Finite Group Databasebeta

← #22581265

Subgroups — #22581265

Order 8896.

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

normal subgroups only

This group has 114 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#17984813C211yesmaximal, characteristic
2C4⋊C4×D139C211yesmaximal, characteristic, complemented
3#17984776C211yesmaximal, characteristic, complemented
4#17984775C211yesmaximal, characteristic, complemented
5#17984763C211yesmaximal, characteristic, complemented
6(C2×D139)⋊C8C211yesmaximal, characteristic, complemented
7#102×C139C211yesmaximal, characteristic, complemented
8C2×C22⋊D139—21no—
9C2×C4×D139—21no—
10C2×C4×D139C2211yescharacteristic
11C2×C139⋊C8C2211yescharacteristic
12C4⋊Dic139C2211yescharacteristic
13C4⋊Dic139C2211yescharacteristic
14Dic139⋊C4—21no—
15C22⋊Dic139—21no—
16C2×D4×C139C2211yescharacteristic
17C2×C8×C139C2211yescharacteristic
18C4⋊C4×C139C2211yescharacteristic
19C22×D139D411yescharacteristic
20C22⋊D139—42no—
21C2×Dic139—21no—
22C2×Dic139—21no—
23C2×Dic139D411yescharacteristic
24C4×D139—21no—
25C4×D139—21no—
26C4×D139—42no—
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—21no—
39C2×D139—21no—
40C2×D139D812yes—
41C4×C139—41no—
42C4×C139#4111yescharacteristic
43C4×C139#4111yescharacteristic
44Dic139—21no—
45Dic139—41no—
46Dic139—41no—
47C2×C139—81no—
48C2×C139#12311yescharacteristic
49C2×C139C2×D811yescharacteristic
50C2×C139#13711yescharacteristic
51D139—22no—
52C139#48011yescharacteristic, complemented, Sylow
53#480—1391nomaximal, Sylow
54#121—1391no—
55C2×C4⋊C4—1391no—
56#107—1391no—
57#107—1391no—
58#102—1391no—
59#102D13911yescharacteristic, complemented
60C22⋊C8—1391no—
61C2×D4—2781no—
62C2×D4C2×D13911yescharacteristic
63C22×C4—2781no—
64C22×C4—1391no—
65C2×C8—1391no—
66C2×C8C2×D13911yescharacteristic
67C4⋊C4—2781no—
68C4⋊C4—1391no—
69C4⋊C4—1391no—
70C4⋊C4C2×D13911yescharacteristic
71C22⋊C4—2781no—
72C23—21no—
73C23—1391no—
74D4—21no—
75D4—21no—
76D4—5562no—
77C2×C4—21no—
78C2×C4—2781no—
79C2×C4—2781no—
80C2×C4—2781no—
81C2×C4—2781no—
82C2×C4—5562no—
83C2×C4—1391no—
84C2×C4C22×D13911yescharacteristic
85C8—21no—
86C8—2781no—
87C22—41no—
88C22—41no—
89C22—41no—
90C22—2781no—
91C22—2781no—
92C22—1392no—
93C22D4×D13911yescharacteristic
94C4—41no—
95C4—2781no—
96C4—5561no—
97C4—5561no—
98C4#1455578411yescharacteristic
99C4#1455578511yescharacteristic
100C2—81no—
101C2—2782no—
102C2#1798482411yescharacteristic
103C2D8×D13911yescharacteristic
104C2#1798487111yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#102×C139C2
socleC22×C139C2×D4
hypercenter#102D139
hypocenterC139#480
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. C4⋊C4×D139C2semidirect
3. #17984776C2semidirect
4. #17984775C2semidirect
5. #17984763C2semidirect
6. (C2×D139)⋊C8C2semidirect
7. #102×C139C2semidirect
52. C139#480semidirect
59. #102D139semidirect