Finite Group Databasebeta

← #21456581

Subgroups — #21456581

Order 7808.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#16840272C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3#16840098C211yesmaximal, characteristic, complemented
4#16840084C212yesmaximal, complemented
5#16840078C211yesmaximal, characteristic, complemented
6#16839995C212yesmaximal, complemented
7#16839990C212yesmaximal, complemented
8#16839913C211yesmaximal, characteristic, complemented
9#16839904C212yesmaximal, complemented
10C22⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic, complemented
13C22×C22⋊D61—21no—
14C22×C4×D61C2211yescharacteristic
15C2×#11758200C2212yescomplemented
16C2×C8×D61C2212yescomplemented
17#14519759—21no—
18#14519757C2211yescharacteristic, complemented
19#14519756C2211yescharacteristic
20#14519748—21no—
21#14519748—21no—
22#14519748C2212yes—
23#14519748C2212yes—
24#14519748C2211yescharacteristic, complemented
25#14519745—21no—
26D4×Dic61—21no—
27#14519737—21no—
28#14519735C2211yescharacteristic, complemented
29C2×C4⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61—21no—
31#14519711C2212yescomplemented
32#14519708C2212yescomplemented
33#14519702C2212yescomplemented
34#14519698C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×D8×C61C2212yescomplemented
40#121×C61C2211yescharacteristic
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61D411yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61C2311yescharacteristic
49C2×D4×C61C2312yes—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—21no—
55C2×C22⋊D61—44no—
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61D411yescharacteristic
59#11758224—42no—
60C2×C4×D61—42no—
61C2×C4×D61D411yescharacteristic
62C2×C4×D61D411yescharacteristic
63C2×C4×D61C2311yescharacteristic
64C2×C4×D61C2311yescharacteristic
65C2×Dic122C2311yescharacteristic
66D8×C61—42no—
67C2×C8×C61C2312yes—
68C4⋊C4×C61C2311yescharacteristic
69C22⋊C4×C61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—22no—
72C22⋊Dic61—22no—
73C22⋊Dic61—21no—
74#11758200—42no—
75#11758198—21no—
76#11758198—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2311yescharacteristic
80C4⋊Dic61C2312yes—
81#11758196—21no—
82C4×Dic61—21no—
83C2×#92418C2312yes—
84C8×D61—42no—
85C23×C61—22no—
86C23×C61—21no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61C2×D411yescharacteristic
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—41no—
94C22×D61C2×D411yescharacteristic
95C22×D61C2×D411yescharacteristic
96D4×C61—22no—
97D4×C61—22no—
98D4×C61—22no—
99D4×C61—42no—
100D4×C61—42no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2411yescharacteristic
105C22⋊D61—42no—
106C22⋊D61—44no—
107C22⋊D61—42no—
108C22⋊D61—44no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61C2×D411yescharacteristic
116C2×Dic61C2×D411yescharacteristic
117C4×D61—22no—
118C4×D61—22no—
119C4×D61—41no—
120C4×D61—41no—
121Dic122—22no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—84no—
133C22×C61#13512yes—
134C22×C61C22×D411yescharacteristic
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—44no—
141C2×D61AGL(1,ℤ/8)12yes—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61H(5,𝔽2)12yes—
145Dic61—21no—
146Dic61—21no—
147Dic61—41no—
148Dic61—42no—
149Dic61—41no—
150#3188—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—81no—
153C2×C61—82no—
154C2×C61#53411yescharacteristic
155C2×C61C2×#13511yescharacteristic
156C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
157D61—22no—
158D61—41no—
159#525—611no—
160C2×#121—611no—
161#484—611no—
162#482—612no—
163#481—611no—
164#466—612no—
165#465—612no—
166#450—611no—
167#449—612no—
168#447D6111yescharacteristic, complemented
169C2×C22⋊C8—611no—
170C61#318811yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C22×D4—1221no—
173C22×D4C2×D6111yescharacteristic
174C23×C4—611no—
175C2×SD16—612no—
176C2×D8C2×D6112yescomplemented
177C22×C8—612no—
178#123—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—611no—
181#121—612no—
182#121—612no—
183#121—611no—
184#121—1221no—
185#121—1221no—
186#121C2×D6111yescharacteristic
187#120—1221no—
188C4×D4—1221no—
189C4×D4—1221no—
190#117—611no—
191C2×C4⋊C4—611no—
192C2×C22⋊C4—1221no—
193#107—612no—
194#106—612no—
195#103—612no—
196#102—612no—
197#102—612no—
198#102C2×D6112yescomplemented
199C22⋊C8—611no—
200C22⋊C8—612no—
201C22⋊C8C2×D6111yescharacteristic
202C24—21no—
203C24—611no—
204#41—2442no—
205C2×Q8—611no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—1222no—
212C2×D4—1222no—
213C2×D4—2444no—
214C2×D4C22×D6111yescharacteristic
215C2×D4C22×D6112yes—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—2442no—
224C22×C4C22×D6111yescharacteristic
225SD16—2442no—
226D8—42no—
227C2×C8—612no—
228C2×C8—2442no—
229C2×C8C22×D6112yes—
230C4⋊C4—611no—
231C4⋊C4—612no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4C22×D6111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1222no—
240C22⋊C4—1222no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C42—1221no—
244C23—21no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—611no—
250C23—611no—
251C23—1222no—
252C23—1222no—
253C23—2441no—
254C23D4×D6111yescharacteristic
255Q8—1222no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—2442no—
262D4—2444no—
263D4—2444no—
264D4—2442no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4D4×D6111yescharacteristic
280C2×C4C23×D6111yescharacteristic
281C8—22no—
282C8—1222no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—84no—
292C22—612no—
293C22—1221no—
294C22—1221no—
295C22—1221no—
296C22—1221no—
297C22—1221no—
298C22—2444no—
299C22#1451979612yes—
300C22C2×D4×D6111yescharacteristic
301C4—21no—
302C4—41no—
303C4—1221no—
304C4—1221no—
305C4—2442no—
306C4—2441no—
307C4—2441no—
308C4#1451982212yes—
309C2—22no—
310C2—82no—
311C2—81no—
312C2—1222no—
313C2—2441no—
314C2#1684032211yescharacteristic
315C2C2×#1451979611yescharacteristic
316C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3188
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840272C2semidirect
2. C2×#14519748C2semidirect
3. #16840098C2semidirect
4. #16840084C2semidirect
5. #16840078C2semidirect
6. #16839995C2semidirect
7. #16839990C2semidirect
8. #16839913C2semidirect
9. #16839904C2semidirect
10. C22⋊C8×D61C2semidirect
11. C61×#447C2semidirect
12. C2×#11758224C22semidirect
15. C2×#11758200C22semidirect
16. C2×C8×D61C22semidirect
18. #14519757C22semidirect
24. #14519748C22semidirect
28. #14519735C22semidirect
31. #14519711C22semidirect
32. #14519708C22semidirect
33. #14519702C22semidirect
34. #14519698C22semidirect
35. #14519698C22semidirect
37. #14519689C22semidirect
39. C2×D8×C61C22semidirect
41. #102×C61C22semidirect
168. #447D61semidirect
170. C61#3188semidirect
176. C2×D8C2×D61semidirect
198. #102C2×D61semidirect