Finite Group Databasebeta

← #483×D61 #21455693

Subgroups — #483×D61 #21455693

Order 7808.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D61C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16840094C212yesmaximal, complemented
4#16840093C211yesmaximal, characteristic, complemented
5#16840092C211yesmaximal, characteristic, complemented
6#16840091C212yesmaximal, complemented
7#16840090C211yesmaximal, characteristic, complemented
8#106×D61C212yesmaximal, complemented
9#103×D61C212yesmaximal, complemented
10C22⋊C8×D61C211yesmaximal, characteristic
11C61×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2211yescharacteristic
13C22×C4×D61—21no—
14C22×C4×D61C2211yescharacteristic
15C2×C8×D61C2212yes—
16#14519757C2211yescharacteristic
17#14519756C2211yescharacteristic
18#14519755—21no—
19#14519754—21no—
20#14519753C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196—21no—
23C4⋊C4×D61—21no—
24C4⋊C4×D61—21no—
25C4⋊C4×D61—21no—
26C4⋊C4×D61C2212yes—
27C4⋊C4×D61C2212yes—
28C4⋊C4×D61C2211yescharacteristic
29C22⋊C4×D61—21no—
30#14519709C2212yescomplemented
31#14519708C2212yescomplemented
32#14519708C2212yescomplemented
33#14519702C2212yescomplemented
34#14519701C2212yescomplemented
35#14519700C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yescomplemented
41#103×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61D411yescharacteristic
44C2×Q8×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61D411yescharacteristic
49Q8×D61—24no—
50C2×C4×D61—24no—
51C2×C4×D61—22no—
52C2×C4×D61—22no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—44no—
56C2×C4×D61D411yescharacteristic
57C2×C4×D61D411yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×C4×D61C2311yescharacteristic
60C2×Dic122—21no—
61C2×Dic122C2311yescharacteristic
62C2×C8×C61C2312yes—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—21no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2312yes—
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—22no—
77#11758196—22no—
78#11758196—21no—
79#11758196—21no—
80C2×#92418C2312yes—
81C8×D61—24no—
82C23×C61C2×D411yescharacteristic
83C22×D61—22no—
84C22×D61—22no—
85C22×D61SD1614yes—
86C22×D61C2×D411yescharacteristic
87C22×D61C2×D411yescharacteristic
88Q8×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—42no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—42no—
107C4×D61—44no—
108C4×D61—44no—
109C4×D61—42no—
110C4×D61#4114yes—
111Dic122—22no—
112Dic122—42no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×SD1612yes—
118C22×C61C22×D411yescharacteristic
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—28no—
122C2×D61#12312yes—
123C2×D61C2×SD1612yes—
124C2×D61C2×SD1612yes—
125C2×D61#13712yes—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—42no—
129C4×C61—41no—
130C4×C61C2×#4112yes—
131Dic61—21no—
132Dic61—41no—
133Dic61—42no—
134Dic61—41no—
135Dic61#12312yes—
136C2×#483—611nomaximal, Sylow
137C2×C61—22no—
138C2×C61C2×#12311yescharacteristic
139C2×C61C22×SD1611yescharacteristic
140C2×C61C2×#13711yescharacteristic
141D61—22no—
142D61#48314yesdirect product factor
143C2×C22⋊Q8—611no—
144C22×C4⋊C4—611no—
145#483—611no—
146#483—611no—
147#483—612no—
148#483—612no—
149#483—611no—
150#483D6111yescharacteristic, direct product factor
151C2×#106—612no—
152C2×#103—612no—
153C2×C22⋊C8—611no—
154C61C2×#48311yescharacteristic, complemented, Sylow
155C22×Q8—611no—
156C23×C4—611no—
157C23×C4—1221no—
158C22×C8—612no—
159C22⋊Q8—611no—
160C22⋊Q8—611no—
161C22⋊Q8—611no—
162C22⋊Q8—1221no—
163C22⋊Q8—1221no—
164C22⋊Q8C2×D6111yescharacteristic
165C2×C4⋊C4—611no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4—1221no—
175#106—612no—
176#106—612no—
177#106—612no—
178#106C2×D6112yescomplemented
179#103—612no—
180#103—612no—
181#103—612no—
182#103C2×D6112yescomplemented
183C22⋊C8—611no—
184C22⋊C8—612no—
185C22⋊C8C2×D6111yescharacteristic
186C24—611no—
187C2×Q8—611no—
188C2×Q8—1221no—
189C2×Q8—1224no—
190C2×Q8C22×D6111yescharacteristic
191C22×C4—21no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1224no—
198C22×C4—1221no—
199C22×C4—1221no—
200C22×C4—1222no—
201C22×C4—1222no—
202C22×C4—1221no—
203C22×C4—2444no—
204C22×C4C22×D6111yescharacteristic
205C2×C8—612no—
206C2×C8—1224no—
207C2×C8C22×D6112yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—612no—
211C4⋊C4—611no—
212C4⋊C4—1222no—
213C4⋊C4—1222no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4—1221no—
219C4⋊C4C22×D6112yes—
220C4⋊C4C22×D6111yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C22⋊C4—1221no—
225C23—611no—
226C23—611no—
227C23—614no—
228C23—1222no—
229C23—1222no—
230C23D4×D6111yescharacteristic
231Q8—22no—
232Q8—1222no—
233Q8—2442no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—611no—
240C2×C4—614no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2442no—
250C2×C4—2444no—
251C2×C4—2444no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4D4×D6111yescharacteristic
255C2×C4C23×D6111yescharacteristic
256C8—22no—
257C8—1222no—
258C22—21no—
259C22—21no—
260C22—612no—
261C22—612no—
262C22—612no—
263C22—612no—
264C22—1228no—
265C22—1221no—
266C22—1221no—
267C22SD16×D6112yes—
268C22C2×D4×D6111yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—612no—
274C4—1221no—
275C4—2441no—
276C4—2442no—
277C4—2441no—
278C4#41×D6112yes—
279C2—22no—
280C2—614no—
281C2—1222no—
282C2#123×D6111yescharacteristic
283C2C2×SD16×D6111yescharacteristic
284C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61C2×#483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16840094C2semidirect
4. #16840093C2semidirect
5. #16840092C2semidirect
6. #16840091C2semidirect
7. #16840090C2semidirect
8. #106×D61C2semidirect
9. #103×D61C2semidirect
11. C61×#483C2semidirect
30. #14519709C22semidirect
31. #14519708C22semidirect
32. #14519708C22semidirect
33. #14519702C22semidirect
34. #14519701C22semidirect
35. #14519700C22semidirect
40. #106×C61C22semidirect
41. #103×C61C22semidirect
142. D61#483direct (N × H)
150. #483D61direct (N × H)
154. C61C2×#483semidirect
178. #106C2×D61semidirect
182. #103C2×D61semidirect