Finite Group Databasebeta

← #21456636

Subgroups — #21456636

Order 7808.

466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840275C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3#16840090C211yesmaximal, characteristic, complemented
4#16840084C212yesmaximal, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16840005C212yesmaximal, complemented
8#16839906C212yesmaximal, complemented
9#16839896C211yesmaximal, characteristic, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic, complemented
13C22×C22⋊D61—21no—
14C22×C4×D61C2211yescharacteristic
15C2×#11758199C2212yescomplemented
16C2×#11758189C2212yescomplemented
17#14519762—21no—
18#14519753C2211yescharacteristic, complemented
19#14519752C2211yescharacteristic, complemented
20#14519751C2211yescharacteristic
21#14519748—21no—
22#14519748—21no—
23#14519748C2212yes—
24#14519748C2212yes—
25#14519747—21no—
26#14519739—21no—
27#14519737—21no—
28#14519735C2211yescharacteristic, complemented
29C2×C4⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61—21no—
31#14519711C2212yescomplemented
32#14519708C2212yescomplemented
33#14519701C2212yescomplemented
34#14519699C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×SD16×C61C2212yescomplemented
40C22⋊Q8×C61C2211yescharacteristic
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61D411yescharacteristic
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—44no—
54C22×Dic61—21no—
55C22×Dic61D411yescharacteristic
56#11758226—42no—
57C2×D244—21no—
58C2×D244—21no—
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—42no—
62C2×C4×D61D411yescharacteristic
63C2×C4×D61D411yescharacteristic
64C2×C4×D61C2311yescharacteristic
65C2×C4×D61C2311yescharacteristic
66SD16×C61—42no—
67C2×C8×C61C2312yes—
68C4⋊C4×C61—21no—
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C22⋊Dic61—22no—
72C22⋊Dic61—22no—
73#11758199—42no—
74#11758198—21no—
75#11758198—21no—
76#11758198—21no—
77#11758198—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2311yescharacteristic
80C4⋊Dic61C2312yes—
81#11758196—21no—
82C4×Dic61—21no—
83C2×#92418C2312yes—
84#11758189—42no—
85C23×C61—22no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61C2×D411yescharacteristic
90C22×D61—22no—
91C22×D61—21no—
92C22×D61—41no—
93C22×D61—41no—
94C22×D61C2×D411yescharacteristic
95C22×D61C2×D411yescharacteristic
96Q8×C61—22no—
97D4×C61—22no—
98D4×C61—22no—
99D4×C61—42no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2411yescharacteristic
105C22⋊D61—44no—
106C22⋊D61—44no—
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—41no—
111C2×Dic61—42no—
112C2×Dic61C2×D411yescharacteristic
113C2×Dic61C2×D411yescharacteristic
114D244—22no—
115D244—42no—
116D244—42no—
117C4×D61—22no—
118C4×D61—22no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—42no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—84no—
130C22×C61AGL(1,ℤ/8)12yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—21no—
138C2×D61—44no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—41no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61H(5,𝔽2)12yes—
146Dic61—21no—
147Dic61—21no—
148Dic61—42no—
149Dic61—41no—
150#3194—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—82no—
153C2×C61#53411yescharacteristic
154C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C61#57511yescharacteristic
156D61—41no—
157D61—41no—
158D61—81no—
159#525—611no—
160C2×#121—611no—
161#483—611no—
162#482—612no—
163#480—611no—
164#469—612no—
165#468—612no—
166#450D6111yescharacteristic, complemented
167#449—612no—
168#447—611no—
169#407—611no—
170C61#319411yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C22×D4—1221no—
173C22×D4C2×D6111yescharacteristic
174C23×C4—611no—
175C2×SD16C2×D6112yescomplemented
176C2×D8—612no—
177C2×M16—612no—
178#123—1221no—
179C22⋊Q8—611no—
180C22⋊Q8C2×D6111yescharacteristic
181#121—612no—
182#121—612no—
183#121—611no—
184#121—611no—
185#121—1221no—
186#121—1221no—
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×Q8C22×D6111yescharacteristic
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—611no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—1222no—
212C2×D4—1222no—
213C2×D4—1221no—
214C2×D4—2444no—
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—42no—
226D8—2442no—
227M16—2442no—
228C2×C8—612no—
229C2×C8C22×D6112yes—
230C4⋊C4—21no—
231C4⋊C4—611no—
232C4⋊C4—612no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4C22×D6111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1221no—
240C22⋊C4—1222no—
241C22⋊C4—1222no—
242C22⋊C4—1221no—
243C42—1221no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—611no—
249C23—611no—
250C23—1222no—
251C23—1221no—
252C23—2441no—
253C23—2441no—
254C23D4×D6111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—1222no—
260D4—2442no—
261D4—2442no—
262D4—2444no—
263D4—2444no—
264D4—2442no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4—1222no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2442no—
277C2×C4—2441no—
278C2×C4—2442no—
279C2×C4D4×D6111yescharacteristic
280C2×C4C23×D6111yescharacteristic
281C8—22no—
282C8—1222no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—1221no—
290C22—1221no—
291C22—1221no—
292C22—1221no—
293C22—1221no—
294C22—1221no—
295C22—2444no—
296C22—2441no—
297C22—2441no—
298C22—2441no—
299C22#1451980412yes—
300C22C2×D4×D6111yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—1221no—
305C4—1221no—
306C4—2442no—
307C4—2441no—
308C4#1451982212yes—
309C2—22no—
310C2—82no—
311C2—4881no—
312C2—2441no—
313C2—2441no—
314C2#1684032211yescharacteristic
315C2C2×#1451980411yescharacteristic
316C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840275C2semidirect
2. C2×#14519748C2semidirect
3. #16840090C2semidirect
4. #16840084C2semidirect
5. #16840076C2semidirect
6. #16840014C2semidirect
7. #16840005C2semidirect
8. #16839906C2semidirect
9. #16839896C2semidirect
10. #16839724C2semidirect
11. C61×#450C2semidirect
12. C2×#11758226C22semidirect
15. C2×#11758199C22semidirect
16. C2×#11758189C22semidirect
18. #14519753C22semidirect
19. #14519752C22semidirect
28. #14519735C22semidirect
31. #14519711C22semidirect
32. #14519708C22semidirect
33. #14519701C22semidirect
34. #14519699C22semidirect
35. #14519698C22semidirect
37. #14519689C22semidirect
39. C2×SD16×C61C22semidirect
41. #102×C61C22semidirect
166. #450D61semidirect
170. C61#3194semidirect
175. C2×SD16C2×D61semidirect
198. #102C2×D61semidirect