Finite Group Databasebeta

← #31826654

Subgroups — #31826654

Order 18112.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#22583655C211yesmaximal, characteristic
2#22583593C212yesmaximal, complemented
3#22583525C211yesmaximal, characteristic, complemented
4#22583524C212yesmaximal, complemented
5#123×C283C211yesmaximal, characteristic, complemented
6#17985392—21no—
7#17985391—22no—
8C2×C22⋊D283—21no—
9C2×C22⋊D283C2212yes—
10D4×D283—22no—
11Dic283⋊C4—22no—
12C22⋊Dic283C2212yescomplemented
13(C2×D283)⋊C4—22no—
14C2×D4×C283C2211yescharacteristic
15C22×C4×C283C2211yescharacteristic, complemented
16C4⋊C4×C283—21no—
17C22⋊C4×C283—21no—
18C22⋊C4×C283C2211yescharacteristic, complemented
19C22×D283—21no—
20C22×D283D412yes—
21Dic566—21no—
22D1132—21no—
23C22⋊D283—22no—
24C22⋊D283—22no—
25C22⋊D283—22no—
26C2×Dic283—21no—
27C2×Dic283—22no—
28C2×Dic283D412yes—
29C4×D283—22no—
30C23×C283D411yescharacteristic
31C23×C283C2311yescharacteristic
32D4×C283—22no—
33C2×C4×C283—21no—
34C2×C4×C283—21no—
35C2×C4×C283—22no—
36C2×C4×C283D411yescharacteristic
37C22×C283—21no—
38C22×C283—41no—
39C22×C283—41no—
40C22×C283C2×D412yes—
41C22×C283C2×D411yescharacteristic
42C2×D283—22no—
43C2×D283—42no—
44C2×D283—81no—
45C4×C283—21no—
46C4×C283—41no—
47C4×C283—41no—
48Dic283—22no—
49Dic283—42no—
50C2×C283—22no—
51C2×C283—21no—
52C2×C283—41no—
53C2×C283#12011yescharacteristic
54D283—42no—
55C283#45811yescharacteristic, complemented, Sylow
56#458—2831nomaximal, Sylow
57H(5,𝔽2)—2831no—
58#123—2832no—
59#123D28311yescharacteristic, complemented
60#99—2831no—
61#99—2832no—
62#41—5662no—
63#41—5661no—
64C2×D4—2832no—
65C2×D4—5662no—
66C2×D4—5661no—
67C2×D4C2×D28311yescharacteristic
68C22×C4C2×D28311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—5662no—
71C22⋊C4—21no—
72C22⋊C4—2832no—
73C22⋊C4—5662no—
74C22⋊C4C2×D28311yescharacteristic, complemented
75C23—2832no—
76C23—5661no—
77C23C22⋊D28311yescharacteristic
78C23C22×D28311yescharacteristic
79Q8—5661no—
80D4—22no—
81D4—5661no—
82D4—5662no—
83D4—5662no—
84D4—5662no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—2832no—
89C2×C4—5662no—
90C2×C4—5661no—
91C2×C4—5662no—
92C2×C4C22⋊D28311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—5662no—
97C22—11322no—
98C22—22641no—
99C22D4×D28312yes—
100C22C2×C22⋊D28311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—5662no—
105C4—11322no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—11322no—
110C2#2258357811yescharacteristic
subgroupG/H
centerC2#22583578
commutator, cosocleC23×C283C23
FrattiniC23C22×D283
Fitting#123×C283C2
socleC2×C283#120
prime radical#22583655C2
hypercenter#123D283
hypocenterC283#458
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #22583593C2semidirect
3. #22583525C2semidirect
4. #22583524C2semidirect
5. #123×C283C2semidirect
12. C22⋊Dic283C22semidirect
15. C22×C4×C283C22semidirect
18. C22⋊C4×C283C22semidirect
55. C283#458semidirect
59. #123D283semidirect
68. C22×C4C2×D283semidirect
74. C22⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836552
#225835932
#225835252
#225835242
#123×C2832
#458283