Finite Group Databasebeta

← #21460673

Subgroups — #21460673

Order 7808.

156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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#16840767C211yesmaximal, characteristic
2#16840706C211yesmaximal, characteristic
3#16839813C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×C4⋊#6923—21no—
6#14519844—21no—
7#14519844C412yescomplemented
8(C2×#6923)⋊C4—21no—
9(C2×#6923)⋊C4C412yes—
10C42×D61C2211yescharacteristic
11#14519706—21no—
12#14519689—21no—
13C4×#92418C411yescharacteristic, complemented
14C4×C8×C61C411yescharacteristic, complemented
15C22×#6923—22no—
16C2×C4×D61C2×C411yescharacteristic
17C2×C4×D61D411yescharacteristic
18C2×C4×D61D411yescharacteristic
19C2×#92420—22no—
20C4⋊#6923—41no—
21C4⋊#6923—41no—
22#11758213—41no—
23#11758213—41no—
24C2×C8×C61—21no—
25C42×C61C2×C411yescharacteristic
26C4×Dic61C2×C411yescharacteristic
27C4×Dic61D411yescharacteristic
28C4×Dic61Q811yescharacteristic
29C2×#92418—21no—
30C22×D61C22⋊C411yescharacteristic
31C2×#6923—42no—
32C2×#6923—42no—
33C2×#6923—42no—
34C2×C4×C61C4211yescharacteristic
35C2×C4×C61C22⋊C411yescharacteristic
36C2×C4×C61C4⋊C411yescharacteristic
37C2×Dic61C22⋊C411yescharacteristic
38C2×Dic61C4⋊C411yescharacteristic
39C2×Dic61C4⋊C411yescharacteristic
40C4×D61—41no—
41C4×D61—41no—
42C4×D61D811yescharacteristic
43C4×D61SD1611yescharacteristic
44C4×D61SD1611yescharacteristic
45C4×D61Q1611yescharacteristic
46#92420—42no—
47C8×C61—41no—
48#92418—41no—
49C22×C61#9511yescharacteristic
50C2×D61—21no—
51C2×D61—21no—
52C2×D61#10211yescharacteristic
53C2×D61#10311yescharacteristic
54#6923—82no—
55C4×C61—21no—
56C4×C61—21no—
57C4×C61#10611yescharacteristic
58C4×C61#10711yescharacteristic
59Dic61—21no—
60Dic61—21no—
61Dic61#10211yescharacteristic
62Dic61#10311yescharacteristic
63#1286—611nomaximal, Sylow
64C2×C61H(3,ℤ/4)11yescharacteristic
65C2×C61#34011yescharacteristic
66C2×C61#34411yescharacteristic
67D61—21no—
68D61—21no—
69#431—611no—
70#423—611no—
71#382—611no—
72C61#128611yescharacteristic, complemented, Sylow
73C2×M16—1221no—
74C2×C4⋊C4—1221no—
75C2×C42—611no—
76C4⋊C8—612no—
77C4⋊C8—1221no—
78C4⋊C8—1221no—
79C22⋊C8—1221no—
80C4×C8—611no—
81C4×C8#692311yescharacteristic, complemented
82#95—612no—
83#95—1221no—
84C22×C4—611no—
85C22×C4—611no—
86C22×C4—611no—
87C22×C4—1222no—
88M16—2441no—
89M16—2441no—
90C2×C8—21no—
91C2×C8—1222no—
92C2×C8—1221no—
93C4⋊C4—2441no—
94C4⋊C4—2441no—
95C42—611no—
96C42—611no—
97C42—611no—
98C42C2×#692311yescharacteristic
99C23—611no—
100C2×C4—611no—
101C2×C4—611no—
102C2×C4—611no—
103C2×C4—611no—
104C2×C4—611no—
105C2×C4—611no—
106C2×C4—611no—
107C2×C4—2441no—
108C2×C4—2441no—
109C2×C4—2442no—
110C2×C4—2442no—
111C2×C4—2442no—
112C2×C4C4×#692311yescharacteristic
113C2×C4C4⋊#692311yescharacteristic
114C2×C4C22⋊#692311yescharacteristic
115C8—41no—
116C8—2441no—
117C8—2442no—
118C22—611no—
119C22—611no—
120C22—1221no—
121C22—1221no—
122C22(C2×#6923)⋊C411yescharacteristic
123C4—21no—
124C4—21no—
125C4—611no—
126C4—611no—
127C4—1221no—
128C4—1221no—
129C4—4882no—
130C4#1451984511yescharacteristic
131C4#1451984611yescharacteristic
132C2—1221no—
133C2—1221no—
134C2#1684062911yescharacteristic
135C2#1684063611yescharacteristic
136C2#1684064411yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC42C2×#6923
FittingC4×C8×C61C4
socleC22×C61#95
hypercenterC4×C8#6923
hypocenterC61#1286
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
7. #14519844C4semidirect
13. C4×#92418C4semidirect
14. C4×C8×C61C4semidirect
72. C61#1286semidirect
81. C4×C8#6923semidirect