Finite Group Databasebeta

← #37559554

Subgroups — #37559554

Order 23872.

198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4×D373C211yesmaximal, characteristic, complemented
2C2×#20238595C211yesmaximal, characteristic, complemented
3#26045763C211yesmaximal, characteristic, complemented
4#26045714C211yesmaximal, characteristic, complemented
5#26045713C211yesmaximal, characteristic, complemented
6#26045704C211yesmaximal, characteristic, complemented
7C2×D8×C373C211yesmaximal, characteristic, complemented
8C23×D373—21no—
9C2×D1492C2211yescharacteristic
10C2×C22⋊D373—21no—
11C2×C22⋊D373—21no—
12D4×D373—22no—
13D4×D373—22no—
14C2×C4×D373C2211yescharacteristic
15#20238595—22no—
16C2×#15688412C2211yescharacteristic, complemented
17C4⋊Dic373C2211yescharacteristic, complemented
18C22⋊Dic373—21no—
19C2×D4×C373C2211yescharacteristic
20C2×D4×C373C2211yescharacteristic, complemented
21D8×C373—22no—
22C2×C8×C373C2211yescharacteristic, complemented
23C22×D373—24no—
24C22×D373—21no—
25C22×D373—42no—
26C22×D373—42no—
27C22×D373D411yescharacteristic
28D1492—21no—
29D1492D412yescomplemented
30C22⋊D373—24no—
31C22⋊D373—42no—
32C2×Dic373—21no—
33C2×Dic373D411yescharacteristic
34C4×D373—21no—
35C4×D373—21no—
36#15688412—21no—
37C23×C373—21no—
38C23×C373—21no—
39D4×C373—21no—
40D4×C373—21no—
41D4×C373—21no—
42D4×C373D412yescomplemented
43C2×C4×C373C2311yescharacteristic
44C8×C373—21no—
45C22×C373—22no—
46C22×C373—41no—
47C22×C373—41no—
48C22×C373—41no—
49C22×C373—41no—
50C22×C373—41no—
51C22×C373C2×D411yescharacteristic
52C2×D373—21no—
53C2×D373—21no—
54C2×D373—22no—
55C2×D373—48no—
56C2×D373—41no—
57C2×D373—41no—
58C2×D373D812yescomplemented
59C4×C373C2×D411yescharacteristic
60C4×C373C2×D411yescharacteristic
61Dic373—21no—
62Dic373—41no—
63C2×C373—42no—
64C2×C373—81no—
65C2×C373#12011yescharacteristic
66C2×C373C2×D811yescharacteristic
67C2×C373AGL(1,ℤ/8)11yescharacteristic
68D373—22no—
69D373—42no—
70C373#44711yescharacteristic, complemented, Sylow
71#447—3731nomaximal, Sylow
72C22×D4—3731no—
73C2×D8—3731no—
74C2×D8D37311yescharacteristic, complemented
75#121—3731no—
76#102—3731no—
77#102—3731no—
78C22⋊C8—3731no—
79C24—7461no—
80C2×D4—3731no—
81C2×D4—7461no—
82C2×D4—7462no—
83C2×D4—7461no—
84C2×D4—7462no—
85C2×D4C2×D37311yescharacteristic
86C2×D4C2×D37311yescharacteristic, complemented
87C22×C4—3731no—
88D8—22no—
89D8—7462no—
90C2×C8—3731no—
91C2×C8C2×D37311yescharacteristic, complemented
92C4⋊C4—3731no—
93C22⋊C4—7461no—
94C23—21no—
95C23—21no—
96C23—3731no—
97C23—14922no—
98C23—14922no—
99C23—7464no—
100C23—7461no—
101D4—21no—
102D4—21no—
103D4—21no—
104D4—3732no—
105D4—14922no—
106D4—7464no—
107D4—7461no—
108D4C22⋊D37312yescomplemented
109C2×C4—3731no—
110C2×C4—7461no—
111C2×C4—7461no—
112C2×C4—7461no—
113C2×C4C22×D37311yescharacteristic
114C8—21no—
115C8—7461no—
116C22—22no—
117C22—41no—
118C22—41no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—3732no—
123C22—14928no—
124C22—14921no—
125C22—14921no—
126C22—7462no—
127C22—7461no—
128C22—7461no—
129C22D4×D37311yescharacteristic
130C4—14921no—
131C4—7461no—
132C4D4×D37311yescharacteristic
133C4C2×C22⋊D37311yescharacteristic
134C2—42no—
135C2—81no—
136C2—14922no—
137C2—7462no—
138C2#2604576011yescharacteristic
139C2D8×D37311yescharacteristic
140C2#2604581611yescharacteristic
subgroupG/H
centerC22D4×D373
commutator, cosocleC2×C4×C373C23
FrattiniC2×C4C22×D373
FittingC2×D8×C373C2
socleC22×C373C2×D4
hypercenterC2×D8D373
hypocenterC373#447
LCSG ▷ C2×C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×D373C2semidirect
2. C2×#20238595C2semidirect
3. #26045763C2semidirect
4. #26045714C2semidirect
5. #26045713C2semidirect
6. #26045704C2semidirect
7. C2×D8×C373C2semidirect
16. C2×#15688412C22semidirect
17. C4⋊Dic373C22semidirect
20. C2×D4×C373C22semidirect
22. C2×C8×C373C22semidirect
29. D1492D4semidirect
42. D4×C373D4semidirect
58. C2×D373D8semidirect
70. C373#447semidirect
74. C2×D8D373semidirect
86. C2×D4C2×D373semidirect
91. C2×C8C2×D373semidirect
108. D4C22⋊D373semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3732
C2×#202385952
#260457632
#260457142
#260457132
#260457042
C2×D8×C3732
#447373