Finite Group Databasebeta

← #21461053

Subgroups — #21461053

Order 7808.

264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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#16840779C212yesmaximal, complemented
2#16840607C212yesmaximal, complemented
3#16840606C212yesmaximal
4C2×#14519735C211yesmaximal, characteristic
5#14519844—22no—
6C22⋊#92420C2214yes—
7C4×#92420—22no—
8C22×C4×D61C411yescharacteristic
9#14519735—22no—
10#14519735—22no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198C411yescharacteristic
13C2×#11758198C2211yescharacteristic
14C2×C4×Dic61C411yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16C2×C4⋊C4×C61C411yescharacteristic
17C23×D61C2×C411yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61C2×C411yescharacteristic
21C22×Dic61C2×C411yescharacteristic
22C22×Dic61C2×C411yescharacteristic
23C22×Dic61C2311yescharacteristic
24C2×C4×D61—21no—
25C2×C4×D61—21no—
26C2×C4×D61—22no—
27C2×C4×D61C814yescomplemented
28C2×#92420—24no—
29C4⋊C4×C61—22no—
30#11758198—22no—
31#11758198—22no—
32C4⋊Dic61—22no—
33C4×Dic61—21no—
34C4×Dic61—21no—
35C4×Dic61D412yes—
36C4×Dic61D412yes—
37C23×C61C22×C411yescharacteristic
38C22×D61—21no—
39C22×D61—21no—
40C22×D61—41no—
41C22×D61—41no—
42C22×D61C2×C812yes—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61C22⋊C412yes—
49C2×C4×C61C2×C812yes—
50C2×Dic61—21no—
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C2×C812yes—
56C2×Dic61M1612yes—
57C2×Dic61C2×D412yes—
58C4×D61—24no—
59C4×D61—24no—
60#92420—44no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61C2×C22⋊C411yescharacteristic
64C22×C61C22×C811yescharacteristic
65C22×C61C2×M1611yescharacteristic
66C2×D61—22no—
67C2×D61—42no—
68C2×D61—41no—
69C2×D61—41no—
70C2×D61—42no—
71C4×C61—22no—
72C4×C61—22no—
73C4×C61—41no—
74Dic61—22no—
75Dic61—41no—
76Dic61C22⋊C812yes—
77Dic61C22⋊C812yes—
78#1458—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61C2×C22⋊C811yescharacteristic
82C2×C61#41011yescharacteristic
83C2×C61#41311yescharacteristic
84D61—42no—
85C2×#117—611no—
86#431—612no—
87#324—612no—
88#323—612no—
89C61#145811yescharacteristic, complemented, Sylow
90C23×C4—611no—
91#117—1222no—
92#117—1222no—
93C2×C4⋊C4—611no—
94C2×C4⋊C4#692311yescharacteristic
95C2×C22⋊C4—611no—
96C2×C22⋊C4—611no—
97C2×C42—611no—
98C2×C42—611no—
99C4⋊C8—1222no—
100C22⋊C8—614no—
101C4×C8—1222no—
102C24—611no—
103C22×C4—611no—
104C22×C4—611no—
105C22×C4—614no—
106C22×C4—611no—
107C22×C4—1221no—
108C22×C4—1221no—
109C22×C4—1222no—
110C22×C4C2×#692311yescharacteristic
111C22×C4C2×#692311yescharacteristic
112C22×C4C2×#692311yescharacteristic
113C2×C8—1224no—
114C4⋊C4—22no—
115C4⋊C4—1222no—
116C22⋊C4—1222no—
117C22⋊C4—1222no—
118C42—612no—
119C42—612no—
120C42—1221no—
121C42—1221no—
122C23—612no—
123C23—1221no—
124C23—1221no—
125C23—2441no—
126C23—2441no—
127C23C22×#692311yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—611no—
134C2×C4—611no—
135C2×C4—612no—
136C2×C4—612no—
137C2×C4—612no—
138C2×C4—1224no—
139C2×C4—1224no—
140C2×C4—1221no—
141C2×C4—2441no—
142C2×C4—2441no—
143C2×C4D61⋊C812yes—
144C2×C4C22⋊#692312yes—
145C8—2444no—
146C22—21no—
147C22—21no—
148C22—1222no—
149C22—2442no—
150C22—2442no—
151C22—2441no—
152C22—2441no—
153C22C2×C22⋊#692311yescharacteristic
154C22C2×D61⋊C811yescharacteristic
155C22D61⋊M1611yescharacteristic
156C4—22no—
157C4—22no—
158C4—41no—
159C4—612no—
160C4—612no—
161C4—1222no—
162C4—2441no—
163C2—21no—
164C2—21no—
165C2—2442no—
166C2D61⋊(C22⋊C8)11yescharacteristic
167C2#1684074311yescharacteristic
168C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC22×C61C22×C8
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1458
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840779C2semidirect
2. #16840607C2semidirect
27. C2×C4×D61C8semidirect
89. C61#1458semidirect