Finite Group Databasebeta

← #20260736

Subgroups — #20260736

Order 6208.

162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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×#13095495C211yesmaximal, characteristic, complemented
2C2×C4⋊Dic97C211yesmaximal, characteristic, complemented
3#15690734C212yesmaximal, complemented
4#15690731C212yesmaximal, complemented
5C2×#41×C97C211yesmaximal, characteristic
6C22×Dic97—21no—
7#13095495—22no—
8C2×#11715895C2212yes—
9C4⋊Dic97—21no—
10C4⋊Dic97C2212yes—
11#41×C97—22no—
12#41×C97C414yescomplemented
13C2×Q8×C97C2211yescharacteristic
14C2×D4×C97—21no—
15C2×D4×C97C2211yescharacteristic
16C22×C4×C97—21no—
17C22×C4×C97C2211yescharacteristic
18C23×C97—21no—
19C23×C97D411yescharacteristic
20Q8×C97—21no—
21Q8×C97C2×C412yescomplemented
22D4×C97—24no—
23D4×C97—21no—
24D4×C97C2×C412yescomplemented
25C2×C4×C97—21no—
26C2×C4×C97—24no—
27C2×C4×C97C2×C412yes—
28C2×C4×C97D411yescharacteristic
29C2×C4×C97D412yes—
30C2×C4×C97C2311yescharacteristic
31C2×Dic97—22no—
32C2×Dic97—42no—
33#11715895—22no—
34C22×C97—21no—
35C22×C97—21no—
36C22×C97—22no—
37C22×C97—41no—
38C22×C97—41no—
39C22×C97C22⋊C412yes—
40C22×C97C2×D411yescharacteristic
41C4×C97—22no—
42C4×C97C22⋊C412yes—
43C4×C97C22×C411yescharacteristic
44C4×C97C2×D411yescharacteristic
45Dic97—42no—
46C2×C97—22no—
47C2×C97—42no—
48C2×C97C2×C22⋊C411yescharacteristic
49C2×C97AGL(1,ℤ/8)11yescharacteristic
50C2×C97#13711yescharacteristic
51C97#41711yescharacteristic, complemented, Sylow
52#417—971nomaximal, Sylow
53C2×#41D9711yescharacteristic
54C2×M16—971no—
55C2×C4⋊C4—971no—
56#103—972no—
57#102—972no—
58#41—22no—
59#41Dic9714yescomplemented
60C2×Q8C2×D9711yescharacteristic
61C2×D4—21no—
62C2×D4C2×D9711yescharacteristic
63C22×C4—21no—
64C22×C4—1941no—
65C22×C4C2×D9711yescharacteristic
66M16—1942no—
67C2×C8—972no—
68C4⋊C4—972no—
69C4⋊C4—1941no—
70C23—21no—
71C23C22⋊D9711yescharacteristic
72Q8—21no—
73Q8C2×Dic9712yescomplemented
74D4—24no—
75D4—21no—
76D4C2×Dic9712yescomplemented
77C2×C4—21no—
78C2×C4—24no—
79C2×C4—3882no—
80C2×C4—1942no—
81C2×C4C2×Dic9712yes—
82C2×C4C22⋊D9711yescharacteristic
83C2×C4C22⋊D9712yes—
84C2×C4C22×D9711yescharacteristic
85C8—1942no—
86C22—21no—
87C22—21no—
88C22—22no—
89C22—41no—
90C22—41no—
91C22C22⋊Dic9712yes—
92C22C2×C22⋊D9711yescharacteristic
93C4—22no—
94C4—3882no—
95C4C22⋊Dic9712yes—
96C4C22×Dic9711yescharacteristic
97C4C2×C22⋊D9711yescharacteristic
98C2—22no—
99C2—42no—
100C2C2×C22⋊Dic9711yescharacteristic
101C2#1569083511yescharacteristic
102C2#1569084011yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×#41×C97C2
socleC22×C97C2×D4
hypercenterC2×#41D97
hypocenterC97#417
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13095495C2semidirect
2. C2×C4⋊Dic97C2semidirect
3. #15690734C2semidirect
4. #15690731C2semidirect
12. #41×C97C4semidirect
21. Q8×C97C2×C4semidirect
24. D4×C97C2×C4semidirect
51. C97#417semidirect
59. #41Dic97semidirect
73. Q8C2×Dic97semidirect
76. D4C2×Dic97semidirect