Finite Group Databasebeta

← #21460700

Subgroups — #21460700

Order 7808.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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#16840733C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16839609C211yesmaximal, characteristic
4C2×#11758213C412yescomplemented
5C2×C22⋊#6923—21no—
6C2×C4×#6923—21no—
7#14519834—21no—
8C22⋊#92420—21no—
9(C2×#6923)⋊C4C412yescomplemented
10C22×C4×D61C2211yescharacteristic
11C2×#11758198—21no—
12C2×C4×Dic61—21no—
13#14519684C411yescharacteristic, complemented
14#95×C61C411yescharacteristic, complemented
15C23×D61D411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61—21no—
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61—21no—
20C22×Dic61D411yescharacteristic
21C2×C4×D61—42no—
22C2×C4×D61C2×C411yescharacteristic
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61D411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C22⋊#6923—22no—
27C22⋊#6923—22no—
28C2×#92420—22no—
29C4×#6923—42no—
30#11758213—42no—
31#11758198—24no—
32C4×Dic61—42no—
33C23×C61C22⋊C411yescharacteristic
34C22×D61—21no—
35C22×D61—21no—
36C22×D61—22no—
37C22×D61—41no—
38C22×D61C22⋊C411yescharacteristic
39C22×D61C4⋊C411yescharacteristic
40C2×#6923—24no—
41C2×#6923—42no—
42C2×#6923—42no—
43C2×C4×C61—22no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C4211yescharacteristic
48C2×C4×C61C4⋊C411yescharacteristic
49C2×Dic61—22no—
50C2×Dic61—22no—
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C4⋊C411yescharacteristic
55C4×D61—22no—
56C4×D61—22no—
57C4×D61—41no—
58C4×D61—41no—
59#92420—42no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61#9511yescharacteristic
63C22×C61#10411yescharacteristic
64C22×C61#10411yescharacteristic
65C2×D61—21no—
66C2×D61—21no—
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61#10412yes—
73#6923—44no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—42no—
77Dic61—21no—
78Dic61—42no—
79Dic61#9912yes—
80#1297—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—21no—
83C2×C61#33911yescharacteristic
84C2×C61#33911yescharacteristic
85C2×C61#34211yescharacteristic
86D61—22no—
87D61—41no—
88#407—611no—
89C4×C22⋊C4—611no—
90C4×C22⋊C4—611no—
91C61#129711yescharacteristic, complemented, Sylow
92C23×C4—611no—
93C2×M16—612no—
94C2×C22⋊C4—1221no—
95C2×C22⋊C4—1221no—
96C2×C42—1221no—
97C2×C42—1221no—
98C22⋊C8—1221no—
99C22⋊C8—1221no—
100#95—612no—
101#95—611no—
102#95#692311yescharacteristic, complemented
103C24—611no—
104C22×C4—21no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4—1222no—
111C22×C4—1221no—
112C22×C4—2442no—
113C22×C4C2×#692311yescharacteristic
114M16—2442no—
115C2×C8—1222no—
116C22⋊C4—1224no—
117C22⋊C4—1222no—
118C22⋊C4—1222no—
119C42—2442no—
120C42—2442no—
121C23—611no—
122C23—611no—
123C23—1222no—
124C23—1221no—
125C23—1221no—
126C23—2441no—
127C23C22⋊#692311yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—611no—
133C2×C4—611no—
134C2×C4—1222no—
135C2×C4—1222no—
136C2×C4—1222no—
137C2×C4—1222no—
138C2×C4—1224no—
139C2×C4—2441no—
140C2×C4—2441no—
141C2×C4—2441no—
142C2×C4—2442no—
143C2×C4—2442no—
144C2×C4—2441no—
145C2×C4C4×#692311yescharacteristic
146C2×C4C4⋊#692311yescharacteristic
147C8—2442no—
148C22—21no—
149C22—21no—
150C22—612no—
151C22—1221no—
152C22—1221no—
153C22—1221no—
154C22—1221no—
155C22—1221no—
156C22—2442no—
157C22—2442no—
158C22(C2×#6923)⋊C411yescharacteristic
159C22#1451984111yescharacteristic
160C22#1451984211yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—612no—
165C4—1221no—
166C4—2442no—
167C4—2444no—
168C2—21no—
169C2—21no—
170C2—1222no—
171C2—2441no—
172C2#1684063211yescharacteristic
173C2#1684063311yescharacteristic
174C2#1684063911yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
Fitting#95×C61C4
socleC22×C61#95
hypercenter#95#6923
hypocenterC61#1297
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#11758213C4semidirect
9. (C2×#6923)⋊C4C4semidirect
13. #14519684C4semidirect
14. #95×C61C4semidirect
91. C61#1297semidirect
102. #95#6923semidirect