Finite Group Databasebeta

← #21452865

Subgroups — #21452865

Order 7808.

560 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 125 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#16839690C212yesmaximal, complemented
2#16839687C211yesmaximal, characteristic, complemented
3#16839674C211yesmaximal, characteristic, complemented
4#16839674C212yesmaximal, complemented
5#16839656C212yesmaximal, complemented
6#16839655C212yesmaximal, complemented
7#16839650C212yesmaximal, complemented
8#16839618C212yesmaximal
9C61×#379C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic, complemented
11C2×C4⋊Dic61C2211yescharacteristic, complemented
12C2×#11758196C2212yescomplemented
13C2×C22⋊Dic61C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C4×Dic61C2212yescomplemented
20#14519684C2211yescharacteristic, complemented
21#14519684C2212yescomplemented
22#14519684C2212yescomplemented
23#14519684C2212yescomplemented
24#14519684C2212yescomplemented
25#14519684C2211yescharacteristic, complemented
26C25×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C24×C61—22no—
32C24×C61—24no—
33C24×C61—42no—
34C24×C61—41no—
35C24×C61—41no—
36C24×C61C2312yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C2×Dic122—42no—
46C2×Dic122—41no—
47C22⋊C4×C61—24no—
48C22⋊C4×C61—41no—
49C22⋊C4×C61—42no—
50C22⋊C4×C61—41no—
51C22⋊Dic61—24no—
52C22⋊Dic61—24no—
53C22⋊Dic61—42no—
54C22⋊Dic61—42no—
55C22⋊Dic61—42no—
56C22⋊Dic61—42no—
57C4⋊Dic61—41no—
58#11758196—42no—
59C4×Dic61—42no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61—48no—
71C23×C61—44no—
72C23×C61—48no—
73C23×C61—44no—
74C23×C61—44no—
75C23×C61#4112yes—
76C23×C61#4114yes—
77C23×C61C2411yescharacteristic
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97Dic122—44no—
98C22×C61—24no—
99C22×C61—22no—
100C22×C61—24no—
101C22×C61—24no—
102C22×C61—24no—
103C22×C61—416no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—41no—
109C22×C61—42no—
110C22×C61—41no—
111C22×C61C2×#4112yes—
112C22×C61C2×#4111yescharacteristic
113C22×C61H(5,𝔽2)11yescharacteristic
114C22×C61H(5,𝔽2)12yes—
115C22×C61H(5,𝔽2)11yescharacteristic
116C4×C61—42no—
117C4×C61—41no—
118C4×C61—41no—
119Dic61—42no—
120Dic61—42no—
121Dic61—42no—
122Dic61—42no—
123#2736—611nomaximal, Sylow
124C2×C61—44no—
125C2×C61—42no—
126C2×C61#53812yes—
127C2×C61#53811yescharacteristic
128C2×C61#55112yes—
129C2×C61#55111yescharacteristic
130C2×C61H(3,𝔽4)11yescharacteristic
131#397—611no—
132#397—612no—
133#393—611no—
134#393—612no—
135#388—612no—
136#388—612no—
137#388—612no—
138#379—612no—
139#379D6111yescharacteristic
140C61#273611yescharacteristic, complemented, Sylow
141C25C2×D6111yescharacteristic
142C22×Q8—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—611no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4C2×D6112yes—
152C2×C22⋊C4C2×D6111yescharacteristic
153C2×C22⋊C4C2×D6112yes—
154C2×C22⋊C4C2×D6111yescharacteristic
155C2×C42—612no—
156#95—612no—
157#95—611no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95—611no—
162C24—22no—
163C24—24no—
164C24—41no—
165C24—42no—
166C24—41no—
167C24C22×D6111yescharacteristic
168C24C22×D6112yes—
169C2×Q8—2442no—
170C2×Q8—2441no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C22×C4C22×D6112yes—
178C4⋊C4—2442no—
179C4⋊C4—2441no—
180C22⋊C4—24no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C22⋊C4—1224no—
185C22⋊C4—1224no—
186C22⋊C4—2442no—
187C22⋊C4—2442no—
188C22⋊C4—2442no—
189C22⋊C4—2442no—
190C42—2442no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—48no—
202C23—44no—
203C23—48no—
204C23—44no—
205C23—44no—
206C23#1175822212yes—
207C23#1175822414yes—
208C23C23×D6111yescharacteristic
209Q8—2444no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C22—24no—
230C22—22no—
231C22—24no—
232C22—24no—
233C22—24no—
234C22—416no—
235C22—42no—
236C22—41no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22C2×#1175822412yes—
243C22C2×#1175822211yescharacteristic
244C22#1451982212yes—
245C22#1451982211yescharacteristic
246C22#1451982211yescharacteristic
247C4—41no—
248C4—42no—
249C4—41no—
250C4—2442no—
251C4—2442no—
252C4—2442no—
253C4—2442no—
254C2—44no—
255C2—42no—
256C2#1684034712yes—
257C2#1684035011yescharacteristic
258C2#1684043812yes—
259C2#1684044311yescharacteristic
260C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#379C2
hypercenter#379D61
hypocenterC61#2736
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #16839690C2semidirect
2. #16839687C2semidirect
3. #16839674C2semidirect
4. #16839674C2semidirect
5. #16839656C2semidirect
6. #16839655C2semidirect
7. #16839650C2semidirect
10. C22×Dic122C22semidirect
11. C2×C4⋊Dic61C22semidirect
12. C2×#11758196C22semidirect
19. C2×C4×Dic61C22semidirect
20. #14519684C22semidirect
21. #14519684C22semidirect
22. #14519684C22semidirect
23. #14519684C22semidirect
24. #14519684C22semidirect
25. #14519684C22semidirect
140. C61#2736semidirect