Finite Group Databasebeta

← #21452045

Subgroups — #21452045

Order 7808.

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

normal subgroups only

This group has 796 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×#14519763C212yesmaximal, complemented
2C2×#14519746C212yesmaximal, complemented
3#16839677C212yesmaximal, complemented
4#16839674C211yesmaximal, characteristic, complemented
5#16839671C212yesmaximal, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839662C212yesmaximal, complemented
8#16839656C212yesmaximal, complemented
9C61×#379C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic, complemented
11C22×D244C2211yescharacteristic, complemented
12C22×C22⋊D61C2212yes—
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2212yes—
15#14519763—28no—
16#14519746—28no—
17C2×#11758196C2212yescomplemented
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×#11758198C2212yescomplemented
22C2×#11758198C2212yescomplemented
23C2×#11758198C2212yescomplemented
24C2×C4×Dic61C2212yescomplemented
25#14519684C2211yescharacteristic, complemented
26#14519684C2212yescomplemented
27#14519684C2211yescharacteristic, complemented
28C25×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2211yescharacteristic
32C2×C22⋊C4×C61C2211yescharacteristic
33C24×C61—24no—
34C24×C61—22no—
35C24×C61—41no—
36C24×C61—42no—
37C24×C61—41no—
38C24×C61C2312yes—
39C24×C61C2311yescharacteristic
40C23×D61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—42no—
50C2×C22⋊D61—42no—
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C2×D244—42no—
57C2×D244—41no—
58C2×Dic122—24no—
59C2×Dic122—41no—
60C22⋊C4×C61—24no—
61C22⋊C4×C61—42no—
62C22⋊C4×C61—41no—
63C22⋊C4×C61—41no—
64C22⋊Dic61—24no—
65C22⋊Dic61—24no—
66C22⋊Dic61D418yescomplemented
67#11758198—24no—
68#11758198—24no—
69#11758198—42no—
70#11758196—42no—
71C4×Dic61—24no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—44no—
83C23×C61—48no—
84C23×C61—48no—
85C23×C61—44no—
86C23×C61—44no—
87C23×C61C2×D414yes—
88C23×C61#4112yes—
89C23×C61C2411yescharacteristic
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—22no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C22⋊D61—48no—
105C22⋊D61—48no—
106C22⋊D61—48no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61C2×D414yes—
115C2×Dic61C2×D414yes—
116D244—44no—
117Dic122—44no—
118C22×C61—24no—
119C22×C61—22no—
120C22×C61—24no—
121C22×C61—24no—
122C22×C61—24no—
123C22×C61—416no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—41no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—41no—
131C22×C61C22×D412yes—
132C22×C61C2×#4111yescharacteristic
133C22×C61H(5,𝔽2)11yescharacteristic
134C22×C61H(5,𝔽2)12yes—
135C22×C61H(5,𝔽2)11yescharacteristic
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—41no—
146Dic61—24no—
147Dic61—24no—
148Dic61—42no—
149#2670—611nomaximal, Sylow
150C2×C61—44no—
151C2×C61—42no—
152C2×C61#53512yes—
153C2×C61#53811yescharacteristic
154C2×C61D4211yescharacteristic
155C2×C61#54612yes—
156C2×C61H(3,𝔽4)11yescharacteristic
157D61—82no—
158C2×#124—612no—
159C2×#120—612no—
160#394—612no—
161#393—611no—
162#392—611no—
163#392—612no—
164#390—612no—
165#388—612no—
166#379D6111yescharacteristic, complemented
167C61#267011yescharacteristic, complemented, Sylow
168C25C2×D6111yescharacteristic
169C22×Q8—611no—
170C22×D4—612no—
171C22×D4—612no—
172C22×D4—612no—
173C22×D4—611no—
174#124—1228no—
175#120—1228no—
176C2×C4⋊C4—612no—
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⋊C4C2×D6112yes—
184C2×C22⋊C4C2×D6112yes—
185C2×C22⋊C4C2×D6111yescharacteristic
186C2×C22⋊C4C2×D6111yescharacteristic
187C2×C42—612no—
188#95—611no—
189#95—612no—
190#95—611no—
191C24—22no—
192C24—24no—
193C24—41no—
194C24—42no—
195C24—41no—
196C24—612no—
197C24C22×D6111yescharacteristic
198C24C22×D6112yes—
199C2×Q8—1224no—
200C2×Q8—2441no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1224no—
205C2×D4—1224no—
206C2×D4—2442no—
207C2×D4—2441no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2442no—
212C22×C4—612no—
213C22×C4—612no—
214C22×C4—612no—
215C22×C4C22×D6111yescharacteristic
216C22×C4C22×D6111yescharacteristic
217C22×C4C22×D6112yes—
218C4⋊C4—2442no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—618no—
224C22⋊C4—1224no—
225C22⋊C4—1224no—
226C22⋊C4—1224no—
227C22⋊C4—1224no—
228C22⋊C4—2442no—
229C42—1224no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—44no—
241C23—48no—
242C23—48no—
243C23—44no—
244C23—44no—
245C23—1222no—
246C23—1222no—
247C23—1222no—
248C23—1222no—
249C23—1222no—
250C23—1222no—
251C23—1222no—
252C23#1175822212yes—
253C23D4×D6114yes—
254C23C23×D6111yescharacteristic
255Q8—2444no—
256D4—2444no—
257D4—2448no—
258D4—2448no—
259D4—2448no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—614no—
268C2×C4—614no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1222no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—416no—
282C22—42no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—42no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22—2442no—
293C22—2442no—
294C22—2442no—
295C22—2442no—
296C22C2×D4×D6112yes—
297C22C2×#1175822211yescharacteristic
298C22#1451982212yes—
299C22#1451982211yescharacteristic
300C22#1451982211yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—1224no—
305C4—1224no—
306C4—2442no—
307C2—44no—
308C2—42no—
309C2—4882no—
310C2#1684032712yes—
311C2#1684035011yescharacteristic
312C2#1684039411yescharacteristic
313C2#1684040212yes—
314C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#379C2
hypercenter#379D61
hypocenterC61#2670
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519746C2semidirect
3. #16839677C2semidirect
4. #16839674C2semidirect
5. #16839671C2semidirect
6. #16839671C2semidirect
7. #16839662C2semidirect
8. #16839656C2semidirect
9. C61×#379C2semidirect
10. C22×Dic122C22semidirect
11. C22×D244C22semidirect
17. C2×#11758196C22semidirect
21. C2×#11758198C22semidirect
22. C2×#11758198C22semidirect
23. C2×#11758198C22semidirect
24. C2×C4×Dic61C22semidirect
25. #14519684C22semidirect
26. #14519684C22semidirect
27. #14519684C22semidirect
66. C22⋊Dic61D4semidirect
166. #379D61semidirect
167. C61#2670semidirect