Finite Group Databasebeta

← #22581142

Subgroups — #22581142

Order 8896.

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#17984887C211yesmaximal, characteristic
2#17984825C212yesmaximal, complemented
3#17984757C211yesmaximal, characteristic, complemented
4#17984756C212yesmaximal, complemented
5#123×C139C211yesmaximal, characteristic, complemented
6#14555785—21no—
7#14555784—22no—
8C2×C22⋊D139—21no—
9C2×C22⋊D139C2212yes—
10D4×D139—22no—
11Dic139⋊C4—22no—
12C22⋊Dic139C2212yescomplemented
13(C2×D139)⋊C4—22no—
14C2×D4×C139C2211yescharacteristic
15C22×C4×C139C2211yescharacteristic, complemented
16C4⋊C4×C139—21no—
17C22⋊C4×C139—21no—
18C22⋊C4×C139C2211yescharacteristic, complemented
19C22×D139—21no—
20C22×D139D412yes—
21Dic278—21no—
22D556—21no—
23C22⋊D139—22no—
24C22⋊D139—22no—
25C22⋊D139—22no—
26C2×Dic139—21no—
27C2×Dic139—22no—
28C2×Dic139D412yes—
29C4×D139—22no—
30C23×C139D411yescharacteristic
31C23×C139C2311yescharacteristic
32D4×C139—22no—
33C2×C4×C139—21no—
34C2×C4×C139—21no—
35C2×C4×C139—22no—
36C2×C4×C139D411yescharacteristic
37C22×C139—21no—
38C22×C139—41no—
39C22×C139—41no—
40C22×C139C2×D412yes—
41C22×C139C2×D411yescharacteristic
42C2×D139—22no—
43C2×D139—42no—
44C2×D139—81no—
45C4×C139—21no—
46C4×C139—41no—
47C4×C139—41no—
48Dic139—22no—
49Dic139—42no—
50C2×C139—22no—
51C2×C139—21no—
52C2×C139—41no—
53C2×C139#12011yescharacteristic
54D139—42no—
55C139#45811yescharacteristic, complemented, Sylow
56#458—1391nomaximal, Sylow
57H(5,𝔽2)—1391no—
58#123—1392no—
59#123D13911yescharacteristic, complemented
60#99—1391no—
61#99—1392no—
62#41—2782no—
63#41—2781no—
64C2×D4—2782no—
65C2×D4—2781no—
66C2×D4—1392no—
67C2×D4C2×D13911yescharacteristic
68C22×C4C2×D13911yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—2782no—
71C22⋊C4—21no—
72C22⋊C4—2782no—
73C22⋊C4—1392no—
74C22⋊C4C2×D13911yescharacteristic, complemented
75C23—2781no—
76C23—1392no—
77C23C22⋊D13911yescharacteristic
78C23C22×D13911yescharacteristic
79Q8—2781no—
80D4—22no—
81D4—2781no—
82D4—2782no—
83D4—2782no—
84D4—2782no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—2782no—
89C2×C4—2781no—
90C2×C4—2782no—
91C2×C4—1392no—
92C2×C4C22⋊D13911yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—2782no—
97C22—5562no—
98C22—11121no—
99C22D4×D13912yes—
100C22C2×C22⋊D13911yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—2782no—
105C4—5562no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—5562no—
110C2#1798481011yescharacteristic
subgroupG/H
centerC2#17984810
commutatorC23×C139C23
FrattiniC23C22×D139
Fitting#123×C139C2
socleC2×C139#120
hypercenter#123D139
hypocenterC139#458
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #17984825C2semidirect
3. #17984757C2semidirect
4. #17984756C2semidirect
5. #123×C139C2semidirect
12. C22⋊Dic139C22semidirect
15. C22×C4×C139C22semidirect
18. C22⋊C4×C139C22semidirect
55. C139#458semidirect
59. #123D139semidirect
68. C22×C4C2×D139semidirect
74. C22⋊C4C2×D139semidirect