Finite Group Databasebeta

← #15690783

Subgroups — #15690783

Order 3104.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D388C211yesmaximal, characteristic, complemented
2C2×C22⋊D97C211yesmaximal, characteristic, complemented
3C2×C22⋊D97C211yesmaximal, characteristic, complemented
4C2×C4×D97C211yesmaximal, characteristic, complemented
5#13095490C211yesmaximal, characteristic, complemented
6#13095488C211yesmaximal, characteristic, complemented
7C22⋊C4×C97C211yesmaximal, characteristic, complemented
8C23×C97C2211yescharacteristic
9C22×D97C2211yescharacteristic
10C22×D97C2211yescharacteristic
11C2×C4×C97C2211yescharacteristic
12C2×C4×C97C2211yescharacteristic
13C22⋊D97—22no—
14C22⋊D97—22no—
15C2×Dic97C2211yescharacteristic
16C2×Dic97C2211yescharacteristic
17D388—22no—
18C4×D97—22no—
19C22×C97—21no—
20C22×C97—21no—
21C22×C97—21no—
22C22×C97C2311yescharacteristic
23C2×D97—21no—
24C2×D97—21no—
25C2×D97—21no—
26C2×D97—21no—
27C2×D97—21no—
28C2×D97D412yescomplemented
29C4×C97—21no—
30C4×C97—21no—
31Dic97—21no—
32Dic97D412yescomplemented
33C2×C97—41no—
34C2×C97C2×D411yescharacteristic
35C2×C97C2×D411yescharacteristic
36C2×C97#4111yescharacteristic
37D97—22no—
38D97—41no—
39C97#12111yescharacteristic, complemented, Sylow
40#121—971nomaximal, Sylow
41C2×D4—971no—
42C2×D4—971no—
43C2×D4—971no—
44C22×C4—971no—
45C4⋊C4—971no—
46C22⋊C4—971no—
47C22⋊C4D9711yescharacteristic, complemented
48C23—971no—
49C23—971no—
50C23C2×D9711yescharacteristic
51D4—1942no—
52D4—1942no—
53D4—1942no—
54C2×C4—971no—
55C2×C4—971no—
56C2×C4—1942no—
57C2×C4C2×D9711yescharacteristic
58C2×C4C2×D9711yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—972no—
63C22—1941no—
64C22—1941no—
65C22—1941no—
66C22—1941no—
67C22—1941no—
68C22C22×D9711yescharacteristic
69C4—21no—
70C4—21no—
71C4—972no—
72C4—1941no—
73C2—41no—
74C2—3881no—
75C2—1942no—
76C2D4×D9711yescharacteristic
77C2D4×D9711yescharacteristic
78C2#1309551111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D97
commutator, socle, cosocleC22×C97C23
FittingC22⋊C4×C97C2
hypercenterC22⋊C4D97
hypocenterC97#121
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D388C2semidirect
2. C2×C22⋊D97C2semidirect
3. C2×C22⋊D97C2semidirect
4. C2×C4×D97C2semidirect
5. #13095490C2semidirect
6. #13095488C2semidirect
7. C22⋊C4×C97C2semidirect
28. C2×D97D4semidirect
32. Dic97D4semidirect
39. C97#121semidirect
47. C22⋊C4D97semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3882
C2×C22⋊D972
C2×C4×D972
#130954902
#130954882
C22⋊C4×C972
#12197