. #2486C22semidirect
56. #2485C22semidirect
58. #2442C22semidirect
59. #2441C22semidirect
72. #2352C22semidirect
74. D4×C4⋊C4C22semidirect
75. #2347C22semidirect
76. #2344C22semidirect
82. #2101C22semidirect
83. #2100C22semidirect
84. #2100C22semidirect
85. #2100C22semidirect
86. #2087C22semidirect
87. #2086C22semidirect
88. #2083C22semidirect
89. #2083C22semidirect
92. #2077C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
101. #2076C22semidirect
102. #2076C22semidirect
103. #2075C22semidirect
104. #2073C22semidirect
105. #2071C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
110. #2057C22semidirect
111. #2057C22semidirect
112. #2034C22semidirect
117. #2033C22semidirect
118. #2033C22semidirect
119. #2033C22semidirect
120. #2025C22semidirect
121. #2025C22semidirect
122. #1992C22semidirect
123. #1990C22semidirect
124. #1989C22semidirect
125. #1988C22semidirect
127. #1955C22semidirect
128. #1947C22semidirect
129. #1947C22semidirect
130. #1943C22semidirect
131. #1942C22semidirect
132. #1936C22semidirect
133. #1936C22semidirect
134. #1936C22semidirect
135. #1934C22semidirect
136. #1926C22semidirect
137. #1926C22semidirect
138. #1925C22semidirect
139. #1925C22semidirect
141. #1924C22semidirect
143. #1923C22semidirect
144. #1921C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1919C22semidirect
152. #1893C22semidirect
153. #1893C22semidirect
160. #1874C22semidirect
161. #1874C22semidirect
163. #1869C22semidirect
164. #1869C22semidirect
165. #1864C22semidirect
166. #1862C22semidirect
167. #1862C22semidirect
168. #1862C22semidirect
169. #1854C22semidirect
170. #1854C22semidirect
171. #1853C22semidirect
174. #1852C22semidirect
175. #1852C22semidirect
176. #1852C22semidirect
177. #1850C22semidirect
178. #1836C22semidirect
179. #1825C22semidirect
180. #1825C22semidirect
183. #1824C22semidirect
184. #1823C22semidirect
185. #1823C22semidirect
186. #1823C22semidirect
187. #1808C22semidirect
188. #1804C22semidirect
189. #1802C22semidirect
195. #1776C22semidirect
196. #1762C22semidirect
197. C4×#102C22semidirect
198. #1752C22semidirect
199. C2×#340C22semidirect
200. C2×#340C22semidirect
201. C2×#340C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#592062
#590152
#320032
#317862
#317392
#317082
#316802
#314282
#313672
#312662
#277172
#276022
#275412
#275252
#273542
#271672
#264202
#263082
#262082
#262022
#252322
#249812
#249392
#245762
#240882
#240022
C2×#20762
#229382
#224852
#220302
#217612