Finite Group Databasebeta

← #21455952

Subgroups — #21455952

Order 7808.

450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840293C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3#16840093C211yesmaximal, characteristic, complemented
4#16840073C211yesmaximal, characteristic, complemented
5#16840064C212yesmaximal, complemented
6#16839975C212yesmaximal, complemented
7#16839913C211yesmaximal, characteristic, complemented
8#16839874C212yesmaximal, complemented
9#16839859C212yesmaximal, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic
12C23×Dic61—21no—
13C2×#11758200C2212yes—
14#14519770—21no—
15#14519768C2211yescharacteristic, complemented
16#14519764C2211yescharacteristic, complemented
17#14519758—21no—
18#14519756C2211yescharacteristic
19#14519742C2211yescharacteristic, complemented
20D4×Dic61—21no—
21D4×Dic61—21no—
22D4×Dic61—21no—
23D4×Dic61C2212yes—
24D4×Dic61C2212yes—
25D4×Dic61C2211yescharacteristic, complemented
26#14519733—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519710C2212yescomplemented
31#14519709C2212yescomplemented
32#14519706C2212yescomplemented
33#14519702C2212yescomplemented
34#14519698C2212yes—
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×D8×C61C2212yes—
40#121×C61C2211yescharacteristic
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C2×D4×C61—24no—
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C2×D4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—21no—
54C22×Dic61—44no—
55C22×Dic61D411yescharacteristic
56C22×Dic61D411yescharacteristic
57C2×Dic122C2311yescharacteristic
58D8×C61—24no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65C22⋊Dic61—21no—
66C22⋊Dic61—21no—
67C22⋊Dic61—21no—
68#11758200—24no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2311yescharacteristic
72C4⋊Dic61C2312yes—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82C23×C61—24no—
83C23×C61—22no—
84C23×C61—21no—
85C23×C61—42no—
86C23×C61—42no—
87C23×C61C2×D411yescharacteristic
88D4×C61—24no—
89D4×C61—22no—
90D4×C61—22no—
91D4×C61—42no—
92D4×C61#4114yes—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61—44no—
104C2×Dic61—44no—
105C2×Dic61—42no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110Dic122—22no—
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—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61AGL(1,ℤ/8)12yes—
123C22×C61C22×D411yescharacteristic
124C4×C61—21no—
125C4×C61—41no—
126C4×C61C2×#4112yes—
127Dic61—21no—
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—41no—
132Dic61—42no—
133Dic61—41no—
134#3114—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—44no—
137C2×C61—81no—
138C2×C61#52511yescharacteristic
139C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
140C2×C61#57511yescharacteristic
141#529—611no—
142C2×C4×D4—611no—
143#483—611no—
144#480—611no—
145#478—612no—
146#463—612no—
147#450—611no—
148#447D6111yescharacteristic
149#442—612no—
150#440—612no—
151#432—611no—
152C61#311411yescharacteristic, complemented, Sylow
153C22×D4C2×D6111yescharacteristic
154C23×C4—1221no—
155C2×SD16—612no—
156C2×D8C2×D6112yes—
157#126—1221no—
158#125—611no—
159#124—611no—
160#123—1221no—
161C22⋊Q8—611no—
162#121C2×D6111yescharacteristic
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
183#97—612no—
184C24—21no—
185C2×Q8—611no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4C22×D6111yescharacteristic
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—1224no—
200D8—24no—
201C2×C8—612no—
202C2×C8C22×D6112yes—
203C4⋊C4—611no—
204C4⋊C4—612no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4C22×D6111yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C42—611no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—1221no—
223C23—24no—
224C23—22no—
225C23—21no—
226C23—42no—
227C23—42no—
228C23D4×D6111yescharacteristic
229Q8—1222no—
230D4—24no—
231D4—22no—
232D4—22no—
233D4—42no—
234D4#1175822414yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—2441no—
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—41no—
261C22—41no—
262C22—41no—
263C22#1451980112yes—
264C22C2×D4×D6111yescharacteristic
265C4—21no—
266C4—41no—
267C4—1221no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2441no—
272C4—2442no—
273C4—2441no—
274C4C2×#1175822412yes—
275C2—22no—
276C2—44no—
277C2—81no—
278C2#1684026811yescharacteristic
279C2C2×#1451980111yescharacteristic
280C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3114
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. #16840293C2semidirect
2. C2×D4×Dic61C2semidirect
3. #16840093C2semidirect
4. #16840073C2semidirect
5. #16840064C2semidirect
6. #16839975C2semidirect
7. #16839913C2semidirect
8. #16839874C2semidirect
9. #16839859C2semidirect
10. #16839816C2semidirect
15. #14519768C22semidirect
16. #14519764C22semidirect
19. #14519742C22semidirect
25. D4×Dic61C22semidirect
30. #14519710C22semidirect
31. #14519709C22semidirect
32. #14519706C22semidirect
33. #14519702C22semidirect
35. #14519698C22semidirect
37. #14519687C22semidirect
152. C61#3114semidirect