Finite Group Databasebeta

← #22581166

Subgroups — #22581166

Order 8896.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14555773C211yesmaximal, characteristic, complemented
2#17984829C211yesmaximal, characteristic, complemented
3D4×Dic139C211yesmaximal, characteristic, complemented
4Dic139⋊C8C211yesmaximal, characteristic, complemented
5#17984767C211yesmaximal, characteristic, complemented
6#17984763C211yesmaximal, characteristic, complemented
7C2×D8×C139C211yesmaximal, characteristic
8C2×Dic278C2211yescharacteristic
9C22×Dic139—21no—
10#14555773—22no—
11C2×C139⋊C8C2211yescharacteristic
12C4⋊Dic139C2211yescharacteristic
13C22⋊Dic139—21no—
14C22⋊Dic139—21no—
15C22⋊Dic139—21no—
16C4×Dic139C2211yescharacteristic
17C2×D4×C139C2211yescharacteristic
18C2×D4×C139C2211yescharacteristic
19D8×C139—22no—
20C2×C8×C139C2211yescharacteristic
21Dic278—21no—
22Dic278—21no—
23C2×Dic139—21no—
24C2×Dic139—21no—
25C2×Dic139—42no—
26C2×Dic139D411yescharacteristic
27C2×Dic139D411yescharacteristic
28C139⋊C8—21no—
29C23×C139—21no—
30C23×C139—21no—
31D4×C139—21no—
32D4×C139—21no—
33D4×C139—21no—
34D4×C139D412yes—
35C2×C4×C139C2311yescharacteristic
36C8×C139—21no—
37C22×C139—22no—
38C22×C139—41no—
39C22×C139—41no—
40C22×C139—41no—
41C22×C139—41no—
42C22×C139—41no—
43C22×C139C2×D411yescharacteristic
44C4×C139C2×D411yescharacteristic
45C4×C139#4111yescharacteristic
46Dic139—21no—
47Dic139—21no—
48Dic139—41no—
49Dic139—41no—
50C2×C139—42no—
51C2×C139—81no—
52C2×C139#12111yescharacteristic
53C2×C139#13511yescharacteristic
54C2×C139AGL(1,ℤ/8)11yescharacteristic
55C139#46311yescharacteristic, complemented, Sylow
56#463—1391nomaximal, Sylow
57C2×SD16—1391no—
58C2×D8D13911yescharacteristic
59#124—1391no—
60C4×D4—1391no—
61C4⋊C8—1391no—
62#103—1391no—
63#102—1391no—
64C2×Q8—1391no—
65C2×D4C2×D13911yescharacteristic
66C2×D4C2×D13911yescharacteristic
67C22×C4—2781no—
68SD16—2782no—
69D8—22no—
70C2×C8—1391no—
71C2×C8C2×D13911yescharacteristic
72C4⋊C4—1391no—
73C22⋊C4—2781no—
74C22⋊C4—2781no—
75C22⋊C4—2781no—
76C42—1391no—
77C23—21no—
78C23—21no—
79Q8—2781no—
80Q8—2781no—
81D4—21no—
82D4—21no—
83D4—21no—
84D4C22⋊D13912yes—
85C2×C4—2781no—
86C2×C4—2781no—
87C2×C4—5562no—
88C2×C4—1391no—
89C2×C4—1391no—
90C2×C4C22×D13911yescharacteristic
91C8—21no—
92C8—2781no—
93C22—22no—
94C22—41no—
95C22—41no—
96C22—41no—
97C22—41no—
98C22—41no—
99C22D4×D13911yescharacteristic
100C4—2781no—
101C4—2781no—
102C4—5561no—
103C4—5561no—
104C4C2×C22⋊D13911yescharacteristic
105C4#1455578411yescharacteristic
106C2—42no—
107C2—81no—
108C2#1798481411yescharacteristic
109C2#1798486111yescharacteristic
110C2#1798486611yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
FittingC2×D8×C139C2
socleC22×C139C2×D4
hypercenterC2×D8D139
hypocenterC139#463
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14555773C2semidirect
2. #17984829C2semidirect
3. D4×Dic139C2semidirect
4. Dic139⋊C8C2semidirect
5. #17984767C2semidirect
6. #17984763C2semidirect
55. C139#463semidirect