Finite Group Databasebeta

← #20261733

Subgroups — #20261733

Order 6208.

154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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
1D97⋊M16C211yesmaximal, characteristic, complemented
2#15690889C211yesmaximal, characteristic, complemented
3#15690874C214yesmaximal, complemented
4C2×#13095510C211yesmaximal, characteristic
5#13095521C2212yescomplemented
6#13095520—21no—
7#13095519—21no—
8C4⋊#87604—21no—
9C22⋊#87604—21no—
10C4×#87604C2212yescomplemented
11#13095510—21no—
12#13095510—21no—
13#13095510C412yescomplemented
14#13095510C2212yes—
15C2×Dic194C411yescharacteristic, complemented
16C2×C22⋊D97—21no—
17C22×Dic97—21no—
18C2×C4×D97C2211yescharacteristic
19C2×D4×C97C411yescharacteristic, complemented
20C23×C97—21no—
21C22×D97D411yescharacteristic
22C2×#87604—22no—
23D4×C97—21no—
24D4×C97C2×C412yes—
25C2×C4×C97C2×C411yescharacteristic
26C22⋊D97—22no—
27C22⋊D97—22no—
28C2×Dic97—21no—
29C2×Dic97—22no—
30C2×Dic97—22no—
31C2×Dic97D411yescharacteristic
32C4×D97C2×C411yescharacteristic
33C4×D97D411yescharacteristic
34C4×D97D411yescharacteristic
35C4×D97C2311yescharacteristic
36Dic194—21no—
37Dic194C2×C412yes—
38#11715897—22no—
39C22×C97—22no—
40C22×C97—42no—
41C22×C97C22⋊C411yescharacteristic
42C2×D97—41no—
43C2×D97C22⋊C411yescharacteristic
44C2×D97C2×D411yescharacteristic
45#87604—42no—
46C4×C97C22⋊C411yescharacteristic
47C4×C97C22×C411yescharacteristic
48Dic97—22no—
49Dic97C22⋊C411yescharacteristic
50Dic97C2×D411yescharacteristic
51C2×C97—21no—
52C2×C97—42no—
53C2×C97C2×C22⋊C411yescharacteristic
54D97—21no—
55D97—21no—
56C97#42111yescharacteristic, complemented, Sylow
57#421—971nomaximal, Sylow
58C2×#41—971no—
59C2×M16—971no—
60#117—971no—
61#104—974no—
62#41—972no—
63#41—972no—
64#41—1941no—
65#41—1941no—
66C2×Q8—971no—
67C2×D4—1941no—
68C2×D4#8760411yescharacteristic, complemented
69C22×C4—971no—
70C22×C4—1941no—
71M16—972no—
72M16—1941no—
73C2×C8—1941no—
74C4⋊C4—1941no—
75C22⋊C4—1941no—
76C42—972no—
77C23—21no—
78C23—971no—
79Q8—972no—
80Q8—1941no—
81D4—21no—
82D4—1942no—
83D4—1942no—
84D4C2×#8760412yes—
85C2×C4—971no—
86C2×C4—971no—
87C2×C4—971no—
88C2×C4—971no—
89C2×C4—971no—
90C2×C4—1942no—
91C2×C4—1942no—
92C2×C4—1942no—
93C2×C4—1941no—
94C2×C4C2×#8760411yescharacteristic
95C8—1942no—
96C22—22no—
97C22—42no—
98C22—971no—
99C22—971no—
100C22—3881no—
101C22C22⋊#8760411yescharacteristic
102C4—971no—
103C4—971no—
104C4—3882no—
105C4—1942no—
106C4C22⋊#8760411yescharacteristic
107C4C22×#8760411yescharacteristic
108C2—21no—
109C2—42no—
110C2—1941no—
111C2—1941no—
112C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×D4×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC2×D4#87604
hypocenterC97#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D97⋊M16C2semidirect
2. #15690889C2semidirect
3. #15690874C2semidirect
5. #13095521C22semidirect
10. C4×#87604C22semidirect
13. #13095510C4semidirect
15. C2×Dic194C4semidirect
19. C2×D4×C97C4semidirect
56. C97#421semidirect
68. C2×D4#87604semidirect