Finite Group Databasebeta

← #21461068

Subgroups — #21461068

Order 7808.

312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840733C212yesmaximal
2#16840608C212yesmaximal, complemented
3#16840607C212yesmaximal, complemented
4C2×C4⋊C4×D61C211yesmaximal, characteristic
5C2×#11758213—22no—
6#14519834—22no—
7C22⋊#92420C2214yes—
8C22×C4×D61C411yescharacteristic
9C22×C4×D61C411yescharacteristic
10C22×C4×D61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C411yescharacteristic
13C2×#11758196C2211yescharacteristic
14C4⋊C4×D61—22no—
15C4⋊C4×D61—22no—
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×D61—22no—
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61—42no—
31C2×C4×D61—42no—
32C2×C4×D61D412yes—
33C2×C4×D61D412yes—
34C2×#92420—24no—
35#11758213—44no—
36C4⋊C4×C61—22no—
37C4⋊Dic61—22no—
38#11758196—22no—
39#11758196—22no—
40C23×C61C22×C411yescharacteristic
41C22×D61—21no—
42C22×D61—21no—
43C22×D61—22no—
44C22×D61—22no—
45C22×D61C22⋊C411yescharacteristic
46C22×D61C22⋊C411yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61C22⋊C412yes—
53C2×C4×C61M1612yescomplemented
54C2×Dic61—21no—
55C2×Dic61—21no—
56C2×Dic61—21no—
57C2×Dic61—41no—
58C2×Dic61—41no—
59C2×Dic61M1612yescomplemented
60C2×Dic61C2×D412yes—
61C4×D61—24no—
62C4×D61—24no—
63C4×D61—24no—
64C4×D61—42no—
65C4×D61—42no—
66C4×D61—42no—
67#92420—44no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61C2×C22⋊C411yescharacteristic
71C22×C61C2×M1611yescharacteristic
72C22×C61C2×M1611yescharacteristic
73C2×D61—24no—
74C2×D61—24no—
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—21no—
78C2×D61—21no—
79C2×D61#9912yes—
80C2×D61#10112yes—
81C4×C61—22no—
82C4×C61—22no—
83C4×C61—41no—
84Dic61—22no—
85Dic61—22no—
86Dic61—41no—
87#1463—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—21no—
90C2×C61#40711yescharacteristic
91C2×C61C2×#9911yescharacteristic
92C2×C61C2×#10111yescharacteristic
93D61—22no—
94D61—22no—
95C22×C4⋊C4—611no—
96#407—612no—
97#324—612no—
98#324—612no—
99C61#146311yescharacteristic, complemented, Sylow
100C23×C4—611no—
101C23×C4—611no—
102C23×C4—611no—
103C2×M16—1222no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4—611no—
106C2×C4⋊C4—611no—
107C2×C4⋊C4—1222no—
108C2×C4⋊C4—1222no—
109C2×C4⋊C4#692311yescharacteristic
110C22⋊C8—614no—
111C22⋊C8—1222no—
112C24—611no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4—612no—
116C22×C4—612no—
117C22×C4—611no—
118C22×C4—1222no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4—1221no—
122C22×C4—1221no—
123C22×C4—1222no—
124C22×C4—2442no—
125C22×C4—2442no—
126C22×C4C2×#692311yescharacteristic
127C22×C4C2×#692311yescharacteristic
128C22×C4C2×#692311yescharacteristic
129M16—2444no—
130C2×C8—1224no—
131C4⋊C4—22no—
132C4⋊C4—1222no—
133C4⋊C4—1222no—
134C4⋊C4—1222no—
135C23—611no—
136C23—611no—
137C23—1222no—
138C23—1222no—
139C23—1221no—
140C23—1221no—
141C23C22×#692311yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—612no—
148C2×C4—612no—
149C2×C4—1224no—
150C2×C4—1224no—
151C2×C4—1224no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4#1175821312yescomplemented
161C2×C4C22⋊#692312yes—
162C8—2444no—
163C22—21no—
164C22—21no—
165C22—612no—
166C22—612no—
167C22—1224no—
168C22—1224no—
169C22—1221no—
170C22—1221no—
171C22—1221no—
172C22—1221no—
173C22C2×C22⋊#692311yescharacteristic
174C22D61⋊M1611yescharacteristic
175C22C2×#1175821311yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—1222no—
180C4—1222no—
181C4—2441no—
182C2—21no—
183C2—21no—
184C2—1222no—
185C2—1222no—
186C2#1684073311yescharacteristic
187C2D61⋊#9911yescharacteristic
188C2D61⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1463
LCSG ▷ C23×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
2. #16840608C2semidirect
3. #16840607C2semidirect
53. C2×C4×C61M16semidirect
59. C2×Dic61M16semidirect
99. C61#1463semidirect
160. C2×C4#11758213semidirect