Finite Group Databasebeta

← #14580902

Subgroups — #14580902

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×#10620306C211yesmaximal, characteristic, complemented
2C2×D4×D41C211yesmaximal, characteristic, complemented
3#13050160C212yesmaximal, complemented
4#13050150C212yesmaximal, complemented
5#13050139C211yesmaximal, characteristic, complemented
6#13050138C211yesmaximal, characteristic, complemented
7#13050135C211yesmaximal, characteristic, complemented
8#13050134C212yesmaximal, complemented
9#13050132C212yesmaximal, complemented
10#13050122C211yesmaximal, characteristic, complemented
11#121×C41C211yesmaximal, characteristic, complemented
12C23×D41C2212yes—
13C2×D4×C41C2211yescharacteristic
14C2×D4×C41C2212yescomplemented
15C22×C4×C41C2211yescharacteristic, complemented
16C2×C22⋊D41C2211yescharacteristic
17C2×C22⋊D41C2212yes—
18C2×C22⋊D41C2211yescharacteristic, complemented
19C2×C22⋊D41C2212yescomplemented
20C2×C22⋊D41C2212yescomplemented
21D4×D41—24no—
22#10620306—24no—
23C2×D164C2211yescharacteristic
24C2×D164C2211yescharacteristic
25C2×D164C2212yescomplemented
26C2×C4×D41C2211yescharacteristic
27C2×C4×D41C2211yescharacteristic, complemented
28C2×Dic82C2211yescharacteristic, complemented
29C4⋊C4×C41C2211yescharacteristic, complemented
30C22⋊C4×C41C2212yescomplemented
31C22⋊Dic41C2212yescomplemented
32#10620281C2212yes—
33#10620281C2212yescomplemented
34#10620281C2212yescomplemented
35C4⋊Dic41C2211yescharacteristic, complemented
36C4×Dic41C2212yescomplemented
37C23×C41C2312yes—
38C23×C41C2311yescharacteristic
39C22×D41—24no—
40C22×D41—42no—
41C22×D41—42no—
42C22×D41C2312yes—
43C22×D41C2311yescharacteristic
44C22×D41C2311yescharacteristic
45D4×C41—22no—
46D4×C41—42no—
47C2×C4×C41—22no—
48C2×C4×C41C2312yes—
49C2×C4×C41C2311yescharacteristic
50C2×C4×C41C2311yescharacteristic
51C22⋊D41—22no—
52C22⋊D41—22no—
53C22⋊D41—24no—
54C22⋊D41—42no—
55C22⋊D41—42no—
56C2×Dic41C2312yes—
57C2×Dic41C2311yescharacteristic
58C2×Dic41C2311yescharacteristic
59D164—22no—
60D164—22no—
61D164—42no—
62C4×D41—22no—
63C4×D41D414yescomplemented
64Dic82—22no—
65C22×C41—21no—
66C22×C41—22no—
67C22×C41—21no—
68C22×C41—22no—
69C22×C41—21no—
70C22×C41—22no—
71C22×C41C2411yescharacteristic
72C2×D41—21no—
73C2×D41—21no—
74C2×D41—21no—
75C2×D41—22no—
76C2×D41—21no—
77C2×D41—22no—
78C2×D41—21no—
79C2×D41—22no—
80C2×D41—48no—
81C2×D41C2×D412yes—
82C4×C41—21no—
83C4×C41—22no—
84C4×C41C2×D412yes—
85Dic41—21no—
86Dic41—22no—
87Dic41C2×D412yes—
88C2×C41—42no—
89C2×C41—41no—
90C2×C41C22×D411yescharacteristic
91C2×C41H(5,𝔽2)11yescharacteristic
92C2×C41H(5,𝔽2)11yescharacteristic
93D41—22no—
94D41—41no—
95D41—42no—
96#535—411nomaximal, Sylow
97C41#53511yescharacteristic, complemented, Sylow
98C2×#41—411no—
99C22×D4—411no—
100#127—412no—
101#124—412no—
102#121—411no—
103#121—411no—
104#121—411no—
105#121D4111yescharacteristic, complemented
106#120—412no—
107#120—412no—
108#117—411no—
109C24—412no—
110#41—824no—
111C2×Q8—411no—
112C2×D4—411no—
113C2×D4—412no—
114C2×D4—411no—
115C2×D4—412no—
116C2×D4—412no—
117C2×D4—411no—
118C2×D4—411no—
119C2×D4—412no—
120C2×D4—824no—
121C2×D4C2×D4111yescharacteristic
122C2×D4C2×D4112yescomplemented
123C22×C4—411no—
124C22×C4—411no—
125C22×C4C2×D4111yescharacteristic, complemented
126C4⋊C4—411no—
127C4⋊C4C2×D4111yescharacteristic, complemented
128C22⋊C4—412no—
129C22⋊C4—412no—
130C22⋊C4—412no—
131C22⋊C4—412no—
132C22⋊C4C2×D4112yescomplemented
133C42—412no—
134C23—411no—
135C23—412no—
136C23—411no—
137C23—824no—
138C23—1642no—
139C23—1642no—
140C23C22×D4112yes—
141C23C22×D4111yescharacteristic
142Q8—822no—
143D4—22no—
144D4—42no—
145D4—822no—
146D4—824no—
147D4—822no—
148D4—822no—
149D4—822no—
150D4—1642no—
151D4—1642no—
152D4—1642no—
153C2×C4—22no—
154C2×C4—411no—
155C2×C4—414no—
156C2×C4—412no—
157C2×C4—411no—
158C2×C4—822no—
159C2×C4C22×D4112yes—
160C2×C4C22×D4111yescharacteristic
161C2×C4C22×D4111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—412no—
169C22—821no—
170C22—821no—
171C22—821no—
172C22—822no—
173C22—821no—
174C22—822no—
175C22—821no—
176C22—822no—
177C22—1648no—
178C22C23×D4111yescharacteristic
179C4—21no—
180C4—22no—
181C4—412no—
182C4—821no—
183C4—822no—
184C4D4×D4112yes—
185C2—42no—
186C2—41no—
187C2—822no—
188C2—1642no—
189C2—1641no—
190C2C2×D4×D4111yescharacteristic
191C2#1305020911yescharacteristic
192C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#121×C41C2
hypercenter#121D41
hypocenterC41#535
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10620306C2semidirect
2. C2×D4×D41C2semidirect
3. #13050160C2semidirect
4. #13050150C2semidirect
5. #13050139C2semidirect
6. #13050138C2semidirect
7. #13050135C2semidirect
8. #13050134C2semidirect
9. #13050132C2semidirect
10. #13050122C2semidirect
11. #121×C41C2semidirect
14. C2×D4×C41C22semidirect
15. C22×C4×C41C22semidirect
18. C2×C22⋊D41C22semidirect
19. C2×C22⋊D41C22semidirect
20. C2×C22⋊D41C22semidirect
25. C2×D164C22semidirect
27. C2×C4×D41C22semidirect
28. C2×Dic82C22semidirect
29. C4⋊C4×C41C22semidirect
30. C22⋊C4×C41C22semidirect
31. C22⋊Dic41C22semidirect
33. #10620281C22semidirect
34. #10620281C22semidirect
35. C4⋊Dic41C22semidirect
36. C4×Dic41C22semidirect
63. C4×D41D4semidirect
97. C41#535semidirect
105. #121D41semidirect
122. C2×D4C2×D41semidirect
125. C22×C4C2×D41semidirect
127. C4⋊C4C2×D41semidirect
132. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
C2×#106203062
C2×D4×D412
#130501602
#130501502
#130501392
#130501382
#130501352
#130501342
#130501322
#130501222
#121×C412
#53541