Finite Group Databasebeta

← #38734571

Subgroups — #38734571

Order 24896.

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×D389C211yesmaximal, characteristic
2C4×D1556C211yesmaximal, characteristic, complemented
3D4×Dic389C211yesmaximal, characteristic, complemented
4#27159346C211yesmaximal, characteristic, complemented
5C4×C22⋊D389C212yesmaximal, complemented
6#27159344C212yesmaximal, complemented
7#27159342C211yesmaximal, characteristic, complemented
8#27159341C211yesmaximal, characteristic, complemented
9C2×#20261943C212yesmaximal, complemented
10C22⋊C4×D389C212yesmaximal, complemented
11C4×D4×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yes—
13C2×D1556C2211yescharacteristic
14C2×C22⋊D389C2212yes—
15D4×D389C418yescomplemented
16C22×Dic389C2212yescomplemented
17C2×C4×D389C2211yescharacteristic
18C2×C4×D389C2212yescomplemented
19C2×C4×D389C2212yescomplemented
20C4⋊Dic389C2211yescharacteristic, complemented
21#20261945C2211yescharacteristic, complemented
22#20261945C2211yescharacteristic, complemented
23C22⋊Dic389C2212yescomplemented
24#20261943C2211yescharacteristic
25#20261943C2212yes—
26#20261943C2211yescharacteristic
27#20261943C2212yescomplemented
28#20261943C2212yescomplemented
29C4×Dic389C2211yescharacteristic, complemented
30C4×Dic389C2212yescomplemented
31C2×D4×C389C2211yescharacteristic
32C22×C4×C389C2212yescomplemented
33C4⋊C4×C389C2211yescharacteristic, complemented
34C22⋊C4×C389C2212yescomplemented
35C42×C389C2211yescharacteristic, complemented
36C22×D389—42no—
37C22×D389—42no—
38C22×D389C2×C418yescomplemented
39C22×D389C2311yescharacteristic
40C22×D389C2312yes—
41D1556C2×C414yescomplemented
42C22⋊D389C2×C418yescomplemented
43C2×Dic389—42no—
44C2×Dic389C2311yescharacteristic
45C2×Dic389C2312yes—
46C2×Dic389C2311yescharacteristic
47C2×Dic389C2311yescharacteristic
48C4×D389—42no—
49C4×D389—42no—
50C4×D389C2×C414yescomplemented
51C23×C389C2312yes—
52D4×C389C2×C414yescomplemented
53C2×C4×C389—42no—
54C2×C4×C389C2311yescharacteristic
55C2×C4×C389C2311yescharacteristic
56C2×C4×C389C2312yes—
57C2×C4×C389C2311yescharacteristic
58C22×C389—22no—
59C22×C389—22no—
60C22×C389C22×C414yes—
61C22×C389C2411yescharacteristic
62C2×D389—21no—
63C2×D389—21no—
64C2×D389—22no—
65C2×D389—22no—
66C2×D389—48no—
67C2×D389C22×C414yes—
68C2×D389C22×C412yes—
69C4×C389—21no—
70C4×C389—22no—
71C4×C389—21no—
72C4×C389C22×C412yes—
73Dic389—21no—
74Dic389—22no—
75Dic389—21no—
76Dic389C22×C412yes—
77C2×C389—24no—
78C2×C389C23×C411yescharacteristic
79C2×C389H(5,𝔽2)11yescharacteristic
80C2×C389H(5,𝔽2)11yescharacteristic
81D389—22no—
82D389—24no—
83C389#51811yescharacteristic, complemented, Sylow
84#518—3891nomaximal, Sylow
85C22×D4—3891no—
86C4×D4—3891no—
87C4×D4—3892no—
88C4×D4—3891no—
89C4×D4—3892no—
90C4×D4—3891no—
91C4×D4D38911yescharacteristic, complemented
92#117—3891no—
93#117—3891no—
94C2×C22⋊C4—3892no—
95C2×C22⋊C4—3892no—
96C24—3892no—
97C2×D4—3892no—
98C2×D4—3898no—
99C2×D4—3891no—
100C2×D4C2×D38911yescharacteristic
101C22×C4—3892no—
102C22×C4—3892no—
103C22×C4—3892no—
104C22×C4—3891no—
105C22×C4C2×D38912yescomplemented
106C4⋊C4—3891no—
107C4⋊C4—3891no—
108C4⋊C4—3891no—
109C4⋊C4C2×D38911yescharacteristic, complemented
110C22⋊C4—3892no—
111C22⋊C4—3892no—
112C22⋊C4—3891no—
113C22⋊C4—3891no—
114C22⋊C4—3892no—
115C22⋊C4—3892no—
116C22⋊C4C2×D38912yescomplemented
117C42—3891no—
118C42—3892no—
119C42C2×D38911yescharacteristic, complemented
120C23—15562no—
121C23—15562no—
122C23—3891no—
123C23—3892no—
124C23—3898no—
125C23C22×D38912yes—
126D4—3898no—
127D4—3894no—
128D4C4×D38914yescomplemented
129C2×C4—42no—
130C2×C4—15562no—
131C2×C4—15562no—
132C2×C4—15562no—
133C2×C4—3891no—
134C2×C4—3892no—
135C2×C4—3891no—
136C2×C4—3891no—
137C2×C4—3894no—
138C2×C4C22×D38912yes—
139C2×C4C22×D38911yescharacteristic
140C2×C4C22×D38911yescharacteristic
141C2×C4C22×D38911yescharacteristic
142C22—22no—
143C22—22no—
144C22—7782no—
145C22—7781no—
146C22—7782no—
147C22—7781no—
148C22—15568no—
149C22—3892no—
150C22—3894no—
151C22C2×C4×D38914yes—
152C22C23×D38911yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—7781no—
157C4—7782no—
158C4—7781no—
159C4—3892no—
160C4C2×C4×D38912yes—
161C2—24no—
162C2—7782no—
163C2—7784no—
164C2C22×C4×D38911yescharacteristic
165C2#2715942911yescharacteristic
166C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutatorC2×C389C23×C4
FittingC4×D4×C389C2
socle, cosocleC22×C389C24
prime radicalC2×D4×D389C2
hypercenterC4×D4D389
hypocenterC389#518
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1556C2semidirect
3. D4×Dic389C2semidirect
4. #27159346C2semidirect
5. C4×C22⋊D389C2semidirect
6. #27159344C2semidirect
7. #27159342C2semidirect
8. #27159341C2semidirect
9. C2×#20261943C2semidirect
10. C22⋊C4×D389C2semidirect
11. C4×D4×C389C2semidirect
15. D4×D389C4semidirect
16. C22×Dic389C22semidirect
18. C2×C4×D389C22semidirect
19. C2×C4×D389C22semidirect
20. C4⋊Dic389C22semidirect
21. #20261945C22semidirect
22. #20261945C22semidirect
23. C22⋊Dic389C22semidirect
27. #20261943C22semidirect
28. #20261943C22semidirect
29. C4×Dic389C22semidirect
30. C4×Dic389C22semidirect
32. C22×C4×C389C22semidirect
33. C4⋊C4×C389C22semidirect
34. C22⋊C4×C389C22semidirect
35. C42×C389C22semidirect
38. C22×D389C2×C4semidirect
41. D1556C2×C4semidirect
42. C22⋊D389C2×C4semidirect
50. C4×D389C2×C4semidirect
52. D4×C389C2×C4semidirect
83. C389#518semidirect
91. C4×D4D389semidirect
105. C22×C4C2×D389semidirect
109. C4⋊C4C2×D389semidirect
116. C22⋊C4C2×D389semidirect
119. C42C2×D389semidirect
128. D4C4×D389semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3892
C4×D15562
D4×Dic3892
#271593462
C4×C22⋊D3892
#271593442
#271593422
#271593412
C2×#202619432
C22⋊C4×D3892
C4×D4×C3892
#518389