Finite Group Databasebeta

← #21449169

Subgroups — #21449169

Order 7808.

1232 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 205 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×#14519748C212yesmaximal, complemented
2C2×#14519746C212yesmaximal, complemented
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4#16839676C212yesmaximal, complemented
5#16839670C212yesmaximal, complemented
6#16839665C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8#16839618C212yesmaximal, complemented
9C23×D4×C61C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2211yescharacteristic
11C22×C22⋊D61C2214yescomplemented
12C22×C4×D61C2211yescharacteristic, complemented
13#14519748—28no—
14#14519746—28no—
15C4×C22⋊D61—24no—
16C2×C4⋊Dic61C2212yescomplemented
17C2×#11758196C2211yescharacteristic, complemented
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2214yescomplemented
21C2×C22⋊Dic61C2214yescomplemented
22C2×C22⋊Dic61C2214yescomplemented
23C2×#11758198C2211yescharacteristic, complemented
24C2×C4×Dic61C2211yescharacteristic, complemented
25#14519684C2212yescomplemented
26C25×C61C2212yes—
27C22×D4×C61—28no—
28C22×D4×C61—24no—
29C22×D4×C61C2212yes—
30C22×D4×C61C2212yes—
31C23×C4×C61C2211yescharacteristic
32C24×C61—28no—
33C24×C61—24no—
34C24×C61—24no—
35C24×C61—24no—
36C24×C61—44no—
37C24×C61C2314yes—
38C24×C61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C2×D4×C61—232no—
41C2×D4×C61—28no—
42C2×D4×C61—24no—
43C2×D4×C61—24no—
44C2×D4×C61—24no—
45C2×D4×C61D418yescomplemented
46C22×C4×C61—24no—
47C22×C4×C61D414yescomplemented
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—28no—
53C2×C22⋊D61—28no—
54C2×C22⋊D61—44no—
55C2×C22⋊D61D414yescomplemented
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2314yes—
58C22×Dic61C2311yescharacteristic
59C22×Dic61C2311yescharacteristic
60C2×C4×D61—22no—
61C2×C4×D61—24no—
62C22⋊Dic61—22no—
63C22⋊Dic61—24no—
64C22⋊Dic61—28no—
65C22⋊Dic61—28no—
66C22⋊Dic61—44no—
67#11758198—22no—
68C4⋊Dic61—24no—
69#11758196—22no—
70C4×Dic61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—216no—
74C23×C61—24no—
75C23×C61—24no—
76C23×C61—24no—
77C23×C61—24no—
78C23×C61—24no—
79C23×C61—24no—
80C23×C61—416no—
81C23×C61—416no—
82C23×C61—48no—
83C23×C61—48no—
84C23×C61C2×D418yes—
85C23×C61C2×D412yes—
86C23×C61C2×D412yes—
87C23×C61#4112yes—
88C23×C61C2411yescharacteristic
89C22×D61—21no—
90C22×D61—22no—
91C22×D61—21no—
92C22×D61—22no—
93C22×D61C2×D412yescomplemented
94D4×C61—216no—
95D4×C61—216no—
96C2×C4×C61—22no—
97C2×C4×C61—28no—
98C2×C4×C61C2×D412yes—
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D414yes—
101C22⋊D61—28no—
102C22⋊D61—416no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—24no—
108C2×Dic61—22no—
109C2×Dic61—24no—
110C2×Dic61—22no—
111C2×Dic61—24no—
112C2×Dic61C2×D412yescomplemented
113C4×D61—44no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—24no—
117C22×C61—24no—
118C22×C61—28no—
119C22×C61—28no—
120C22×C61—28no—
121C22×C61—432no—
122C22×C61—44no—
123C22×C61—44no—
124C22×C61—44no—
125C22×C61—44no—
126C22×C61#12114yescomplemented
127C22×C61C22×D411yescharacteristic
128C22×C61C22×D411yescharacteristic
129C22×C61C22×D412yes—
130C22×C61C2×#4111yescharacteristic
131C22×C61H(5,𝔽2)12yes—
132C2×D61—22no—
133C2×D61—24no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—42no—
137C4×C61—22no—
138C4×C61#12014yescomplemented
139Dic61—22no—
140Dic61—41no—
141Dic61—41no—
142Dic61—44no—
143#2408—611nomaximal, Sylow
144C2×C61—24no—
145C2×C61—48no—
146C2×C61C2×#12011yescharacteristic
147C2×C61C2×#12111yescharacteristic
148C2×C61#53511yescharacteristic
149C2×C61D4212yes—
150C2×C61#54612yes—
151D61—42no—
152C23×D4D6111yescharacteristic, complemented
153C2×#121—612no—
154C2×#120—612no—
155C2×C4×D4—611no—
156#394—612no—
157#392—612no—
158#390—612no—
159#380—611no—
160#379—612no—
161C61#240811yescharacteristic, complemented, Sylow
162C25C2×D6112yes—
163C22×D4—28no—
164C22×D4—24no—
165C22×D4—611no—
166C22×D4—614no—
167C22×D4C2×D6112yes—
168C22×D4C2×D6112yes—
169C23×C4—611no—
170C23×C4C2×D6111yescharacteristic
171#121—1228no—
172#120—1228no—
173C4×D4—1224no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—612no—
176C2×C22⋊C4—611no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4—614no—
179C2×C22⋊C4—614no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—614no—
182C2×C42—611no—
183#95—612no—
184C24—28no—
185C24—24no—
186C24—24no—
187C24—24no—
188C24—44no—
189C24—611no—
190C24C22×D6114yes—
191C24C22×D6111yescharacteristic
192C2×D4—232no—
193C2×D4—28no—
194C2×D4—24no—
195C2×D4—24no—
196C2×D4—24no—
197C2×D4—614no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—1228no—
201C2×D4—1228no—
202C2×D4—2444no—
203C2×D4C22⋊D6118yescomplemented
204C22×C4—24no—
205C22×C4—611no—
206C22×C4—614no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1222no—
210C22×C4—1224no—
211C22×C4C22⋊D6114yescomplemented
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6111yescharacteristic
214C4⋊C4—1222no—
215C4⋊C4—1224no—
216C22⋊C4—1228no—
217C22⋊C4—1224no—
218C22⋊C4—1222no—
219C22⋊C4—1228no—
220C22⋊C4—1222no—
221C22⋊C4—2444no—
222C42—1222no—
223C23—22no—
224C23—22no—
225C23—216no—
226C23—24no—
227C23—24no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—24no—
232C23—416no—
233C23—416no—
234C23—48no—
235C23—48no—
236C23—612no—
237C23—1221no—
238C23—1222no—
239C23—1221no—
240C23—1222no—
241C23D4×D6112yes—
242C23#1175822412yes—
243C23C2×C22⋊D6118yes—
244C23C2×C22⋊D6112yes—
245C23C23×D6111yescharacteristic
246D4—216no—
247D4—216no—
248D4—1228no—
249D4—24416no—
250C2×C4—22no—
251C2×C4—28no—
252C2×C4—612no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1224no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1224no—
260C2×C4—1222no—
261C2×C4—1224no—
262C2×C4—2444no—
263C2×C4C2×C22⋊D6112yes—
264C2×C4C2×C22⋊D6112yes—
265C2×C4C2×C22⋊D6114yes—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—28no—
271C22—28no—
272C22—28no—
273C22—432no—
274C22—44no—
275C22—44no—
276C22—44no—
277C22—44no—
278C22—1222no—
279C22—1224no—
280C22—2441no—
281C22—2441no—
282C22—2442no—
283C22#1451974814yescomplemented
284C22C2×D4×D6111yescharacteristic
285C22C22×C22⋊D6111yescharacteristic
286C22C22×C22⋊D6112yes—
287C22C2×#1175822411yescharacteristic
288C22#1451982212yes—
289C4—22no—
290C4—1222no—
291C4—2441no—
292C4—2441no—
293C4—2444no—
294C4#1451974614yescomplemented
295C2—24no—
296C2—48no—
297C2—2442no—
298C2C2×#1451974611yescharacteristic
299C2C2×#1451974811yescharacteristic
300C2#1684032911yescharacteristic
301C2D4×C22⋊D6112yes—
302C2#1684040612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC23×D4×C61C2
hypercenterC23×D4D61
hypocenterC61#2408
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519748C2semidirect
2. C2×#14519746C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. #16839676C2semidirect
5. #16839670C2semidirect
6. #16839665C2semidirect
7. #16839622C2semidirect
8. #16839618C2semidirect
9. C23×D4×C61C2semidirect
11. C22×C22⋊D61C22semidirect
12. C22×C4×D61C22semidirect
16. C2×C4⋊Dic61C22semidirect
17. C2×#11758196C22semidirect
20. C2×C22⋊Dic61C22semidirect
21. C2×C22⋊Dic61C22semidirect
22. C2×C22⋊Dic61C22semidirect
23. C2×#11758198C22semidirect
24. C2×C4×Dic61C22semidirect
25. #14519684C22semidirect
45. C2×D4×C61D4semidirect
47. C22×C4×C61D4semidirect
55. C2×C22⋊D61D4semidirect
93. C22×D61C2×D4semidirect
112. C2×Dic61C2×D4semidirect
126. C22×C61#121semidirect
138. C4×C61#120semidirect
152. C23×D4D61semidirect
161. C61#2408semidirect
203. C2×D4C22⋊D61semidirect
211. C22×C4C22⋊D61semidirect
283. C22#14519748semidirect
294. C4#14519746semidirect