Finite Group Databasebeta

← #21452854

Subgroups — #21452854

Order 7808.

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

normal subgroups only

This group has 552 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#16839698C211yesmaximal, characteristic, complemented
2#16839689C212yesmaximal, complemented
3#16839684C212yesmaximal, complemented
4#16839655C212yesmaximal, complemented
5#16839654C212yesmaximal, complemented
6#16839651C212yesmaximal, complemented
7#16839617C212yesmaximal
8#16839617C211yesmaximal, characteristic
9C61×#397C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C2×C4⋊Dic61C2212yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic, complemented
13C2×#11758196C2212yescomplemented
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×C4×Dic61C2212yescomplemented
23#14519684C2212yescomplemented
24#14519684C2211yescharacteristic, complemented
25#14519684C2212yescomplemented
26C2×C4⋊C4×C61C2211yescharacteristic, complemented
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2212yescomplemented
30#95×C61C2211yescharacteristic, complemented
31C24×C61C2311yescharacteristic
32C23×D61—22no—
33C23×D61—24no—
34C23×D61—41no—
35C23×D61—42no—
36C23×D61—41no—
37C23×D61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C4⋊C4×C61—41no—
46C22⋊C4×C61—24no—
47C22⋊C4×C61—41no—
48C22⋊Dic61—42no—
49C22⋊Dic61—41no—
50#11758198—24no—
51#11758198—24no—
52#11758198—42no—
53#11758198—42no—
54#11758198—42no—
55#11758198—42no—
56C4⋊Dic61—41no—
57C4⋊Dic61—42no—
58#11758196—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—21no—
86C2×C4×C61—22no—
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—
97C22×C61—22no—
98C22×C61—24no—
99C22×C61—42no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61C2×#4112yes—
103C22×C61C2×#4111yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C61H(5,𝔽2)12yes—
107C2×D61—24no—
108C2×D61—24no—
109C2×D61—24no—
110C2×D61—416no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C4×C61—42no—
116C4×C61—42no—
117C4×C61—41no—
118C4×C61—41no—
119Dic61—42no—
120Dic61—42no—
121Dic61—42no—
122#2735—611nomaximal, Sylow
123C2×C61—42no—
124C2×C61#53811yescharacteristic
125C2×C61#53812yes—
126C2×C61#55112yes—
127C2×C61#55111yescharacteristic
128C2×C61#56011yescharacteristic
129D61—44no—
130#399—611no—
131#397—612no—
132#397D6111yescharacteristic, complemented
133#396—612no—
134#388—612no—
135#388—612no—
136#388—612no—
137#379—611no—
138#379—612no—
139C61#273511yescharacteristic, complemented, Sylow
140C25—611no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—612no—
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—612no—
158#95—611no—
159#95C2×D6111yescharacteristic, complemented
160#95C2×D6112yescomplemented
161C24—612no—
162C24—1224no—
163C24—1222no—
164C24—2441no—
165C24—2442no—
166C24—2441no—
167C24C22×D6111yescharacteristic
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4C22×D6112yes—
172C22×C4C22×D6111yescharacteristic
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—2442no—
177C4⋊C4—2441no—
178C4⋊C4—2442no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—1224no—
182C22⋊C4—1224no—
183C22⋊C4—2442no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C22⋊C4—2442no—
188C22⋊C4—2441no—
189C42—2442no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—22no—
194C23—614no—
195C23—1222no—
196C23—1222no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—1222no—
201C23—2448no—
202C23—2444no—
203C23—2444no—
204C23—2448no—
205C23—2444no—
206C23#1175822412yes—
207C23C23×D6111yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
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—
227C22—22no—
228C22—24no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—1224no—
233C22—1224no—
234C22—1224no—
235C22—24416no—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22#41×D6112yes—
241C22C2×#1175822411yescharacteristic
242C22#1451982211yescharacteristic
243C22#1451982312yes—
244C22#1451982311yescharacteristic
245C4—41no—
246C4—42no—
247C4—42no—
248C4—41no—
249C4—2442no—
250C4—2442no—
251C4—2442no—
252C2—42no—
253C2—2444no—
254C2#1684034911yescharacteristic
255C2#1684035112yes—
256C2#1684043512yes—
257C2#1684044211yescharacteristic
258C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2735
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16839698C2semidirect
2. #16839689C2semidirect
3. #16839684C2semidirect
4. #16839655C2semidirect
5. #16839654C2semidirect
6. #16839651C2semidirect
9. C61×#397C2semidirect
11. C2×C4⋊Dic61C22semidirect
12. C2×C4⋊Dic61C22semidirect
13. C2×#11758196C22semidirect
22. C2×C4×Dic61C22semidirect
23. #14519684C22semidirect
24. #14519684C22semidirect
25. #14519684C22semidirect
26. C2×C4⋊C4×C61C22semidirect
29. #95×C61C22semidirect
30. #95×C61C22semidirect
132. #397D61semidirect
139. C61#2735semidirect
144. C2×C4⋊C4C2×D61semidirect
159. #95C2×D61semidirect
160. #95C2×D61semidirect