Finite Group Databasebeta

← #21452866

Subgroups — #21452866

Order 7808.

560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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#16839689C212yesmaximal, complemented
2#16839675C212yesmaximal, complemented
3#16839674C211yesmaximal, characteristic, complemented
4#16839655C212yesmaximal, complemented
5#16839654C212yesmaximal, complemented
6#16839652C212yesmaximal, complemented
7#16839617C212yesmaximal
8#16839617C211yesmaximal, characteristic
9C61×#397C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C22×Dic122C2211yescharacteristic, complemented
12C2×C4⋊Dic61C2212yescomplemented
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2212yescomplemented
22#14519684C2212yescomplemented
23#14519684C2212yescomplemented
24#14519684C2212yescomplemented
25#14519684C2211yescharacteristic, complemented
26C2×C4⋊C4×C61C2211yescharacteristic, complemented
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic, complemented
30#95×C61C2212yescomplemented
31C24×C61C2311yescharacteristic
32C23×D61—22no—
33C23×D61—24no—
34C23×D61—41no—
35C23×D61—42no—
36C23×D61—41no—
37C23×D61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C2×Dic122—41no—
46C2×Dic122—42no—
47C4⋊C4×C61—41no—
48C22⋊C4×C61—24no—
49C22⋊C4×C61—41no—
50C22⋊Dic61—41no—
51C22⋊Dic61—42no—
52#11758198—24no—
53#11758198—24no—
54#11758198—42no—
55#11758198—42no—
56#11758198—42no—
57#11758198—42no—
58C4⋊Dic61—42no—
59C4×Dic61—42no—
60C23×C61—22no—
61C23×C61—21no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61#4112yes—
65C23×C61C2411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—44no—
73C22×D61—48no—
74C22×D61—48no—
75C22×D61—44no—
76C22×D61—44no—
77C22×D61#4114yes—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
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—22no—
99C22×C61—24no—
100C22×C61—42no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61C2×#4112yes—
104C22×C61C2×#4111yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C61H(5,𝔽2)11yescharacteristic
107C22×C61H(5,𝔽2)12yes—
108C2×D61—24no—
109C2×D61—24no—
110C2×D61—24no—
111C2×D61—416no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61—41no—
119C4×C61—41no—
120Dic61—42no—
121Dic61—42no—
122Dic61—42no—
123#2736—611nomaximal, Sylow
124C2×C61—42no—
125C2×C61#53811yescharacteristic
126C2×C61#53812yes—
127C2×C61#55112yes—
128C2×C61#55111yescharacteristic
129C2×C61H(3,𝔽4)11yescharacteristic
130D61—44no—
131#397—612no—
132#397D6111yescharacteristic, complemented
133#393—611no—
134#393—612no—
135#388—612no—
136#388—612no—
137#388—612no—
138#379—611no—
139#379—612no—
140C61#273611yescharacteristic, complemented, Sylow
141C25—611no—
142C22×Q8—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4C2×D6111yescharacteristic, complemented
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—611no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4C2×D6112yes—
154C2×C22⋊C4C2×D6111yescharacteristic
155C2×C42—612no—
156#95—612no—
157#95—611no—
158#95—612no—
159#95—612no—
160#95C2×D6112yescomplemented
161#95C2×D6111yescharacteristic, complemented
162C24—612no—
163C24—1224no—
164C24—1222no—
165C24—2441no—
166C24—2442no—
167C24—2441no—
168C24C22×D6111yescharacteristic
169C2×Q8—2441no—
170C2×Q8—2442no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6112yes—
176C22×C4C22×D6111yescharacteristic
177C22×C4C22×D6112yes—
178C4⋊C4—41no—
179C4⋊C4—2442no—
180C22⋊C4—24no—
181C22⋊C4—41no—
182C22⋊C4—1224no—
183C22⋊C4—1224no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C22⋊C4—2442no—
188C22⋊C4—2441no—
189C22⋊C4—2442no—
190C42—2442no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23—614no—
196C23—1222no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—1222no—
201C23—1222no—
202C23—2448no—
203C23—2444no—
204C23—2444no—
205C23—2448no—
206C23—2444no—
207C23#1175822412yes—
208C23C23×D6111yescharacteristic
209Q8—2444no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
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—22no—
230C22—24no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—1224no—
235C22—1224no—
236C22—1224no—
237C22—24416no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22—2442no—
242C22#41×D6112yes—
243C22C2×#1175822411yescharacteristic
244C22#1451982211yescharacteristic
245C22#1451982312yes—
246C22#1451982311yescharacteristic
247C4—41no—
248C4—42no—
249C4—42no—
250C4—41no—
251C4—2442no—
252C4—2442no—
253C4—2442no—
254C2—42no—
255C2—2444no—
256C2#1684034911yescharacteristic
257C2#1684035112yes—
258C2#1684043512yes—
259C2#1684044011yescharacteristic
260C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2736
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16839689C2semidirect
2. #16839675C2semidirect
3. #16839674C2semidirect
4. #16839655C2semidirect
5. #16839654C2semidirect
6. #16839652C2semidirect
9. C61×#397C2semidirect
11. C22×Dic122C22semidirect
12. C2×C4⋊Dic61C22semidirect
21. C2×C4×Dic61C22semidirect
22. #14519684C22semidirect
23. #14519684C22semidirect
24. #14519684C22semidirect
25. #14519684C22semidirect
26. C2×C4⋊C4×C61C22semidirect
29. #95×C61C22semidirect
30. #95×C61C22semidirect
132. #397D61semidirect
140. C61#2736semidirect
144. C2×C4⋊C4C2×D61semidirect
160. #95C2×D61semidirect
161. #95C2×D61semidirect