Finite Group Databasebeta

← #38734731

Subgroups — #38734731

Order 24896.

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⋊D389C212yesmaximal, complemented
2C2×D4×D389C212yesmaximal, complemented
3#27159380C211yesmaximal, characteristic, complemented
4#27159357C212yesmaximal, complemented
5#27159356C212yesmaximal, complemented
6#27159354C212yesmaximal, complemented
7#27159352C211yesmaximal, characteristic, complemented
8#27159344C212yesmaximal, complemented
9#120×C389C211yesmaximal, characteristic, complemented
10C23×D389C2211yescharacteristic, complemented
11C23×D389C2212yescomplemented
12C2×D1556C2212yescomplemented
13C2×D1556C2211yescharacteristic, complemented
14C2×C22⋊D389—28no—
15C2×C22⋊D389C2212yes—
16C2×C22⋊D389C2212yescomplemented
17C2×C22⋊D389C2212yescomplemented
18C2×C22⋊D389C2212yescomplemented
19C2×C22⋊D389C2212yescomplemented
20D4×D389—28no—
21C22×Dic389C2212yescomplemented
22C2×C4×D389C2212yescomplemented
23#20261945C2212yescomplemented
24C22⋊Dic389C2211yescharacteristic, complemented
25#20261943C2212yescomplemented
26#20261943C2212yescomplemented
27C4×Dic389C2211yescharacteristic, complemented
28C24×C389C2211yescharacteristic, complemented
29C2×D4×C389C2212yescomplemented
30C2×D4×C389C2211yescharacteristic, complemented
31C22⋊C4×C389C2212yescomplemented
32C22⋊C4×C389C2211yescharacteristic, complemented
33C22×D389—24no—
34C22×D389—24no—
35C22×D389—24no—
36C22×D389—41no—
37C22×D389—42no—
38C22×D389C2312yes—
39C22×D389C2312yes—
40D1556—24no—
41D1556—41no—
42C22⋊D389—24no—
43C22⋊D389—24no—
44C22⋊D389—24no—
45C22⋊D389—24no—
46C22⋊D389D418yescomplemented
47C2×Dic389—24no—
48C2×Dic389C2312yes—
49C2×Dic389C2312yes—
50C4×D389—24no—
51C23×C389—24no—
52C23×C389—41no—
53C23×C389C2311yescharacteristic
54C23×C389C2311yescharacteristic
55C23×C389C2312yes—
56D4×C389—24no—
57D4×C389—41no—
58C2×C4×C389C2311yescharacteristic
59C2×C4×C389C2312yes—
60C22×C389—22no—
61C22×C389—22no—
62C22×C389—22no—
63C22×C389—22no—
64C22×C389—21no—
65C22×C389—21no—
66C22×C389—44no—
67C22×C389C2×D414yescomplemented
68C22×C389C2411yescharacteristic
69C2×D389—22no—
70C2×D389—22no—
71C2×D389—22no—
72C2×D389—22no—
73C2×D389—22no—
74C2×D389—44no—
75C2×D389—48no—
76C2×D389C2×D414yescomplemented
77C4×C389—22no—
78C4×C389—21no—
79Dic389—22no—
80Dic389C2×D414yescomplemented
81C2×C389—24no—
82C2×C389—41no—
83C2×C389—41no—
84C2×C389C22×D412yes—
85C2×C389H(5,𝔽2)11yescharacteristic
86D389—24no—
87D389—42no—
88C389D4211yescharacteristic, complemented, Sylow
89D42—3891nomaximal, Sylow
90C22×D4—3892no—
91C22×D4—3892no—
92#127—3891no—
93#121—3892no—
94#121—3892no—
95#120—3891no—
96#120—3892no—
97#120D38911yescharacteristic, complemented
98C4×D4—3892no—
99C24—3891no—
100C24—3892no—
101C24C2×D38911yescharacteristic, complemented
102C2×D4—7788no—
103C2×D4—7788no—
104C2×D4—3892no—
105C2×D4—3892no—
106C2×D4—3892no—
107C2×D4—3892no—
108C2×D4—3892no—
109C2×D4—3892no—
110C2×D4—3891no—
111C2×D4C2×D38912yescomplemented
112C2×D4C2×D38911yescharacteristic, complemented
113C22×C4—3892no—
114C22×C4—3892no—
115C4⋊C4—3892no—
116C22⋊C4—3891no—
117C22⋊C4—3892no—
118C22⋊C4—3892no—
119C22⋊C4C2×D38912yescomplemented
120C22⋊C4C2×D38911yescharacteristic, complemented
121C42—3891no—
122C23—24no—
123C23—41no—
124C23—7784no—
125C23—7784no—
126C23—7784no—
127C23—15562no—
128C23—15561no—
129C23—3892no—
130C23—3892no—
131C23C22×D38911yescharacteristic
132C23C22×D38911yescharacteristic
133C23C22×D38912yes—
134D4—24no—
135D4—41no—
136D4—7784no—
137D4—7784no—
138D4—7784no—
139D4—7784no—
140D4—7784no—
141D4—15561no—
142D4—3898no—
143C2×C4—7784no—
144C2×C4—7784no—
145C2×C4—3892no—
146C2×C4—3892no—
147C2×C4C22×D38911yescharacteristic
148C2×C4C22×D38912yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—7782no—
157C22—7782no—
158C22—7782no—
159C22—7782no—
160C22—7782no—
161C22—15568no—
162C22—15564no—
163C22—3894no—
164C22D4×D38914yescomplemented
165C22C23×D38911yescharacteristic
166C4—22no—
167C4—21no—
168C4—7782no—
169C4—3894no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—7784no—
174C2—15562no—
175C2C2×D4×D38912yes—
176C2#2715942911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#120×C389C2
hypercenter#120D389
hypocenterC389D42
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D389C2semidirect
2. C2×D4×D389C2semidirect
3. #27159380C2semidirect
4. #27159357C2semidirect
5. #27159356C2semidirect
6. #27159354C2semidirect
7. #27159352C2semidirect
8. #27159344C2semidirect
9. #120×C389C2semidirect
10. C23×D389C22semidirect
11. C23×D389C22semidirect
12. C2×D1556C22semidirect
13. C2×D1556C22semidirect
16. C2×C22⋊D389C22semidirect
17. C2×C22⋊D389C22semidirect
18. C2×C22⋊D389C22semidirect
19. C2×C22⋊D389C22semidirect
21. C22×Dic389C22semidirect
22. C2×C4×D389C22semidirect
23. #20261945C22semidirect
24. C22⋊Dic389C22semidirect
25. #20261943C22semidirect
26. #20261943C22semidirect
27. C4×Dic389C22semidirect
28. C24×C389C22semidirect
29. C2×D4×C389C22semidirect
30. C2×D4×C389C22semidirect
31. C22⋊C4×C389C22semidirect
32. C22⋊C4×C389C22semidirect
46. C22⋊D389D4semidirect
67. C22×C389C2×D4semidirect
76. C2×D389C2×D4semidirect
80. Dic389C2×D4semidirect
88. C389D42semidirect
97. #120D389semidirect
101. C24C2×D389semidirect
111. C2×D4C2×D389semidirect
112. C2×D4C2×D389semidirect
119. C22⋊C4C2×D389semidirect
120. C22⋊C4C2×D389semidirect
164. C22D4×D389semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D3892
C2×D4×D3892
#271593802
#271593572
#271593562
#271593542
#271593522
#271593442
#120×C3892
D42389