Finite Group Databasebeta

← #20261728

Subgroups — #20261728

Order 6208.

150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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
2#15690889C211yesmaximal, characteristic
3#15690873C214yesmaximal, complemented
4C2×Q8×D97C211yesmaximal, characteristic
5#13095521—21no—
6#13095520—21no—
7#13095519C2212yes—
8C4⋊#87604C2212yes—
9C22⋊#87604—21no—
10C4×#87604—21no—
11C2×Dic194—21no—
12C2×Dic194C411yescharacteristic, complemented
13Q8×D97—21no—
14Q8×D97—21no—
15Q8×D97C412yescomplemented
16Q8×D97C2212yes—
17C2×C4×D97—21no—
18C2×C4×D97C2211yescharacteristic
19C2×Q8×C97C411yescharacteristic, complemented
20C22×D97D411yescharacteristic
21C2×#87604—22no—
22Q8×C97—21no—
23Q8×C97C2×C412yes—
24C2×C4×C97—21no—
25C2×C4×C97C2×C411yescharacteristic
26C2×Dic97—21no—
27C2×Dic97D411yescharacteristic
28C4×D97—22no—
29C4×D97—22no—
30C4×D97C2×C411yescharacteristic
31C4×D97D411yescharacteristic
32C4×D97D411yescharacteristic
33C4×D97C2311yescharacteristic
34Dic194—21no—
35Dic194—22no—
36Dic194—22no—
37Dic194C2×C412yes—
38#11715897—22no—
39C22×C97C22⋊C411yescharacteristic
40C2×D97—22no—
41C2×D97C22⋊C411yescharacteristic
42C2×D97C2×D411yescharacteristic
43#87604—42no—
44C4×C97—22no—
45C4×C97C22⋊C411yescharacteristic
46C4×C97C22×C411yescharacteristic
47Dic97—22no—
48Dic97C22⋊C411yescharacteristic
49Dic97C2×D411yescharacteristic
50C2×C97—21no—
51C2×C97C2×C22⋊C411yescharacteristic
52D97—21no—
53D97#13712yes—
54C97#41911yescharacteristic, complemented, Sylow
55#419—971nomaximal, Sylow
56C22×Q8—971no—
57C2×M16—971no—
58#117—971no—
59#103—974no—
60C2×Q8—972no—
61C2×Q8—972no—
62C2×Q8—971no—
63C2×Q8—1941no—
64C2×Q8—1941no—
65C2×Q8—1941no—
66C2×Q8#8760411yescharacteristic, complemented
67C22×C4—971no—
68C22×C4—1941no—
69M16—1941no—
70M16—1941no—
71C2×C8—972no—
72C4⋊C4—972no—
73C22⋊C4—1941no—
74C42—1941no—
75C23—971no—
76Q8—21no—
77Q8—972no—
78Q8—1942no—
79Q8—1942no—
80Q8—1941no—
81Q8C2×#8760412yes—
82C2×C4—21no—
83C2×C4—971no—
84C2×C4—971no—
85C2×C4—971no—
86C2×C4—971no—
87C2×C4—971no—
88C2×C4—1942no—
89C2×C4—1942no—
90C2×C4—1942no—
91C2×C4—1941no—
92C2×C4C2×#8760411yescharacteristic
93C8—1942no—
94C22—971no—
95C22—971no—
96C22—1942no—
97C22C22⋊#8760411yescharacteristic
98C4—22no—
99C4—971no—
100C4—971no—
101C4—3882no—
102C4—1942no—
103C4C22⋊#8760411yescharacteristic
104C4C22×#8760411yescharacteristic
105C2—21no—
106C2—972no—
107C2—1941no—
108C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×Q8×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC2×Q8#87604
hypocenterC97#419
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
3. #15690873C2semidirect
12. C2×Dic194C4semidirect
15. Q8×D97C4semidirect
19. C2×Q8×C97C4semidirect
54. C97#419semidirect
66. C2×Q8#87604semidirect