Finite Group Databasebeta

← #21455867

Subgroups — #21455867

Order 7808.

454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840298C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3#16840095C211yesmaximal, characteristic, complemented
4#16840081C211yesmaximal, characteristic, complemented
5#16840064C212yesmaximal, complemented
6#16839979C212yesmaximal, complemented
7#16839896C211yesmaximal, characteristic
8SD16×Dic61C212yesmaximal, complemented
9#16839842C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C23×Dic61—21no—
13C2×#11758199C2212yes—
14#14519772—21no—
15#14519768C2211yescharacteristic, complemented
16#14519766C2211yescharacteristic, complemented
17#14519761—21no—
18#14519751C2211yescharacteristic
19Q8×Dic61C2211yescharacteristic, complemented
20D4×Dic61—21no—
21D4×Dic61—21no—
22D4×Dic61C2212yes—
23D4×Dic61C2212yes—
24#14519739C2211yescharacteristic, complemented
25#14519737—21no—
26#14519735—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519710C2212yescomplemented
31#14519709C2212yescomplemented
32#14519706C2212yescomplemented
33#14519701C2212yescomplemented
34#14519699C2212yescomplemented
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×SD16×C61C2212yes—
40C22⋊Q8×C61C2211yescharacteristic
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—24no—
46C2×D4×C61—21no—
47C2×D4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C22×Dic61—21no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—44no—
54C22×Dic61D411yescharacteristic
55C22×Dic61D411yescharacteristic
56C2×D244C2311yescharacteristic
57C2×C4×D61—21no—
58SD16×C61—24no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61C2311yescharacteristic
62C22⋊C4×C61—21no—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65#11758199—24no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69#11758198—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2312yes—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82C23×C61—24no—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—42no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88Q8×C61—22no—
89D4×C61—24no—
90D4×C61—22no—
91D4×C61#4114yes—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—42no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—44no—
103C2×Dic61—42no—
104C2×Dic61—44no—
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109D244—22no—
110C4×D61—42no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—24no—
116C22×C61—48no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61#13512yes—
120C22×C61C22×D411yescharacteristic
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61C2×#4112yes—
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—41no—
132Dic61—42no—
133Dic61AGL(1,ℤ/8)12yes—
134#3105—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—44no—
137C2×C61#52511yescharacteristic
138C2×C61C2×#13511yescharacteristic
139C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
140D61—81no—
141#529—611no—
142C2×C4×D4—611no—
143#484—611no—
144#481—611no—
145#478—612no—
146#463—612no—
147#450D6111yescharacteristic, complemented
148#447—611no—
149C4×SD16—612no—
150C4×D8—612no—
151#431—611no—
152C61#310511yescharacteristic, complemented, Sylow
153C22×D4C2×D6111yescharacteristic
154C23×C4—1221no—
155C2×SD16C2×D6112yes—
156C2×D8—612no—
157#126—1221no—
158#125—611no—
159#124—611no—
160#123—1221no—
161C22⋊Q8C2×D6111yescharacteristic
162#121—611no—
163C4×Q8—611no—
164C4×D4—612no—
165C4×D4—612no—
166C4×D4—611no—
167C4×D4—1221no—
168C4×D4—1221no—
169C4×D4—1221no—
170#117—1221no—
171C2×C4⋊C4—611no—
172C2×C22⋊C4—1221no—
173C2×C42—611no—
174#107—612no—
175#106—612no—
176C4⋊C8—612no—
177#103—612no—
178#102—612no—
179#102—612no—
180#102C2×D6112yes—
181C22⋊C8—611no—
182C22⋊C8C2×D6111yescharacteristic
183C4×C8—612no—
184C24—21no—
185C2×Q8C22×D6111yescharacteristic
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—611no—
189C2×D4—1221no—
190C2×D4C22×D6112yes—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—2444no—
198C22×C4C22×D6111yescharacteristic
199SD16—24no—
200D8—1224no—
201C2×C8—612no—
202C2×C8C22×D6112yes—
203C4⋊C4—21no—
204C4⋊C4—611no—
205C4⋊C4—612no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4C22×D6111yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1222no—
216C22⋊C4—1222no—
217C22⋊C4—1221no—
218C42—611no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—1221no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—1221no—
228C23D4×D6111yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232D4—1222no—
233D4—2442no—
234D4#1175822414yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—2442no—
247C2×C4—2444no—
248C2×C4—2444no—
249C2×C4—2442no—
250C2×C4D4×D6111yescharacteristic
251C2×C4C23×D6111yescharacteristic
252C8—22no—
253C8—1222no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—2441no—
261C22—2441no—
262C22—2441no—
263C22#1451979812yes—
264C22C2×D4×D6111yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—612no—
269C4—1221no—
270C4—1221no—
271C4—1221no—
272C4—2441no—
273C4—2442no—
274C4C2×#1175822412yes—
275C2—22no—
276C2—44no—
277C2—4881no—
278C2#1684026811yescharacteristic
279C2C2×#1451979811yescharacteristic
280C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3105
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. #16840298C2semidirect
2. C2×D4×Dic61C2semidirect
3. #16840095C2semidirect
4. #16840081C2semidirect
5. #16840064C2semidirect
6. #16839979C2semidirect
8. SD16×Dic61C2semidirect
9. #16839842C2semidirect
10. #16839812C2semidirect
11. C61×#450C2semidirect
15. #14519768C22semidirect
16. #14519766C22semidirect
19. Q8×Dic61C22semidirect
24. #14519739C22semidirect
30. #14519710C22semidirect
31. #14519709C22semidirect
32. #14519706C22semidirect
33. #14519701C22semidirect
34. #14519699C22semidirect
37. C8×Dic61C22semidirect
147. #450D61semidirect
152. C61#3105semidirect