Finite Group Databasebeta

← #22581141

Subgroups — #22581141

Order 8896.

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

normal subgroups only

This group has 198 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#17984887C211yesmaximal, characteristic, complemented
2#17984812C212yesmaximal, complemented
3#17984810C211yesmaximal, characteristic, complemented
4#17984756C212yesmaximal, complemented
5#99×C139C211yesmaximal, characteristic, complemented
6C23×D139C2211yescharacteristic, complemented
7#14555785—21no—
8#14555784—22no—
9C2×D556—22no—
10C2×C22⋊D139—21no—
11C2×C22⋊D139—21no—
12C2×C22⋊D139C2212yes—
13D4×D139—22no—
14C22⋊Dic139C2211yescharacteristic, complemented
15(C2×D139)⋊C4—22no—
16(C2×D139)⋊C4—21no—
17C2×D4×C139C2211yescharacteristic
18C22⋊C4×C139C2212yescomplemented
19C22×D139—21no—
20C22×D139—22no—
21C22×D139—21no—
22C22×D139—42no—
23C22×D139D412yescomplemented
24Dic278—21no—
25D556—21no—
26D556—44no—
27C22⋊D139—22no—
28C22⋊D139—22no—
29C22⋊D139—22no—
30C22⋊D139—42no—
31C2×Dic139—21no—
32C2×Dic139—21no—
33C2×Dic139D412yescomplemented
34C4×D139—22no—
35C23×C139D411yescharacteristic, complemented
36C23×C139C2311yescharacteristic
37D4×C139—22no—
38C2×C4×C139—22no—
39C2×C4×C139D411yescharacteristic, complemented
40C22×C139—21no—
41C22×C139—41no—
42C22×C139—41no—
43C22×C139C2×D412yes—
44C22×C139C2×D411yescharacteristic
45C2×D139—22no—
46C2×D139—24no—
47C2×D139—22no—
48C2×D139—41no—
49C2×D139—42no—
50C2×D139—41no—
51C2×D139—42no—
52C2×D139—81no—
53C4×C139—21no—
54C4×C139—42no—
55Dic139—22no—
56Dic139—41no—
57C2×C139—21no—
58C2×C139—22no—
59C2×C139—41no—
60C2×C139#12011yescharacteristic
61D139—42no—
62D139—42no—
63C139B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—1391nomaximal, Sylow
65H(5,𝔽2)—1391no—
66#120—1391no—
67#120—1392no—
68#99—1392no—
69#99D13911yescharacteristic, complemented
70C24—1391no—
71#41—2782no—
72#41—2781no—
73C2×D4—2782no—
74C2×D4—2782no—
75C2×D4—2781no—
76C2×D4—2781no—
77C2×D4—1392no—
78C2×D4C2×D13911yescharacteristic
79C22⋊C4—2782no—
80C22⋊C4—2781no—
81C22⋊C4—1391no—
82C22⋊C4C2×D13912yescomplemented
83C23—2781no—
84C23—2782no—
85C23—2781no—
86C23—5562no—
87C23—1392no—
88C23D55611yescharacteristic, complemented
89C23C22×D13911yescharacteristic
90Q8—2781no—
91D4—22no—
92D4—2781no—
93D4—2782no—
94D4—2782no—
95D4—2782no—
96D4—5564no—
97D4—5562no—
98C2×C4—22no—
99C2×C4—2782no—
100C2×C4—2781no—
101C2×C4—2781no—
102C2×C4—1392no—
103C2×C4D55611yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—2784no—
108C22—2782no—
109C22—2782no—
110C22—5562no—
111C22—5562no—
112C22—5561no—
113C22—5561no—
114C22—11121no—
115C22D4×D13912yes—
116C22C2×D55611yescharacteristic
117C4—21no—
118C4—42no—
119C4—2782no—
120C4—5561no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—5562no—
125C2—5562no—
126C2#1798481211yescharacteristic
subgroupG/H
centerC2#17984812
commutatorC23×C139C23
FrattiniC23C22×D139
Fitting#99×C139C2
socleC2×C139#120
hypercenter#99D139
hypocenterC139B(4,𝔽2)
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #17984887C2semidirect
2. #17984812C2semidirect
3. #17984810C2semidirect
4. #17984756C2semidirect
5. #99×C139C2semidirect
6. C23×D139C22semidirect
14. C22⋊Dic139C22semidirect
18. C22⋊C4×C139C22semidirect
23. C22×D139D4semidirect
33. C2×Dic139D4semidirect
35. C23×C139D4semidirect
39. C2×C4×C139D4semidirect
63. C139B(4,𝔽2)semidirect
69. #99D139semidirect
82. C22⋊C4C2×D139semidirect
88. C23D556semidirect
103. C2×C4D556semidirect