Finite Group Databasebeta

← #44543680

Subgroups — #44543680

Order 31936.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#30630346C211yesmaximal, characteristic, complemented
2#30630344C211yesmaximal, characteristic, complemented
3#30630338C211yesmaximal, characteristic, complemented
4#30630337C211yesmaximal, characteristic, complemented
5#30630334C211yesmaximal, characteristic, complemented
6#30630332C211yesmaximal, characteristic, complemented
7#30630329C211yesmaximal, characteristic, complemented
8#30630323C211yesmaximal, characteristic, complemented
9#30630322C211yesmaximal, characteristic, complemented
10#30630319C211yesmaximal, characteristic, complemented
11#30630319C211yesmaximal, characteristic, complemented
12C4×C22⋊D499C211yesmaximal, characteristic, complemented
13(C22⋊D499)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D499C211yesmaximal, characteristic, complemented
15#121×C499C211yesmaximal, characteristic, complemented
16C23×D499C2211yescharacteristic
17C2×Dic998C2211yescharacteristic, complemented
18C2×C22⋊D499C2211yescharacteristic
19C2×C22⋊D499C2211yescharacteristic
20C2×C22⋊D499C2211yescharacteristic
21C2×C22⋊D499C2211yescharacteristic
22C22×Dic499C2211yescharacteristic, complemented
23C2×C4×D499C2211yescharacteristic
24C2×C4×D499C2211yescharacteristic
25C4⋊Dic499C2211yescharacteristic, complemented
26Dic499⋊C4C2211yescharacteristic, complemented
27Dic499⋊C4C2211yescharacteristic, complemented
28Dic499⋊C4C2211yescharacteristic, complemented
29Dic499⋊C4C2211yescharacteristic, complemented
30C22⋊Dic499C2211yescharacteristic
31C22⋊Dic499C2211yescharacteristic
32C22⋊Dic499C2211yescharacteristic
33C22⋊Dic499C2211yescharacteristic, complemented
34C22⋊Dic499C2211yescharacteristic, complemented
35C22⋊Dic499C2211yescharacteristic, complemented
36(C2×D499)⋊C4C2211yescharacteristic
37(C2×D499)⋊C4C2211yescharacteristic
38(C2×D499)⋊C4C2211yescharacteristic
39(C2×D499)⋊C4C2211yescharacteristic
40(C2×D499)⋊C4C2211yescharacteristic
41(C2×D499)⋊C4C2211yescharacteristic
42C4×Dic499C2211yescharacteristic, complemented
43C4×Dic499C2211yescharacteristic, complemented
44C2×D4×C499C2211yescharacteristic
45C2×D4×C499C2211yescharacteristic
46C2×D4×C499C2211yescharacteristic, complemented
47C22×C4×C499C2211yescharacteristic, complemented
48C4⋊C4×C499C2211yescharacteristic, complemented
49C22⋊C4×C499C2211yescharacteristic
50C22⋊C4×C499C2211yescharacteristic, complemented
51C22×D499—22no—
52C22×D499—41no—
53C22×D499—41no—
54C22×D499C2311yescharacteristic
55C22×D499C2311yescharacteristic
56Dic998—41no—
57C22⋊D499—22no—
58C22⋊D499—22no—
59C22⋊D499—41no—
60C22⋊D499—41no—
61C2×Dic499—41no—
62C2×Dic499C2311yescharacteristic
63C2×Dic499C2311yescharacteristic
64C2×Dic499C2311yescharacteristic
65C2×Dic499C2311yescharacteristic
66C2×Dic499C2311yescharacteristic
67C2×Dic499C2311yescharacteristic
68C4×D499—41no—
69C4×D499—41no—
70C23×C499C2311yescharacteristic
71C23×C499C2311yescharacteristic
72C23×C499C2311yescharacteristic
73D4×C499—41no—
74D4×C499—41no—
75D4×C499—41no—
76C2×C4×C499—41no—
77C2×C4×C499C2311yescharacteristic
78C2×C4×C499C2311yescharacteristic
79C2×C4×C499C2311yescharacteristic
80C2×C4×C499C2311yescharacteristic
81C22×C499—21no—
82C22×C499—21no—
83C22×C499—21no—
84C22×C499—21no—
85C22×C499—21no—
86C22×C499—21no—
87C22×C499—21no—
88C22×C499—21no—
89C22×C499—21no—
90C22×C499C2411yescharacteristic
91C2×D499—21no—
92C2×D499—21no—
93C2×D499—21no—
94C2×D499—21no—
95C2×D499—21no—
96C2×D499—44no—
97C2×D499#4112yes—
98C4×C499—21no—
99C4×C499—21no—
100C4×C499—21no—
101C4×C499—21no—
102Dic499—21no—
103Dic499—21no—
104Dic499—21no—
105Dic499—21no—
106Dic499—21no—
107Dic499—21no—
108C2×C499—41no—
109C2×C499—41no—
110C2×C499—41no—
111C2×C499C2×#4111yescharacteristic
112C2×C499H(5,𝔽2)11yescharacteristic
113C2×C499H(5,𝔽2)11yescharacteristic
114D499—22no—
115D499—41no—
116C499#53811yescharacteristic, complemented, Sylow
117#538—4991nomaximal, Sylow
118#126—4991no—
119#126—4991no—
120#124—4991no—
121#124—4991no—
122#123—4991no—
123#123—4991no—
124C22⋊Q8—4991no—
125#121—4991no—
126#121—4991no—
127#121D49911yescharacteristic, complemented
128#120—4991no—
129#120—4991no—
130C4×D4—4991no—
131C4×D4—4991no—
132C2×C22⋊C4—4991no—
133C24—4991no—
134C2×Q8—4991no—
135C2×D4—4991no—
136C2×D4—4991no—
137C2×D4—4991no—
138C2×D4—4991no—
139C2×D4C2×D49911yescharacteristic
140C2×D4C2×D49911yescharacteristic
141C2×D4C2×D49911yescharacteristic, complemented
142C22×C4—4991no—
143C22×C4—4991no—
144C22×C4—4991no—
145C22×C4C2×D49911yescharacteristic, complemented
146C4⋊C4—4991no—
147C4⋊C4—4991no—
148C4⋊C4—4991no—
149C4⋊C4—4991no—
150C4⋊C4—4991no—
151C4⋊C4C2×D49911yescharacteristic, complemented
152C22⋊C4—4991no—
153C22⋊C4—4991no—
154C22⋊C4—4991no—
155C22⋊C4—4991no—
156C22⋊C4—4991no—
157C22⋊C4—4991no—
158C22⋊C4—4991no—
159C22⋊C4—4991no—
160C22⋊C4—4991no—
161C22⋊C4—4991no—
162C22⋊C4—4991no—
163C22⋊C4—4991no—
164C22⋊C4C2×D49911yescharacteristic
165C22⋊C4C2×D49911yescharacteristic, complemented
166C42—4991no—
167C42—4991no—
168C23—19961no—
169C23—19961no—
170C23—9982no—
171C23—4991no—
172C23—4991no—
173C23C22×D49911yescharacteristic
174C23C22×D49911yescharacteristic
175C23C22×D49911yescharacteristic
176Q8—19961no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—19961no—
181D4—19961no—
182D4—9982no—
183D4—9982no—
184C2×C4—41no—
185C2×C4—19961no—
186C2×C4—19961no—
187C2×C4—19961no—
188C2×C4—4991no—
189C2×C4—4991no—
190C2×C4—4991no—
191C2×C4—4991no—
192C2×C4—4991no—
193C2×C4—4991no—
194C2×C4C22×D49911yescharacteristic
195C2×C4C22×D49911yescharacteristic
196C2×C4C22×D49911yescharacteristic
197C2×C4C22×D49911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—19964no—
208C22—9981no—
209C22—9981no—
210C22—9981no—
211C22—9981no—
212C22—9981no—
213C22—4992no—
214C22C23×D49911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—9981no—
220C4—9981no—
221C4—9981no—
222C4—9981no—
223C4—9981no—
224C4—9981no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—19961no—
229C2—9982no—
230C2#41×D49911yescharacteristic
231C2#3063039611yescharacteristic
232C2#3063039611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#121×C499C2
hypercenter#121D499
hypocenterC499#538
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #30630346C2semidirect
2. #30630344C2semidirect
3. #30630338C2semidirect
4. #30630337C2semidirect
5. #30630334C2semidirect
6. #30630332C2semidirect
7. #30630329C2semidirect
8. #30630323C2semidirect
9. #30630322C2semidirect
10. #30630319C2semidirect
11. #30630319C2semidirect
12. C4×C22⋊D499C2semidirect
13. (C22⋊D499)⋊C4C2semidirect
14. C22⋊C4×D499C2semidirect
15. #121×C499C2semidirect
17. C2×Dic998C22semidirect
22. C22×Dic499C22semidirect
25. C4⋊Dic499C22semidirect
26. Dic499⋊C4C22semidirect
27. Dic499⋊C4C22semidirect
28. Dic499⋊C4C22semidirect
29. Dic499⋊C4C22semidirect
33. C22⋊Dic499C22semidirect
34. C22⋊Dic499C22semidirect
35. C22⋊Dic499C22semidirect
42. C4×Dic499C22semidirect
43. C4×Dic499C22semidirect
46. C2×D4×C499C22semidirect
47. C22×C4×C499C22semidirect
48. C4⋊C4×C499C22semidirect
50. C22⋊C4×C499C22semidirect
116. C499#538semidirect
127. #121D499semidirect
141. C2×D4C2×D499semidirect
145. C22×C4C2×D499semidirect
151. C4⋊C4C2×D499semidirect
165. C22⋊C4C2×D499semidirect

Maximal subgroups

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

subgroupindex
#306303462
#306303442
#306303382
#306303372
#306303342
#306303322
#306303292
#306303232
#306303222
#306303192
C4×C22⋊D4992
(C22⋊D499)⋊C42
C22⋊C4×D4992
#121×C4992
#538499