Finite Group Databasebeta

← #21462101

Subgroups — #21462101

Order 7808.

238 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 54 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
1#16840741C212yesmaximal
2#16840668C214yesmaximal, complemented
3#16840336C211yesmaximal, characteristic
4#14519856—22no—
5#14519836C2214yes—
6#14519835—22no—
7C2×#11758222C2211yescharacteristic
8#14519775C412yescomplemented
9#14519766C2212yes—
10#14519760—22no—
11#14519753—22no—
12#14519736C411yescharacteristic, complemented
13C22×Q8×C61C411yescharacteristic, complemented
14C2×Q8×C61—21no—
15C2×Q8×C61—42no—
16C2×Q8×C61C2×C412yes—
17C22×C4×C61—21no—
18C22×C4×C61C2×C411yescharacteristic
19C2×C22⋊D61D412yes—
20#11758222—42no—
21C2×D244C2311yescharacteristic
22C2×C4×D61D412yes—
23C2×Dic122C2×C411yescharacteristic
24C22⋊#6923—24no—
25C4⋊#6923—42no—
26C4×#6923—42no—
27C22⋊Dic61—21no—
28#11758198—24no—
29C4⋊Dic61—21no—
30#11758196—24no—
31C4×Dic61C2×C412yes—
32C23×C61C22⋊C411yescharacteristic
33C22×D61C2×D412yes—
34C2×#6923—44no—
35Q8×C61—42no—
36Q8×C61—42no—
37C2×C4×C61—22no—
38C2×C4×C61—22no—
39C2×C4×C61—42no—
40C2×C4×C61C22⋊C411yescharacteristic
41C2×C4×C61C22×C411yescharacteristic
42C22⋊D61—42no—
43C2×Dic61—22no—
44C2×Dic61C22⋊C412yes—
45D244—41no—
46C4×D61—22no—
47C4×D61—22no—
48Dic122—41no—
49C22×C61—21no—
50C22×C61—41no—
51C22×C61C2×C22⋊C411yescharacteristic
52C2×D61—22no—
53C2×D61—42no—
54#6923—84no—
55C4×C61—21no—
56C4×C61—42no—
57C4×C61#9912yes—
58Dic61—22no—
59Dic61—42no—
60#2129—611nomaximal, Sylow
61C2×C61—21no—
62C2×C61—41no—
63C2×C61C2×#9911yescharacteristic
64D61—42no—
65#536—611no—
66#410—612no—
67#354—614no—
68C61#212911yescharacteristic, complemented, Sylow
69C2×#41—611no—
70C22×Q8#692311yescharacteristic, complemented
71C4⋊Q8—612no—
72#124—612no—
73#123—1222no—
74C22⋊Q8—1222no—
75#117—611no—
76#117—1222no—
77#99—614no—
78#99—1222no—
79#41—2442no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8—611no—
83C2×Q8C2×#692312yes—
84C2×D4—612no—
85C2×D4—611no—
86C22×C4—21no—
87C22×C4—612no—
88C22×C4C2×#692311yescharacteristic
89C4⋊C4—1224no—
90C4⋊C4—1221no—
91C4⋊C4—2442no—
92C22⋊C4—1224no—
93C22⋊C4—1221no—
94C22⋊C4—1224no—
95C42—612no—
96C42—2442no—
97C23—612no—
98C23C22⋊#692311yescharacteristic
99Q8—42no—
100Q8—42no—
101Q8—2441no—
102D4—2441no—
103D4—2442no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—42no—
107C2×C4—612no—
108C2×C4—1222no—
109C2×C4—1222no—
110C2×C4—1222no—
111C2×C4—2444no—
112C2×C4C22⋊#692311yescharacteristic
113C2×C4C22×#692311yescharacteristic
114C22—21no—
115C22—41no—
116C22—1222no—
117C22—2442no—
118C22C2×C22⋊#692311yescharacteristic
119C4—21no—
120C4—42no—
121C4—1222no—
122C4—4884no—
123C4—2442no—
124C4#1451983512yes—
125C2—21no—
126C2—41no—
127C2—2442no—
128C2C2×#1451983511yescharacteristic
subgroupG/H
centerC2C2×#14519835
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC2×C61C2×#99
hypercenterC22×Q8#6923
hypocenterC61#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #16840668C2semidirect
8. #14519775C4semidirect
12. #14519736C4semidirect
13. C22×Q8×C61C4semidirect
68. C61#2129semidirect
70. C22×Q8#6923semidirect