Finite Group Databasebeta

← #20260734

Subgroups — #20260734

Order 6208.

162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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
2C2×#13095495C211yesmaximal, characteristic, complemented
3#15690733C212yesmaximal, complemented
4#15690730C212yesmaximal, complemented
5C2×C4⋊C4×C97C211yesmaximal, characteristic, complemented
6#13095511—22no—
7#13095511C414yescomplemented
8C2×Dic194C2211yescharacteristic
9C2×D388C2211yescharacteristic
10C2×C22⋊D97—21no—
11C2×C4×D97—21no—
12#13095495—22no—
13C2×#11715895C2212yes—
14C22×C4×C97—21no—
15C22×C4×C97C2211yescharacteristic
16C4⋊C4×C97—21no—
17C4⋊C4×C97C2212yes—
18C23×C97D411yescharacteristic
19C22×D97—21no—
20C2×C4×C97—22no—
21C2×C4×C97—42no—
22C2×C4×C97C2×C412yes—
23C2×C4×C97D412yes—
24C2×C4×C97D411yescharacteristic
25C2×C4×C97C2311yescharacteristic
26C22⋊D97—24no—
27C2×Dic97—21no—
28D388—21no—
29D388C2×C412yescomplemented
30C4×D97—24no—
31Dic194—21no—
32Dic194C2×C412yescomplemented
33#11715895—22no—
34C22×C97—21no—
35C22×C97—21no—
36C22×C97C22⋊C412yes—
37C22×C97C2×D411yescharacteristic
38C2×D97—22no—
39C2×D97—41no—
40C2×D97—41no—
41C4×C97—42no—
42C4×C97C22⋊C412yes—
43C4×C97C22×C411yescharacteristic
44C4×C97C2×D411yescharacteristic
45Dic97—22no—
46C2×C97—22no—
47C2×C97C2×C22⋊C411yescharacteristic
48C2×C97AGL(1,ℤ/8)11yescharacteristic
49C2×C97#13711yescharacteristic
50D97—42no—
51C97#41711yescharacteristic, complemented, Sylow
52#417—971nomaximal, Sylow
53C2×#41—971no—
54C2×M16—971no—
55C2×C4⋊C4D9711yescharacteristic, complemented
56#103—972no—
57#102—972no—
58#41—974no—
59#41—1942no—
60C2×Q8—971no—
61C2×D4—971no—
62C2×D4—1941no—
63C22×C4—21no—
64C22×C4—1941no—
65C22×C4C2×D9711yescharacteristic
66M16—1942no—
67C2×C8—972no—
68C4⋊C4—21no—
69C4⋊C4C2×D9712yes—
70C23—1941no—
71C23C22⋊D9711yescharacteristic
72Q8—972no—
73Q8—1941no—
74D4—972no—
75D4—1944no—
76D4—1941no—
77C2×C4—22no—
78C2×C4—42no—
79C2×C4—1941no—
80C2×C4—1944no—
81C2×C4C4×D9712yes—
82C2×C4D38812yes—
83C2×C4C22⋊D9711yescharacteristic
84C2×C4C22×D9711yescharacteristic
85C8—1942no—
86C22—21no—
87C22—21no—
88C22—3881no—
89C22—3881no—
90C22—1942no—
91C22#1309548812yes—
92C22C2×C22⋊D9711yescharacteristic
93C4—42no—
94C4—1942no—
95C4#1309548812yes—
96C4C2×C4×D9711yescharacteristic
97C4C2×D38811yescharacteristic
98C2—22no—
99C2—3882no—
100C2C2×#1309548811yescharacteristic
101C2#1569083611yescharacteristic
102C2#1569084111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×C4⋊C4×C97C2
socleC22×C97C2×D4
hypercenterC2×C4⋊C4D97
hypocenterC97#417
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13095495C2semidirect
3. #15690733C2semidirect
4. #15690730C2semidirect
5. C2×C4⋊C4×C97C2semidirect
7. #13095511C4semidirect
29. D388C2×C4semidirect
32. Dic194C2×C4semidirect
51. C97#417semidirect
55. C2×C4⋊C4D97semidirect