Finite Group Databasebeta

← #22581205

Subgroups — #22581205

Order 8896.

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

normal subgroups only

This group has 130 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
1C2×#14555770C211yesmaximal, characteristic, complemented
2C2×#14555768C211yesmaximal, characteristic, complemented
3#17984817C211yesmaximal, characteristic, complemented
4#17984813C211yesmaximal, characteristic, complemented
5#17984773C211yesmaximal, characteristic, complemented
6#17984764C211yesmaximal, characteristic, complemented
7#102×C139C211yesmaximal, characteristic, complemented
8C2×D556—21no—
9C2×D556C2211yescharacteristic
10C2×C22⋊D139—21no—
11C2×C4×D139C2211yescharacteristic
12#14555770—22no—
13#14555768—22no—
14C2×C139⋊C8C2211yescharacteristic
15C4⋊Dic139C2211yescharacteristic
16C22⋊Dic139—21no—
17(C2×D139)⋊C4—21no—
18C2×D4×C139C2211yescharacteristic
19C2×C8×C139C2211yescharacteristic
20C4⋊C4×C139C2211yescharacteristic
21C22×D139—21no—
22C22×D139D411yescharacteristic
23D556—21no—
24D556—21no—
25D556—42no—
26C22⋊D139—42no—
27C2×Dic139—21no—
28C2×Dic139D411yescharacteristic
29C4×D139—21no—
30C4×D139—21no—
31C139⋊C8D412yescomplemented
32C23×C139—21no—
33D4×C139—21no—
34D4×C139—21no—
35C2×C4×C139—21no—
36C2×C4×C139C2311yescharacteristic
37C8×C139—21no—
38C22×C139—41no—
39C22×C139—41no—
40C22×C139—41no—
41C22×C139C2×D411yescharacteristic
42C2×D139—21no—
43C2×D139—21no—
44C2×D139—21no—
45C2×D139—41no—
46C2×D139—41no—
47C2×D139—41no—
48C4×C139—41no—
49C4×C139C2×D411yescharacteristic
50C4×C139#4111yescharacteristic
51Dic139—21no—
52Dic139—41no—
53C2×C139—81no—
54C2×C139#12111yescharacteristic
55C2×C139AGL(1,ℤ/8)11yescharacteristic
56C2×C139AGL(1,ℤ/8)11yescharacteristic
57D139—41no—
58D139—81no—
59C139#46911yescharacteristic, complemented, Sylow
60#469—1391nomaximal, Sylow
61C2×D8—1391no—
62C2×M16—1391no—
63#121—1391no—
64#121—1391no—
65#106—1391no—
66#102—1391no—
67#102D13911yescharacteristic, complemented
68C2×D4—2781no—
69C2×D4—2781no—
70C2×D4—1391no—
71C2×D4C2×D13911yescharacteristic
72C22×C4—1391no—
73D8—2782no—
74M16—2782no—
75C2×C8—1391no—
76C2×C8C2×D13911yescharacteristic
77C4⋊C4—1391no—
78C4⋊C4C2×D13911yescharacteristic
79C22⋊C4—2781no—
80C22⋊C4—2781no—
81C23—21no—
82C23—2781no—
83C23—1391no—
84D4—21no—
85D4—21no—
86D4—2781no—
87D4—2781no—
88D4—5562no—
89D4—5562no—
90C2×C4—21no—
91C2×C4—2781no—
92C2×C4—2781no—
93C2×C4—2781no—
94C2×C4—1391no—
95C2×C4C22×D13911yescharacteristic
96C8—21no—
97C8—1392no—
98C22—41no—
99C22—41no—
100C22—41no—
101C22—2781no—
102C22—2781no—
103C22—2781no—
104C22—5561no—
105C22—5561no—
106C22—5561no—
107C22D4×D13911yescharacteristic
108C4—41no—
109C4—2781no—
110C4—5561no—
111C4D4×D13911yescharacteristic
112C4#1455578511yescharacteristic
113C2—81no—
114C2—5561no—
115C2—11121no—
116C2#1798481511yescharacteristic
117C2#1798486611yescharacteristic
118C2#1798486911yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#102×C139C2
socleC22×C139C2×D4
hypercenter#102D139
hypocenterC139#469
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
1. C2×#14555770C2semidirect
2. C2×#14555768C2semidirect
3. #17984817C2semidirect
4. #17984813C2semidirect
5. #17984773C2semidirect
6. #17984764C2semidirect
7. #102×C139C2semidirect
31. C139⋊C8D4semidirect
59. C139#469semidirect
67. #102D139semidirect