Finite Group Databasebeta

← #38786586

Subgroups — #38786586

Order 25664.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×D401C211yesmaximal, characteristic
2C4×D1604C211yesmaximal, characteristic, complemented
3D4×Dic401C211yesmaximal, characteristic, complemented
4#27165699C211yesmaximal, characteristic, complemented
5C4×C22⋊D401C212yesmaximal, complemented
6#27165697C212yesmaximal, complemented
7#27165695C211yesmaximal, characteristic, complemented
8#27165694C211yesmaximal, characteristic, complemented
9C2×#20264343C212yesmaximal, complemented
10C22⋊C4×D401C212yesmaximal, complemented
11C4×D4×C401C211yesmaximal, characteristic, complemented
12C23×D401C2212yes—
13C2×D1604C2211yescharacteristic
14C2×C22⋊D401C2212yes—
15D4×D401C418yescomplemented
16C22×Dic401C2212yescomplemented
17C2×C4×D401C2211yescharacteristic
18C2×C4×D401C2212yescomplemented
19C2×C4×D401C2212yescomplemented
20C4⋊Dic401C2211yescharacteristic, complemented
21#20264345C2211yescharacteristic, complemented
22#20264345C2211yescharacteristic, complemented
23C22⋊Dic401C2212yescomplemented
24#20264343C2211yescharacteristic
25#20264343C2212yes—
26#20264343C2211yescharacteristic
27#20264343C2212yescomplemented
28#20264343C2212yescomplemented
29C4×Dic401C2212yescomplemented
30C4×Dic401C2211yescharacteristic, complemented
31C2×D4×C401C2211yescharacteristic
32C22×C4×C401C2212yescomplemented
33C4⋊C4×C401C2211yescharacteristic, complemented
34C22⋊C4×C401C2212yescomplemented
35C42×C401C2211yescharacteristic, complemented
36C22×D401—42no—
37C22×D401—42no—
38C22×D401C2×C418yescomplemented
39C22×D401C2311yescharacteristic
40C22×D401C2312yes—
41D1604C2×C414yescomplemented
42C22⋊D401C2×C418yescomplemented
43C2×Dic401—42no—
44C2×Dic401C2311yescharacteristic
45C2×Dic401C2312yes—
46C2×Dic401C2311yescharacteristic
47C2×Dic401C2311yescharacteristic
48C4×D401—42no—
49C4×D401—42no—
50C4×D401C2×C414yescomplemented
51C23×C401C2312yes—
52D4×C401C2×C414yescomplemented
53C2×C4×C401—42no—
54C2×C4×C401C2311yescharacteristic
55C2×C4×C401C2311yescharacteristic
56C2×C4×C401C2312yes—
57C2×C4×C401C2311yescharacteristic
58C22×C401—22no—
59C22×C401—22no—
60C22×C401C22×C414yes—
61C22×C401C2411yescharacteristic
62C2×D401—22no—
63C2×D401—22no—
64C2×D401—21no—
65C2×D401—21no—
66C2×D401—48no—
67C2×D401C22×C412yes—
68C2×D401C22×C414yes—
69C4×C401—21no—
70C4×C401—22no—
71C4×C401—21no—
72C4×C401C22×C412yes—
73Dic401—21no—
74Dic401—22no—
75Dic401—21no—
76Dic401C22×C412yes—
77C2×C401—24no—
78C2×C401C23×C411yescharacteristic
79C2×C401H(5,𝔽2)11yescharacteristic
80C2×C401H(5,𝔽2)11yescharacteristic
81D401—22no—
82D401—24no—
83C401#51811yescharacteristic, complemented, Sylow
84#518—4011nomaximal, Sylow
85C22×D4—4011no—
86C4×D4—4011no—
87C4×D4—4012no—
88C4×D4—4011no—
89C4×D4—4012no—
90C4×D4—4011no—
91C4×D4D40111yescharacteristic, complemented
92#117—4011no—
93#117—4011no—
94C2×C22⋊C4—4012no—
95C2×C22⋊C4—4012no—
96C24—4012no—
97C2×D4—4012no—
98C2×D4—4018no—
99C2×D4—4011no—
100C2×D4C2×D40111yescharacteristic
101C22×C4—4012no—
102C22×C4—4012no—
103C22×C4—4012no—
104C22×C4—4011no—
105C22×C4C2×D40112yescomplemented
106C4⋊C4—4011no—
107C4⋊C4—4011no—
108C4⋊C4—4011no—
109C4⋊C4C2×D40111yescharacteristic, complemented
110C22⋊C4—4012no—
111C22⋊C4—4012no—
112C22⋊C4—4011no—
113C22⋊C4—4011no—
114C22⋊C4—4012no—
115C22⋊C4—4012no—
116C22⋊C4C2×D40112yescomplemented
117C42—4011no—
118C42—4012no—
119C42C2×D40111yescharacteristic, complemented
120C23—16042no—
121C23—16042no—
122C23—4011no—
123C23—4012no—
124C23—4018no—
125C23C22×D40112yes—
126D4—4018no—
127D4—4014no—
128D4C4×D40114yescomplemented
129C2×C4—42no—
130C2×C4—16042no—
131C2×C4—16042no—
132C2×C4—16042no—
133C2×C4—4011no—
134C2×C4—4012no—
135C2×C4—4011no—
136C2×C4—4011no—
137C2×C4—4014no—
138C2×C4C22×D40112yes—
139C2×C4C22×D40111yescharacteristic
140C2×C4C22×D40111yescharacteristic
141C2×C4C22×D40111yescharacteristic
142C22—22no—
143C22—22no—
144C22—8022no—
145C22—8021no—
146C22—8022no—
147C22—8021no—
148C22—16048no—
149C22—4012no—
150C22—4014no—
151C22C2×C4×D40114yes—
152C22C23×D40111yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—8021no—
157C4—8022no—
158C4—8021no—
159C4—4012no—
160C4C2×C4×D40112yes—
161C2—24no—
162C2—8022no—
163C2—8024no—
164C2C22×C4×D40111yescharacteristic
165C2#2716578211yescharacteristic
166C2#2716578311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D401
commutatorC2×C401C23×C4
FittingC4×D4×C401C2
socle, cosocleC22×C401C24
prime radicalC2×D4×D401C2
hypercenterC4×D4D401
hypocenterC401#518
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1604C2semidirect
3. D4×Dic401C2semidirect
4. #27165699C2semidirect
5. C4×C22⋊D401C2semidirect
6. #27165697C2semidirect
7. #27165695C2semidirect
8. #27165694C2semidirect
9. C2×#20264343C2semidirect
10. C22⋊C4×D401C2semidirect
11. C4×D4×C401C2semidirect
15. D4×D401C4semidirect
16. C22×Dic401C22semidirect
18. C2×C4×D401C22semidirect
19. C2×C4×D401C22semidirect
20. C4⋊Dic401C22semidirect
21. #20264345C22semidirect
22. #20264345C22semidirect
23. C22⋊Dic401C22semidirect
27. #20264343C22semidirect
28. #20264343C22semidirect
29. C4×Dic401C22semidirect
30. C4×Dic401C22semidirect
32. C22×C4×C401C22semidirect
33. C4⋊C4×C401C22semidirect
34. C22⋊C4×C401C22semidirect
35. C42×C401C22semidirect
38. C22×D401C2×C4semidirect
41. D1604C2×C4semidirect
42. C22⋊D401C2×C4semidirect
50. C4×D401C2×C4semidirect
52. D4×C401C2×C4semidirect
83. C401#518semidirect
91. C4×D4D401semidirect
105. C22×C4C2×D401semidirect
109. C4⋊C4C2×D401semidirect
116. C22⋊C4C2×D401semidirect
119. C42C2×D401semidirect
128. D4C4×D401semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4012
C4×D16042
D4×Dic4012
#271656992
C4×C22⋊D4012
#271656972
#271656952
#271656942
C2×#202643432
C22⋊C4×D4012
C4×D4×C4012
#518401