Finite Group Databasebeta

← #21453813

Subgroups — #21453813

Order 7808.

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

normal subgroups only

This group has 712 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
1C2×#14519745C212yesmaximal, complemented
2#16839691C212yesmaximal, complemented
3#16839687C211yesmaximal, characteristic, complemented
4#16839678C212yesmaximal, complemented
5#16839677C212yesmaximal, complemented
6#16839676C212yesmaximal, complemented
7#16839670C212yesmaximal, complemented
8#16839617C211yesmaximal, characteristic, complemented
9C61×#392C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13#14519745—28no—
14C2×C4⋊Dic61C2211yescharacteristic, complemented
15C2×#11758196C2212yescomplemented
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2211yescharacteristic
18C2×C22⋊Dic61C2212yescomplemented
19C2×C22⋊Dic61C2212yescomplemented
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24#14519684C2212yescomplemented
25#14519684C2211yescharacteristic, complemented
26#14519684C2212yescomplemented
27C22×D4×C61C2212yes—
28C22×D4×C61C2211yescharacteristic, complemented
29C2×C22⋊C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yescomplemented
31#95×C61C2211yescharacteristic, complemented
32C24×C61C2312yes—
33C24×C61C2311yescharacteristic
34C23×D61—42no—
35C23×D61—42no—
36C23×D61—41no—
37C23×D61—41no—
38C23×D61D414yescomplemented
39C23×D61C2312yes—
40C2×D4×C61—24no—
41C2×D4×C61—42no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C2×D4×C61—41no—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—24no—
49C2×C22⋊D61—24no—
50C2×C22⋊D61—42no—
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C22⋊C4×C61—41no—
58C22⋊C4×C61—42no—
59C22⋊Dic61—24no—
60C22⋊Dic61—41no—
61C22⋊Dic61—42no—
62C22⋊Dic61—42no—
63#11758198—24no—
64#11758198—24no—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—41no—
68#11758196—42no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61C2×D412yes—
81C23×C61C2411yescharacteristic
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—44no—
89C22×D61—48no—
90C22×D61—44no—
91C22×D61—48no—
92C22×D61—44no—
93C22×D61C2×D414yes—
94D4×C61—48no—
95D4×C61—44no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C22⋊D61—48no—
104C22⋊D61—48no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C22×C61—24no—
115C22×C61—22no—
116C22×C61—41no—
117C22×C61—42no—
118C22×C61—41no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61C22×D411yescharacteristic
127C22×C61H(5,𝔽2)12yes—
128C22×C61H(5,𝔽2)11yescharacteristic
129C22×C61H(5,𝔽2)12yes—
130C22×C61H(5,𝔽2)11yescharacteristic
131C2×D61—24no—
132C2×D61—24no—
133C2×D61—24no—
134C2×D61—416no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—42no—
140C4×C61—41no—
141C4×C61—41no—
142Dic61—42no—
143Dic61—42no—
144Dic61—42no—
145#2812—611nomaximal, Sylow
146C2×C61—42no—
147C2×C61—82no—
148C2×C61#53411yescharacteristic
149C2×C61#53412yes—
150C2×C61#56011yescharacteristic
151C2×C61#56012yes—
152C2×C61H(3,𝔽4)11yescharacteristic
153D61—44no—
154C2×#120—612no—
155#397—611no—
156#397—612no—
157#394—612no—
158#394—612no—
159#394—612no—
160#392—612no—
161#392D6111yescharacteristic, complemented
162#379—611no—
163C61#281211yescharacteristic, complemented, Sylow
164C25—611no—
165C22×D4—612no—
166C22×D4—612no—
167C22×D4C2×D6112yes—
168C22×D4C2×D6111yescharacteristic, complemented
169#120—1228no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—611no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—611no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4C2×D6111yescharacteristic
181C2×C22⋊C4C2×D6112yescomplemented
182#95—612no—
183#95—611no—
184#95—612no—
185#95C2×D6111yescharacteristic, complemented
186C24—612no—
187C24—614no—
188C24—2441no—
189C24—2442no—
190C24—2442no—
191C24—2441no—
192C24C22×D6112yes—
193C24C22×D6111yescharacteristic
194C2×D4—24no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—41no—
198C2×D4—42no—
199C2×D4—1224no—
200C2×D4—1224no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—612no—
208C22×C4C22×D6111yescharacteristic
209C22×C4C22×D6112yes—
210C22×C4C22×D6111yescharacteristic
211C4⋊C4—2442no—
212C4⋊C4—2441no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—1224no—
216C22⋊C4—1224no—
217C22⋊C4—1224no—
218C22⋊C4—2442no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2441no—
222C22⋊C4—2442no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—614no—
235C23—1222no—
236C23—1222no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—2444no—
242C23—2448no—
243C23—2444no—
244C23—2448no—
245C23—2444no—
246C23D4×D6112yes—
247C23C23×D6111yescharacteristic
248D4—48no—
249D4—44no—
250D4—2448no—
251D4—2448no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—1224no—
281C22—1224no—
282C22—1224no—
283C22—24416no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22C2×D4×D6111yescharacteristic
289C22#1451982212yes—
290C22#1451982211yescharacteristic
291C22#1451982212yes—
292C22#1451982311yescharacteristic
293C4—41no—
294C4—41no—
295C4—42no—
296C4—2442no—
297C4—2442no—
298C4—2442no—
299C2—42no—
300C2—82no—
301C2—2444no—
302C2#1684032011yescharacteristic
303C2#1684032212yes—
304C2#1684049911yescharacteristic
305C2#1684050012yes—
306C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2812
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519745C2semidirect
2. #16839691C2semidirect
3. #16839687C2semidirect
4. #16839678C2semidirect
5. #16839677C2semidirect
6. #16839676C2semidirect
7. #16839670C2semidirect
8. #16839617C2semidirect
9. C61×#392C2semidirect
14. C2×C4⋊Dic61C22semidirect
15. C2×#11758196C22semidirect
18. C2×C22⋊Dic61C22semidirect
19. C2×C22⋊Dic61C22semidirect
24. #14519684C22semidirect
25. #14519684C22semidirect
26. #14519684C22semidirect
28. C22×D4×C61C22semidirect
30. C2×C22⋊C4×C61C22semidirect
31. #95×C61C22semidirect
38. C23×D61D4semidirect
161. #392D61semidirect
163. C61#2812semidirect
168. C22×D4C2×D61semidirect
181. C2×C22⋊C4C2×D61semidirect
185. #95C2×D61semidirect