Finite Group Databasebeta

← #21460819

Subgroups — #21460819

Order 7808.

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

normal subgroups only

This group has 140 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
2#16840608C211yesmaximal, characteristic
3#16839683C211yesmaximal, characteristic
4C2×#11758217—21no—
5C22⋊#92420—21no—
6C22×Dic122C411yescharacteristic
7C2×C4⋊Dic61—21no—
8C2×#11758196C2211yescharacteristic
9#14519684—21no—
10#95×C61C411yescharacteristic
11C22×C4×C61—21no—
12C22×C4×C61C2×C411yescharacteristic
13C22×Dic61—21no—
14C22×Dic61D411yescharacteristic
15C22×Dic61D411yescharacteristic
16C2×Dic122—41no—
17C2×Dic122—42no—
18#11758217—22no—
19#11758217—41no—
20C2×#92420—41no—
21C2×#92420—41no—
22C4⋊Dic61—42no—
23#11758196—41no—
24C23×C61C22⋊C411yescharacteristic
25C2×C4×C61—22no—
26C2×C4×C61—21no—
27C2×C4×C61—41no—
28C2×C4×C61—41no—
29C2×C4×C61—41no—
30C2×Dic61—21no—
31C2×Dic61—21no—
32C2×Dic61—22no—
33C2×Dic61—21no—
34C2×Dic61—41no—
35C2×Dic61—41no—
36C2×Dic61—41no—
37C2×Dic61SD1611yescharacteristic
38C2×Dic61Q1611yescharacteristic
39Dic122—42no—
40Dic122—42no—
41#92420—42no—
42#92420—81no—
43C22×C61—21no—
44C22×C61—21no—
45C22×C61#9911yescharacteristic
46C22×C61#10311yescharacteristic
47C22×C61#10411yescharacteristic
48C4×C61—42no—
49C4×C61—41no—
50Dic61—21no—
51Dic61—21no—
52Dic61—41no—
53Dic61—42no—
54#1354—611nomaximal, Sylow
55C2×C61—21no—
56C2×C61—21no—
57C2×C61#32811yescharacteristic
58C2×C61AΣL(1,𝔽16)11yescharacteristic
59C2×C61#35611yescharacteristic
60#395—611no—
61#343—611no—
62#324—611no—
63C61#135411yescharacteristic, complemented, Sylow
64C22×Q8—611no—
65C2×M16—1221no—
66C2×C4⋊C4—611no—
67C2×C4⋊C4—1221no—
68C22⋊C8—1221no—
69#95—1221no—
70#95#692311yescharacteristic
71C2×Q8—2441no—
72C2×Q8—2442no—
73C22×C4—21no—
74C22×C4—611no—
75C22×C4—611no—
76C22×C4—1221no—
77C22×C4C2×#692311yescharacteristic
78M16—1222no—
79M16—2441no—
80C2×C8—2441no—
81C2×C8—2441no—
82C4⋊C4—2441no—
83C4⋊C4—2442no—
84C23C22⋊#692311yescharacteristic
85Q8—2442no—
86Q8—2442no—
87C2×C4—22no—
88C2×C4—21no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—611no—
93C2×C4—611no—
94C2×C4—1221no—
95C2×C4—1221no—
96C2×C4—1222no—
97C2×C4—1221no—
98C2×C4—2441no—
99C2×C4—2441no—
100C2×C4—2441no—
101C8—4881no—
102C8—2442no—
103C22—21no—
104C22—21no—
105C22#1451983611yescharacteristic
106C22#1451984011yescharacteristic
107C22#1451984111yescharacteristic
108C4—42no—
109C4—41no—
110C4—1221no—
111C4—1221no—
112C4—2441no—
113C4—2442no—
114C2—21no—
115C2—21no—
116C2#1684061511yescharacteristic
117C2#1684066311yescharacteristic
118C2#1684067311yescharacteristic
subgroupG/H
centerC22#14519836
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
Fitting#95×C61C4
socleC22×C61#99
hypercenter#95#6923
hypocenterC61#1354
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
63. C61#1354semidirect