Finite Group Databasebeta

← #44543658

Subgroups — #44543658

Order 31936.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×C22⋊D499C211yesmaximal, characteristic, complemented
2C2×D4×D499C211yesmaximal, characteristic, complemented
3#30630335C211yesmaximal, characteristic, complemented
4#30630333C212yesmaximal, complemented
5#30630332C211yesmaximal, characteristic, complemented
6#30630324C212yesmaximal, complemented
7#30630322C212yesmaximal, complemented
8#30630320C211yesmaximal, characteristic, complemented
9#30630319C212yesmaximal, complemented
10C22⋊C4×D499C211yesmaximal, characteristic, complemented
11#120×C499C211yesmaximal, characteristic, complemented
12C23×D499C2211yescharacteristic
13C23×D499C2211yescharacteristic, complemented
14C2×D1996C2211yescharacteristic, complemented
15C2×C22⋊D499—24no—
16C2×C22⋊D499C2212yes—
17C2×C22⋊D499C2211yescharacteristic
18C2×C22⋊D499C2211yescharacteristic, complemented
19C2×C22⋊D499C2212yescomplemented
20C2×C22⋊D499C2212yescomplemented
21D4×D499—24no—
22C22×Dic499C2211yescharacteristic, complemented
23C2×C4×D499C2211yescharacteristic, complemented
24C2×C4×D499C2212yescomplemented
25C4⋊Dic499C2212yescomplemented
26Dic499⋊C4C2212yescomplemented
27C22⋊Dic499C2211yescharacteristic, complemented
28C22⋊Dic499C2212yescomplemented
29C22⋊Dic499C2212yescomplemented
30(C2×D499)⋊C4C2212yescomplemented
31(C2×D499)⋊C4C2212yescomplemented
32C24×C499C2211yescharacteristic, complemented
33C2×D4×C499C2211yescharacteristic
34C2×D4×C499C2212yescomplemented
35C22⋊C4×C499C2211yescharacteristic, complemented
36C22⋊C4×C499C2212yescomplemented
37C22×D499—22no—
38C22×D499—42no—
39C22×D499—42no—
40C22×D499D414yescomplemented
41C22×D499C2311yescharacteristic
42C22×D499C2311yescharacteristic
43C22×D499C2311yescharacteristic
44D1996—22no—
45C22⋊D499—22no—
46C22⋊D499—22no—
47C22⋊D499—24no—
48C22⋊D499—24no—
49C22⋊D499—42no—
50C2×Dic499—22no—
51C2×Dic499C2312yes—
52C2×Dic499C2312yes—
53C2×Dic499C2311yescharacteristic
54C4×D499—22no—
55C4×D499—42no—
56C23×C499—22no—
57C23×C499—42no—
58C23×C499C2312yes—
59C23×C499C2311yescharacteristic
60C23×C499C2311yescharacteristic
61D4×C499—22no—
62D4×C499—42no—
63C2×C4×C499C2311yescharacteristic
64C2×C4×C499C2312yes—
65C22×C499—22no—
66C22×C499—22no—
67C22×C499—21no—
68C22×C499—22no—
69C22×C499—22no—
70C22×C499—22no—
71C22×C499—44no—
72C22×C499C2×D412yes—
73C22×C499C2411yescharacteristic
74C2×D499—22no—
75C2×D499—22no—
76C2×D499—21no—
77C2×D499—22no—
78C2×D499—44no—
79C2×D499—44no—
80C2×D499C2×D412yes—
81C2×D499C2×D412yes—
82C4×C499—21no—
83C4×C499—22no—
84Dic499—21no—
85Dic499—22no—
86Dic499—22no—
87C2×C499—22no—
88C2×C499—41no—
89C2×C499—42no—
90C2×C499C22×D411yescharacteristic
91C2×C499H(5,𝔽2)12yes—
92D499—22no—
93D499—22no—
94D499—41no—
95C499#53411yescharacteristic, complemented, Sylow
96#534—4991nomaximal, Sylow
97C22×D4—4991no—
98C22×D4—4991no—
99#123—4991no—
100#123—4992no—
101#123—4991no—
102#121—4992no—
103#121—4992no—
104#120—4991no—
105#120—4992no—
106#120D49911yescharacteristic, complemented
107C2×C22⋊C4—4991no—
108C24—4991no—
109C24—4991no—
110C24C2×D49911yescharacteristic, complemented
111C2×D4—9984no—
112C2×D4—9984no—
113C2×D4—4992no—
114C2×D4—4992no—
115C2×D4—4991no—
116C2×D4—4991no—
117C2×D4—4992no—
118C2×D4—4991no—
119C2×D4C2×D49911yescharacteristic
120C2×D4C2×D49912yescomplemented
121C22×C4—4992no—
122C22×C4—4991no—
123C22×C4—4991no—
124C4⋊C4—4992no—
125C4⋊C4—4992no—
126C22⋊C4—4991no—
127C22⋊C4—4992no—
128C22⋊C4—4992no—
129C22⋊C4—4992no—
130C22⋊C4—4992no—
131C22⋊C4C2×D49911yescharacteristic, complemented
132C22⋊C4C2×D49912yescomplemented
133C23—22no—
134C23—42no—
135C23—19962no—
136C23—19962no—
137C23—9982no—
138C23—4994no—
139C23—4991no—
140C23—4991no—
141C23—4991no—
142C23C22×D49911yescharacteristic
143C23C22×D49912yes—
144C23C22×D49911yescharacteristic
145D4—22no—
146D4—42no—
147D4—19962no—
148D4—9982no—
149D4—9982no—
150D4—9984no—
151D4—9984no—
152D4—9982no—
153C2×C4—19962no—
154C2×C4—9982no—
155C2×C4—9982no—
156C2×C4—4992no—
157C2×C4—4992no—
158C2×C4—4991no—
159C2×C4C22×D49912yes—
160C2×C4C22×D49911yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—19964no—
169C22—19964no—
170C22—9981no—
171C22—9982no—
172C22—9982no—
173C22—9982no—
174C22—4992no—
175C22—4992no—
176C22D4×D49912yes—
177C22C23×D49911yescharacteristic
178C4—21no—
179C4—22no—
180C4—9981no—
181C4—9982no—
182C4—9982no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—19961no—
187C2—9982no—
188C2—9982no—
189C2C2×D4×D49911yescharacteristic
190C2#3063039612yes—
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#120×C499C2
hypercenter#120D499
hypocenterC499#534
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D499C2semidirect
2. C2×D4×D499C2semidirect
3. #30630335C2semidirect
4. #30630333C2semidirect
5. #30630332C2semidirect
6. #30630324C2semidirect
7. #30630322C2semidirect
8. #30630320C2semidirect
9. #30630319C2semidirect
10. C22⋊C4×D499C2semidirect
11. #120×C499C2semidirect
13. C23×D499C22semidirect
14. C2×D1996C22semidirect
18. C2×C22⋊D499C22semidirect
19. C2×C22⋊D499C22semidirect
20. C2×C22⋊D499C22semidirect
22. C22×Dic499C22semidirect
23. C2×C4×D499C22semidirect
24. C2×C4×D499C22semidirect
25. C4⋊Dic499C22semidirect
26. Dic499⋊C4C22semidirect
27. C22⋊Dic499C22semidirect
28. C22⋊Dic499C22semidirect
29. C22⋊Dic499C22semidirect
30. (C2×D499)⋊C4C22semidirect
31. (C2×D499)⋊C4C22semidirect
32. C24×C499C22semidirect
34. C2×D4×C499C22semidirect
35. C22⋊C4×C499C22semidirect
36. C22⋊C4×C499C22semidirect
40. C22×D499D4semidirect
95. C499#534semidirect
106. #120D499semidirect
110. C24C2×D499semidirect
120. C2×D4C2×D499semidirect
131. C22⋊C4C2×D499semidirect
132. C22⋊C4C2×D499semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4992
C2×D4×D4992
#306303352
#306303332
#306303322
#306303242
#306303222
#306303202
#306303192
C22⋊C4×D4992
#120×C4992
#534499