Finite Group Databasebeta

← #21462295

Subgroups — #21462295

Order 7808.

672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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#16840712C218yesmaximal, complemented
2#16840704C212yesmaximal, complemented
3#16840703C212yesmaximal
4C4×C22⋊#6923C212yesmaximal, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic
6C2×C4⋊#6923C2214yescomplemented
7C2×C22⋊#6923C2214yes—
8C2×C22⋊#6923C2214yes—
9C2×C22⋊#6923C2214yes—
10C2×C4×#6923C2214yescomplemented
11(C2×#6923)⋊C4C2214yescomplemented
12(C2×#6923)⋊C4C2214yescomplemented
13C24×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C2×C22⋊Dic61C411yescharacteristic, complemented
17C2×#11758198C411yescharacteristic, complemented
18C2×#11758198C411yescharacteristic, complemented
19C22⋊C4×D61C414yescomplemented
20C22⋊C4×D61C2214yes—
21C2×C22⋊C4×C61C411yescharacteristic, complemented
22C24×C61C2×C411yescharacteristic
23C23×D61—24no—
24C23×D61—42no—
25C23×D61—42no—
26C23×D61C2×C412yes—
27C23×D61C2×C411yescharacteristic
28C23×D61C2312yes—
29C23×D61C2311yescharacteristic
30C22×#6923C2318yes—
31C22×C4×C61C2×C411yescharacteristic
32C22×C4×C61C2×C411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C22×Dic61C2×C411yescharacteristic
35C2×C4×D61—42no—
36C2×C4×D61—42no—
37C2×C4×D61C2×C412yes—
38C2×C4×D61C2×C412yes—
39C2×C4×D61C2312yes—
40C2×C4×D61C2312yes—
41C22⋊#6923—28no—
42C22⋊#6923—44no—
43C22⋊#6923—44no—
44C4⋊#6923—44no—
45C4×#6923—44no—
46C22⋊C4×C61C2×C414yes—
47C22⋊Dic61C2×C414yes—
48#11758198C2×C414yes—
49#11758198C2×C414yes—
50C23×C61—22no—
51C23×C61—41no—
52C23×C61—41no—
53C23×C61C22×C412yes—
54C23×C61C22×C411yescharacteristic
55C22×D61—22no—
56C22×D61—22no—
57C22×D61—22no—
58C22×D61—24no—
59C22×D61—24no—
60C22×D61—24no—
61C22×D61—24no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61—41no—
65C22×D61—41no—
66C22×D61—416no—
67C22×D61C22×C412yes—
68C22×D61C22×C411yescharacteristic
69C22×D61#4114yes—
70C22×D61C2411yescharacteristic
71C2×#6923—28no—
72C2×#6923—28no—
73C2×#6923—28no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C22×C412yes—
77C2×C4×C61C22×C412yes—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61C22×C412yes—
81C2×Dic61C22×C412yes—
82C4×D61—24no—
83C4×D61—24no—
84C4×D61—42no—
85C4×D61—42no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—44no—
92C22×C61#11712yes—
93C22×C61C23×C411yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—28no—
97C2×D61—22no—
98C2×D61—22no—
99C2×D61—22no—
100C2×D61—48no—
101C2×D61—44no—
102C2×D61—48no—
103C2×D61#11712yes—
104C2×D61C2×#4112yes—
105C2×D61H(5,𝔽2)12yes—
106C2×D61H(5,𝔽2)12yes—
107#6923—48no—
108C4×C61—22no—
109C4×C61—22no—
110Dic61—22no—
111Dic61—22no—
112#2312—611nomaximal, Sylow
113C2×C61—22no—
114C2×C61—42no—
115C2×C61C2×#11711yescharacteristic
116C2×C61#51811yescharacteristic
117C2×C61#51811yescharacteristic
118D61—22no—
119D61—42no—
120D61#53814yes—
121C22×C22⋊C4—611no—
122#388—618no—
123#380—612no—
124#379—612no—
125C4×C22⋊C4—612no—
126C61#231211yescharacteristic, complemented, Sylow
127C25—611no—
128C23×C4—611no—
129C23×C4—611no—
130C2×C4⋊C4—614no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4—611no—
134C2×C22⋊C4—614no—
135C2×C22⋊C4—614no—
136C2×C22⋊C4—614no—
137C2×C22⋊C4—614no—
138C2×C22⋊C4—614no—
139C2×C22⋊C4#692311yescharacteristic, complemented
140C2×C42—614no—
141#95—614no—
142#95—614no—
143C24—611no—
144C24—612no—
145C24—612no—
146C24—611no—
147C24—1224no—
148C24—2442no—
149C24—2442no—
150C24C2×#692311yescharacteristic
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—612no—
154C22×C4—612no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—618no—
158C22×C4—2442no—
159C22×C4—2442no—
160C22×C4C2×#692311yescharacteristic
161C22×C4C2×#692311yescharacteristic
162C4⋊C4—2444no—
163C22⋊C4—614no—
164C22⋊C4—614no—
165C22⋊C4—614no—
166C22⋊C4—1228no—
167C22⋊C4—2444no—
168C22⋊C4—2444no—
169C22⋊C4C2×#692314yes—
170C42—2444no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—611no—
175C23—614no—
176C23—611no—
177C23—612no—
178C23—1222no—
179C23—1222no—
180C23—1224no—
181C23—1224no—
182C23—1224no—
183C23—1224no—
184C23—1222no—
185C23—2441no—
186C23—2441no—
187C23—2442no—
188C23—2442no—
189C23—24416no—
190C23C22×#692312yes—
191C23C22×#692311yescharacteristic
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—612no—
195C2×C4—612no—
196C2×C4—1224no—
197C2×C4—1224no—
198C2×C4—1228no—
199C2×C4—1228no—
200C2×C4—1228no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4C22×#692312yes—
206C2×C4C22×#692312yes—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—22no—
211C22—22no—
212C22—44no—
213C22—612no—
214C22—612no—
215C22—612no—
216C22—612no—
217C22—1228no—
218C22—1221no—
219C22—1221no—
220C22—1222no—
221C22—1222no—
222C22—1222no—
223C22—2444no—
224C22—2448no—
225C22—2448no—
226C22#1451985612yes—
227C22C23×#692311yescharacteristic
228C4—22no—
229C4—22no—
230C4—1222no—
231C4—1222no—
232C4—2448no—
233C2—22no—
234C2—42no—
235C2—614no—
236C2—1222no—
237C2—2442no—
238C2C2×#1451985611yescharacteristic
239C2#1684082911yescharacteristic
240C2#1684082911yescharacteristic
subgroupG/H
center, FrattiniC22C23×#6923
commutator, socleC22×C61C23×C4
FittingC2×C22⋊C4×C61C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#2312
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840712C2semidirect
2. #16840704C2semidirect
4. C4×C22⋊#6923C2semidirect
6. C2×C4⋊#6923C22semidirect
10. C2×C4×#6923C22semidirect
11. (C2×#6923)⋊C4C22semidirect
12. (C2×#6923)⋊C4C22semidirect
16. C2×C22⋊Dic61C4semidirect
17. C2×#11758198C4semidirect
18. C2×#11758198C4semidirect
19. C22⋊C4×D61C4semidirect
21. C2×C22⋊C4×C61C4semidirect
126. C61#2312semidirect
139. C2×C22⋊C4#6923semidirect