Finite Group Databasebeta

← #21452028

Subgroups — #21452028

Order 7808.

816 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519752C212yesmaximal, complemented
2C2×#14519747C212yesmaximal, complemented
3#16839688C212yesmaximal, complemented
4#16839679C212yesmaximal, complemented
5#16839671C211yesmaximal, characteristic, complemented
6#16839640C212yesmaximal, complemented
7#16839638C212yesmaximal, complemented
8#16839617C211yesmaximal, characteristic, complemented
9C61×#399C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C22×D244C2212yes—
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic, complemented
14C22×C22⋊D61C2212yes—
15C22×C4×D61C2212yescomplemented
16#14519752—28no—
17#14519747—28no—
18C2×C22⋊Dic61C2211yescharacteristic
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yescomplemented
24C2×#11758198C2212yescomplemented
25#14519684C2211yescharacteristic, complemented
26#14519684C2212yescomplemented
27#14519684C2212yescomplemented
28C2×C4⋊C4×C61C2212yescomplemented
29C2×C4⋊C4×C61C2211yescharacteristic, complemented
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2211yescharacteristic, complemented
33C24×C61C2311yescharacteristic
34C23×D61—22no—
35C23×D61—24no—
36C23×D61—42no—
37C23×D61—41no—
38C23×D61—41no—
39C23×D61C2312yes—
40C23×D61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—42no—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C2×D244—24no—
51C2×D244—24no—
52C2×D244—24no—
53C2×D244—42no—
54C2×D244—42no—
55C2×D244—42no—
56C2×D244—41no—
57C2×D244D418yescomplemented
58C2×C4×D61—24no—
59C2×C4×D61—42no—
60C2×C4×D61—42no—
61C4⋊C4×C61—24no—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—24no—
64C22⋊C4×C61—41no—
65C22⋊Dic61—41no—
66#11758198—24no—
67#11758198—24no—
68#11758198—24no—
69#11758198—24no—
70#11758198—42no—
71#11758198—42no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61#4112yes—
77C23×C61C2411yescharacteristic
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—44no—
91C22×D61—48no—
92C22×D61—48no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61C2×D414yes—
96C22×D61C2×D414yes—
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—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61C2×D414yes—
107C22⋊D61—48no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114D244—48no—
115D244—44no—
116D244—48no—
117C4×D61—48no—
118C22×C61—22no—
119C22×C61—24no—
120C22×C61—42no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C22×D412yes—
124C22×C61C2×#4111yescharacteristic
125C22×C61H(5,𝔽2)11yescharacteristic
126C22×C61H(5,𝔽2)11yescharacteristic
127C22×C61H(5,𝔽2)12yes—
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—24no—
131C2×D61—24no—
132C2×D61—24no—
133C2×D61—24no—
134C2×D61—416no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C4×C61—24no—
144C4×C61—42no—
145C4×C61—41no—
146C4×C61—41no—
147Dic61—42no—
148Dic61—42no—
149#2668—611nomaximal, Sylow
150C2×C61—42no—
151C2×C61#53412yes—
152C2×C61#53811yescharacteristic
153C2×C61D4211yescharacteristic
154C2×C61#54612yes—
155C2×C61#56011yescharacteristic
156D61—44no—
157D61—44no—
158C2×#121—612no—
159C2×#120—612no—
160#399D6111yescharacteristic, complemented
161#397—612no—
162#394—612no—
163#392—611no—
164#386—612no—
165#386—612no—
166#379—611no—
167C61#266811yescharacteristic, complemented, Sylow
168C25—611no—
169C22×D4—612no—
170C22×D4—612no—
171C22×D4—612no—
172C22×D4—611no—
173C23×C4—612no—
174#121—1228no—
175#120—1228no—
176C2×C4⋊C4C2×D6112yescomplemented
177C2×C4⋊C4C2×D6111yescharacteristic, complemented
178C2×C22⋊C4—612no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4C2×D6112yes—
186C2×C22⋊C4C2×D6111yescharacteristic
187#95—612no—
188#95—612no—
189#95—611no—
190#95C2×D6111yescharacteristic, complemented
191C24—612no—
192C24—612no—
193C24—1224no—
194C24—1222no—
195C24—2441no—
196C24—2441no—
197C24—2442no—
198C24C22×D6111yescharacteristic
199C2×D4—618no—
200C2×D4—1224no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1224no—
205C2×D4—2442no—
206C2×D4—2442no—
207C2×D4—2441no—
208C2×D4—2442no—
209C2×D4—2442no—
210C22×C4—612no—
211C22×C4—612no—
212C22×C4—1224no—
213C22×C4—2442no—
214C22×C4—2442no—
215C22×C4C22×D6112yes—
216C22×C4C22×D6111yescharacteristic
217C22×C4C22×D6111yescharacteristic
218C22×C4C22×D6112yes—
219C4⋊C4—24no—
220C4⋊C4—41no—
221C22⋊C4—24no—
222C22⋊C4—41no—
223C22⋊C4—1224no—
224C22⋊C4—1224no—
225C22⋊C4—1224no—
226C22⋊C4—1224no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C22⋊C4—2441no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—614no—
235C23—614no—
236C23—1222no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23—1222no—
248C23—2448no—
249C23—2444no—
250C23—2444no—
251C23—2448no—
252C23—2444no—
253C23#1175822612yes—
254C23C23×D6111yescharacteristic
255D4—2448no—
256D4—2444no—
257D4—2448no—
258D4—2448no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—2448no—
275C2×C4D4×D6114yes—
276C22—22no—
277C22—24no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—1224no—
282C22—1224no—
283C22—1224no—
284C22—1224no—
285C22—1224no—
286C22—1224no—
287C22—24416no—
288C22—2442no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22—2442no—
293C22—2442no—
294C22—2442no—
295C22—2442no—
296C22C2×D4×D6112yes—
297C22C2×#1175822611yescharacteristic
298C22#1451982211yescharacteristic
299C22#1451982312yes—
300C22#1451982311yescharacteristic
301C4—24no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—2442no—
306C4—2442no—
307C2—42no—
308C2—2444no—
309C2—2444no—
310C2#1684032312yes—
311C2#1684035211yescharacteristic
312C2#1684039711yescharacteristic
313C2#1684040312yes—
314C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2668
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519752C2semidirect
2. C2×#14519747C2semidirect
3. #16839688C2semidirect
4. #16839679C2semidirect
5. #16839671C2semidirect
6. #16839640C2semidirect
7. #16839638C2semidirect
8. #16839617C2semidirect
9. C61×#399C2semidirect
13. C22×D244C22semidirect
15. C22×C4×D61C22semidirect
23. C2×#11758198C22semidirect
24. C2×#11758198C22semidirect
25. #14519684C22semidirect
26. #14519684C22semidirect
27. #14519684C22semidirect
28. C2×C4⋊C4×C61C22semidirect
29. C2×C4⋊C4×C61C22semidirect
32. #95×C61C22semidirect
57. C2×D244D4semidirect
160. #399D61semidirect
167. C61#2668semidirect
176. C2×C4⋊C4C2×D61semidirect
177. C2×C4⋊C4C2×D61semidirect
190. #95C2×D61semidirect