Finite Group Databasebeta

← #21461065

Subgroups — #21461065

Order 7808.

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

normal subgroups only

This group has 440 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, complemented
2#16840606C212yesmaximal, complemented
3#16840605C212yesmaximal, complemented
4C2×C22⋊C4×D61C211yesmaximal, characteristic
5C2×#11758213—22no—
6#14519834—22no—
7C22⋊#92420C2214yescomplemented
8C24×D61C411yescharacteristic
9C22×C4×D61C411yescharacteristic
10C22×C4×D61C2211yescharacteristic
11C2×C22⋊Dic61C2211yescharacteristic
12C2×#11758198C411yescharacteristic
13C2×#11758198C2211yescharacteristic
14C22⋊C4×D61—22no—
15C22⋊C4×D61—22no—
16C2×C22⋊C4×C61C411yescharacteristic
17C24×C61C2×C411yescharacteristic
18C23×D61—22no—
19C23×D61—21no—
20C23×D61—21no—
21C23×D61—22no—
22C23×D61—42no—
23C23×D61—42no—
24C23×D61C2×C411yescharacteristic
25C23×D61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2311yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—42no—
33C2×C4×D61—42no—
34C2×C4×D61D412yes—
35C2×C4×D61D412yes—
36C2×#92420—24no—
37#11758213—44no—
38C22⋊C4×C61—22no—
39C22⋊Dic61—22no—
40#11758198—22no—
41#11758198—22no—
42C23×C61—21no—
43C23×C61—21no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61M1612yescomplemented
47C23×C61C22×C411yescharacteristic
48C22×D61—21no—
49C22×D61—21no—
50C22×D61—22no—
51C22×D61—22no—
52C22×D61—24no—
53C22×D61—24no—
54C22×D61—21no—
55C22×D61—21no—
56C22×D61—48no—
57C22×D61—48no—
58C22×D61—42no—
59C22×D61—42no—
60C22×D61—42no—
61C22×D61—42no—
62C22×D61—41no—
63C22×D61—41no—
64C22×D61C22⋊C411yescharacteristic
65C22×D61C22⋊C411yescharacteristic
66C22×D61M1612yescomplemented
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C22⋊C412yes—
71C2×Dic61—21no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61C2×D412yes—
75C4×D61—24no—
76C4×D61—42no—
77C4×D61—42no—
78C4×D61—42no—
79#92420—44no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—22no—
83C22×C61—42no—
84C22×C61—42no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61C2×C22⋊C411yescharacteristic
88C22×C61C2×M1611yescharacteristic
89C22×C61C2×M1611yescharacteristic
90C2×D61—24no—
91C2×D61—24no—
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—22no—
97C2×D61—48no—
98C2×D61—48no—
99C2×D61—42no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—42no—
103C2×D61#9912yes—
104C2×D61#10012yes—
105C4×C61—22no—
106C4×C61—41no—
107Dic61—22no—
108Dic61—41no—
109#1462—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—42no—
113C2×C61#40711yescharacteristic
114C2×C61C2×#9911yescharacteristic
115C2×C61C2×#10011yescharacteristic
116D61—22no—
117D61—22no—
118D61—42no—
119C22×C22⋊C4—611no—
120#407—612no—
121#323—612no—
122#323—612no—
123C61#146211yescharacteristic, complemented, Sylow
124C25—611no—
125C23×C4—611no—
126C23×C4—611no—
127C2×M16—1222no—
128C2×C22⋊C4—611no—
129C2×C22⋊C4—611no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4—1222no—
132C2×C22⋊C4—1222no—
133C2×C22⋊C4#692311yescharacteristic
134C22⋊C8—614no—
135C22⋊C8—1222no—
136C24—611no—
137C24—611no—
138C24—1221no—
139C24—1221no—
140C24—1222no—
141C24—1222no—
142C24—2442no—
143C24—2442no—
144C24C2×#692311yescharacteristic
145C22×C4—611no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—611no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4—2442no—
152C22×C4—2442no—
153C22×C4C2×#692311yescharacteristic
154C22×C4C2×#692311yescharacteristic
155M16—2444no—
156C2×C8—1224no—
157C22⋊C4—22no—
158C22⋊C4—1222no—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C23—21no—
162C23—21no—
163C23—41no—
164C23—41no—
165C23—611no—
166C23—611no—
167C23—612no—
168C23—1222no—
169C23—1222no—
170C23—1224no—
171C23—1224no—
172C23—1221no—
173C23—1221no—
174C23—1221no—
175C23—1221no—
176C23—2441no—
177C23—2441no—
178C23—2442no—
179C23—2442no—
180C23—2448no—
181C23—2448no—
182C23—2442no—
183C23—2442no—
184C23#1175821312yescomplemented
185C23C22×#692311yescharacteristic
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—612no—
190C2×C4—1224no—
191C2×C4—1221no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4C22⋊#692312yes—
198C8—2444no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—612no—
207C22—612no—
208C22—1224no—
209C22—1224no—
210C22—1221no—
211C22—1221no—
212C22—1221no—
213C22—1221no—
214C22—1222no—
215C22—2442no—
216C22—2442no—
217C22—2448no—
218C22—2448no—
219C22—2441no—
220C22—2441no—
221C22C2×C22⋊#692311yescharacteristic
222C22D61⋊M1611yescharacteristic
223C22C2×#1175821311yescharacteristic
224C4—22no—
225C4—41no—
226C4—1222no—
227C4—2441no—
228C2—21no—
229C2—21no—
230C2—42no—
231C2—1222no—
232C2—1222no—
233C2—2442no—
234C2#1684073311yescharacteristic
235C2D61⋊#9911yescharacteristic
236C2D61⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1462
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. #16840733C2semidirect
2. #16840606C2semidirect
3. #16840605C2semidirect
7. C22⋊#92420C22semidirect
46. C23×C61M16semidirect
66. C22×D61M16semidirect
123. C61#1462semidirect
184. C23#11758213semidirect