Finite Group Databasebeta

← #21460801

Subgroups — #21460801

Order 7808.

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

normal subgroups only

This group has 168 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#16840642C211yesmaximal, characteristic, complemented
2#16840608C211yesmaximal, characteristic, complemented
3#16839676C211yesmaximal, characteristic
4C2×#11758217—21no—
5C22⋊#92420—21no—
6C2×#11758196C2211yescharacteristic
7C2×C22⋊Dic61—21no—
8C2×C22⋊Dic61—21no—
9#14519684C411yescharacteristic
10C22×D4×C61C411yescharacteristic
11C24×C61—21no—
12C2×D4×C61—41no—
13C2×D4×C61—42no—
14C22×C4×C61C2×C411yescharacteristic
15C22×Dic61—21no—
16C22×Dic61D411yescharacteristic
17C22×Dic61D411yescharacteristic
18#11758217—22no—
19#11758217—41no—
20C2×#92420—41no—
21C2×#92420—41no—
22C22⋊Dic61—42no—
23C22⋊Dic61—41no—
24C22⋊Dic61—41no—
25#11758196—41no—
26C23×C61—22no—
27C23×C61—41no—
28C23×C61—41no—
29C23×C61—41no—
30C23×C61—41no—
31C23×C61—41no—
32C23×C61—41no—
33C23×C61C22⋊C411yescharacteristic
34D4×C61—42no—
35D4×C61—42no—
36C2×C4×C61—21no—
37C2×C4×C61—41no—
38C2×Dic61—21no—
39C2×Dic61—21no—
40C2×Dic61—21no—
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61—41no—
45C2×Dic61D811yescharacteristic
46C2×Dic61SD1611yescharacteristic
47#92420—42no—
48#92420—81no—
49C22×C61—21no—
50C22×C61—21no—
51C22×C61—42no—
52C22×C61—42no—
53C22×C61—42no—
54C22×C61—81no—
55C22×C61—81no—
56C22×C61—81no—
57C22×C61—81no—
58C22×C61#9911yescharacteristic
59C22×C61#10211yescharacteristic
60C22×C61#10411yescharacteristic
61C4×C61—41no—
62Dic61—21no—
63Dic61—21no—
64Dic61—41no—
65Dic61—81no—
66#1345—611nomaximal, Sylow
67C2×C61—21no—
68C2×C61—21no—
69C2×C61—82no—
70C2×C61#32711yescharacteristic
71C2×C61AΣL(1,𝔽16)11yescharacteristic
72C2×C61#35511yescharacteristic
73#394—611no—
74#343—611no—
75#324—611no—
76C61#134511yescharacteristic, complemented, Sylow
77C22×D4#692311yescharacteristic
78C2×M16—1221no—
79C2×C4⋊C4—611no—
80C2×C22⋊C4—1221no—
81C2×C22⋊C4—1221no—
82C22⋊C8—1221no—
83#95—611no—
84C24—21no—
85C2×D4—41no—
86C2×D4—42no—
87C22×C4—611no—
88C22×C4—611no—
89C22×C4—1221no—
90C22×C4C2×#692311yescharacteristic
91M16—1222no—
92M16—2441no—
93C2×C8—2441no—
94C2×C8—2441no—
95C4⋊C4—2441no—
96C22⋊C4—2441no—
97C22⋊C4—2441no—
98C22⋊C4—2442no—
99C23—22no—
100C23—41no—
101C23—41no—
102C23—41no—
103C23—41no—
104C23—41no—
105C23—41no—
106C23C22⋊#692311yescharacteristic
107D4—42no—
108D4—42no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—611no—
112C2×C4—611no—
113C2×C4—1221no—
114C2×C4—1221no—
115C2×C4—1221no—
116C2×C4—2441no—
117C2×C4—2441no—
118C2×C4—2441no—
119C2×C4—2441no—
120C8—4881no—
121C8—2442no—
122C22—21no—
123C22—21no—
124C22—42no—
125C22—42no—
126C22—42no—
127C22—81no—
128C22—81no—
129C22—81no—
130C22—81no—
131C22#1451983511yescharacteristic
132C22#1451983911yescharacteristic
133C22#1451984111yescharacteristic
134C4—41no—
135C4—1221no—
136C4—1221no—
137C4—4881no—
138C4—2441no—
139C2—21no—
140C2—21no—
141C2—82no—
142C2#1684061311yescharacteristic
143C2#1684066211yescharacteristic
144C2#1684067011yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
FittingC22×D4×C61C4
socleC22×C61#99
hypercenterC22×D4#6923
hypocenterC61#1345
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840642C2semidirect
2. #16840608C2semidirect
76. C61#1345semidirect