Finite Group Databasebeta

← #14580974

Subgroups — #14580974

Order 2624.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×D4×D41C211yesmaximal, characteristic, complemented
2#13050153C211yesmaximal, characteristic, complemented
3#13050147C212yesmaximal, complemented
4#13050140C211yesmaximal, characteristic, complemented
5#13050138C211yesmaximal, characteristic, complemented
6#13050136C212yesmaximal, complemented
7#13050132C212yesmaximal, complemented
8D4×Dic41C211yesmaximal, characteristic, complemented
9C4×C22⋊D41C211yesmaximal, characteristic, complemented
10C2×#10620281C212yesmaximal, complemented
11C2×#41×C41C211yesmaximal, characteristic, complemented
12C23×D41C2212yes—
13#41×C41—24no—
14C2×Q8×C41C2211yescharacteristic, complemented
15C2×D4×C41C2211yescharacteristic
16C2×D4×C41C2212yescomplemented
17C22×C4×C41C2212yescomplemented
18C22×C4×C41C2211yescharacteristic, complemented
19C2×C22⋊D41C2211yescharacteristic
20C2×C22⋊D41C2212yes—
21C2×C22⋊D41C2212yescomplemented
22C22×Dic41C2212yescomplemented
23D4×D41—24no—
24C2×D164C2211yescharacteristic
25C2×C4×D41C2211yescharacteristic
26C22⋊Dic41C2211yescharacteristic, complemented
27C22⋊Dic41C2212yescomplemented
28#10620281C2211yescharacteristic
29#10620281C2212yes—
30#10620281C2212yescomplemented
31#10620281C2212yescomplemented
32#10620281C2212yescomplemented
33C4⋊Dic41C2211yescharacteristic, complemented
34#10620279C2211yescharacteristic, complemented
35#10620279C2212yescomplemented
36C4×Dic41C2211yescharacteristic, complemented
37C23×C41C2311yescharacteristic
38C23×C41C2312yes—
39C22×D41—24no—
40C22×D41—24no—
41C22×D41—42no—
42C22×D41C2312yes—
43C22×D41C2311yescharacteristic
44Q8×C41—22no—
45D4×C41—24no—
46D4×C41D414yescomplemented
47C2×C4×C41—24no—
48C2×C4×C41—22no—
49C2×C4×C41C2311yescharacteristic
50C2×C4×C41C2312yes—
51C2×C4×C41C2311yescharacteristic
52C22⋊D41—24no—
53C22⋊D41—22no—
54C22⋊D41—42no—
55C2×Dic41—42no—
56C2×Dic41C2311yescharacteristic
57C2×Dic41C2311yescharacteristic
58C2×Dic41C2311yescharacteristic
59C2×Dic41C2312yes—
60D164—22no—
61C4×D41—22no—
62C22×C41—22no—
63C22×C41—22no—
64C22×C41—21no—
65C22×C41—21no—
66C22×C41—21no—
67C22×C41C2×D414yes—
68C22×C41C2411yescharacteristic
69C2×D41—21no—
70C2×D41—21no—
71C2×D41—22no—
72C2×D41—22no—
73C2×D41—22no—
74C2×D41—48no—
75C2×D41#4112yescomplemented
76C4×C41—21no—
77C4×C41—22no—
78C4×C41C2×D412yes—
79Dic41—21no—
80Dic41—21no—
81Dic41—21no—
82Dic41—22no—
83C2×C41—24no—
84C2×C41—41no—
85C2×C41C22×D411yescharacteristic
86C2×C41C2×#4111yescharacteristic
87C2×C41H(5,𝔽2)11yescharacteristic
88D41—22no—
89D41—42no—
90#546—411nomaximal, Sylow
91C41#54611yescharacteristic, complemented, Sylow
92C2×#41D4111yescharacteristic, complemented
93C22×D4—411no—
94#124—411no—
95#123—412no—
96C22⋊Q8—411no—
97#121—412no—
98#121—411no—
99#120—412no—
100C4×D4—411no—
101C4×D4—411no—
102C2×C22⋊C4—412no—
103C24—412no—
104#41—24no—
105C2×Q8C2×D4111yescharacteristic, complemented
106C2×D4—411no—
107C2×D4—412no—
108C2×D4—412no—
109C2×D4—411no—
110C2×D4—824no—
111C2×D4C2×D4111yescharacteristic
112C2×D4C2×D4112yescomplemented
113C22×C4—412no—
114C22×C4—411no—
115C22×C4C2×D4112yescomplemented
116C22×C4C2×D4111yescharacteristic, complemented
117C4⋊C4—411no—
118C4⋊C4—411no—
119C4⋊C4—412no—
120C22⋊C4—412no—
121C22⋊C4—411no—
122C22⋊C4—411no—
123C22⋊C4—412no—
124C22⋊C4—412no—
125C22⋊C4—412no—
126C22⋊C4—412no—
127C42—411no—
128C23—411no—
129C23—412no—
130C23—824no—
131C23—824no—
132C23—1642no—
133C23C22×D4111yescharacteristic
134C23C22×D4112yes—
135Q8—22no—
136D4—24no—
137D4—822no—
138D4—824no—
139D4—822no—
140D4—1642no—
141D4C22⋊D4114yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—411no—
145C2×C4—411no—
146C2×C4—412no—
147C2×C4—411no—
148C2×C4—822no—
149C2×C4—1642no—
150C2×C4C22×D4111yescharacteristic
151C2×C4C22×D4112yes—
152C2×C4C22×D4111yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—412no—
159C22—821no—
160C22—821no—
161C22—822no—
162C22—822no—
163C22—822no—
164C22—1648no—
165C22C2×C22⋊D4114yes—
166C22C23×D4111yescharacteristic
167C4—21no—
168C4—22no—
169C4—821no—
170C4—821no—
171C4—821no—
172C4—822no—
173C4C2×C22⋊D4112yes—
174C2—24no—
175C2—41no—
176C2—822no—
177C2—1642no—
178C2C22×C22⋊D4111yescharacteristic
179C2#41×D4111yescharacteristic
180C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC2×#41×C41C2
hypercenterC2×#41D41
hypocenterC41#546
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D41C2semidirect
2. #13050153C2semidirect
3. #13050147C2semidirect
4. #13050140C2semidirect
5. #13050138C2semidirect
6. #13050136C2semidirect
7. #13050132C2semidirect
8. D4×Dic41C2semidirect
9. C4×C22⋊D41C2semidirect
10. C2×#10620281C2semidirect
11. C2×#41×C41C2semidirect
14. C2×Q8×C41C22semidirect
16. C2×D4×C41C22semidirect
17. C22×C4×C41C22semidirect
18. C22×C4×C41C22semidirect
21. C2×C22⋊D41C22semidirect
22. C22×Dic41C22semidirect
26. C22⋊Dic41C22semidirect
27. C22⋊Dic41C22semidirect
30. #10620281C22semidirect
31. #10620281C22semidirect
32. #10620281C22semidirect
33. C4⋊Dic41C22semidirect
34. #10620279C22semidirect
35. #10620279C22semidirect
36. C4×Dic41C22semidirect
46. D4×C41D4semidirect
75. C2×D41#41semidirect
91. C41#546semidirect
92. C2×#41D41semidirect
105. C2×Q8C2×D41semidirect
112. C2×D4C2×D41semidirect
115. C22×C4C2×D41semidirect
116. C22×C4C2×D41semidirect
141. D4C22⋊D41semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D412
#130501532
#130501472
#130501402
#130501382
#130501362
#130501322
D4×Dic412
C4×C22⋊D412
C2×#106202812
C2×#41×C412
#54641