Finite Group Databasebeta

← #14580901

Subgroups — #14580901

Order 2624.

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×#10620308C211yesmaximal, characteristic, complemented
2C22×C22⋊D41C211yesmaximal, characteristic, complemented
3#13050160C212yesmaximal, complemented
4#13050150C212yesmaximal, complemented
5#13050137C212yesmaximal, complemented
6#13050136C212yesmaximal, complemented
7#13050134C211yesmaximal, characteristic, complemented
8#13050133C211yesmaximal, characteristic, complemented
9#13050132C211yesmaximal, characteristic, complemented
10#13050120C211yesmaximal, characteristic, complemented
11#120×C41C211yesmaximal, characteristic, complemented
12C24×C41C2211yescharacteristic
13C23×D41C2211yescharacteristic
14C2×D4×C41C2211yescharacteristic
15C2×D4×C41C2212yescomplemented
16C2×C22⋊D41—24no—
17C2×C22⋊D41C2211yescharacteristic
18C2×C22⋊D41C2212yes—
19C2×C22⋊D41C2212yes—
20C2×C22⋊D41C2211yescharacteristic, complemented
21C2×C22⋊D41C2212yescomplemented
22C2×C22⋊D41C2212yescomplemented
23C22×Dic41C2211yescharacteristic
24C22×Dic41C2211yescharacteristic, complemented
25#10620308—24no—
26C2×D164C2212yescomplemented
27C2×C4×D41C2211yescharacteristic, complemented
28C2×Dic82C2211yescharacteristic, complemented
29C22⋊C4×C41C2211yescharacteristic
30C22⋊C4×C41C2212yescomplemented
31C22⋊Dic41C2211yescharacteristic
32C22⋊Dic41C2212yescomplemented
33#10620281C2212yescomplemented
34#10620281C2212yescomplemented
35#10620279C2212yescomplemented
36C4×Dic41C2212yescomplemented
37C23×C41—22no—
38C23×C41—42no—
39C23×C41C2312yes—
40C23×C41C2311yescharacteristic
41C23×C41C2311yescharacteristic
42C22×D41—22no—
43C22×D41—42no—
44C22×D41C2312yes—
45C22×D41C2311yescharacteristic
46D4×C41—22no—
47D4×C41—42no—
48C2×C4×C41C2312yes—
49C2×C4×C41C2311yescharacteristic
50C22⋊D41—22no—
51C22⋊D41—22no—
52C22⋊D41—24no—
53C22⋊D41—24no—
54C22⋊D41—42no—
55C22⋊D41—42no—
56C2×Dic41—22no—
57C2×Dic41D414yescomplemented
58C2×Dic41C2312yes—
59C2×Dic41C2311yescharacteristic
60C2×Dic41C2311yescharacteristic
61C2×Dic41C2311yescharacteristic
62D164—42no—
63C4×D41—22no—
64Dic82—22no—
65C22×C41—22no—
66C22×C41—21no—
67C22×C41—22no—
68C22×C41—22no—
69C22×C41—22no—
70C22×C41—22no—
71C22×C41—44no—
72C22×C41C2×D412yes—
73C22×C41C2411yescharacteristic
74C2×D41—21no—
75C2×D41—22no—
76C2×D41—22no—
77C2×D41—22no—
78C2×D41—22no—
79C2×D41—44no—
80C4×C41—21no—
81C4×C41—22no—
82Dic41—21no—
83Dic41—22no—
84Dic41C2×D412yes—
85Dic41C2×D412yes—
86C2×C41—22no—
87C2×C41—41no—
88C2×C41—42no—
89C2×C41C22×D411yescharacteristic
90C2×C41H(5,𝔽2)12yes—
91D41—41no—
92D41—42no—
93#535—411nomaximal, Sylow
94C41#53511yescharacteristic, complemented, Sylow
95C2×#41—411no—
96C22×D4—411no—
97#127—412no—
98#124—412no—
99#121—412no—
100#121—412no—
101#120—411no—
102#120—411no—
103#120—411no—
104#120D4111yescharacteristic, complemented
105#117—411no—
106C24—411no—
107C24C2×D4111yescharacteristic
108#41—824no—
109C2×Q8—411no—
110C2×D4—411no—
111C2×D4—412no—
112C2×D4—412no—
113C2×D4—411no—
114C2×D4—412no—
115C2×D4—412no—
116C2×D4—412no—
117C2×D4—824no—
118C2×D4C2×D4111yescharacteristic
119C2×D4C2×D4112yescomplemented
120C22×C4—411no—
121C22×C4—411no—
122C22×C4—411no—
123C4⋊C4—412no—
124C22⋊C4—411no—
125C22⋊C4—412no—
126C22⋊C4—412no—
127C22⋊C4—412no—
128C22⋊C4C2×D4111yescharacteristic
129C22⋊C4C2×D4112yescomplemented
130C42—412no—
131C23—22no—
132C23—42no—
133C23—412no—
134C23—411no—
135C23—822no—
136C23—1642no—
137C23C22×D4112yes—
138C23C22×D4111yescharacteristic
139C23C22×D4111yescharacteristic
140Q8—822no—
141D4—22no—
142D4—42no—
143D4—824no—
144D4—824no—
145D4—822no—
146D4—822no—
147D4—1642no—
148D4—1642no—
149D4—1642no—
150C2×C4—414no—
151C2×C4—411no—
152C2×C4—411no—
153C2×C4—412no—
154C2×C4—411no—
155C2×C4—822no—
156C2×C4—822no—
157C2×C4C22×D4112yes—
158C2×C4C22×D4111yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—821no—
167C22—822no—
168C22—822no—
169C22—822no—
170C22—822no—
171C22—1644no—
172C22D4×D4112yes—
173C22C23×D4111yescharacteristic
174C4—21no—
175C4—22no—
176C4—412no—
177C4—412no—
178C4—821no—
179C4—822no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—1642no—
184C2—1641no—
185C2C2×D4×D4111yescharacteristic
186C2#1305020912yes—
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#120×C41C2
hypercenter#120D41
hypocenterC41#535
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#10620308C2semidirect
2. C22×C22⋊D41C2semidirect
3. #13050160C2semidirect
4. #13050150C2semidirect
5. #13050137C2semidirect
6. #13050136C2semidirect
7. #13050134C2semidirect
8. #13050133C2semidirect
9. #13050132C2semidirect
10. #13050120C2semidirect
11. #120×C41C2semidirect
15. C2×D4×C41C22semidirect
20. C2×C22⋊D41C22semidirect
21. C2×C22⋊D41C22semidirect
22. C2×C22⋊D41C22semidirect
24. C22×Dic41C22semidirect
26. C2×D164C22semidirect
27. C2×C4×D41C22semidirect
28. C2×Dic82C22semidirect
30. C22⋊C4×C41C22semidirect
32. C22⋊Dic41C22semidirect
33. #10620281C22semidirect
34. #10620281C22semidirect
35. #10620279C22semidirect
36. C4×Dic41C22semidirect
57. C2×Dic41D4semidirect
94. C41#535semidirect
104. #120D41semidirect
119. C2×D4C2×D41semidirect
129. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
C2×#106203082
C22×C22⋊D412
#130501602
#130501502
#130501372
#130501362
#130501342
#130501332
#130501322
#130501202
#120×C412
#53541