Finite Group Databasebeta

← #44543663

Subgroups — #44543663

Order 31936.

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

normal subgroups only

This group has 334 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
1C2×#22547810C211yesmaximal, characteristic, complemented
2C22×C22⋊D499C211yesmaximal, characteristic, complemented
3#30630347C212yesmaximal, complemented
4#30630337C212yesmaximal, complemented
5#30630324C212yesmaximal, complemented
6#30630323C212yesmaximal, complemented
7#30630321C211yesmaximal, characteristic, complemented
8#30630320C211yesmaximal, characteristic, complemented
9#30630319C211yesmaximal, characteristic, complemented
10#30630307C211yesmaximal, characteristic, complemented
11#120×C499C211yesmaximal, characteristic, complemented
12C23×D499C2211yescharacteristic
13#22547810—24no—
14C2×Dic998C2211yescharacteristic, complemented
15C2×D1996C2212yescomplemented
16C2×C22⋊D499—24no—
17C2×C22⋊D499C2211yescharacteristic
18C2×C22⋊D499C2212yes—
19C2×C22⋊D499C2212yes—
20C2×C22⋊D499C2211yescharacteristic, complemented
21C2×C22⋊D499C2212yescomplemented
22C2×C22⋊D499C2212yescomplemented
23C22×Dic499C2211yescharacteristic
24C22×Dic499C2211yescharacteristic, complemented
25C2×C4×D499C2211yescharacteristic, complemented
26Dic499⋊C4C2212yescomplemented
27C22⋊Dic499C2211yescharacteristic
28C22⋊Dic499C2212yescomplemented
29(C2×D499)⋊C4C2212yescomplemented
30(C2×D499)⋊C4C2212yescomplemented
31C4×Dic499C2212yescomplemented
32C24×C499C2211yescharacteristic
33C2×D4×C499C2211yescharacteristic
34C2×D4×C499C2212yescomplemented
35C22⋊C4×C499C2211yescharacteristic
36C22⋊C4×C499C2212yescomplemented
37C22×D499—22no—
38C22×D499—42no—
39C22×D499C2312yes—
40C22×D499C2311yescharacteristic
41Dic998—22no—
42D1996—42no—
43C22⋊D499—22no—
44C22⋊D499—24no—
45C22⋊D499—24no—
46C22⋊D499—22no—
47C22⋊D499—42no—
48C22⋊D499—42no—
49C2×Dic499—22no—
50C2×Dic499D414yescomplemented
51C2×Dic499C2312yes—
52C2×Dic499C2311yescharacteristic
53C2×Dic499C2311yescharacteristic
54C2×Dic499C2311yescharacteristic
55C4×D499—22no—
56C23×C499—22no—
57C23×C499—42no—
58C23×C499C2312yes—
59C23×C499C2311yescharacteristic
60C23×C499C2311yescharacteristic
61D4×C499—22no—
62D4×C499—42no—
63C2×C4×C499C2312yes—
64C2×C4×C499C2311yescharacteristic
65C22×C499—22no—
66C22×C499—21no—
67C22×C499—22no—
68C22×C499—22no—
69C22×C499—22no—
70C22×C499—22no—
71C22×C499—44no—
72C22×C499C2×D412yes—
73C22×C499C2411yescharacteristic
74C2×D499—21no—
75C2×D499—22no—
76C2×D499—22no—
77C2×D499—22no—
78C2×D499—22no—
79C2×D499—44no—
80C4×C499—21no—
81C4×C499—22no—
82Dic499—21no—
83Dic499—22no—
84Dic499C2×D412yes—
85Dic499C2×D412yes—
86C2×C499—22no—
87C2×C499—41no—
88C2×C499—42no—
89C2×C499C22×D411yescharacteristic
90C2×C499H(5,𝔽2)12yes—
91D499—41no—
92D499—42no—
93C499#53511yescharacteristic, complemented, Sylow
94#535—4991nomaximal, Sylow
95C2×#41—4991no—
96C22×D4—4991no—
97#127—4992no—
98#124—4992no—
99#121—4992no—
100#121—4992no—
101#120—4991no—
102#120—4991no—
103#120—4991no—
104#120D49911yescharacteristic, complemented
105#117—4991no—
106C24—4991no—
107C24C2×D49911yescharacteristic
108#41—9984no—
109C2×Q8—4991no—
110C2×D4—9984no—
111C2×D4—4992no—
112C2×D4—4992no—
113C2×D4—4991no—
114C2×D4—4992no—
115C2×D4—4992no—
116C2×D4—4991no—
117C2×D4—4992no—
118C2×D4C2×D49911yescharacteristic
119C2×D4C2×D49912yescomplemented
120C22×C4—4991no—
121C22×C4—4991no—
122C22×C4—4991no—
123C4⋊C4—4992no—
124C22⋊C4—4991no—
125C22⋊C4—4992no—
126C22⋊C4—4992no—
127C22⋊C4—4992no—
128C22⋊C4C2×D49911yescharacteristic
129C22⋊C4C2×D49912yescomplemented
130C42—4992no—
131C23—22no—
132C23—42no—
133C23—19962no—
134C23—9982no—
135C23—4992no—
136C23—4991no—
137C23C22×D49912yes—
138C23C22×D49911yescharacteristic
139C23C22×D49911yescharacteristic
140Q8—9982no—
141D4—22no—
142D4—42no—
143D4—19962no—
144D4—19962no—
145D4—19962no—
146D4—9982no—
147D4—9984no—
148D4—9984no—
149D4—9982no—
150C2×C4—9982no—
151C2×C4—9982no—
152C2×C4—4992no—
153C2×C4—4991no—
154C2×C4—4994no—
155C2×C4—4991no—
156C2×C4—4991no—
157C2×C4C22×D49912yes—
158C2×C4C22×D49911yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—19964no—
167C22—9981no—
168C22—9982no—
169C22—9982no—
170C22—9982no—
171C22—9982no—
172C22D4×D49912yes—
173C22C23×D49911yescharacteristic
174C4—21no—
175C4—22no—
176C4—9981no—
177C4—9982no—
178C4—4992no—
179C4—4992no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—19962no—
184C2—19961no—
185C2C2×D4×D49911yescharacteristic
186C2#3063039612yes—
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#120×C499C2
hypercenter#120D499
hypocenterC499#535
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#22547810C2semidirect
2. C22×C22⋊D499C2semidirect
3. #30630347C2semidirect
4. #30630337C2semidirect
5. #30630324C2semidirect
6. #30630323C2semidirect
7. #30630321C2semidirect
8. #30630320C2semidirect
9. #30630319C2semidirect
10. #30630307C2semidirect
11. #120×C499C2semidirect
14. C2×Dic998C22semidirect
15. C2×D1996C22semidirect
20. C2×C22⋊D499C22semidirect
21. C2×C22⋊D499C22semidirect
22. C2×C22⋊D499C22semidirect
24. C22×Dic499C22semidirect
25. C2×C4×D499C22semidirect
26. Dic499⋊C4C22semidirect
28. C22⋊Dic499C22semidirect
29. (C2×D499)⋊C4C22semidirect
30. (C2×D499)⋊C4C22semidirect
31. C4×Dic499C22semidirect
34. C2×D4×C499C22semidirect
36. C22⋊C4×C499C22semidirect
50. C2×Dic499D4semidirect
93. C499#535semidirect
104. #120D499semidirect
119. C2×D4C2×D499semidirect
129. C22⋊C4C2×D499semidirect

Maximal subgroups

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

subgroupindex
C2×#225478102
C22×C22⋊D4992
#306303472
#306303372
#306303242
#306303232
#306303212
#306303202
#306303192
#306303072
#120×C4992
#535499