Finite Group Databasebeta

← #20260974

Subgroups — #20260974

Order 6208.

114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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×#13095501C211yesmaximal, characteristic, complemented
2C22×#11715895C211yesmaximal, characteristic
3#15690789C211yesmaximal, characteristic
4#15690743C211yesmaximal, characteristic, complemented
5#15690734C211yesmaximal, characteristic, complemented
6#15690733C211yesmaximal, characteristic, complemented
7C22⋊Q8×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9#13095501—22no—
10C2×#11715895—22no—
11C2×#11715895C2211yescharacteristic
12C2×#11715895C2211yescharacteristic
13C4⋊Dic97C2211yescharacteristic
14#13095490—21no—
15C22⋊Dic97—21no—
16C2×Q8×C97C2211yescharacteristic
17C22×C4×C97C2211yescharacteristic
18C4⋊C4×C97—21no—
19C4⋊C4×C97C2211yescharacteristic
20C22⋊C4×C97—21no—
21C23×C97D411yescharacteristic
22Q8×C97—21no—
23Q8×C97—21no—
24C2×C4×C97—21no—
25C2×C4×C97—21no—
26C2×C4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97D411yescharacteristic
29C2×C4×C97C2311yescharacteristic
30C2×Dic97—21no—
31C2×Dic97—21no—
32Dic194—21no—
33Dic194—21no—
34#11715895—21no—
35#11715895D412yes—
36C22×C97—21no—
37C22×C97—21no—
38C22×C97Q1612yescomplemented
39C22×C97C2×D411yescharacteristic
40C4×C97—21no—
41C4×C97—41no—
42C4×C97—41no—
43C4×C97C2×D411yescharacteristic
44C4×C97#4111yescharacteristic
45Dic97—41no—
46Dic97—41no—
47C2×C97—22no—
48C2×C97#12111yescharacteristic
49C2×C97C2×Q1611yescharacteristic
50C2×C97#13511yescharacteristic
51C97#46711yescharacteristic, complemented, Sylow
52#467—971nomaximal, Sylow
53C2×Q16—971no—
54C22×C8—971no—
55C22⋊Q8—971no—
56C22⋊Q8D9711yescharacteristic
57#107—971no—
58#103—971no—
59#103—971no—
60C2×Q8—971no—
61C2×Q8C2×D9711yescharacteristic
62C22×C4C2×D9711yescharacteristic
63Q16—1942no—
64C2×C8—971no—
65C2×C8—971no—
66C2×C8—1942no—
67C4⋊C4—21no—
68C4⋊C4—971no—
69C4⋊C4—1941no—
70C4⋊C4C2×D9711yescharacteristic
71C22⋊C4—21no—
72C22⋊C4—1941no—
73C23C22⋊D9711yescharacteristic
74Q8—21no—
75Q8—21no—
76Q8—1941no—
77Q8—1941no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—1941no—
83C2×C4—1941no—
84C2×C4C22⋊D9711yescharacteristic
85C2×C4C22×D9711yescharacteristic
86C8—972no—
87C8—1941no—
88C22—21no—
89C22—21no—
90C22#1309550112yescomplemented
91C22C2×C22⋊D9711yescharacteristic
92C4—21no—
93C4—41no—
94C4—41no—
95C4—3881no—
96C4—3881no—
97C4D4×D9711yescharacteristic
98C4#1309551011yescharacteristic
99C2—22no—
100C2#1569078211yescharacteristic
101C2C2×#1309550111yescharacteristic
102C2#1569083011yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊Q8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊Q8D97
hypocenterC97#467
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13095501C2semidirect
4. #15690743C2semidirect
5. #15690734C2semidirect
6. #15690733C2semidirect
38. C22×C97Q16semidirect
51. C97#467semidirect
90. C22#13095501semidirect