Finite Group Databasebeta

← #21455049

Subgroups — #21455049

Order 7808.

994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×D244C211yesmaximal, characteristic, complemented
2C2×#14519805C212yesmaximal, complemented
3#16840273C211yesmaximal, characteristic, complemented
4#16839915C214yesmaximal, complemented
5#16839898C214yesmaximal, complemented
6#16839768C212yesmaximal, complemented
7C61×#407C211yesmaximal, characteristic, complemented
8C24×D61—21no—
9C2×#11758222C2211yescharacteristic, complemented
10C22×D244—22no—
11C22×D244—21no—
12C22×D244—28no—
13C22×D244C2214yes—
14C22×D244C2212yes—
15#14519805—28no—
16C2×#11758190C2214yescomplemented
17C2×D488C2214yescomplemented
18#14519760—21no—
19#14519756C2212yescomplemented
20#14519751C2212yescomplemented
21#14519746—21no—
22C4×C22⋊D61—22no—
23#14519736C2211yescharacteristic, complemented
24#14519699C2218yescomplemented
25C23×C4×C61C2211yescharacteristic
26C2×M16×C61C2212yescomplemented
27C22⋊C8×C61C2214yescomplemented
28C24×C61D411yescharacteristic
29C23×D61—28no—
30C23×D61—24no—
31C23×D61—22no—
32C23×D61—48no—
33C22×C4×C61—24no—
34C22×C4×C61D412yes—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C2×C22⋊D61—22no—
40#11758222—24no—
41C2×D244—28no—
42C2×D244—216no—
43C2×D244—24no—
44C2×D244—22no—
45C2×D244—24no—
46C2×D244—216no—
47C2×D244D418yescomplemented
48C2×D244C2314yes—
49C2×D244C2311yescharacteristic, complemented
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic, complemented
52M16×C61—24no—
53C2×C8×C61C2314yescomplemented
54C22⋊Dic61—21no—
55C22⋊Dic61—22no—
56#11758198—22no—
57C4⋊Dic61C2312yescomplemented
58#11758196—22no—
59C4×Dic61—21no—
60D488—28no—
61#11758190—28no—
62C23×C61—22no—
63C23×C61—24no—
64C23×C61C2×D411yescharacteristic
65C23×C61C2×D412yes—
66C22×D61—216no—
67C22×D61—28no—
68C22×D61—24no—
69C22×D61—21no—
70C22×D61—432no—
71C22×D61—48no—
72C22×D61—48no—
73C22×D61—48no—
74C2×C4×C61—22no—
75C2×C4×C61—24no—
76C2×C4×C61—24no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D414yes—
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—44no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85D244—216no—
86D244—28no—
87D244—24no—
88D244—22no—
89D244C2×D418yes—
90C4×D61—42no—
91Dic122—22no—
92C8×C61—24no—
93C22×C61—28no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61#12012yes—
98C22×C61AGL(1,ℤ/8)14yescomplemented
99C22×C61C22×D411yescharacteristic
100C2×D61—28no—
101C2×D61—416no—
102C2×D61—432no—
103C2×D61—48no—
104C2×D61—41no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61#12012yes—
108C4×C61C22×D412yes—
109Dic61—41no—
110Dic61—42no—
111#3003—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—24no—
114C2×C61C2×#12011yescharacteristic
115C2×C61C2×AGL(1,ℤ/8)12yes—
116D61—48no—
117D61—81no—
118C23×D4—611no—
119C2×AGL(1,ℤ/8)—612no—
120#525—611no—
121#450—614no—
122#447—614no—
123#418—612no—
124#407D6111yescharacteristic, complemented
125C61#300311yescharacteristic, complemented, Sylow
126C25—1221no—
127C2×#41—611no—
128C22×D4—612no—
129C22×D4—614no—
130C22×D4—1228no—
131C22×D4—1222no—
132C22×D4—1221no—
133C23×C4C2×D6111yescharacteristic
134AGL(1,ℤ/8)—1228no—
135C2×SD16—614no—
136C2×D8—614no—
137C2×M16C2×D6112yescomplemented
138#123—1221no—
139C22⋊Q8—612no—
140#121—612no—
141#120—1221no—
142C4×D4—1222no—
143#117—611no—
144#102—618no—
145C22⋊C8C2×D6114yescomplemented
146C24—1228no—
147C24—1224no—
148C24—1222no—
149C24—2448no—
150C24D24411yescharacteristic
151#41—1224no—
152C2×Q8—611no—
153C2×D4—618no—
154C2×D4—614no—
155C2×D4—611no—
156C2×D4—12216no—
157C2×D4—1228no—
158C2×D4—12216no—
159C2×D4—1222no—
160C2×D4—1221no—
161C2×D4—1224no—
162C2×D4—1222no—
163C2×D4—1224no—
164C22×C4—24no—
165C22×C4—1221no—
166C22×C4D24412yes—
167C22×C4D24411yescharacteristic
168C22×C4C22×D6112yes—
169C22×C4C22×D6111yescharacteristic
170SD16—1228no—
171D8—1228no—
172M16—24no—
173C2×C8C22×D6114yescomplemented
174C4⋊C4—612no—
175C4⋊C4—1222no—
176C22⋊C4—1221no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C42—1221no—
180C23—22no—
181C23—24no—
182C23—12216no—
183C23—1224no—
184C23—1228no—
185C23—1221no—
186C23—24432no—
187C23—2448no—
188C23—2448no—
189C23—2448no—
190C23C2×D24411yescharacteristic
191C23C2×D24412yes—
192Q8—1222no—
193D4—618no—
194D4—12216no—
195D4—1224no—
196D4—1222no—
197D4—1228no—
198D4—2442no—
199D4—2444no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4C2×D24412yes—
207C2×C4C2×D24411yescharacteristic
208C2×C4D4×D6114yes—
209C2×C4C23×D6111yescharacteristic
210C8—24no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—1228no—
216C22—24416no—
217C22—24432no—
218C22—2441no—
219C22—2442no—
220C22—2448no—
221C22#1451974712yes—
222C22#1451980514yescomplemented
223C22C22×D24411yescharacteristic
224C4—22no—
225C4—2441no—
226C4—2442no—
227C4#1451974712yes—
228C4C2×D4×D6112yes—
229C2—22no—
230C2—24no—
231C2—4881no—
232C2—2448no—
233C2C2×#1451974711yescharacteristic
234C2C2×#1451980512yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3003
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×D244C2semidirect
2. C2×#14519805C2semidirect
3. #16840273C2semidirect
4. #16839915C2semidirect
5. #16839898C2semidirect
6. #16839768C2semidirect
7. C61×#407C2semidirect
9. C2×#11758222C22semidirect
16. C2×#11758190C22semidirect
17. C2×D488C22semidirect
19. #14519756C22semidirect
20. #14519751C22semidirect
23. #14519736C22semidirect
24. #14519699C22semidirect
26. C2×M16×C61C22semidirect
27. C22⋊C8×C61C22semidirect
47. C2×D244D4semidirect
49. C2×D244C23semidirect
51. C2×Dic122C23semidirect
53. C2×C8×C61C23semidirect
57. C4⋊Dic61C23semidirect
98. C22×C61AGL(1,ℤ/8)semidirect
124. #407D61semidirect
125. C61#3003semidirect
137. C2×M16C2×D61semidirect
145. C22⋊C8C2×D61semidirect
173. C2×C8C22×D61semidirect
222. C22#14519805semidirect