Finite Group Databasebeta

← #22581316

Subgroups — #22581316

Order 8896.

110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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#17984838C211yesmaximal, characteristic
2#17984833C211yesmaximal, characteristic, complemented
3#17984764C211yesmaximal, characteristic, complemented
4#17984763C211yesmaximal, characteristic, complemented
5#17984762C211yesmaximal, characteristic, complemented
6#17984752C211yesmaximal, characteristic, complemented
7#102×C139C211yesmaximal, characteristic, complemented
8C2×D556C2211yescharacteristic
9C2×C22⋊D139—21no—
10C2×C22⋊D139—21no—
11C2×C139⋊C8C2211yescharacteristic
12C4⋊Dic139—21no—
13C4⋊Dic139C2211yescharacteristic
14Dic139⋊C4—21no—
15C4×Dic139C2211yescharacteristic
16C2×D4×C139C2211yescharacteristic
17C2×C8×C139C2211yescharacteristic
18C4⋊C4×C139C2211yescharacteristic
19C22×D139—21no—
20D556—21no—
21D556—21no—
22C22⋊D139—42no—
23C22⋊D139—42no—
24C2×Dic139—21no—
25C2×Dic139D411yescharacteristic
26C2×Dic139D411yescharacteristic
27C139⋊C8—21no—
28C23×C139—21no—
29D4×C139—21no—
30D4×C139—21no—
31C2×C4×C139—21no—
32C2×C4×C139C2311yescharacteristic
33C8×C139—21no—
34C22×C139—41no—
35C22×C139—41no—
36C22×C139—41no—
37C22×C139C2×D411yescharacteristic
38C2×D139—41no—
39C2×D139—41no—
40C2×D139—41no—
41C4×C139—41no—
42C4×C139#4111yescharacteristic
43C4×C139#4111yescharacteristic
44Dic139—21no—
45Dic139—21no—
46Dic139—41no—
47C2×C139—81no—
48C2×C139#12411yescharacteristic
49C2×C139AGL(1,ℤ/8)11yescharacteristic
50C2×C139AGL(1,ℤ/8)11yescharacteristic
51D139—81no—
52C139#49011yescharacteristic, complemented, Sylow
53#490—1391nomaximal, Sylow
54#127—1391no—
55#125—1391no—
56#102—1391no—
57#102—1391no—
58#102—1391no—
59#102D13911yescharacteristic, complemented
60#97—1391no—
61C2×D4—2781no—
62C2×D4—2781no—
63C2×D4—1391no—
64C2×D4C2×D13911yescharacteristic
65C2×C8—1391no—
66C2×C8C2×D13911yescharacteristic
67C4⋊C4—2781no—
68C4⋊C4—2781no—
69C4⋊C4—1391no—
70C4⋊C4C2×D13911yescharacteristic
71C42—1391no—
72C23—21no—
73C23—2781no—
74D4—21no—
75D4—21no—
76D4—2781no—
77D4—2781no—
78D4—5562no—
79D4—5562no—
80C2×C4—21no—
81C2×C4—2781no—
82C2×C4—1391no—
83C2×C4—1391no—
84C2×C4C22×D13911yescharacteristic
85C8—21no—
86C8—2781no—
87C22—41no—
88C22—41no—
89C22—41no—
90C22—5561no—
91C22—5561no—
92C22—5561no—
93C22D4×D13911yescharacteristic
94C4—41no—
95C4—2781no—
96C4—2781no—
97C4—5561no—
98C4#1455578411yescharacteristic
99C4#1455578511yescharacteristic
100C2—81no—
101C2—11121no—
102C2#1798482811yescharacteristic
103C2#1798486611yescharacteristic
104C2#1798486911yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#102×C139C2
socleC22×C139C2×D4
hypercenter#102D139
hypocenterC139#490
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #17984833C2semidirect
3. #17984764C2semidirect
4. #17984763C2semidirect
5. #17984762C2semidirect
6. #17984752C2semidirect
7. #102×C139C2semidirect
52. C139#490semidirect
59. #102D139semidirect