Finite Group Databasebeta

← #21455824

Subgroups — #21455824

Order 7808.

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

normal subgroups only

This group has 448 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
1#16840314C211yesmaximal, characteristic, complemented
2C2×#14519739C211yesmaximal, characteristic
3#16840092C211yesmaximal, characteristic, complemented
4#16840051C212yesmaximal, complemented
5#16839966C212yesmaximal, complemented
6#16839915C211yesmaximal, characteristic
7#16839912C211yesmaximal, characteristic
8#16839849C212yesmaximal, complemented
9#16839847C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#483C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C4×D61—21no—
14C2×#11758190C2212yes—
15C2×#11758201C2212yes—
16#14519776C2211yescharacteristic, complemented
17#14519775C2211yescharacteristic, complemented
18#14519767—21no—
19#14519756C2211yescharacteristic
20#14519754—21no—
21Q8×Dic61C2211yescharacteristic, complemented
22#14519742—21no—
23#14519742C2211yescharacteristic, complemented
24#14519739—21no—
25#14519739—21no—
26#14519739C2212yes—
27#14519739C2212yes—
28#14519733—21no—
29C2×#11758198—21no—
30C2×C4×Dic61C2211yescharacteristic
31#14519708C2212yescomplemented
32#14519706C2212yescomplemented
33#14519700C2212yescomplemented
34#14519699C2212yes—
35#14519697C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yescomplemented
41#103×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61—21no—
44C2×Q8×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61D411yescharacteristic
48C22×Dic61D411yescharacteristic
49C2×D244—21no—
50C2×D244—24no—
51C2×D244C2312yes—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—44no—
55C2×Dic122—21no—
56C2×Dic122C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C22⋊C4×C61—21no—
63C22⋊Dic61—21no—
64#11758201—24no—
65#11758198—22no—
66#11758198—22no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2311yescharacteristic
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758190—24no—
82C23×C61C2×D411yescharacteristic
83C22×D61—24no—
84C22×D61—22no—
85C22×D61—42no—
86C22×D61—42no—
87Q8×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61SD1614yescomplemented
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103D244—24no—
104D244—22no—
105D244#4114yes—
106C4×D61—44no—
107C4×D61—44no—
108Dic122—22no—
109Dic122—42no—
110C8×C61—22no—
111#92418—22no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61C2×SD1612yes—
115C22×C61C22×D411yescharacteristic
116C2×D61—24no—
117C2×D61—48no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61C2×#4112yes—
125Dic61—21no—
126Dic61—21no—
127Dic61—41no—
128Dic61—41no—
129Dic61C2×SD1612yes—
130Dic61C2×SD1612yes—
131#3101—611nomaximal, Sylow
132C2×C61—22no—
133C2×C61#52511yescharacteristic
134C2×C61C22×SD1611yescharacteristic
135C2×C61#57511yescharacteristic
136D61—44no—
137#533—611no—
138C2×C4×D4—611no—
139#483—611no—
140#483D6111yescharacteristic, complemented
141#476—612no—
142#461—612no—
143#450—611no—
144#450—611no—
145C4×SD16—612no—
146C4×SD16—612no—
147#431—611no—
148C61#310111yescharacteristic, complemented, Sylow
149C22×D4—611no—
150C23×C4—1221no—
151C2×SD16—612no—
152C2×SD16—612no—
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⋊C4C2×D6111yescharacteristic
168C2×C22⋊C4—1221no—
169C2×C42—611no—
170#106—612no—
171#106C2×D6112yescomplemented
172C4⋊C8—612no—
173#103—612no—
174#103C2×D6112yescomplemented
175#102—612no—
176#102—612no—
177C22⋊C8—611no—
178C22⋊C8C2×D6111yescharacteristic
179C4×C8—612no—
180C24—1221no—
181C2×Q8—611no—
182C2×Q8—1221no—
183C2×Q8C22×D6111yescharacteristic
184C2×D4—612no—
185C2×D4—1224no—
186C2×D4—1221no—
187C22×C4—21no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1222no—
191C22×C4—1222no—
192C22×C4—2444no—
193C22×C4C22×D6111yescharacteristic
194SD16—1224no—
195SD16—1224no—
196C2×C8—612no—
197C2×C8C22×D6112yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—611no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4C22×D6111yescharacteristic
208C4⋊C4C22×D6112yes—
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—1224no—
220C23—1222no—
221C23—2442no—
222C23—2442no—
223C23D4×D6111yescharacteristic
224Q8—22no—
225Q8—1222no—
226Q8—2442no—
227D4—614no—
228D4—1224no—
229D4—1222no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—614no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—2444no—
243C2×C4—2444no—
244C2×C4—2441no—
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—22no—
248C8—1222no—
249C22—21no—
250C22—21no—
251C22—1224no—
252C22—2448no—
253C22—2442no—
254C22—2442no—
255C22SD16×D6112yes—
256C22C2×D4×D6111yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—612no—
262C4—612no—
263C4—1221no—
264C4—1221no—
265C4—2441no—
266C4—2441no—
267C4#41×D6112yes—
268C2—22no—
269C2—2444no—
270C2#1684027011yescharacteristic
271C2C2×SD16×D6111yescharacteristic
272C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3101
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
1. #16840314C2semidirect
3. #16840092C2semidirect
4. #16840051C2semidirect
5. #16839966C2semidirect
8. #16839849C2semidirect
9. #16839847C2semidirect
10. #16839812C2semidirect
11. C61×#483C2semidirect
16. #14519776C22semidirect
17. #14519775C22semidirect
21. Q8×Dic61C22semidirect
23. #14519742C22semidirect
31. #14519708C22semidirect
32. #14519706C22semidirect
33. #14519700C22semidirect
37. C8×Dic61C22semidirect
40. #106×C61C22semidirect
41. #103×C61C22semidirect
98. C2×Dic61SD16semidirect
140. #483D61semidirect
148. C61#3101semidirect
171. #106C2×D61semidirect
174. #103C2×D61semidirect