Finite Group Databasebeta

← #44543608

Subgroups — #44543608

Order 31936.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4×D499C211yesmaximal, characteristic, complemented
3#30630333C212yesmaximal, complemented
4#30630331C211yesmaximal, characteristic, complemented
5#30630330C211yesmaximal, characteristic, complemented
6#30630322C211yesmaximal, characteristic, complemented
7#30630319C212yesmaximal, complemented
8D4×Dic499C212yesmaximal, complemented
9(C22⋊D499)⋊C4C212yesmaximal, complemented
10#30630309C211yesmaximal, characteristic, complemented
11#121×C499C211yesmaximal, characteristic, complemented
12C23×D499C2211yescharacteristic
13#22547810—24no—
14C2×Dic998C2211yescharacteristic, complemented
15C2×C22⋊D499C2212yes—
16C2×C22⋊D499C2212yes—
17C22×Dic499C2211yescharacteristic
18C22×Dic499C2212yescomplemented
19C2×C4×D499—24no—
20C2×C4×D499C2211yescharacteristic
21C2×C4×D499C2211yescharacteristic
22C2×C4×D499C2211yescharacteristic
23C2×C4×D499C2211yescharacteristic
24C4⋊Dic499C2211yescharacteristic, complemented
25C4⋊Dic499C2212yescomplemented
26Dic499⋊C4C2212yescomplemented
27C22⋊Dic499C2212yes—
28C22⋊Dic499C2212yescomplemented
29(C2×D499)⋊C4C2212yes—
30(C2×D499)⋊C4C2212yes—
31C4×Dic499C2212yescomplemented
32C2×D4×C499C2212yes—
33C2×D4×C499C2211yescharacteristic, complemented
34C22×C4×C499C2211yescharacteristic
35C4⋊C4×C499C2211yescharacteristic, complemented
36C22⋊C4×C499C2212yescomplemented
37C22×D499—22no—
38C22×D499—22no—
39C22×D499—22no—
40C22×D499C2311yescharacteristic
41C22×D499C2311yescharacteristic
42Dic998—22no—
43C22⋊D499—24no—
44C22⋊D499—24no—
45C2×Dic499—22no—
46C2×Dic499—24no—
47C2×Dic499C2312yes—
48C2×Dic499C2312yes—
49C2×Dic499C2311yescharacteristic
50C2×Dic499C2311yescharacteristic
51C4×D499—22no—
52C4×D499—22no—
53C4×D499—22no—
54C4×D499D414yescomplemented
55C23×C499C2312yes—
56C23×C499C2311yescharacteristic
57D4×C499—24no—
58D4×C499—22no—
59C2×C4×C499—22no—
60C2×C4×C499C2311yescharacteristic
61C2×C4×C499C2312yes—
62C2×C4×C499C2311yescharacteristic
63C22×C499—21no—
64C22×C499—21no—
65C22×C499—22no—
66C22×C499—22no—
67C22×C499—22no—
68C22×C499#4112yescomplemented
69C22×C499C2411yescharacteristic
70C2×D499—28no—
71C2×D499—21no—
72C2×D499—21no—
73C2×D499—21no—
74C2×D499—21no—
75C2×D499C2×D412yes—
76C2×D499#4112yescomplemented
77C4×C499—21no—
78C4×C499—22no—
79C4×C499C2×D412yes—
80Dic499—21no—
81Dic499—22no—
82Dic499—22no—
83Dic499C2×D412yes—
84C2×C499—22no—
85C2×C499—42no—
86C2×C499C22×D411yescharacteristic
87C2×C499C2×#4111yescharacteristic
88C2×C499C2×#4111yescharacteristic
89D499—22no—
90D499—22no—
91C499#52511yescharacteristic, complemented, Sylow
92#525—4991nomaximal, Sylow
93C2×#41—4991no—
94C23×C4—4991no—
95#123—4992no—
96C22⋊Q8—4991no—
97C22⋊Q8—4991no—
98#121—4991no—
99#121D49911yescharacteristic, complemented
100#120—4992no—
101C4×D4—4992no—
102C4×D4—4992no—
103#117—4991no—
104C24—4991no—
105#41—9984no—
106C2×Q8—4991no—
107C2×D4—4992no—
108C2×D4—4992no—
109C2×D4C2×D49912yes—
110C2×D4C2×D49911yescharacteristic, complemented
111C22×C4—9984no—
112C22×C4—4991no—
113C22×C4—4992no—
114C22×C4—4991no—
115C22×C4—4991no—
116C22×C4—4991no—
117C22×C4—4991no—
118C22×C4C2×D49911yescharacteristic
119C4⋊C4—4992no—
120C4⋊C4—4991no—
121C4⋊C4—4992no—
122C4⋊C4C2×D49911yescharacteristic, complemented
123C22⋊C4—4992no—
124C22⋊C4—4992no—
125C22⋊C4—4992no—
126C22⋊C4—4992no—
127C22⋊C4C2×D49912yescomplemented
128C42—4992no—
129C23—9982no—
130C23—9982no—
131C23—9982no—
132C23—4991no—
133C23—4991no—
134C23C22×D49912yes—
135C23C22×D49911yescharacteristic
136Q8—9982no—
137D4—24no—
138D4—22no—
139D4—9984no—
140D4—9984no—
141C2×C4—22no—
142C2×C4—9982no—
143C2×C4—9982no—
144C2×C4—9982no—
145C2×C4—9984no—
146C2×C4—9982no—
147C2×C4—4992no—
148C2×C4—4991no—
149C2×C4—4992no—
150C2×C4—4991no—
151C2×C4—4994no—
152C2×C4C22×D49912yes—
153C2×C4C22×D49911yescharacteristic
154C2×C4C22×D49911yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—9988no—
161C22—9981no—
162C22—9981no—
163C22—9981no—
164C22—9981no—
165C22—4992no—
166C22—4992no—
167C22#2254781012yescomplemented
168C22C23×D49911yescharacteristic
169C4—21no—
170C4—22no—
171C4—9981no—
172C4—9982no—
173C4—9982no—
174C4—4992no—
175C4D4×D49912yes—
176C2—22no—
177C2—42no—
178C2—9982no—
179C2—9982no—
180C2C2×D4×D49911yescharacteristic
181C2#41×D49911yescharacteristic
182C2C2×#2254781011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#121×C499C2
hypercenter#121D499
hypocenterC499#525
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22547810C2semidirect
2. C22×C4×D499C2semidirect
3. #30630333C2semidirect
4. #30630331C2semidirect
5. #30630330C2semidirect
6. #30630322C2semidirect
7. #30630319C2semidirect
8. D4×Dic499C2semidirect
9. (C22⋊D499)⋊C4C2semidirect
10. #30630309C2semidirect
11. #121×C499C2semidirect
14. C2×Dic998C22semidirect
18. C22×Dic499C22semidirect
24. C4⋊Dic499C22semidirect
25. C4⋊Dic499C22semidirect
26. Dic499⋊C4C22semidirect
28. C22⋊Dic499C22semidirect
31. C4×Dic499C22semidirect
33. C2×D4×C499C22semidirect
35. C4⋊C4×C499C22semidirect
36. C22⋊C4×C499C22semidirect
54. C4×D499D4semidirect
68. C22×C499#41semidirect
76. C2×D499#41semidirect
91. C499#525semidirect
99. #121D499semidirect
110. C2×D4C2×D499semidirect
122. C4⋊C4C2×D499semidirect
127. C22⋊C4C2×D499semidirect
167. C22#22547810semidirect

Maximal subgroups

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

subgroupindex
C2×#225478102
C22×C4×D4992
#306303332
#306303312
#306303302
#306303222
#306303192
D4×Dic4992
(C22⋊D499)⋊C42
#306303092
#121×C4992
#525499