Finite Group Databasebeta

← #37559556

Subgroups — #37559556

Order 23872.

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

normal subgroups only

This group has 198 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×#20238595C212yesmaximal, complemented
2#26045766C211yesmaximal, characteristic, complemented
3#26045713C212yesmaximal, complemented
4C22⋊#15688412C211yesmaximal, characteristic, complemented
5C22×D4×C373C211yesmaximal, characteristic, complemented
6C2×D1492C2211yescharacteristic, complemented
7C2×C22⋊D373—21no—
8#20238595—24no—
9C2×#15688412C2212yescomplemented
10C4⋊Dic373C2211yescharacteristic, complemented
11#20238587—21no—
12C24×C373—21no—
13C2×D4×C373—24no—
14C2×D4×C373—21no—
15C2×D4×C373C2212yes—
16C22×C4×C373C2211yescharacteristic
17C22×D373—21no—
18D1492—22no—
19C22⋊D373—42no—
20C2×Dic373—21no—
21#15688412—22no—
22C23×C373—24no—
23C23×C373—22no—
24C23×C373—42no—
25C23×C373—42no—
26C23×C373D411yescharacteristic
27D4×C373—24no—
28D4×C373—22no—
29D4×C373D414yescomplemented
30C2×C4×C373—22no—
31C2×C4×C373D411yescharacteristic
32C2×C4×C373C2311yescharacteristic
33C22×C373—21no—
34C22×C373—21no—
35C22×C373—24no—
36C22×C373—48no—
37C22×C373—42no—
38C22×C373—42no—
39C22×C373D812yescomplemented
40C22×C373C2×D411yescharacteristic
41C2×D373—41no—
42C2×D373—41no—
43C2×D373—41no—
44C4×C373—21no—
45C4×C373C2×D412yes—
46Dic373—41no—
47C2×C373—22no—
48C2×C373—44no—
49C2×C373#12011yescharacteristic
50C2×C373C2×D811yescharacteristic
51C2×C373AGL(1,ℤ/8)11yescharacteristic
52D373—81no—
53C373#44711yescharacteristic, complemented, Sylow
54#447—3731nomaximal, Sylow
55C22×D4D37311yescharacteristic, complemented
56C2×D8—3732no—
57#121—3731no—
58#102—3732no—
59C22⋊C8—3731no—
60C24—21no—
61C2×D4—24no—
62C2×D4—21no—
63C2×D4—3731no—
64C2×D4—7461no—
65C2×D4C2×D37312yes—
66C22×C4C2×D37311yescharacteristic
67D8—7464no—
68C2×C8—3732no—
69C4⋊C4—3731no—
70C22⋊C4—7461no—
71C23—24no—
72C23—22no—
73C23—42no—
74C23—42no—
75C23—7461no—
76C23C22⋊D37311yescharacteristic
77D4—24no—
78D4—22no—
79D4—14922no—
80D4—7462no—
81D4C22⋊D37314yescomplemented
82C2×C4—22no—
83C2×C4—7461no—
84C2×C4C22⋊D37311yescharacteristic
85C2×C4C22×D37311yescharacteristic
86C8—7462no—
87C22—21no—
88C22—21no—
89C22—24no—
90C22—48no—
91C22—42no—
92C22—42no—
93C22—14921no—
94C22—14921no—
95C22—14921no—
96C22#2023859512yescomplemented
97C22C2×C22⋊D37311yescharacteristic
98C4—21no—
99C4—14921no—
100C4C2×C22⋊D37312yes—
101C2—22no—
102C2—44no—
103C2—29841no—
104C2#2604576111yescharacteristic
105C2C2×#2023859511yescharacteristic
106C2#2604581811yescharacteristic
subgroupG/H
centerC22C2×C22⋊D373
commutator, cosocleC2×C4×C373C23
FrattiniC2×C4C22×D373
FittingC22×D4×C373C2
socleC22×C373C2×D4
hypercenterC22×D4D373
hypocenterC373#447
LCSG ▷ C2×C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#20238595C2semidirect
2. #26045766C2semidirect
3. #26045713C2semidirect
4. C22⋊#15688412C2semidirect
5. C22×D4×C373C2semidirect
6. C2×D1492C22semidirect
9. C2×#15688412C22semidirect
10. C4⋊Dic373C22semidirect
29. D4×C373D4semidirect
39. C22×C373D8semidirect
53. C373#447semidirect
55. C22×D4D373semidirect
81. D4C22⋊D373semidirect
96. C22#20238595semidirect

Maximal subgroups

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

subgroupindex
C2×#202385952
#260457662
#260457132
C22⋊#156884122
C22×D4×C3732
#447373