Finite Group Databasebeta

← #21451630

Subgroups — #21451630

Order 7808.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519754C211yesmaximal, characteristic, complemented
2C22×#11758198C211yesmaximal, characteristic
3#16839697C212yesmaximal, complemented
4#16839686C212yesmaximal, complemented
5#16839684C212yesmaximal, complemented
6#16839675C212yesmaximal, complemented
7#16839635C211yesmaximal, characteristic, complemented
8#16839620C211yesmaximal, characteristic, complemented
9#16839617C211yesmaximal, characteristic
10#16839617C211yesmaximal, characteristic
11C61×#385C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×Dic122C2211yescharacteristic, complemented
14C23×Dic61C2211yescharacteristic
15#14519754—24no—
16C2×C4⋊Dic61C2211yescharacteristic, complemented
17C2×#11758196C2211yescharacteristic, complemented
18C2×#11758196C2211yescharacteristic, complemented
19C2×#11758196C2212yescomplemented
20C2×#11758196C2212yescomplemented
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198—24no—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30#14519684C2212yescomplemented
31#14519684C2212yescomplemented
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yescomplemented
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36#95×C61C2212yescomplemented
37C24×C61C2311yescharacteristic
38C23×D61—22no—
39C23×D61—22no—
40C23×D61—42no—
41C23×D61—42no—
42C23×D61Q814yescomplemented
43C23×D61C2312yes—
44C22×C4×C61—22no—
45C22×C4×C61—42no—
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2312yes—
48C22×C4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—42no—
51C22×Dic61D414yes—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2312yes—
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2311yescharacteristic
57C2×Dic122—22no—
58C2×Dic122—42no—
59C4⋊C4×C61—42no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—22no—
62C22⋊Dic61—22no—
63C22⋊Dic61—22no—
64#11758198—24no—
65#11758198—24no—
66#11758198—42no—
67#11758198—42no—
68#11758198—42no—
69#11758198—42no—
70C4⋊Dic61—22no—
71#11758196—22no—
72#11758196—22no—
73#11758196—42no—
74#11758196—42no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61C2×D412yes—
78C23×C61C2×Q812yes—
79C23×C61#4112yes—
80C23×C61C2411yescharacteristic
81C22×D61—28no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—48no—
89C22×D61—44no—
90C22×D61—44no—
91C22×D61—48no—
92C22×D61C2×Q814yes—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—44no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—44no—
114C2×Dic61C2×D412yes—
115C2×Dic61C2×D412yes—
116Dic122—44no—
117C22×C61—22no—
118C22×C61—22no—
119C22×C61—24no—
120C22×C61—24no—
121C22×C61C22⋊Q814yes—
122C22×C61C22×D411yescharacteristic
123C22×C61C22×Q811yescharacteristic
124C22×C61C2×#4111yescharacteristic
125C22×C61H(5,𝔽2)12yes—
126C22×C61H(5,𝔽2)12yes—
127C2×D61—24no—
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—416no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61—42no—
139Dic61—22no—
140Dic61—22no—
141Dic61—41no—
142Dic61—41no—
143Dic61—42no—
144#2626—611nomaximal, Sylow
145C2×C61—24no—
146C2×C61C2×C22⋊Q811yescharacteristic
147C2×C61#53411yescharacteristic
148C2×C61#53511yescharacteristic
149C2×C61#53812yes—
150C2×C61#54312yes—
151D61—44no—
152C2×C22⋊Q8—611no—
153C22×C22⋊C4—611no—
154#399—612no—
155#396—612no—
156#396—612no—
157#393—612no—
158#385—611no—
159#385D6111yescharacteristic, complemented
160#380—611no—
161#379—611no—
162#379—611no—
163C61#262611yescharacteristic, complemented, Sylow
164C25—611no—
165C22×Q8—611no—
166C23×C4—611no—
167C23×C4C2×D6111yescharacteristic
168C22⋊Q8—1224no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—612no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4C2×D6112yescomplemented
175C2×C22⋊C4—611no—
176C2×C22⋊C4—611no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—1224no—
184C2×C22⋊C4C2×D6111yescharacteristic
185C2×C22⋊C4C2×D6111yescharacteristic
186#95—612no—
187#95—612no—
188#95C2×D6112yescomplemented
189C24—612no—
190C24—614no—
191C24—1222no—
192C24—1222no—
193C24—2442no—
194C24—2442no—
195C24C22×D6111yescharacteristic
196C2×Q8—1222no—
197C2×Q8—2442no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—614no—
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—2442no—
207C22×C4C22×D6112yes—
208C22×C4C22×D6112yes—
209C22×C4C22×D6111yescharacteristic
210C22×C4C22×D6111yescharacteristic
211C4⋊C4—42no—
212C4⋊C4—1222no—
213C4⋊C4—1222no—
214C4⋊C4—1222no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—1224no—
220C22⋊C4—1224no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C22⋊C4—2442no—
224C22⋊C4—2442no—
225C22⋊C4—2442no—
226C22⋊C4—2442no—
227C23—22no—
228C23—22no—
229C23—614no—
230C23—1222no—
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23—1222no—
235C23—1222no—
236C23—1228no—
237C23—2448no—
238C23—2444no—
239C23—2444no—
240C23—2448no—
241C23#1175822212yes—
242C23D4×D6112yes—
243C23Q8×D6112yes—
244C23C23×D6111yescharacteristic
245Q8—2444no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—44no—
257C2×C4—612no—
258C2×C4—612no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—2444no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—24no—
273C22—1224no—
274C22—1224no—
275C22—1224no—
276C22—24416no—
277C22—2442no—
278C22—2442no—
279C22—2442no—
280C22—2442no—
281C22#1451975514yes—
282C22C2×D4×D6111yescharacteristic
283C22C2×Q8×D6111yescharacteristic
284C22C2×#1175822211yescharacteristic
285C22#1451982212yes—
286C22#1451982312yes—
287C4—41no—
288C4—41no—
289C4—42no—
290C4—42no—
291C4—1222no—
292C4—1222no—
293C4—2441no—
294C4—2441no—
295C4—2442no—
296C2—24no—
297C2—2444no—
298C2C2×#1451975511yescharacteristic
299C2#1684032311yescharacteristic
300C2#1684032711yescharacteristic
301C2#1684034512yes—
302C2#1684038712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2626
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14519754C2semidirect
3. #16839697C2semidirect
4. #16839686C2semidirect
5. #16839684C2semidirect
6. #16839675C2semidirect
7. #16839635C2semidirect
8. #16839620C2semidirect
11. C61×#385C2semidirect
13. C22×Dic122C22semidirect
16. C2×C4⋊Dic61C22semidirect
17. C2×#11758196C22semidirect
18. C2×#11758196C22semidirect
19. C2×#11758196C22semidirect
20. C2×#11758196C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
33. C2×C4⋊C4×C61C22semidirect
36. #95×C61C22semidirect
42. C23×D61Q8semidirect
159. #385D61semidirect
163. C61#2626semidirect
174. C2×C4⋊C4C2×D61semidirect
188. #95C2×D61semidirect