Finite Group Databasebeta

← #22581052

Subgroups — #22581052

Order 8896.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14555774C211yesmaximal, characteristic
2#17984807C211yesmaximal, characteristic, complemented
3#17984804C211yesmaximal, characteristic
4#17984765C211yesmaximal, characteristic, complemented
5#17984762C211yesmaximal, characteristic
6#17984752C211yesmaximal, characteristic, complemented
7#107×C139C211yesmaximal, characteristic, complemented
8C2×Dic278C2211yescharacteristic
9C2×D556C2211yescharacteristic
10C2×C4×D139—21no—
11#14555774C414yescomplemented
12C2×C139⋊C8C2211yescharacteristic
13Dic139⋊C4—21no—
14(C2×D139)⋊C4—21no—
15C4×Dic139—21no—
16C4×Dic139C2211yescharacteristic
17C2×C8×C139C2211yescharacteristic
18C4⋊C4×C139C2211yescharacteristic
19C4⋊C4×C139C2211yescharacteristic
20C22×D139—21no—
21Dic278—21no—
22Dic278C2×C412yescomplemented
23D556—21no—
24D556C2×C412yes—
25C2×Dic139—21no—
26C2×Dic139D411yescharacteristic
27C2×Dic139D411yescharacteristic
28C4×D139—42no—
29C139⋊C8—21no—
30C2×C4×C139—21no—
31C2×C4×C139—21no—
32C2×C4×C139C2311yescharacteristic
33C8×C139C2×C412yescomplemented
34C22×C139C2×D411yescharacteristic
35C2×D139—22no—
36C2×D139—41no—
37C2×D139—41no—
38C4×C139—41no—
39C4×C139—41no—
40C4×C139C22×C411yescharacteristic
41C4×C139#4111yescharacteristic
42Dic139—22no—
43Dic139—21no—
44Dic139—21no—
45C2×C139C4×D411yescharacteristic
46C2×C139AGL(1,ℤ/8)11yescharacteristic
47C2×C139#13711yescharacteristic
48D139—42no—
49C139#44011yescharacteristic, complemented, Sylow
50#440—1391nomaximal, Sylow
51C2×SD16—1391no—
52C4×Q8—1391no—
53C4×D4—1391no—
54#107D13911yescharacteristic, complemented
55#103—1391no—
56#102—1391no—
57#97—1391no—
58C2×Q8—1391no—
59C2×D4—1391no—
60C22×C4—2781no—
61SD16—1394no—
62C2×C8—1391no—
63C2×C8C2×D13911yescharacteristic
64C4⋊C4—2781no—
65C4⋊C4C2×D13911yescharacteristic
66C4⋊C4C2×D13911yescharacteristic
67C22⋊C4—2781no—
68C42—2781no—
69C42—1391no—
70C23—2781no—
71Q8—2781no—
72Q8—1392no—
73D4—2781no—
74D4—1392no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—2781no—
78C2×C4—5562no—
79C2×C4—1391no—
80C2×C4—1391no—
81C2×C4C22×D13911yescharacteristic
82C8—2781no—
83C8C4×D13912yescomplemented
84C22—2782no—
85C22—5561no—
86C22—5561no—
87C22D4×D13911yescharacteristic
88C4—41no—
89C4—41no—
90C4—2782no—
91C4—2781no—
92C4—2781no—
93C4C2×C4×D13911yescharacteristic
94C4#1455578611yescharacteristic
95C2—5562no—
96C2#1798480411yescharacteristic
97C2#1798486611yescharacteristic
98C2#1798487411yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC4×C139C22×C4
FrattiniC2×C4C22×D139
Fitting#107×C139C2
socleC22×C139C2×D4
hypercenter#107D139
hypocenterC139#440
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #17984807C2semidirect
4. #17984765C2semidirect
6. #17984752C2semidirect
7. #107×C139C2semidirect
11. #14555774C4semidirect
22. Dic278C2×C4semidirect
33. C8×C139C2×C4semidirect
49. C139#440semidirect
54. #107D139semidirect
83. C8C4×D139semidirect