Finite Group Databasebeta

← #21460814

Subgroups — #21460814

Order 7808.

162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 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#16840640C211yesmaximal, characteristic
2#16840606C211yesmaximal, characteristic
3#16839673C211yesmaximal, characteristic
4C2×C22⋊#6923—21no—
5C22⋊#92420—21no—
6C2×#11758198—21no—
7C2×#11758198C2211yescharacteristic
8#14519684—21no—
9#14519684C411yescharacteristic, complemented
10C22×Q8×C61C411yescharacteristic, complemented
11C23×D61D411yescharacteristic
12C22×#6923—41no—
13C2×Q8×C61—42no—
14C2×Q8×C61—41no—
15C22×C4×C61—21no—
16C22×C4×C61C2×C411yescharacteristic
17C22×Dic61—21no—
18C22×Dic61D411yescharacteristic
19C22⋊#6923—22no—
20C22⋊#6923—41no—
21C2×#92420—41no—
22#11758198—41no—
23#11758198—42no—
24C23×C61C22⋊C411yescharacteristic
25C22×D61—21no—
26C22×D61—21no—
27C22×D61—41no—
28C22×D61—41no—
29C22×D61SD1611yescharacteristic
30C22×D61Q1611yescharacteristic
31C2×#6923—42no—
32C2×#6923—81no—
33C2×#6923—81no—
34Q8×C61—42no—
35Q8×C61—42no—
36C2×C4×C61—22no—
37C2×C4×C61—21no—
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×Dic61—21no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61—41no—
45C2×Dic61—41no—
46#92420—81no—
47C22×C61—21no—
48C22×C61—21no—
49C22×C61#9911yescharacteristic
50C22×C61#10311yescharacteristic
51C22×C61#10411yescharacteristic
52C2×D61—21no—
53C2×D61—21no—
54C2×D61—41no—
55C2×D61—41no—
56C2×D61—41no—
57C2×D61—41no—
58C2×D61—81no—
59#6923—82no—
60C4×C61—42no—
61C4×C61—41no—
62Dic61—41no—
63Dic61—81no—
64#1351—611nomaximal, Sylow
65C2×C61—21no—
66C2×C61—21no—
67C2×C61#32811yescharacteristic
68C2×C61AΣL(1,𝔽16)11yescharacteristic
69C2×C61#35411yescharacteristic
70D61—41no—
71D61—41no—
72#393—611no—
73#342—611no—
74#323—611no—
75C61#135111yescharacteristic, complemented, Sylow
76C22×Q8#692311yescharacteristic, complemented
77C2×C22⋊C4—611no—
78C2×C22⋊C4—1221no—
79C2×C22⋊C4—1221no—
80C22⋊C8—1221no—
81#95—611no—
82#95—1221no—
83C24—611no—
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—611no—
88C22×C4—1221no—
89C22×C4—2441no—
90C22×C4C2×#692311yescharacteristic
91C2×C8—2441no—
92C22⋊C4—1222no—
93C22⋊C4—2441no—
94C22⋊C4—2442no—
95C22⋊C4—2441no—
96C23—611no—
97C23—611no—
98C23—1221no—
99C23—1221no—
100C23—2441no—
101C23—2441no—
102C23C22⋊#692311yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—1221no—
111C2×C4—4881no—
112C2×C4—4881no—
113C2×C4—2441no—
114C2×C4—2441no—
115C2×C4—2442no—
116C2×C4—2441no—
117C2×C4—2441no—
118C8—4881no—
119C22—21no—
120C22—21no—
121C22—1221no—
122C22—1221no—
123C22—4881no—
124C22—2441no—
125C22—2441no—
126C22—2441no—
127C22—2441no—
128C22#1451983511yescharacteristic
129C22#1451984011yescharacteristic
130C22#1451984211yescharacteristic
131C4—42no—
132C4—41no—
133C4—4881no—
134C4—4882no—
135C4—2441no—
136C2—21no—
137C2—21no—
138C2—2441no—
139C2—2441no—
140C2#1684061611yescharacteristic
141C2#1684066211yescharacteristic
142C2#1684066811yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
FittingC22×Q8×C61C4
socleC22×C61#99
hypercenterC22×Q8#6923
hypocenterC61#1351
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. #14519684C4semidirect
10. C22×Q8×C61C4semidirect
75. C61#1351semidirect
76. C22×Q8#6923semidirect