Finite Group Databasebeta

← #44543664

Subgroups — #44543664

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×#22547811C211yesmaximal, characteristic, complemented
2C2×D4×D499C211yesmaximal, characteristic, complemented
3#30630347C212yesmaximal, complemented
4#30630337C212yesmaximal, complemented
5#30630326C211yesmaximal, characteristic, complemented
6#30630325C211yesmaximal, characteristic, complemented
7#30630322C211yesmaximal, characteristic, complemented
8#30630321C212yesmaximal, complemented
9#30630319C212yesmaximal, complemented
10#30630309C211yesmaximal, characteristic, complemented
11#121×C499C211yesmaximal, characteristic, complemented
12C23×D499C2212yes—
13#22547811—24no—
14C2×Dic998C2211yescharacteristic, complemented
15C2×D1996C2211yescharacteristic
16C2×D1996C2211yescharacteristic
17C2×D1996C2212yescomplemented
18C2×C22⋊D499C2211yescharacteristic
19C2×C22⋊D499C2212yes—
20C2×C22⋊D499C2211yescharacteristic, complemented
21C2×C22⋊D499C2212yescomplemented
22C2×C22⋊D499C2212yescomplemented
23D4×D499—24no—
24C2×C4×D499C2211yescharacteristic
25C2×C4×D499C2211yescharacteristic, complemented
26C4⋊Dic499C2211yescharacteristic, complemented
27C22⋊Dic499C2212yescomplemented
28(C2×D499)⋊C4C2212yes—
29(C2×D499)⋊C4C2212yescomplemented
30(C2×D499)⋊C4C2212yescomplemented
31C4×Dic499C2212yescomplemented
32C2×D4×C499C2211yescharacteristic
33C2×D4×C499C2212yescomplemented
34C22×C4×C499C2211yescharacteristic, complemented
35C4⋊C4×C499C2211yescharacteristic, complemented
36C22⋊C4×C499C2212yescomplemented
37C22×D499—24no—
38C22×D499—42no—
39C22×D499—42no—
40C22×D499C2312yes—
41C22×D499C2311yescharacteristic
42C22×D499C2311yescharacteristic
43Dic998—22no—
44D1996—22no—
45D1996—22no—
46D1996—42no—
47C22⋊D499—22no—
48C22⋊D499—24no—
49C22⋊D499—22no—
50C22⋊D499—42no—
51C22⋊D499—42no—
52C2×Dic499C2312yes—
53C2×Dic499C2311yescharacteristic
54C2×Dic499C2311yescharacteristic
55C4×D499—22no—
56C4×D499D414yescomplemented
57C23×C499C2312yes—
58C23×C499C2311yescharacteristic
59D4×C499—22no—
60D4×C499—42no—
61C2×C4×C499—22no—
62C2×C4×C499C2311yescharacteristic
63C2×C4×C499C2312yes—
64C2×C4×C499C2311yescharacteristic
65C22×C499—21no—
66C22×C499—22no—
67C22×C499—21no—
68C22×C499—22no—
69C22×C499—22no—
70C22×C499—21no—
71C22×C499C2411yescharacteristic
72C2×D499—21no—
73C2×D499—21no—
74C2×D499—21no—
75C2×D499—22no—
76C2×D499—21no—
77C2×D499—22no—
78C2×D499—21no—
79C2×D499—22no—
80C2×D499—48no—
81C2×D499C2×D412yes—
82C4×C499—21no—
83C4×C499—22no—
84C4×C499C2×D412yes—
85Dic499—21no—
86Dic499—22no—
87Dic499C2×D412yes—
88C2×C499—42no—
89C2×C499—41no—
90C2×C499C22×D411yescharacteristic
91C2×C499H(5,𝔽2)11yescharacteristic
92C2×C499H(5,𝔽2)11yescharacteristic
93D499—22no—
94D499—41no—
95D499—42no—
96C499#53511yescharacteristic, complemented, Sylow
97#535—4991nomaximal, Sylow
98C2×#41—4991no—
99C22×D4—4991no—
100#127—4992no—
101#124—4992no—
102#121—4991no—
103#121—4991no—
104#121—4991no—
105#121D49911yescharacteristic, complemented
106#120—4992no—
107#120—4992no—
108#117—4991no—
109C24—4992no—
110#41—9984no—
111C2×Q8—4991no—
112C2×D4—9984no—
113C2×D4—4992no—
114C2×D4—4992no—
115C2×D4—4991no—
116C2×D4—4992no—
117C2×D4—4991no—
118C2×D4—4992no—
119C2×D4—4991no—
120C2×D4—4991no—
121C2×D4C2×D49911yescharacteristic
122C2×D4C2×D49912yescomplemented
123C22×C4—4991no—
124C22×C4—4991no—
125C22×C4C2×D49911yescharacteristic, complemented
126C4⋊C4—4991no—
127C4⋊C4C2×D49911yescharacteristic, complemented
128C22⋊C4—4992no—
129C22⋊C4—4992no—
130C22⋊C4—4992no—
131C22⋊C4—4992no—
132C22⋊C4C2×D49912yescomplemented
133C42—4992no—
134C23—19962no—
135C23—19962no—
136C23—9984no—
137C23—4992no—
138C23—4991no—
139C23—4991no—
140C23C22×D49912yes—
141C23C22×D49911yescharacteristic
142Q8—9982no—
143D4—22no—
144D4—42no—
145D4—19962no—
146D4—19962no—
147D4—19962no—
148D4—9982no—
149D4—9982no—
150D4—9984no—
151D4—9982no—
152D4—9982no—
153C2×C4—22no—
154C2×C4—9982no—
155C2×C4—4992no—
156C2×C4—4991no—
157C2×C4—4991no—
158C2×C4—4994no—
159C2×C4C22×D49912yes—
160C2×C4C22×D49911yescharacteristic
161C2×C4C22×D49911yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—19968no—
169C22—9981no—
170C22—9982no—
171C22—9981no—
172C22—9982no—
173C22—9981no—
174C22—9982no—
175C22—9981no—
176C22—9981no—
177C22—4992no—
178C22C23×D49911yescharacteristic
179C4—21no—
180C4—22no—
181C4—9981no—
182C4—9982no—
183C4—4992no—
184C4D4×D49912yes—
185C2—42no—
186C2—41no—
187C2—19962no—
188C2—19961no—
189C2—9982no—
190C2C2×D4×D49911yescharacteristic
191C2#3063039611yescharacteristic
192C2#3063039711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#121×C499C2
hypercenter#121D499
hypocenterC499#535
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22547811C2semidirect
2. C2×D4×D499C2semidirect
3. #30630347C2semidirect
4. #30630337C2semidirect
5. #30630326C2semidirect
6. #30630325C2semidirect
7. #30630322C2semidirect
8. #30630321C2semidirect
9. #30630319C2semidirect
10. #30630309C2semidirect
11. #121×C499C2semidirect
14. C2×Dic998C22semidirect
17. C2×D1996C22semidirect
20. C2×C22⋊D499C22semidirect
21. C2×C22⋊D499C22semidirect
22. C2×C22⋊D499C22semidirect
25. C2×C4×D499C22semidirect
26. C4⋊Dic499C22semidirect
27. C22⋊Dic499C22semidirect
29. (C2×D499)⋊C4C22semidirect
30. (C2×D499)⋊C4C22semidirect
31. C4×Dic499C22semidirect
33. C2×D4×C499C22semidirect
34. C22×C4×C499C22semidirect
35. C4⋊C4×C499C22semidirect
36. C22⋊C4×C499C22semidirect
56. C4×D499D4semidirect
96. C499#535semidirect
105. #121D499semidirect
122. C2×D4C2×D499semidirect
125. C22×C4C2×D499semidirect
127. C4⋊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
C2×#225478112
C2×D4×D4992
#306303472
#306303372
#306303262
#306303252
#306303222
#306303212
#306303192
#306303092
#121×C4992
#535499