Finite Group Databasebeta

← #20260924

Subgroups — #20260924

Order 6208.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15690855C211yesmaximal, characteristic
2#15690793C212yesmaximal, complemented
3#15690725C211yesmaximal, characteristic, complemented
4#15690724C212yesmaximal, complemented
5#123×C97C211yesmaximal, characteristic, complemented
6#13095511—21no—
7#13095510—22no—
8C2×C22⋊D97—21no—
9C2×C22⋊D97C2212yes—
10D4×D97—22no—
11#13095490—22no—
12C22⋊Dic97C2212yescomplemented
13#13095488—22no—
14C2×D4×C97C2211yescharacteristic
15C22×C4×C97C2211yescharacteristic, complemented
16C4⋊C4×C97—21no—
17C22⋊C4×C97—21no—
18C22⋊C4×C97C2211yescharacteristic, complemented
19C23×C97D411yescharacteristic
20C23×C97C2311yescharacteristic
21C22×D97—21no—
22C22×D97D412yes—
23D4×C97—22no—
24C2×C4×C97—21no—
25C2×C4×C97—21no—
26C2×C4×C97—22no—
27C2×C4×C97D411yescharacteristic
28C22⋊D97—22no—
29C22⋊D97—22no—
30C22⋊D97—22no—
31C2×Dic97—21no—
32C2×Dic97—22no—
33C2×Dic97D412yes—
34D388—21no—
35C4×D97—22no—
36Dic194—21no—
37C22×C97—21no—
38C22×C97—41no—
39C22×C97—41no—
40C22×C97C2×D412yes—
41C22×C97C2×D411yescharacteristic
42C2×D97—22no—
43C2×D97—42no—
44C2×D97—81no—
45C4×C97—21no—
46C4×C97—41no—
47C4×C97—41no—
48Dic97—22no—
49Dic97—42no—
50C2×C97—22no—
51C2×C97—21no—
52C2×C97—41no—
53C2×C97#12011yescharacteristic
54D97—42no—
55C97#45811yescharacteristic, complemented, Sylow
56#458—971nomaximal, Sylow
57H(5,𝔽2)—971no—
58#123—972no—
59#123D9711yescharacteristic, complemented
60#99—971no—
61#99—972no—
62#41—1942no—
63#41—1941no—
64C2×D4—972no—
65C2×D4—1942no—
66C2×D4—1941no—
67C2×D4C2×D9711yescharacteristic
68C22×C4C2×D9711yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—1942no—
71C22⋊C4—21no—
72C22⋊C4—972no—
73C22⋊C4—1942no—
74C22⋊C4C2×D9711yescharacteristic, complemented
75C23—972no—
76C23—1941no—
77C23C22⋊D9711yescharacteristic
78C23C22×D9711yescharacteristic
79Q8—1941no—
80D4—22no—
81D4—1941no—
82D4—1942no—
83D4—1942no—
84D4—1942no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—972no—
89C2×C4—1942no—
90C2×C4—1942no—
91C2×C4—1941no—
92C2×C4C22⋊D9711yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—7761no—
97C22—3882no—
98C22—1942no—
99C22D4×D9712yes—
100C22C2×C22⋊D9711yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—3882no—
105C4—1942no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—3882no—
110C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC23×C97C23
FrattiniC23C22×D97
Fitting#123×C97C2
socleC2×C97#120
hypercenter#123D97
hypocenterC97#458
LCSG ▷ C23×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #15690793C2semidirect
3. #15690725C2semidirect
4. #15690724C2semidirect
5. #123×C97C2semidirect
12. C22⋊Dic97C22semidirect
15. C22×C4×C97C22semidirect
18. C22⋊C4×C97C22semidirect
55. C97#458semidirect
59. #123D97semidirect
68. C22×C4C2×D97semidirect
74. C22⋊C4C2×D97semidirect