Finite Group Databasebeta

← #49130738

Subgroups — #49130738

Order 36224.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C212yesmaximal, complemented
2#127×D283C211yesmaximal, characteristic, complemented
3C4×#17985393C211yesmaximal, characteristic, complemented
4#31826665C211yesmaximal, characteristic, complemented
5#31826663C212yesmaximal, complemented
6#31826661C211yesmaximal, characteristic, complemented
7#31826659C212yesmaximal, complemented
8#31826657C211yesmaximal, characteristic, complemented
9#31826487C211yesmaximal, characteristic, complemented
10#31826468C212yesmaximal, complemented
11#460×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2211yescharacteristic
13C2×D4×D283—21no—
14C2×D4×D283—21no—
15C2×D4×D283C2212yes—
16#22583637—28no—
17C2×#17985379C2212yescomplemented
18C2×D2264C2212yescomplemented
19C2×#17985377C2212yescomplemented
20C2×#17985375C2212yes—
21#22583607C2211yescharacteristic
22#22583606—21no—
23#22583606—21no—
24#22583606C2212yes—
25Q8×Dic283C2211yescharacteristic, complemented
26C4×D1132—21no—
27C4×D1132C2211yescharacteristic, complemented
28#22583572—21no—
29#22583572C2211yescharacteristic, complemented
30#22583568—21no—
31#22583568C2211yescharacteristic
32C42×D283—21no—
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic, complemented
35Dic283⋊C8C2212yescomplemented
36#22583532C2212yescomplemented
37#22583531C2212yescomplemented
38#22583530C2212yescomplemented
39C2×SD16×C283C2212yescomplemented
40#127×C283C2211yescharacteristic
41C4×Q8×C283C2211yescharacteristic, complemented
42C4⋊C8×C283C2211yescharacteristic, complemented
43#102×C283C2212yescomplemented
44C23×D283—22no—
45#17985393—22no—
46#17985393D414yescomplemented
47C2×D1132—21no—
48C2×D1132—21no—
49C2×D1132—21no—
50C2×D1132C2312yes—
51C2×D1132C2311yescharacteristic
52C2×C22⋊D283—22no—
53C2×C22⋊D283—22no—
54C2×C22⋊D283—22no—
55D4×D283—24no—
56D4×D283—24no—
57D4×D283—44no—
58D4×D283—44no—
59C2×C4×D283—21no—
60C2×C4×D283—21no—
61C2×C4×D283—21no—
62C2×C4×D283D411yescharacteristic
63C2×C4×D283D411yescharacteristic
64C2×C4×D283C2311yescharacteristic
65#17985379—24no—
66D2264—24no—
67#17985377—24no—
68#17985375—24no—
69C2×C283⋊C8C2312yes—
70C4⋊Dic283—21no—
71C4⋊Dic283C2311yescharacteristic
72(C2×D283)⋊C4—21no—
73(C2×D283)⋊C4—21no—
74(C2×D283)⋊C4—21no—
75C4×Dic283—21no—
76C4×Dic283—21no—
77C4×Dic283D411yescharacteristic
78C4×Dic283D411yescharacteristic
79C4×Dic283C2311yescharacteristic
80C2×Q8×C283C2311yescharacteristic
81C2×D4×C283—21no—
82C2×D4×C283—21no—
83C2×D4×C283C2312yes—
84SD16×C283—24no—
85C2×C8×C283C2312yes—
86C4⋊C4×C283—21no—
87C4⋊C4×C283C2311yescharacteristic
88C42×C283—21no—
89C42×C283C2311yescharacteristic
90C22×D283—21no—
91C22×D283—22no—
92C22×D283—44no—
93C22×D283—44no—
94C22×D283—44no—
95C22×D283C2×D411yescharacteristic
96D1132—24no—
97D1132—22no—
98D1132—21no—
99D1132—22no—
100D1132—42no—
101D1132—42no—
102D1132C2×D412yescomplemented
103C22⋊D283—44no—
104C22⋊D283—44no—
105C22⋊D283—44no—
106C2×Dic283—21no—
107C2×Dic283C2×D411yescharacteristic
108C2×Dic283C2×D411yescharacteristic
109C2×Dic283C2×D411yescharacteristic
110C4×D283—22no—
111C4×D283—24no—
112C4×D283—22no—
113C4×D283—42no—
114C4×D283—42no—
115C4×D283C2×D412yes—
116C4×D283#4112yes—
117C283⋊C8—22no—
118C23×C283—22no—
119Q8×C283—21no—
120Q8×C283C2×D412yescomplemented
121D4×C283—22no—
122D4×C283—22no—
123D4×C283—42no—
124D4×C283—42no—
125C2×C4×C283—21no—
126C2×C4×C283—21no—
127C2×C4×C283C2×D411yescharacteristic
128C2×C4×C283C2×D411yescharacteristic
129C2×C4×C283C2411yescharacteristic
130C8×C283—22no—
131C22×C283—42no—
132C22×C283—42no—
133C22×C283—42no—
134C22×C283C22×D411yescharacteristic
135C2×D283—21no—
136C2×D283—21no—
137C2×D283—22no—
138C2×D283—41no—
139C2×D283—41no—
140C2×D283—42no—
141C2×D283—42no—
142C2×D283—42no—
143C2×D283—88no—
144C2×D283#12112yes—
145C4×C283—22no—
146C4×C283—21no—
147C4×C283—41no—
148C4×C283AGL(1,ℤ/8)12yescomplemented
149C4×C283C22×D411yescharacteristic
150C4×C283C2×#4111yescharacteristic
151Dic283—21no—
152Dic283—41no—
153Dic283#12112yes—
154Dic283AGL(1,ℤ/8)12yescomplemented
155C2×C283—82no—
156C2×C283C2×#12111yescharacteristic
157C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
158C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
159D283—22no—
160D283—42no—
161D283—82no—
162C283#303811yescharacteristic, complemented, Sylow
163#3038—2831nomaximal, Sylow
164C2×AGL(1,ℤ/8)—2832no—
165C2×#127—2831no—
166C4×#41—2831no—
167#460—2832no—
168#460—2831no—
169#460D28311yescharacteristic, complemented
170#459—2831no—
171#459—2831no—
172#459—2832no—
173#423—2831no—
174#418—2832no—
175C2×#41—2831no—
176C22×D4—2832no—
177C22×D4—5661no—
178C22×D4—5661no—
179AGL(1,ℤ/8)—5668no—
180C2×SD16—2832no—
181C2×SD16C2×D28312yescomplemented
182C2×D8—2832no—
183C2×D8—2832no—
184C2×M16—2832no—
185#127—2832no—
186#127—2831no—
187#127—5661no—
188#127—5661no—
189#127C2×D28311yescharacteristic
190C4×Q8—2831no—
191C4×Q8C2×D28311yescharacteristic, complemented
192C4×D4—2831no—
193C4×D4—2831no—
194C4×D4—5661no—
195C4×D4—5661no—
196#117—2831no—
197#117—5661no—
198C2×C42—2831no—
199C2×C42—5661no—
200C4⋊C8—2832no—
201C4⋊C8—2831no—
202C4⋊C8C2×D28311yescharacteristic, complemented
203#102—2832no—
204#102—2832no—
205#102—2832no—
206#102C2×D28312yescomplemented
207C24—5662no—
208#41—2834no—
209#41—5662no—
210C2×Q8C22×D28311yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—2831no—
214C2×D4—2832no—
215C2×D4—5661no—
216C2×D4—5664no—
217C2×D4—5664no—
218C2×D4—5662no—
219C2×D4—5662no—
220C2×D4—5662no—
221C2×D4—5661no—
222C2×D4—5661no—
223C2×D4—11324no—
224C2×D4—11324no—
225C2×D4C22×D28312yes—
226C22×C4—2831no—
227C22×C4—2831no—
228C22×C4—2831no—
229C22×C4—5661no—
230C22×C4—5661no—
231C22×C4—5661no—
232SD16—24no—
233SD16—5664no—
234D8—5664no—
235D8—5664no—
236M16—5664no—
237C2×C8—2832no—
238C2×C8C22×D28312yes—
239C4⋊C4—21no—
240C4⋊C4—2831no—
241C4⋊C4—5661no—
242C4⋊C4C22×D28311yescharacteristic
243C22⋊C4—5661no—
244C22⋊C4—5661no—
245C22⋊C4—5661no—
246C42—21no—
247C42—2831no—
248C42—2831no—
249C42—2831no—
250C42—5661no—
251C42—5661no—
252C42C22×D28311yescharacteristic
253C23—22no—
254C23—2831no—
255C23—5661no—
256C23—5662no—
257C23—11324no—
258C23—11324no—
259C23—11324no—
260Q8—21no—
261Q8D4×D28312yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—2832no—
267D4—5664no—
268D4—5662no—
269D4—5661no—
270D4—5662no—
271D4—11322no—
272D4—11324no—
273D4—11324no—
274D4—11324no—
275D4—11322no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2831no—
279C2×C4—2831no—
280C2×C4—2832no—
281C2×C4—2832no—
282C2×C4—2831no—
283C2×C4—5662no—
284C2×C4—5664no—
285C2×C4—5662no—
286C2×C4—5661no—
287C2×C4—11322no—
288C2×C4—11322no—
289C2×C4D4×D28311yescharacteristic
290C2×C4D4×D28311yescharacteristic
291C2×C4C23×D28311yescharacteristic
292C8—22no—
293C8—5662no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—2832no—
298C22—5661no—
299C22—5661no—
300C22—5662no—
301C22—11321no—
302C22—11321no—
303C22—11322no—
304C22—11322no—
305C22—11322no—
306C22—22648no—
307C22C2×D4×D28311yescharacteristic
308C4—22no—
309C4—21no—
310C4—41no—
311C4—2832no—
312C4—2832no—
313C4—5661no—
314C4—11321no—
315C4#2258363712yescomplemented
316C4C2×D4×D28311yescharacteristic
317C4#41×D28311yescharacteristic
318C2—82no—
319C2—5662no—
320C2—11322no—
321C2—22642no—
322C2#121×D28311yescharacteristic
323C2AGL(1,ℤ/8)×D28311yescharacteristic
324C2C2×#2258363711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#460×C283C2
socleC22×C283C22×D4
hypercenter#460D283
hypocenterC283#3038
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. #127×D283C2semidirect
3. C4×#17985393C2semidirect
4. #31826665C2semidirect
5. #31826663C2semidirect
6. #31826661C2semidirect
7. #31826659C2semidirect
8. #31826657C2semidirect
9. #31826487C2semidirect
10. #31826468C2semidirect
11. #460×C283C2semidirect
17. C2×#17985379C22semidirect
18. C2×D2264C22semidirect
19. C2×#17985377C22semidirect
25. Q8×Dic283C22semidirect
27. C4×D1132C22semidirect
29. #22583572C22semidirect
34. C4⋊(C283⋊C8)C22semidirect
35. Dic283⋊C8C22semidirect
36. #22583532C22semidirect
37. #22583531C22semidirect
38. #22583530C22semidirect
39. C2×SD16×C283C22semidirect
41. C4×Q8×C283C22semidirect
42. C4⋊C8×C283C22semidirect
43. #102×C283C22semidirect
46. #17985393D4semidirect
102. D1132C2×D4semidirect
120. Q8×C283C2×D4semidirect
148. C4×C283AGL(1,ℤ/8)semidirect
154. Dic283AGL(1,ℤ/8)semidirect
162. C283#3038semidirect
169. #460D283semidirect
181. C2×SD16C2×D283semidirect
191. C4×Q8C2×D283semidirect
202. C4⋊C8C2×D283semidirect
206. #102C2×D283semidirect
261. Q8D4×D283semidirect
315. C4#22583637semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
#127×D2832
C4×#179853932
#318266652
#318266632
#318266612
#318266592
#318266572
#318264872
#318264682
#460×C2832
#3038283