Finite Group Databasebeta

← #20260897

Subgroups — #20260897

Order 6208.

152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13095499C211yesmaximal, characteristic, complemented
3#15690789C211yesmaximal, characteristic, complemented
4#15690734C211yesmaximal, characteristic, complemented
5#15690731C211yesmaximal, characteristic, complemented
6C22⋊#11715895C211yesmaximal, characteristic, complemented
7C2×#41×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9#13095501—22no—
10#13095499—22no—
11C2×#11715895C2211yescharacteristic
12C2×#11715895C2211yescharacteristic
13C4⋊Dic97C2211yescharacteristic
14#13095490—21no—
15C22⋊Dic97—21no—
16#41×C97—22no—
17#41×C97—22no—
18C2×Q8×C97C2211yescharacteristic
19C2×D4×C97—21no—
20C2×D4×C97C2211yescharacteristic
21C22×C4×C97—21no—
22C22×C4×C97C2211yescharacteristic
23C23×C97—21no—
24C23×C97D411yescharacteristic
25Q8×C97—21no—
26Q8×C97D412yes—
27D4×C97—24no—
28D4×C97—21no—
29D4×C97D412yes—
30C2×C4×C97—24no—
31C2×C4×C97—21no—
32C2×C4×C97—21no—
33C2×C4×C97—21no—
34C2×C4×C97D411yescharacteristic
35C2×C4×C97C2311yescharacteristic
36C2×Dic97—21no—
37C2×Dic97—21no—
38Dic194—21no—
39Dic194—21no—
40#11715895—21no—
41#11715895—21no—
42C22×C97—21no—
43C22×C97—22no—
44C22×C97—21no—
45C22×C97—21no—
46C22×C97—41no—
47C22×C97—41no—
48C22×C97C2×D411yescharacteristic
49C4×C97—21no—
50C4×C97—22no—
51C4×C97C2×D411yescharacteristic
52C4×C97C2×D411yescharacteristic
53Dic97—41no—
54Dic97—41no—
55C2×C97—41no—
56C2×C97—42no—
57C2×C97#12011yescharacteristic
58C2×C97#13511yescharacteristic
59C2×C97#13711yescharacteristic
60C97#45211yescharacteristic, complemented, Sylow
61#452—971nomaximal, Sylow
62C2×#41D9711yescharacteristic
63C2×Q16—971no—
64C2×SD16—971no—
65C22⋊Q8—971no—
66#103—971no—
67#102—971no—
68C22⋊C8—971no—
69#41—22no—
70#41—22no—
71C2×Q8—971no—
72C2×Q8C2×D9711yescharacteristic
73C2×D4—21no—
74C2×D4C2×D9711yescharacteristic
75C22×C4—21no—
76C22×C4C2×D9711yescharacteristic
77Q16—1942no—
78SD16—1942no—
79C2×C8—971no—
80C2×C8—971no—
81C4⋊C4—971no—
82C4⋊C4—1941no—
83C22⋊C4—1941no—
84C23—21no—
85C23C22⋊D9711yescharacteristic
86Q8—21no—
87Q8—1941no—
88Q8—1941no—
89Q8C22⋊D9712yes—
90D4—24no—
91D4—21no—
92D4C22⋊D9712yes—
93C2×C4—24no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—1941no—
98C2×C4—1941no—
99C2×C4C22⋊D9711yescharacteristic
100C2×C4C22×D9711yescharacteristic
101C8—1941no—
102C8—1941no—
103C22—21no—
104C22—22no—
105C22—21no—
106C22—21no—
107C22—41no—
108C22—41no—
109C22C2×C22⋊D9711yescharacteristic
110C4—21no—
111C4—22no—
112C4—3881no—
113C4—3881no—
114C4C2×C22⋊D9711yescharacteristic
115C4C2×C22⋊D9711yescharacteristic
116C2—41no—
117C2—42no—
118C2#1569077911yescharacteristic
119C2#1569083011yescharacteristic
120C2#1569084011yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×#41×C97C2
socleC22×C97C2×D4
hypercenterC2×#41D97
hypocenterC97#452
LCSG ▷ C2×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×#13095501C2semidirect
2. C2×#13095499C2semidirect
3. #15690789C2semidirect
4. #15690734C2semidirect
5. #15690731C2semidirect
6. C22⋊#11715895C2semidirect
60. C97#452semidirect