Finite Group Databasebeta

← #20261116

Subgroups — #20261116

Order 6208.

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

normal subgroups only

This group has 130 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×#13095501C211yesmaximal, characteristic, complemented
2C2×#13095500C211yesmaximal, characteristic, complemented
3C2×#13095496C211yesmaximal, characteristic
4#15690799C211yesmaximal, characteristic, complemented
5#15690797C211yesmaximal, characteristic, complemented
6C8×Dic97C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8C2×Dic194C2211yescharacteristic
9C2×D388C2211yescharacteristic
10#13095501—22no—
11#13095500—22no—
12#13095496—22no—
13C2×#11715895C2211yescharacteristic
14C22⋊Dic97—22no—
15#13095488—22no—
16C4×Dic97C2211yescharacteristic
17C2×Q8×C97C2211yescharacteristic
18C2×D4×C97C2211yescharacteristic
19SD16×C97—22no—
20C2×C8×C97C2211yescharacteristic
21C23×C97—21no—
22C22×D97—21no—
23Q8×C97—21no—
24Q8×C97—21no—
25D4×C97—21no—
26D4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97C2311yescharacteristic
29C2×Dic97—21no—
30C2×Dic97D412yes—
31D388—21no—
32D388—21no—
33Dic194—21no—
34Dic194—21no—
35C8×C97D412yes—
36#11715895D412yes—
37C22×C97—41no—
38C22×C97—42no—
39C22×C97C2×D411yescharacteristic
40C2×D97—41no—
41C2×D97—42no—
42C4×C97—41no—
43C4×C97C2×D411yescharacteristic
44C4×C97C2×D411yescharacteristic
45Dic97—22no—
46Dic97—41no—
47C2×C97—81no—
48C2×C97#12711yescharacteristic
49C2×C97#13512yes—
50D97—81no—
51C97#49511yescharacteristic, complemented, Sylow
52#495—971nomaximal, Sylow
53C2×Q16—971no—
54C2×SD16—971no—
55C2×SD16D9711yescharacteristic, complemented
56C2×D8—971no—
57#124—971no—
58#124—971no—
59C4×C8—971no—
60C2×Q8—971no—
61C2×Q8C2×D9711yescharacteristic
62C2×D4—971no—
63C2×D4C2×D9711yescharacteristic
64Q16—1942no—
65SD16—22no—
66SD16—1942no—
67D8—1942no—
68C2×C8—971no—
69C2×C8C2×D9711yescharacteristic
70C22⋊C4—1942no—
71C22⋊C4—1942no—
72C42—971no—
73C23—21no—
74C23—1941no—
75Q8—21no—
76Q8—21no—
77Q8—1941no—
78Q8—1941no—
79D4—21no—
80D4—21no—
81D4—1941no—
82D4—1941no—
83C2×C4—21no—
84C2×C4—972no—
85C2×C4—1941no—
86C2×C4C22×D9711yescharacteristic
87C8—972no—
88C8C22⋊D9712yes—
89C22—41no—
90C22—42no—
91C22—3881no—
92C22—3882no—
93C22D4×D9711yescharacteristic
94C4—41no—
95C4—3881no—
96C4—1942no—
97C4D4×D9711yescharacteristic
98C4C2×C22⋊D9711yescharacteristic
99C2—81no—
100C2—7761no—
101C2#1569080611yescharacteristic
102C2#1569083112yes—
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#495
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×#13095501C2semidirect
2. C2×#13095500C2semidirect
4. #15690799C2semidirect
5. #15690797C2semidirect
6. C8×Dic97C2semidirect
7. C2×SD16×C97C2semidirect
51. C97#495semidirect
55. C2×SD16D97semidirect