Finite Group Databasebeta

← #20263927

Subgroups — #20263927

Order 6368.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊D199C211yesmaximal, characteristic, complemented
2C2×C22⋊D199C211yesmaximal, characteristic, complemented
3C22×Dic199C211yesmaximal, characteristic, complemented
4Dic199⋊C4C211yesmaximal, characteristic, complemented
5C22⋊Dic199C211yesmaximal, characteristic, complemented
6(C2×D199)⋊C4C211yesmaximal, characteristic, complemented
7C2×D4×C199C211yesmaximal, characteristic, complemented
8C22×D199C2211yescharacteristic
9C22⋊D199—22no—
10C22⋊D199—22no—
11C2×Dic199—22no—
12C2×Dic199C2211yescharacteristic
13C2×Dic199C2211yescharacteristic
14C2×Dic199C2211yescharacteristic
15C23×C199C2211yescharacteristic
16C23×C199C2211yescharacteristic
17D4×C199—22no—
18C2×C4×C199C2211yescharacteristic
19C22×C199—21no—
20C22×C199—21no—
21C22×C199—21no—
22C22×C199—21no—
23C22×C199—21no—
24C22×C199D412yescomplemented
25C22×C199C2311yescharacteristic
26C2×D199—21no—
27C2×D199—21no—
28C2×D199—21no—
29C4×C199—21no—
30Dic199—21no—
31Dic199—21no—
32Dic199D412yescomplemented
33C2×C199—22no—
34C2×C199—41no—
35C2×C199C2×D411yescharacteristic
36C2×C199C2×D411yescharacteristic
37C2×C199#4111yescharacteristic
38D199—41no—
39C199#12111yescharacteristic, complemented, Sylow
40#121—1991nomaximal, Sylow
41C2×D4—1991no—
42C2×D4—1991no—
43C2×D4D19911yescharacteristic, complemented
44C22×C4—1991no—
45C4⋊C4—1991no—
46C22⋊C4—1991no—
47C22⋊C4—1991no—
48C23—1991no—
49C23C2×D19911yescharacteristic
50C23C2×D19911yescharacteristic
51D4—22no—
52D4—3982no—
53D4—3982no—
54C2×C4—3982no—
55C2×C4—1991no—
56C2×C4—1991no—
57C2×C4—1991no—
58C2×C4C2×D19911yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—21no—
63C22—21no—
64C22—3981no—
65C22—3981no—
66C22—3981no—
67C22C22⋊D19912yescomplemented
68C22C22×D19911yescharacteristic
69C4—21no—
70C4—3981no—
71C4—3981no—
72C4—1992no—
73C2—22no—
74C2—41no—
75C2—7961no—
76C2D4×D19911yescharacteristic
77C2C2×C22⋊D19911yescharacteristic
78C2#1569188511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D199
commutator, socleC22×C199C23
FittingC2×D4×C199C2
hypercenterC2×D4D199
hypocenterC199#121
LCSG ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊D199C2semidirect
2. C2×C22⋊D199C2semidirect
3. C22×Dic199C2semidirect
4. Dic199⋊C4C2semidirect
5. C22⋊Dic199C2semidirect
6. (C2×D199)⋊C4C2semidirect
7. C2×D4×C199C2semidirect
24. C22×C199D4semidirect
32. Dic199D4semidirect
39. C199#121semidirect
43. C2×D4D199semidirect
67. C22C22⋊D199semidirect