Finite Group Databasebeta

← #20260879

Subgroups — #20260879

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×#13095512C211yesmaximal, characteristic, complemented
2C2×#13095496C211yesmaximal, characteristic, complemented
3#15690781C211yesmaximal, characteristic, complemented
4#15690734C211yesmaximal, characteristic, complemented
5#15690732C211yesmaximal, characteristic, complemented
6#15690722C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8#13095512—22no—
9#13095512—22no—
10C2×D388—21no—
11C2×D388C2211yescharacteristic
12C2×C22⋊D97—21no—
13C2×C4×D97—21no—
14C2×C4×D97C2211yescharacteristic
15#13095496—22no—
16C2×#11715895C2211yescharacteristic
17C4⋊Dic97C2211yescharacteristic
18C22⋊Dic97—21no—
19C2×Q8×C97C2211yescharacteristic
20C2×D4×C97C2211yescharacteristic
21SD16×C97—22no—
22C2×C8×C97C2211yescharacteristic
23C23×C97—21no—
24C22×D97—21no—
25C22×D97D411yescharacteristic
26Q8×C97—21no—
27Q8×C97D412yescomplemented
28D4×C97—21no—
29D4×C97—21no—
30C2×C4×C97—21no—
31C2×C4×C97C2311yescharacteristic
32C22⋊D97—42no—
33C2×Dic97—21no—
34C2×Dic97D411yescharacteristic
35D388—24no—
36D388—21no—
37D388D412yescomplemented
38C4×D97—24no—
39C4×D97—21no—
40C4×D97—21no—
41C8×C97—21no—
42#11715895—21no—
43C22×C97—41no—
44C22×C97—41no—
45C22×C97—41no—
46C22×C97C2×D411yescharacteristic
47C2×D97—21no—
48C2×D97—22no—
49C2×D97—21no—
50C2×D97—21no—
51C2×D97—41no—
52C2×D97—41no—
53C4×C97—22no—
54C4×C97C2×D411yescharacteristic
55C4×C97C2×D411yescharacteristic
56Dic97—21no—
57Dic97—41no—
58C2×C97—81no—
59C2×C97#12011yescharacteristic
60C2×C97#13511yescharacteristic
61C2×C97AGL(1,ℤ/8)11yescharacteristic
62D97—41no—
63D97—42no—
64C97#44911yescharacteristic, complemented, Sylow
65#449—971nomaximal, Sylow
66C2×#41—971no—
67C2×SD16D9711yescharacteristic, complemented
68C2×D8—971no—
69#121—971no—
70#103—971no—
71#102—971no—
72C22⋊C8—971no—
73#41—1942no—
74#41—1942no—
75C2×Q8C2×D9711yescharacteristic
76C2×D4—971no—
77C2×D4—1941no—
78C2×D4—1941no—
79C2×D4C2×D9711yescharacteristic
80C22×C4—971no—
81C22×C4—1941no—
82SD16—22no—
83D8—1942no—
84C2×C8—971no—
85C2×C8C2×D9711yescharacteristic
86C4⋊C4—971no—
87C22⋊C4—1941no—
88C23—21no—
89C23—971no—
90C23—1941no—
91Q8—21no—
92Q8C22⋊D9712yescomplemented
93D4—21no—
94D4—21no—
95D4—972no—
96D4—3882no—
97D4—1944no—
98D4—1941no—
99C2×C4—21no—
100C2×C4—971no—
101C2×C4—1944no—
102C2×C4—1941no—
103C2×C4—1941no—
104C2×C4—1941no—
105C2×C4C22×D9711yescharacteristic
106C8—21no—
107C8—1941no—
108C22—41no—
109C22—41no—
110C22—41no—
111C22—3881no—
112C22—3881no—
113C22—1942no—
114C22—1941no—
115C22—1941no—
116C22—1941no—
117C22D4×D9711yescharacteristic
118C4—22no—
119C4—3881no—
120C4—1941no—
121C4D4×D9711yescharacteristic
122C4C2×C22⋊D9711yescharacteristic
123C2—81no—
124C2—3882no—
125C2—3881no—
126C2#1569077811yescharacteristic
127C2#1569083111yescharacteristic
128C2#1569083711yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#449
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13095512C2semidirect
2. C2×#13095496C2semidirect
3. #15690781C2semidirect
4. #15690734C2semidirect
5. #15690732C2semidirect
6. #15690722C2semidirect
7. C2×SD16×C97C2semidirect
27. Q8×C97D4semidirect
37. D388D4semidirect
64. C97#449semidirect
67. C2×SD16D97semidirect
92. Q8C22⋊D97semidirect