Finite Group Databasebeta

← #20261734

Subgroups — #20261734

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#15690875C214yesmaximal, complemented
4C2×#13095512C211yesmaximal, characteristic
5#13095521C2212yescomplemented
6#13095520—21no—
7#13095519—21no—
8C4⋊#87604—21no—
9C22⋊#87604—21no—
10C4×#87604C2212yescomplemented
11#13095512—21no—
12#13095512—21no—
13#13095512C412yescomplemented
14#13095512C2212yes—
15C2×D388—21no—
16C2×D388C411yescharacteristic, complemented
17C2×C4×D97—21no—
18C2×C4×D97C2211yescharacteristic
19C2×Q8×C97C411yescharacteristic, complemented
20C22×D97—21no—
21C22×D97D411yescharacteristic
22C2×#87604—22no—
23Q8×C97—21no—
24Q8×C97C2×C412yes—
25C2×C4×C97—21no—
26C2×C4×C97C2×C411yescharacteristic
27C2×Dic97D411yescharacteristic
28D388—22no—
29D388—22no—
30D388—21no—
31D388C2×C412yes—
32C4×D97—22no—
33C4×D97—22no—
34C4×D97C2×C411yescharacteristic
35C4×D97D411yescharacteristic
36C4×D97D411yescharacteristic
37C4×D97C2311yescharacteristic
38#11715897—22no—
39C22×C97C22⋊C411yescharacteristic
40C2×D97—22no—
41C2×D97—41no—
42C2×D97—42no—
43C2×D97C22⋊C411yescharacteristic
44C2×D97C2×D411yescharacteristic
45#87604—42no—
46C4×C97—22no—
47C4×C97C22⋊C411yescharacteristic
48C4×C97C22×C411yescharacteristic
49Dic97C22⋊C411yescharacteristic
50Dic97C2×D411yescharacteristic
51C2×C97—21no—
52C2×C97C2×C22⋊C411yescharacteristic
53D97—21no—
54D97—21no—
55D97—42no—
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#8760411yescharacteristic, complemented
67C2×D4—971no—
68C2×D4—1941no—
69C22×C4—971no—
70C22×C4—1941no—
71M16—972no—
72M16—1941no—
73C2×C8—1941no—
74C4⋊C4—1941no—
75C22⋊C4—1941no—
76C42—972no—
77C23—971no—
78C23—1941no—
79Q8—21no—
80Q8C2×#8760412yes—
81D4—972no—
82D4—1942no—
83D4—1942no—
84D4—1941no—
85C2×C4—21no—
86C2×C4—971no—
87C2×C4—971no—
88C2×C4—971no—
89C2×C4—971no—
90C2×C4—971no—
91C2×C4—1942no—
92C2×C4—1942no—
93C2×C4—1942no—
94C2×C4C2×#8760411yescharacteristic
95C8—1942no—
96C22—971no—
97C22—971no—
98C22—3882no—
99C22—3881no—
100C22—1942no—
101C22C22⋊#8760411yescharacteristic
102C4—22no—
103C4—971no—
104C4—971no—
105C4—3882no—
106C4C22⋊#8760411yescharacteristic
107C4C22×#8760411yescharacteristic
108C2—21no—
109C2—3882no—
110C2—1941no—
111C2—1941no—
112C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×Q8×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC2×Q8#87604
hypocenterC97#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. D97⋊M16C2semidirect
2. #15690889C2semidirect
3. #15690875C2semidirect
5. #13095521C22semidirect
10. C4×#87604C22semidirect
13. #13095512C4semidirect
16. C2×D388C4semidirect
19. C2×Q8×C97C4semidirect
56. C97#421semidirect
66. C2×Q8#87604semidirect