Finite Group Databasebeta

← #21461071

Subgroups — #21461071

Order 7808.

252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 64 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#16840783C212yesmaximal, complemented
2#16840608C212yesmaximal, complemented
3#16840605C212yesmaximal
4C2×#14519733C211yesmaximal, characteristic
5C4⋊#92420—22no—
6C22⋊#92420C2214yes—
7#14519832—22no—
8C23×Dic61C411yescharacteristic
9#14519733—22no—
10#14519733—22no—
11C2×#11758196C411yescharacteristic
12C2×#11758196C2211yescharacteristic
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C4×Dic61C411yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16C2×C22⋊C4×C61C411yescharacteristic
17C24×C61C2×C411yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C22×Dic61—22no—
21C22×Dic61—21no—
22C22×Dic61—21no—
23C22×Dic61—22no—
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61C2×C411yescharacteristic
26C22×Dic61C2×C411yescharacteristic
27C22×Dic61C2311yescharacteristic
28C2×#92420—24no—
29C22⋊C4×C61—22no—
30C22⋊Dic61—22no—
31#11758196—22no—
32#11758196—22no—
33C4×Dic61—21no—
34C4×Dic61—21no—
35C4×Dic61D412yes—
36C4×Dic61D412yes—
37C23×C61—21no—
38C23×C61—21no—
39C23×C61—41no—
40C23×C61—41no—
41C23×C61M1612yes—
42C23×C61C22×C411yescharacteristic
43C2×C4×C61—21no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C412yes—
47C2×Dic61—24no—
48C2×Dic61—24no—
49C2×Dic61—21no—
50C2×Dic61—21no—
51C2×Dic61—21no—
52C2×Dic61—21no—
53C2×Dic61—21no—
54C2×Dic61—41no—
55C2×Dic61—41no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61M1612yes—
59C2×Dic61C2×D412yes—
60#92420—44no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61—22no—
64C22×C61—42no—
65C22×C61—42no—
66C22×C61—41no—
67C22×C61—41no—
68C22×C61C2×C22⋊C411yescharacteristic
69C22×C61C2×M1611yescharacteristic
70C22×C61C2×M1611yescharacteristic
71C4×C61—22no—
72C4×C61—41no—
73Dic61—21no—
74Dic61—21no—
75Dic61—22no—
76Dic61—22no—
77Dic61—41no—
78#1464—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61—42no—
82C2×C61#40711yescharacteristic
83C2×C61#41011yescharacteristic
84C2×C61#41311yescharacteristic
85C2×#117—611no—
86#432—612no—
87#324—612no—
88#323—612no—
89C61#146411yescharacteristic, complemented, Sylow
90C23×C4—611no—
91#117—1222no—
92#117—1222no—
93C2×C4⋊C4—611no—
94C2×C4⋊C4—611no—
95C2×C22⋊C4—611no—
96C2×C22⋊C4#692311yescharacteristic
97C2×C42—611no—
98C2×C42—611no—
99C4⋊C8—1222no—
100C22⋊C8—614no—
101#97—1222no—
102C24C2×#692311yescharacteristic
103C22×C4—611no—
104C22×C4—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—1221no—
108C22×C4—1221no—
109C22×C4—1222no—
110C22×C4—1222no—
111C22×C4C2×#692311yescharacteristic
112C22×C4C2×#692311yescharacteristic
113C2×C8—1224no—
114C4⋊C4—1222no—
115C4⋊C4—1222no—
116C22⋊C4—22no—
117C22⋊C4—1222no—
118C42—612no—
119C42—612no—
120C42—1221no—
121C42—1221no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1175821312yes—
127C23C22×#692311yescharacteristic
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—611no—
132C2×C4—611no—
133C2×C4—612no—
134C2×C4—612no—
135C2×C4—1224no—
136C2×C4—1224no—
137C2×C4—1221no—
138C2×C4—1221no—
139C2×C4—1221no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4—2441no—
143C2×C4—2441no—
144C2×C4C22⋊#692312yes—
145C8—2444no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊#692311yescharacteristic
154C22D61⋊M1611yescharacteristic
155C22C2×#1175821311yescharacteristic
156C4—22no—
157C4—41no—
158C4—1221no—
159C4—1221no—
160C4—1222no—
161C4—1222no—
162C4—2441no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1684073311yescharacteristic
167C2#1684074211yescharacteristic
168C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. #16840608C2semidirect
89. C61#1464semidirect