Finite Group Databasebeta

← #489×D61 #21456145

Subgroups — #489×D61 #21456145

Order 7808.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic
3#16840124C211yesmaximal, characteristic, complemented
4#16840123C212yesmaximal, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840121C211yesmaximal, characteristic, complemented
7#16840120C212yesmaximal, complemented
8#103×D61C212yesmaximal, complemented
9#102×D61C212yesmaximal
10#97×D61C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×Q8×D61C2211yescharacteristic
14C2×D4×D61C2211yescharacteristic
15C2×C8×D61C2212yes—
16#14519777C2211yescharacteristic, complemented
17#14519776—21no—
18#14519776C2212yescomplemented
19#14519775—21no—
20#14519766C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519764C2211yescharacteristic
23#14519763—21no—
24#14519763—21no—
25C4⋊C4×D61—21no—
26C4⋊C4×D61C2212yes—
27C22⋊C4×D61—21no—
28C22⋊C4×D61—21no—
29C42×D61C2211yescharacteristic
30#14519702C2212yescomplemented
31#14519701C2212yescomplemented
32#14519700C2212yescomplemented
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519688C2211yescharacteristic, complemented
37#14519687C2212yescomplemented
38C4⋊Q8×C61C2211yescharacteristic, complemented
39#124×C61C2211yescharacteristic
40#103×C61C2212yescomplemented
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C2×Q8×C61—21no—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48Q8×D61—24no—
49Q8×D61—44no—
50D4×D61—24no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—22no—
53C2×C4×D61—21no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122—21no—
58C2×Dic122—22no—
59C2×Dic122—21no—
60C2×Dic122C2311yescharacteristic
61C2×C8×C61C2312yes—
62C4⋊C4×C61—21no—
63C4⋊C4×C61C2312yes—
64C22⋊C4×C61—21no—
65C22⋊C4×C61—21no—
66C42×C61C2311yescharacteristic
67C22⋊Dic61—21no—
68C22⋊Dic61—21no—
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2312yes—
75#11758196—22no—
76#11758196—22no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81C8×D61—24no—
82C23×C61—21no—
83C22×D61—21no—
84C22×D61—42no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61C2×D411yescharacteristic
88Q8×C61—22no—
89Q8×C61—42no—
90D4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—42no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102D244—22no—
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—42no—
106C4×D61—44no—
107C4×D61#4114yes—
108Dic122—22no—
109Dic122—44no—
110Dic122—42no—
111Dic122—42no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—84no—
122C2×D61#12412yes—
123C2×D61AGL(1,ℤ/8)12yes—
124C2×D61#13712yes—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—42no—
129C4×C61C2×#4112yes—
130Dic61—21no—
131Dic61—21no—
132Dic61—41no—
133Dic61—42no—
134Dic61#12412yes—
135C2×#489—611nomaximal, Sylow
136C2×C61—81no—
137C2×C61C2×#12411yescharacteristic
138C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C61C2×#13711yescharacteristic
140D61—81no—
141D61#48914yesdirect product factor
142C2×C4⋊Q8—611no—
143C2×#124—611no—
144#489—611no—
145#489—611no—
146#489—612no—
147#489—612no—
148#489—611no—
149#489D6111yescharacteristic, direct product factor
150C2×#103—612no—
151C2×#102—612no—
152C2×#97—611no—
153C61C2×#48911yescharacteristic, complemented, Sylow
154C22×Q8—611no—
155C22×Q8—1221no—
156C22×D4—611no—
157C22×C8—612no—
158C4⋊Q8—612no—
159C4⋊Q8—611no—
160C4⋊Q8—1221no—
161C4⋊Q8—1221no—
162C4⋊Q8C2×D6111yescharacteristic, complemented
163#124—611no—
164#124—611no—
165#124—611no—
166#124—1221no—
167#124—1221no—
168#124C2×D6111yescharacteristic
169C2×C4⋊C4—612no—
170C2×C4⋊C4—1221no—
171C2×C22⋊C4—1221no—
172C2×C22⋊C4—1221no—
173C2×C42—611no—
174#103—612no—
175#103—612no—
176#103—612no—
177#103C2×D6112yescomplemented
178#102—612no—
179#102—612no—
180#102—612no—
181#102C2×D6112yes—
182#97—612no—
183#97—611no—
184#97C2×D6111yescharacteristic, complemented
185C24—1221no—
186C2×Q8—21no—
187C2×Q8—611no—
188C2×Q8—1221no—
189C2×Q8—1222no—
190C2×Q8—1224no—
191C2×Q8—1221no—
192C2×Q8—2444no—
193C2×Q8C22×D6111yescharacteristic
194C2×D4—611no—
195C2×D4—1224no—
196C2×D4—1221no—
197C2×D4C22×D6111yescharacteristic
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1221no—
202C22×C4—1222no—
203C2×C8—612no—
204C2×C8—1224no—
205C2×C8C22×D6112yes—
206C4⋊C4—21no—
207C4⋊C4—612no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—1221no—
211C4⋊C4C22×D6112yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42C22×D6111yescharacteristic
224C23—21no—
225C23—611no—
226C23—1221no—
227C23—2442no—
228C23—2442no—
229C23—2442no—
230Q8—22no—
231Q8—42no—
232Q8—1222no—
233Q8—2442no—
234Q8—2442no—
235Q8—2444no—
236D4—22no—
237D4—1222no—
238D4—2442no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—611no—
242C2×C4—614no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2442no—
250C2×C4—2444no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—22no—
255C8—1222no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—612no—
260C22—612no—
261C22—612no—
262C22—4884no—
263C22—2441no—
264C22—2441no—
265C22—2441no—
266C22C2×D4×D6111yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—612no—
272C4—1221no—
273C4—1221no—
274C4—2441no—
275C4—2442no—
276C4#41×D6112yes—
277C2—81no—
278C2—614no—
279C2—4881no—
280C2#124×D6111yescharacteristic
281C2AGL(1,ℤ/8)×D6111yescharacteristic
282C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61C2×#489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D61C2semidirect
3. #16840124C2semidirect
4. #16840123C2semidirect
5. #16840122C2semidirect
6. #16840121C2semidirect
7. #16840120C2semidirect
8. #103×D61C2semidirect
10. #97×D61C2semidirect
11. C61×#489C2semidirect
16. #14519777C22semidirect
18. #14519776C22semidirect
30. #14519702C22semidirect
31. #14519701C22semidirect
32. #14519700C22semidirect
36. #14519688C22semidirect
37. #14519687C22semidirect
38. C4⋊Q8×C61C22semidirect
40. #103×C61C22semidirect
42. #97×C61C22semidirect
141. D61#489direct (N × H)
149. #489D61direct (N × H)
153. C61C2×#489semidirect
162. C4⋊Q8C2×D61semidirect
177. #103C2×D61semidirect
184. #97C2×D61semidirect