Finite Group Databasebeta

← #14580968

Subgroups — #14580968

Order 2624.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×C22⋊D41C212yesmaximal, complemented
2C2×D4×D41C212yesmaximal, complemented
3#13050160C211yesmaximal, characteristic, complemented
4#13050137C212yesmaximal, complemented
5#13050136C212yesmaximal, complemented
6#13050134C212yesmaximal, complemented
7#13050132C211yesmaximal, characteristic, complemented
8#13050124C212yesmaximal, complemented
9#120×C41C211yesmaximal, characteristic, complemented
10C24×C41C2211yescharacteristic, complemented
11C23×D41C2211yescharacteristic, complemented
12C23×D41C2212yescomplemented
13C2×D4×C41C2212yescomplemented
14C2×D4×C41C2211yescharacteristic, complemented
15C2×C22⋊D41—28no—
16C2×C22⋊D41C2212yes—
17C2×C22⋊D41C2212yescomplemented
18C2×C22⋊D41C2212yescomplemented
19C2×C22⋊D41C2212yescomplemented
20C2×C22⋊D41C2212yescomplemented
21C22×Dic41C2212yescomplemented
22D4×D41—28no—
23C2×D164C2212yescomplemented
24C2×D164C2211yescharacteristic, complemented
25C2×C4×D41C2212yescomplemented
26C22⋊C4×C41C2212yescomplemented
27C22⋊C4×C41C2211yescharacteristic, complemented
28C22⋊Dic41C2211yescharacteristic, complemented
29#10620281C2212yescomplemented
30#10620281C2212yescomplemented
31#10620279C2212yescomplemented
32C4×Dic41C2211yescharacteristic, complemented
33C23×C41—24no—
34C23×C41—41no—
35C23×C41C2311yescharacteristic
36C23×C41C2311yescharacteristic
37C23×C41C2312yes—
38C22×D41—24no—
39C22×D41—24no—
40C22×D41—24no—
41C22×D41—41no—
42C22×D41—42no—
43C22×D41C2312yes—
44C22×D41C2312yes—
45D4×C41—24no—
46D4×C41—41no—
47C2×C4×C41C2311yescharacteristic
48C2×C4×C41C2312yes—
49C22⋊D41—24no—
50C22⋊D41—24no—
51C22⋊D41—24no—
52C22⋊D41—24no—
53C22⋊D41D418yescomplemented
54C2×Dic41—24no—
55C2×Dic41C2312yes—
56C2×Dic41C2312yes—
57D164—24no—
58D164—41no—
59C4×D41—24no—
60C22×C41—22no—
61C22×C41—22no—
62C22×C41—22no—
63C22×C41—22no—
64C22×C41—21no—
65C22×C41—21no—
66C22×C41—44no—
67C22×C41C2×D414yescomplemented
68C22×C41C2411yescharacteristic
69C2×D41—22no—
70C2×D41—22no—
71C2×D41—22no—
72C2×D41—22no—
73C2×D41—22no—
74C2×D41—44no—
75C2×D41—48no—
76C2×D41C2×D414yescomplemented
77C4×C41—22no—
78C4×C41—21no—
79Dic41—22no—
80Dic41C2×D414yescomplemented
81C2×C41—24no—
82C2×C41—41no—
83C2×C41—41no—
84C2×C41C22×D412yes—
85C2×C41H(5,𝔽2)11yescharacteristic
86D41—24no—
87D41—42no—
88D42—411nomaximal, Sylow
89C41D4211yescharacteristic, complemented, Sylow
90C22×D4—412no—
91C22×D4—412no—
92#127—411no—
93#121—412no—
94#121—412no—
95#120—411no—
96#120—412no—
97#120D4111yescharacteristic, complemented
98C4×D4—412no—
99C24—411no—
100C24—412no—
101C24C2×D4111yescharacteristic, complemented
102C2×D4—412no—
103C2×D4—412no—
104C2×D4—412no—
105C2×D4—412no—
106C2×D4—412no—
107C2×D4—412no—
108C2×D4—411no—
109C2×D4—828no—
110C2×D4—828no—
111C2×D4C2×D4112yescomplemented
112C2×D4C2×D4111yescharacteristic, complemented
113C22×C4—412no—
114C22×C4—412no—
115C4⋊C4—412no—
116C22⋊C4—411no—
117C22⋊C4—412no—
118C22⋊C4—412no—
119C22⋊C4C2×D4112yescomplemented
120C22⋊C4C2×D4111yescharacteristic, complemented
121C42—411no—
122C23—24no—
123C23—41no—
124C23—412no—
125C23—412no—
126C23—824no—
127C23—824no—
128C23—824no—
129C23—1642no—
130C23—1641no—
131C23C22×D4111yescharacteristic
132C23C22×D4111yescharacteristic
133C23C22×D4112yes—
134D4—24no—
135D4—41no—
136D4—418no—
137D4—824no—
138D4—824no—
139D4—824no—
140D4—824no—
141D4—824no—
142D4—1641no—
143C2×C4—412no—
144C2×C4—412no—
145C2×C4—824no—
146C2×C4—824no—
147C2×C4C22×D4111yescharacteristic
148C2×C4C22×D4112yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—414no—
157C22—822no—
158C22—822no—
159C22—822no—
160C22—822no—
161C22—822no—
162C22—1648no—
163C22—1644no—
164C22D4×D4114yescomplemented
165C22C23×D4111yescharacteristic
166C4—22no—
167C4—21no—
168C4—414no—
169C4—822no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—824no—
174C2—1642no—
175C2C2×D4×D4112yes—
176C2#1305020911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#120×C41C2
hypercenter#120D41
hypocenterC41D42
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D41C2semidirect
2. C2×D4×D41C2semidirect
3. #13050160C2semidirect
4. #13050137C2semidirect
5. #13050136C2semidirect
6. #13050134C2semidirect
7. #13050132C2semidirect
8. #13050124C2semidirect
9. #120×C41C2semidirect
10. C24×C41C22semidirect
11. C23×D41C22semidirect
12. C23×D41C22semidirect
13. C2×D4×C41C22semidirect
14. C2×D4×C41C22semidirect
17. C2×C22⋊D41C22semidirect
18. C2×C22⋊D41C22semidirect
19. C2×C22⋊D41C22semidirect
20. C2×C22⋊D41C22semidirect
21. C22×Dic41C22semidirect
23. C2×D164C22semidirect
24. C2×D164C22semidirect
25. C2×C4×D41C22semidirect
26. C22⋊C4×C41C22semidirect
27. C22⋊C4×C41C22semidirect
28. C22⋊Dic41C22semidirect
29. #10620281C22semidirect
30. #10620281C22semidirect
31. #10620279C22semidirect
32. C4×Dic41C22semidirect
53. C22⋊D41D4semidirect
67. C22×C41C2×D4semidirect
76. C2×D41C2×D4semidirect
80. Dic41C2×D4semidirect
89. C41D42semidirect
97. #120D41semidirect
101. C24C2×D41semidirect
111. C2×D4C2×D41semidirect
112. C2×D4C2×D41semidirect
119. C22⋊C4C2×D41semidirect
120. C22⋊C4C2×D41semidirect
164. C22D4×D41semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D412
C2×D4×D412
#130501602
#130501372
#130501362
#130501342
#130501322
#130501242
#120×C412
D4241