Finite Group Databasebeta

← #37559439

Subgroups — #37559439

Order 23872.

154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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×#20238594C211yesmaximal, characteristic, complemented
2#26045751C211yesmaximal, characteristic, complemented
3#26045719C214yesmaximal, complemented
4C2×#41×C373C211yesmaximal, characteristic
5#20238594—21no—
6#20238594C2212yescomplemented
7C2×#15688412—21no—
8C4⋊Dic373—21no—
9C22⋊Dic373—21no—
10C4×Dic373C2212yescomplemented
11#41×C373—21no—
12#41×C373—21no—
13#41×C373C412yescomplemented
14#41×C373C2212yes—
15C2×Q8×C373C411yescharacteristic, complemented
16C2×D4×C373—21no—
17C2×D4×C373C411yescharacteristic, complemented
18C22×C4×C373—21no—
19C22×C4×C373C2211yescharacteristic
20C2×Dic373—22no—
21#15688412—22no—
22C23×C373—21no—
23C23×C373D411yescharacteristic
24Q8×C373—21no—
25Q8×C373C2×C412yes—
26D4×C373—22no—
27D4×C373—22no—
28D4×C373—21no—
29D4×C373C2×C412yes—
30C2×C4×C373—21no—
31C2×C4×C373—22no—
32C2×C4×C373—22no—
33C2×C4×C373C2×C411yescharacteristic
34C2×C4×C373C2×C411yescharacteristic
35C2×C4×C373D411yescharacteristic
36C2×C4×C373D411yescharacteristic
37C2×C4×C373D411yescharacteristic
38C2×C4×C373C2311yescharacteristic
39C22×C373—22no—
40C22×C373—41no—
41C22×C373—42no—
42C22×C373C22⋊C411yescharacteristic
43C22×C373C22⋊C411yescharacteristic
44C22×C373C2×D411yescharacteristic
45C4×C373—22no—
46C4×C373C22⋊C411yescharacteristic
47C4×C373C22⋊C411yescharacteristic
48C4×C373C22×C411yescharacteristic
49C4×C373C2×D411yescharacteristic
50Dic373—42no—
51C2×C373—21no—
52C2×C373—21no—
53C2×C373—21no—
54C2×C373—42no—
55C2×C373C2×C22⋊C411yescharacteristic
56C373#42111yescharacteristic, complemented, Sylow
57#421—3731nomaximal, Sylow
58C2×#41D37311yescharacteristic
59C2×M16—3731no—
60#117—3731no—
61#104—3734no—
62#41—21no—
63#41—21no—
64#41Dic37312yescomplemented
65#41C2×D37312yes—
66C2×Q8Dic37311yescharacteristic, complemented
67C2×D4—21no—
68C2×D4Dic37311yescharacteristic, complemented
69C22×C4—21no—
70C22×C4C2×D37311yescharacteristic
71M16—3732no—
72M16—7461no—
73C2×C8—7461no—
74C4⋊C4—7461no—
75C22⋊C4—7461no—
76C42—3732no—
77C23—21no—
78C23C22⋊D37311yescharacteristic
79Q8—21no—
80Q8C2×Dic37312yes—
81D4—22no—
82D4—22no—
83D4—21no—
84D4C2×Dic37312yes—
85C2×C4—21no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—7462no—
89C2×C4C2×Dic37311yescharacteristic
90C2×C4C2×Dic37311yescharacteristic
91C2×C4C22⋊D37311yescharacteristic
92C2×C4C22⋊D37311yescharacteristic
93C2×C4C22⋊D37311yescharacteristic
94C2×C4C22×D37311yescharacteristic
95C8—7462no—
96C22—22no—
97C22—41no—
98C22—42no—
99C22C22⋊Dic37311yescharacteristic
100C22C22⋊Dic37311yescharacteristic
101C22C2×C22⋊D37311yescharacteristic
102C4—22no—
103C4—14922no—
104C4C22⋊Dic37311yescharacteristic
105C4C22⋊Dic37311yescharacteristic
106C4C22×Dic37311yescharacteristic
107C4C2×C22⋊D37311yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—42no—
112C2C2×C22⋊Dic37311yescharacteristic
subgroupG/H
centerC4C2×C22⋊D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
Fitting, prime radicalC2×#41×C373C2
socleC2×C373C2×C22⋊C4
cosocleC2×C4×C373C23
hypercenterC2×#41D373
hypocenterC373#421
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20238594C2semidirect
2. #26045751C2semidirect
3. #26045719C2semidirect
6. #20238594C22semidirect
10. C4×Dic373C22semidirect
13. #41×C373C4semidirect
15. C2×Q8×C373C4semidirect
17. C2×D4×C373C4semidirect
56. C373#421semidirect
64. #41Dic373semidirect
66. C2×Q8Dic373semidirect
68. C2×D4Dic373semidirect

Maximal subgroups

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

subgroupindex
C2×#202385942
#260457512
#260457192
C2×#41×C3732
#421373