Finite Group Databasebeta

← #21455822

Subgroups — #21455822

Order 7808.

448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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#16840314C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic
3#16840093C211yesmaximal, characteristic, complemented
4#16840090C211yesmaximal, characteristic, complemented
5#16840050C212yesmaximal, complemented
6#16839965C212yesmaximal, complemented
7#16839913C211yesmaximal, characteristic
8#16839853C212yesmaximal, complemented
9SD16×Dic61C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic
12C23×Dic61—21no—
13C2×#11758200C2212yes—
14#14519776C2211yescharacteristic, complemented
15#14519775C2211yescharacteristic, complemented
16#14519767—21no—
17#14519756C2211yescharacteristic
18#14519754—21no—
19Q8×Dic61C2211yescharacteristic, complemented
20#14519742—21no—
21#14519742C2211yescharacteristic, complemented
22D4×Dic61—21no—
23D4×Dic61—21no—
24D4×Dic61C2212yes—
25D4×Dic61C2212yes—
26#14519733—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519709C2212yescomplemented
31#14519708C2212yescomplemented
32#14519706C2212yescomplemented
33#14519702C2212yescomplemented
34#14519701C2212yescomplemented
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
49C22×Dic61—21no—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—44no—
53C22×Dic61D411yescharacteristic
54C22×Dic61D411yescharacteristic
55C2×Dic122—21no—
56C2×Dic122C2311yescharacteristic
57SD16×C61—24no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65#11758200—24no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2312yes—
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—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
87Q8×C61—22no—
88D4×C61—24no—
89D4×C61—22no—
90D4×C61#4114yes—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—42no—
101C2×Dic61—44no—
102C2×Dic61—44no—
103C2×Dic61SD1614yescomplemented
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108Dic122—22no—
109Dic122—42no—
110C8×C61—22no—
111#92418—22no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—24no—
115C22×C61—48no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61C2×SD1612yes—
119C22×C61C22×D411yescharacteristic
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—41no—
123C4×C61C2×#4112yes—
124Dic61—21no—
125Dic61—21no—
126Dic61—41no—
127Dic61—42no—
128Dic61—41no—
129Dic61C2×SD1612yes—
130Dic61C2×SD1612yes—
131#3101—611nomaximal, Sylow
132C2×C61—22no—
133C2×C61—44no—
134C2×C61#52511yescharacteristic
135C2×C61C22×SD1611yescharacteristic
136C2×C61#57511yescharacteristic
137#533—611no—
138C2×C4×D4—611no—
139#483—611no—
140#483—611no—
141#476—612no—
142#461—612no—
143#450—611no—
144#450D6111yescharacteristic
145C4×SD16—612no—
146C4×SD16—612no—
147#431—611no—
148C61#310111yescharacteristic, complemented, Sylow
149C22×D4C2×D6111yescharacteristic
150C23×C4—1221no—
151C2×SD16—612no—
152C2×SD16C2×D6112yes—
153C4⋊Q8—611no—
154C4⋊Q8—611no—
155#125—1221no—
156C22⋊Q8—611no—
157C22⋊Q8—1221no—
158C22⋊Q8C2×D6111yescharacteristic
159C4×Q8—611no—
160C4×Q8—611no—
161C4×Q8—1221no—
162C4×D4—612no—
163C4×D4—612no—
164C4×D4—1221no—
165C4×D4—1221no—
166#117—1221no—
167C2×C4⋊C4—611no—
168C2×C22⋊C4—1221no—
169C2×C42—611no—
170#106—612no—
171#106—612no—
172C4⋊C8—612no—
173#103—612no—
174#103—612no—
175#102—612no—
176#102C2×D6112yes—
177C22⋊C8—611no—
178C22⋊C8C2×D6111yescharacteristic
179C4×C8—612no—
180C24—21no—
181C2×Q8—611no—
182C2×Q8—1221no—
183C2×Q8C22×D6111yescharacteristic
184C2×D4—24no—
185C2×D4—21no—
186C2×D4C22×D6112yes—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1221no—
192C22×C4—2444no—
193C22×C4C22×D6111yescharacteristic
194SD16—24no—
195SD16—1224no—
196C2×C8—612no—
197C2×C8C22×D6112yes—
198C4⋊C4—21no—
199C4⋊C4—611no—
200C4⋊C4—612no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6111yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—611no—
217C42—1221no—
218C42—1221no—
219C23—24no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23D4×D6111yescharacteristic
224Q8—22no—
225Q8—1222no—
226Q8—2442no—
227D4—24no—
228D4—22no—
229D4#1175822414yes—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—614no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—2444no—
242C2×C4—2444no—
243C2×C4—2441no—
244C2×C4—2442no—
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—22no—
248C8—1222no—
249C22—21no—
250C22—21no—
251C22—24no—
252C22—48no—
253C22—42no—
254C22—42no—
255C22SD16×D6112yes—
256C22C2×D4×D6111yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—612no—
261C4—612no—
262C4—1221no—
263C4—1221no—
264C4—2441no—
265C4—2442no—
266C4—2441no—
267C4C2×#1175822412yes—
268C2—22no—
269C2—44no—
270C2#1684026811yescharacteristic
271C2C2×SD16×D6111yescharacteristic
272C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3101
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. #16840314C2semidirect
3. #16840093C2semidirect
4. #16840090C2semidirect
5. #16840050C2semidirect
6. #16839965C2semidirect
8. #16839853C2semidirect
9. SD16×Dic61C2semidirect
10. #16839812C2semidirect
14. #14519776C22semidirect
15. #14519775C22semidirect
19. Q8×Dic61C22semidirect
21. #14519742C22semidirect
30. #14519709C22semidirect
31. #14519708C22semidirect
32. #14519706C22semidirect
33. #14519702C22semidirect
34. #14519701C22semidirect
37. C8×Dic61C22semidirect
103. C2×Dic61SD16semidirect
148. C61#3101semidirect