Finite Group Databasebeta

← #20260896

Subgroups — #20260896

Order 6208.

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

normal subgroups only

This group has 152 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
2C2×#13095498C211yesmaximal, characteristic, complemented
3#15690786C211yesmaximal, characteristic, complemented
4#15690734C211yesmaximal, characteristic, complemented
5#15690732C211yesmaximal, characteristic, complemented
6#15690722C211yesmaximal, characteristic, complemented
7C2×Q16×C97C211yesmaximal, characteristic, complemented
8#13095512—22no—
9#13095512—22no—
10C2×D388—21no—
11C2×D388C2211yescharacteristic
12C2×C4×D97—21no—
13C2×C4×D97C2211yescharacteristic
14#13095498—22no—
15C2×#11715895C2211yescharacteristic
16C4⋊Dic97C2211yescharacteristic
17#13095490—21no—
18#13095488—21no—
19C2×Q8×C97C2211yescharacteristic
20C2×Q8×C97C2211yescharacteristic
21Q16×C97—22no—
22C2×C8×C97C2211yescharacteristic
23C22×D97—21no—
24C22×D97D411yescharacteristic
25Q8×C97—21no—
26Q8×C97—21no—
27Q8×C97—21no—
28Q8×C97D412yes—
29C2×C4×C97—21no—
30C2×C4×C97—21no—
31C2×C4×C97C2311yescharacteristic
32C2×Dic97—21no—
33C2×Dic97D411yescharacteristic
34D388—24no—
35D388—21no—
36D388D412yes—
37C4×D97—24no—
38C4×D97—21no—
39C4×D97—21no—
40C8×C97—21no—
41#11715895—21no—
42C22×C97C2×D411yescharacteristic
43C2×D97—21no—
44C2×D97—22no—
45C2×D97—21no—
46C2×D97—21no—
47C2×D97—41no—
48C2×D97—41no—
49C4×C97—22no—
50C4×C97—41no—
51C4×C97C2×D411yescharacteristic
52C4×C97C2×D411yescharacteristic
53Dic97—21no—
54Dic97—41no—
55C2×C97#12011yescharacteristic
56C2×C97#13511yescharacteristic
57C2×C97#13711yescharacteristic
58D97—41no—
59D97—42no—
60C97#45211yescharacteristic, complemented, Sylow
61#452—971nomaximal, Sylow
62C2×#41—971no—
63C2×Q16D9711yescharacteristic, complemented
64C2×SD16—971no—
65C22⋊Q8—971no—
66#103—971no—
67#102—971no—
68C22⋊C8—971no—
69#41—1942no—
70#41—1942no—
71C2×Q8C2×D9711yescharacteristic
72C2×Q8C2×D9711yescharacteristic
73C2×D4—971no—
74C2×D4—1941no—
75C22×C4—971no—
76C22×C4—1941no—
77Q16—22no—
78SD16—1942no—
79C2×C8—971no—
80C2×C8C2×D9711yescharacteristic
81C4⋊C4—971no—
82C4⋊C4—1941no—
83C22⋊C4—1941no—
84C23—971no—
85C23—1941no—
86Q8—21no—
87Q8—21no—
88Q8—21no—
89Q8C22⋊D9712yes—
90D4—972no—
91D4—1944no—
92D4—1941no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—971no—
96C2×C4—1944no—
97C2×C4—1941no—
98C2×C4—1941no—
99C2×C4—1941no—
100C2×C4C22×D9711yescharacteristic
101C8—21no—
102C8—1941no—
103C22—3881no—
104C22—3881no—
105C22—1942no—
106C22—1941no—
107C22—1941no—
108C22—1941no—
109C22D4×D9711yescharacteristic
110C4—22no—
111C4—41no—
112C4—3881no—
113C4—1941no—
114C4D4×D9711yescharacteristic
115C4C2×C22⋊D9711yescharacteristic
116C2—3882no—
117C2—3881no—
118C2#1569077811yescharacteristic
119C2#1569083311yescharacteristic
120C2#1569084211yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×Q16×C97C2
socleC22×C97C2×D4
hypercenterC2×Q16D97
hypocenterC97#452
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#13095498C2semidirect
3. #15690786C2semidirect
4. #15690734C2semidirect
5. #15690732C2semidirect
6. #15690722C2semidirect
7. C2×Q16×C97C2semidirect
60. C97#452semidirect
63. C2×Q16D97semidirect