Finite Group Databasebeta

← #20260751

Subgroups — #20260751

Order 6208.

154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#13095511C211yesmaximal, characteristic
2#15690769C211yesmaximal, characteristic, complemented
3#15690736C214yesmaximal, complemented
4C2×M16×C97C211yesmaximal, characteristic, complemented
5#13095511—21no—
6#13095511—21no—
7#13095511C412yescomplemented
8#13095511C2212yes—
9C2×Dic194C411yescharacteristic, complemented
10C2×D388C411yescharacteristic, complemented
11C2×C22⋊D97—21no—
12C2×C4×D97—21no—
13C4⋊Dic97—21no—
14C22⋊Dic97—21no—
15C4×Dic97C2212yescomplemented
16C22×C4×C97C2211yescharacteristic
17M16×C97—21no—
18M16×C97C2212yescomplemented
19C2×C8×C97—21no—
20C23×C97D411yescharacteristic
21C22×D97—21no—
22C2×C4×C97C2×C411yescharacteristic
23C2×C4×C97C2×C411yescharacteristic
24C2×C4×C97D411yescharacteristic
25C2×C4×C97D411yescharacteristic
26C2×C4×C97D411yescharacteristic
27C2×C4×C97C2311yescharacteristic
28C22⋊D97—22no—
29C22⋊D97—22no—
30C2×Dic97—21no—
31C2×Dic97—22no—
32D388—21no—
33D388C2×C412yes—
34C4×D97—22no—
35C4×D97—22no—
36Dic194—21no—
37Dic194C2×C412yes—
38C8×C97—22no—
39C22×C97—41no—
40C22×C97C22⋊C411yescharacteristic
41C22×C97C22⋊C411yescharacteristic
42C22×C97C2×D411yescharacteristic
43C2×D97—22no—
44C2×D97—42no—
45C4×C97C22⋊C411yescharacteristic
46C4×C97C22⋊C411yescharacteristic
47C4×C97C22×C411yescharacteristic
48C4×C97C2×D411yescharacteristic
49Dic97—22no—
50Dic97—42no—
51C2×C97—21no—
52C2×C97—21no—
53C2×C97—21no—
54C2×C97C2×C22⋊C411yescharacteristic
55D97—42no—
56C97#42111yescharacteristic, complemented, Sylow
57#421—971nomaximal, Sylow
58C2×#41—971no—
59C2×M16D9711yescharacteristic, complemented
60#117—971no—
61#104—974no—
62#41—972no—
63#41—972no—
64#41—1941no—
65#41—1941no—
66C2×Q8—971no—
67C2×D4—971no—
68C2×D4—1941no—
69C22×C4—1941no—
70C22×C4C2×D9711yescharacteristic
71M16—21no—
72M16C2×D9712yescomplemented
73C2×C8—21no—
74C4⋊C4—1941no—
75C22⋊C4—1941no—
76C42—972no—
77C23—1941no—
78C23D38811yescharacteristic
79Q8—972no—
80Q8—1941no—
81D4—972no—
82D4—1942no—
83D4—1942no—
84D4—1941no—
85C2×C4—1942no—
86C2×C4—1941no—
87C2×C4—1942no—
88C2×C4—1942no—
89C2×C4C4×D9711yescharacteristic
90C2×C4C4×D9711yescharacteristic
91C2×C4D38811yescharacteristic
92C2×C4C22⋊D9711yescharacteristic
93C2×C4C22⋊D9711yescharacteristic
94C2×C4C22×D9711yescharacteristic
95C8—22no—
96C22—41no—
97C22—3882no—
98C22—1942no—
99C22#1309548811yescharacteristic
100C22#1309548811yescharacteristic
101C22C2×D38811yescharacteristic
102C4—3882no—
103C4—1942no—
104C4#1309548811yescharacteristic
105C4#1309548811yescharacteristic
106C4C2×C4×D9711yescharacteristic
107C4C2×C22⋊D9711yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—3882no—
112C2C2×#1309548811yescharacteristic
subgroupG/H
centerC4C2×C22⋊D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×M16×C97C2
socleC2×C97C2×C22⋊C4
hypercenterC2×M16D97
hypocenterC97#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #15690769C2semidirect
3. #15690736C2semidirect
4. C2×M16×C97C2semidirect
7. #13095511C4semidirect
9. C2×Dic194C4semidirect
10. C2×D388C4semidirect
15. C4×Dic97C22semidirect
18. M16×C97C22semidirect
56. C97#421semidirect
59. C2×M16D97semidirect
72. M16C2×D97semidirect