Finite Group Databasebeta

← #37559520

Subgroups — #37559520

Order 23872.

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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×#20238597C211yesmaximal, characteristic
2C4×D1492C211yesmaximal, characteristic
3#26045725C211yesmaximal, characteristic, complemented
4#26045716C211yesmaximal, characteristic, complemented
5#26045712C211yesmaximal, characteristic
6#26045703C211yesmaximal, characteristic, complemented
7C4×Q8×C373C211yesmaximal, characteristic, complemented
8C2×D1492C2211yescharacteristic
9C2×C4×D373—21no—
10#20238597C414yescomplemented
11C2×#15688412C2211yescharacteristic
12C2×#15688412C2211yescharacteristic
13C4⋊Dic373C2211yescharacteristic
14#20238587—21no—
15C2×Q8×C373C2211yescharacteristic
16C4⋊C4×C373—21no—
17C4⋊C4×C373C2211yescharacteristic
18C42×C373—21no—
19C42×C373C2211yescharacteristic
20C22×D373—21no—
21D1492—21no—
22D1492C2×C412yes—
23C2×Dic373—21no—
24C4×D373—42no—
25#15688412—21no—
26#15688412C2×C412yescomplemented
27Q8×C373—21no—
28Q8×C373C2×C412yescomplemented
29C2×C4×C373—21no—
30C2×C4×C373—21no—
31C2×C4×C373D411yescharacteristic
32C2×C4×C373D411yescharacteristic
33C2×C4×C373C2311yescharacteristic
34C22×C373C2×D411yescharacteristic
35C2×D373—22no—
36C2×D373—41no—
37C2×D373—41no—
38C4×C373—22no—
39C4×C373—21no—
40C4×C373—21no—
41C4×C373—41no—
42C4×C373C22×C411yescharacteristic
43C4×C373#4111yescharacteristic
44Dic373—41no—
45C2×C373C4×D411yescharacteristic
46C2×C373AGL(1,ℤ/8)11yescharacteristic
47C2×C373#13711yescharacteristic
48D373—42no—
49C373#44011yescharacteristic, complemented, Sylow
50#440—3731nomaximal, Sylow
51C2×SD16—3731no—
52C4×Q8D37311yescharacteristic, complemented
53C4×D4—3731no—
54#107—3731no—
55#103—3731no—
56#102—3731no—
57#97—3731no—
58C2×Q8C2×D37311yescharacteristic
59C2×D4—3731no—
60C22×C4—7461no—
61SD16—3734no—
62C2×C8—3731no—
63C2×C8—3731no—
64C4⋊C4—21no—
65C4⋊C4—3731no—
66C4⋊C4C2×D37311yescharacteristic
67C22⋊C4—7461no—
68C42—21no—
69C42C2×D37311yescharacteristic
70C23—7461no—
71Q8—21no—
72Q8C4×D37312yescomplemented
73D4—3732no—
74D4—7461no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—14922no—
78C2×C4—7461no—
79C2×C4C22⋊D37311yescharacteristic
80C2×C4C22⋊D37311yescharacteristic
81C2×C4C22×D37311yescharacteristic
82C8—3732no—
83C8—7461no—
84C22—14921no—
85C22—14921no—
86C22—7462no—
87C22C2×C22⋊D37311yescharacteristic
88C4—22no—
89C4—21no—
90C4—21no—
91C4—41no—
92C4—14921no—
93C4C2×C4×D37311yescharacteristic
94C4#2023861011yescharacteristic
95C2—14922no—
96C2C4×C22⋊D37311yescharacteristic
97C2#2604581711yescharacteristic
98C2#2604582311yescharacteristic
subgroupG/H
centerC22C2×C22⋊D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
FittingC4×Q8×C373C2
socleC22×C373C2×D4
prime radicalC2×D1492C22
cosocleC2×C4×C373C23
hypercenterC4×Q8D373
hypocenterC373#440
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #26045725C2semidirect
4. #26045716C2semidirect
6. #26045703C2semidirect
7. C4×Q8×C373C2semidirect
10. #20238597C4semidirect
26. #15688412C2×C4semidirect
28. Q8×C373C2×C4semidirect
49. C373#440semidirect
52. C4×Q8D373semidirect
72. Q8C4×D373semidirect

Maximal subgroups

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

subgroupindex
C2×#202385972
C4×D14922
#260457252
#260457162
#260457122
#260457032
C4×Q8×C3732
#440373