Finite Group Databasebeta

← #20263928

Subgroups — #20263928

Order 6368.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D796C211yesmaximal, characteristic, complemented
2C2×C22⋊D199C211yesmaximal, characteristic, complemented
3C2×C22⋊D199C211yesmaximal, characteristic, complemented
4C2×C4×D199C211yesmaximal, characteristic, complemented
5Dic199⋊C4C211yesmaximal, characteristic, complemented
6(C2×D199)⋊C4C211yesmaximal, characteristic, complemented
7C22⋊C4×C199C211yesmaximal, characteristic, complemented
8C22×D199C2211yescharacteristic
9C22×D199C2211yescharacteristic
10D796—22no—
11C22⋊D199—22no—
12C22⋊D199—22no—
13C2×Dic199C2211yescharacteristic
14C2×Dic199C2211yescharacteristic
15C4×D199—22no—
16C23×C199C2211yescharacteristic
17C2×C4×C199C2211yescharacteristic
18C2×C4×C199C2211yescharacteristic
19C22×C199—21no—
20C22×C199—21no—
21C22×C199—21no—
22C22×C199C2311yescharacteristic
23C2×D199—21no—
24C2×D199—21no—
25C2×D199—21no—
26C2×D199—21no—
27C2×D199—21no—
28C2×D199D412yescomplemented
29C4×C199—21no—
30C4×C199—21no—
31Dic199—21no—
32Dic199D412yescomplemented
33C2×C199—41no—
34C2×C199C2×D411yescharacteristic
35C2×C199C2×D411yescharacteristic
36C2×C199#4111yescharacteristic
37D199—22no—
38D199—41no—
39C199#12111yescharacteristic, complemented, Sylow
40#121—1991nomaximal, Sylow
41C2×D4—1991no—
42C2×D4—1991no—
43C2×D4—1991no—
44C22×C4—1991no—
45C4⋊C4—1991no—
46C22⋊C4—1991no—
47C22⋊C4D19911yescharacteristic, complemented
48C23—1991no—
49C23—1991no—
50C23C2×D19911yescharacteristic
51D4—3982no—
52D4—3982no—
53D4—3982no—
54C2×C4—3982no—
55C2×C4—1991no—
56C2×C4—1991no—
57C2×C4C2×D19911yescharacteristic
58C2×C4C2×D19911yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—3981no—
63C22—3981no—
64C22—3981no—
65C22—3981no—
66C22—3981no—
67C22—1992no—
68C22C22×D19911yescharacteristic
69C4—21no—
70C4—21no—
71C4—3981no—
72C4—1992no—
73C2—41no—
74C2—7961no—
75C2—3982no—
76C2D4×D19911yescharacteristic
77C2D4×D19911yescharacteristic
78C2#1569188611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D199
commutator, socleC22×C199C23
FittingC22⋊C4×C199C2
hypercenterC22⋊C4D199
hypocenterC199#121
LCSG ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D796C2semidirect
2. C2×C22⋊D199C2semidirect
3. C2×C22⋊D199C2semidirect
4. C2×C4×D199C2semidirect
5. Dic199⋊C4C2semidirect
6. (C2×D199)⋊C4C2semidirect
7. C22⋊C4×C199C2semidirect
28. C2×D199D4semidirect
32. Dic199D4semidirect
39. C199#121semidirect
47. C22⋊C4D199semidirect