Finite Group Databasebeta

← #20260882

Subgroups — #20260882

Order 6208.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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, complemented
2C2×#13095500C211yesmaximal, characteristic, complemented
3C2×D776C211yesmaximal, characteristic, complemented
4#15690784C211yesmaximal, characteristic, complemented
5#15690735C211yesmaximal, characteristic, complemented
6#15690732C211yesmaximal, characteristic, complemented
7C22⋊C8×C97C211yesmaximal, characteristic, complemented
8#13095511—22no—
9#13095511—22no—
10C2×Dic194C2211yescharacteristic
11C2×D388C2211yescharacteristic
12C2×D388C2211yescharacteristic
13C2×C22⋊D97—21no—
14C2×C22⋊D97—21no—
15C2×C4×D97—21no—
16#13095500—22no—
17D776—22no—
18C4⋊Dic97C2211yescharacteristic
19#13095488—21no—
20C22×C4×C97C2211yescharacteristic
21C2×C8×C97C2211yescharacteristic
22C2×C8×C97C2211yescharacteristic
23C23×C97D411yescharacteristic
24C22×D97—21no—
25C22×D97—21no—
26C2×C4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97D411yescharacteristic
29C2×C4×C97C2311yescharacteristic
30C22⋊D97—24no—
31C22⋊D97—42no—
32C2×Dic97—21no—
33C2×Dic97—21no—
34D388—21no—
35D388—21no—
36D388—21no—
37D388D412yescomplemented
38C4×D97—24no—
39Dic194—21no—
40Dic194D412yescomplemented
41C8×C97—21no—
42C8×C97—21no—
43C22×C97—21no—
44C22×C97—21no—
45C22×C97—21no—
46C22×C97C2×D411yescharacteristic
47C2×D97—22no—
48C2×D97—41no—
49C2×D97—41no—
50C2×D97—41no—
51C2×D97—41no—
52C2×D97—41no—
53C4×C97—21no—
54C4×C97C2×D411yescharacteristic
55C4×C97C2×D411yescharacteristic
56Dic97—22no—
57Dic97—41no—
58C2×C97—41no—
59C2×C97#12011yescharacteristic
60C2×C97#13511yescharacteristic
61C2×C97AGL(1,ℤ/8)11yescharacteristic
62D97—42no—
63D97—81no—
64C97#44911yescharacteristic, complemented, Sylow
65#449—971nomaximal, Sylow
66C2×#41—971no—
67C2×SD16—971no—
68C2×D8—971no—
69#121—971no—
70#103—971no—
71#102—971no—
72C22⋊C8D9711yescharacteristic, complemented
73#41—1942no—
74#41—1942no—
75C2×Q8—971no—
76C2×D4—971no—
77C2×D4—971no—
78C2×D4—1941no—
79C2×D4—1941no—
80C22×C4—1941no—
81C22×C4C2×D9711yescharacteristic
82SD16—1942no—
83D8—1942no—
84C2×C8C2×D9711yescharacteristic
85C2×C8C2×D9711yescharacteristic
86C4⋊C4—971no—
87C22⋊C4—1941no—
88C23—1941no—
89C23—1941no—
90C23D38811yescharacteristic
91Q8—972no—
92Q8—1941no—
93D4—972no—
94D4—3882no—
95D4—1944no—
96D4—1941no—
97D4—1941no—
98D4—1941no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—1944no—
102C2×C4—1941no—
103C2×C4—1941no—
104C2×C4D38811yescharacteristic
105C2×C4C22×D9711yescharacteristic
106C8—21no—
107C8—21no—
108C22—21no—
109C22—21no—
110C22—21no—
111C22—3881no—
112C22—3881no—
113C22—3881no—
114C22—3881no—
115C22—3881no—
116C22—1942no—
117C22C2×D38811yescharacteristic
118C4—21no—
119C4—3881no—
120C4—1942no—
121C4D4×D9711yescharacteristic
122C4D4×D9711yescharacteristic
123C2—41no—
124C2—7761no—
125C2—3882no—
126C2#1569078011yescharacteristic
127C2#1569083211yescharacteristic
128C2#1569083811yescharacteristic
subgroupG/H
centerC22C2×D388
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊C8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊C8D97
hypocenterC97#449
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#13095511C2semidirect
2. C2×#13095500C2semidirect
3. C2×D776C2semidirect
4. #15690784C2semidirect
5. #15690735C2semidirect
6. #15690732C2semidirect
7. C22⋊C8×C97C2semidirect
37. D388D4semidirect
40. Dic194D4semidirect
64. C97#449semidirect
72. C22⋊C8D97semidirect