Finite Group Databasebeta

← #37560100

Subgroups — #37560100

Order 23872.

248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#26045785C212yesmaximal, complemented
2#26045779C211yesmaximal, characteristic, complemented
3#26045774C212yesmaximal, complemented
4#26045770C212yesmaximal, complemented
5#26045760C211yesmaximal, characteristic
6C4×C22⋊D373C212yesmaximal, complemented
7#26045750C212yesmaximal, complemented
8C22⋊C4×D373C212yesmaximal, complemented
9#123×C373C211yesmaximal, characteristic, complemented
10C23×D373C2211yescharacteristic
11C2×Dic746C2211yescharacteristic, complemented
12C2×C22⋊D373C2212yes—
13C2×C4×D373C2212yes—
14C2×C4×D373C2212yes—
15C4⋊Dic373C2212yescomplemented
16#20238589C2212yescomplemented
17#20238589C2212yescomplemented
18C22⋊Dic373C2212yes—
19C22⋊Dic373C2211yescharacteristic
20C22⋊Dic373C2212yescomplemented
21#20238587C2212yes—
22#20238587C2212yes—
23#20238587C2212yes—
24C4×Dic373C2211yescharacteristic, complemented
25C4×Dic373C2212yescomplemented
26C2×D4×C373C2211yescharacteristic
27C22×C4×C373C2211yescharacteristic, complemented
28C4⋊C4×C373C2212yescomplemented
29C22⋊C4×C373C2212yes—
30C22⋊C4×C373C2211yescharacteristic, complemented
31C22×D373—24no—
32C22×D373—41no—
33C22×D373C2312yes—
34Dic746—41no—
35C22⋊D373—24no—
36C2×Dic373C2312yes—
37C2×Dic373C2312yes—
38C2×Dic373C2312yes—
39C4×D373—24no—
40C4×D373—42no—
41C23×C373C2311yescharacteristic
42C23×C373C2311yescharacteristic
43D4×C373—41no—
44C2×C4×C373—41no—
45C2×C4×C373C2312yes—
46C2×C4×C373C2312yes—
47C2×C4×C373C2311yescharacteristic
48C22×C373—22no—
49C22×C373—22no—
50C22×C373—21no—
51C22×C373—21no—
52C22×C373C2411yescharacteristic
53C2×D373—22no—
54C2×D373—22no—
55C2×D373—44no—
56C2×D373#4114yes—
57C4×C373—22no—
58C4×C373—22no—
59C4×C373—21no—
60Dic373—22no—
61Dic373—22no—
62Dic373—22no—
63C2×C373—41no—
64C2×C373—41no—
65C2×C373C2×#4112yes—
66C2×C373H(5,𝔽2)11yescharacteristic
67D373—24no—
68C373#55111yescharacteristic, complemented, Sylow
69#551—3731nomaximal, Sylow
70#126—3732no—
71#124—3731no—
72#123—3732no—
73#123D37311yescharacteristic, complemented
74C22⋊Q8—3732no—
75#120—3731no—
76C4×D4—3732no—
77#117—3732no—
78C2×C22⋊C4—3732no—
79C24—3731no—
80C2×Q8—3731no—
81C2×D4—3732no—
82C2×D4C2×D37311yescharacteristic
83C22×C4—3732no—
84C22×C4—3732no—
85C22×C4C2×D37311yescharacteristic, complemented
86C4⋊C4—3732no—
87C4⋊C4—3732no—
88C4⋊C4—3732no—
89C4⋊C4C2×D37312yescomplemented
90C22⋊C4—3732no—
91C22⋊C4—3732no—
92C22⋊C4—3731no—
93C22⋊C4—3732no—
94C22⋊C4—3732no—
95C22⋊C4—3732no—
96C22⋊C4C2×D37312yes—
97C22⋊C4C2×D37311yescharacteristic, complemented
98C42—3731no—
99C42—3732no—
100C23—3732no—
101C23—14921no—
102C23—7464no—
103C23C22×D37311yescharacteristic
104C23C22×D37311yescharacteristic
105Q8—14921no—
106D4—41no—
107D4—7464no—
108C2×C4—41no—
109C2×C4—3732no—
110C2×C4—3732no—
111C2×C4—3732no—
112C2×C4—14922no—
113C2×C4—7464no—
114C2×C4C22×D37311yescharacteristic
115C2×C4C22×D37312yes—
116C2×C4C22×D37312yes—
117C22—22no—
118C22—22no—
119C22—21no—
120C22—21no—
121C22—3734no—
122C22—14924no—
123C22—7462no—
124C22—7462no—
125C22C23×D37311yescharacteristic
126C4—22no—
127C4—22no—
128C4—21no—
129C4—7462no—
130C4—7462no—
131C4—7462no—
132C2—41no—
133C2—41no—
134C2—7464no—
135C2#41×D37312yes—
136C2#2604583711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
Fitting#123×C373C2
prime radical#26045760C2
hypercenter#123D373
hypocenterC373#551
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #26045785C2semidirect
2. #26045779C2semidirect
3. #26045774C2semidirect
4. #26045770C2semidirect
6. C4×C22⋊D373C2semidirect
7. #26045750C2semidirect
8. C22⋊C4×D373C2semidirect
9. #123×C373C2semidirect
11. C2×Dic746C22semidirect
15. C4⋊Dic373C22semidirect
16. #20238589C22semidirect
17. #20238589C22semidirect
20. C22⋊Dic373C22semidirect
24. C4×Dic373C22semidirect
25. C4×Dic373C22semidirect
27. C22×C4×C373C22semidirect
28. C4⋊C4×C373C22semidirect
30. C22⋊C4×C373C22semidirect
68. C373#551semidirect
73. #123D373semidirect
85. C22×C4C2×D373semidirect
89. C4⋊C4C2×D373semidirect
97. C22⋊C4C2×D373semidirect

Maximal subgroups

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

subgroupindex
#260457852
#260457792
#260457742
#260457702
#260457602
C4×C22⋊D3732
#260457502
C22⋊C4×D3732
#123×C3732
#551373