Finite Group Databasebeta

← #21455046

Subgroups — #21455046

Order 7808.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#14519803C212yesmaximal, complemented
2#16840273C211yesmaximal, characteristic, complemented
3#16839913C214yesmaximal, complemented
4#16839896C214yesmaximal, complemented
5#16839767C212yesmaximal, complemented
6#16839726C211yesmaximal, characteristic, complemented
7C23×D4×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic, complemented
9#14519803—28no—
10C2×#11758200C2214yescomplemented
11C2×#11758199C2214yescomplemented
12C2×#11758194C2212yescomplemented
13#14519760—21no—
14#14519756C2212yescomplemented
15#14519751C2212yescomplemented
16#14519746—21no—
17C4×C22⋊D61—22no—
18#14519736C2211yescharacteristic, complemented
19#14519698C2218yescomplemented
20C22⋊#92418C2214yescomplemented
21C25×C61—21no—
22C22×D4×C61—28no—
23C22×D4×C61—22no—
24C22×D4×C61—21no—
25C22×D4×C61C2214yes—
26C22×D4×C61C2212yes—
27C23×C4×C61C2211yescharacteristic
28C24×C61—28no—
29C24×C61—24no—
30C24×C61—22no—
31C24×C61—48no—
32C24×C61D411yescharacteristic
33C2×D4×C61—28no—
34C2×D4×C61—216no—
35C2×D4×C61—216no—
36C2×D4×C61—24no—
37C2×D4×C61—22no—
38C2×D4×C61—24no—
39C2×D4×C61D418yescomplemented
40C2×D4×C61C2314yes—
41C22×C4×C61—24no—
42C22×C4×C61D412yes—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61—22no—
48#11758222—24no—
49C2×D244C2311yescharacteristic, complemented
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic, complemented
52C22⋊Dic61—21no—
53C22⋊Dic61—22no—
54#11758200—28no—
55#11758199—28no—
56#11758198—22no—
57C4⋊Dic61C2312yescomplemented
58#11758196—22no—
59C4×Dic61—21no—
60#11758194—24no—
61C2×#92418C2314yescomplemented
62C23×C61—22no—
63C23×C61—24no—
64C23×C61—216no—
65C23×C61—28no—
66C23×C61—24no—
67C23×C61—432no—
68C23×C61—48no—
69C23×C61—48no—
70C23×C61—48no—
71C23×C61C2×D411yescharacteristic
72C23×C61C2×D412yes—
73C22×D61—21no—
74D4×C61—216no—
75D4×C61—28no—
76D4×C61—24no—
77D4×C61C2×D418yes—
78C2×C4×C61—22no—
79C2×C4×C61—24no—
80C2×C4×C61—24no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D414yes—
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—42no—
86C22⋊D61—44no—
87C2×Dic61—22no—
88C2×Dic61—21no—
89D244—22no—
90C4×D61—42no—
91Dic122—22no—
92#92418—24no—
93C22×C61—28no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—28no—
98C22×C61—416no—
99C22×C61—432no—
100C22×C61—48no—
101C22×C61#12012yes—
102C22×C61AGL(1,ℤ/8)14yescomplemented
103C22×C61C22×D411yescharacteristic
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×C61—48no—
115C2×C61C2×#12011yescharacteristic
116C2×C61C2×AGL(1,ℤ/8)12yes—
117D61—81no—
118C23×D4D6111yescharacteristic, complemented
119C2×AGL(1,ℤ/8)—612no—
120#525—611no—
121#450—614no—
122#447—614no—
123#418—612no—
124#407—611no—
125C61#300311yescharacteristic, complemented, Sylow
126C25—21no—
127C2×#41—611no—
128C22×D4—28no—
129C22×D4—22no—
130C22×D4—21no—
131C22×D4C2×D6114yes—
132C22×D4C2×D6112yes—
133C23×C4C2×D6111yescharacteristic
134AGL(1,ℤ/8)—1228no—
135C2×SD16—614no—
136C2×D8—614no—
137C2×M16—612no—
138#123—1221no—
139C22⋊Q8—612no—
140#121—612no—
141#120—1221no—
142C4×D4—1222no—
143#117—611no—
144#102—618no—
145C22⋊C8—614no—
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D6111yescharacteristic
151#41—1224no—
152C2×Q8—611no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—611no—
160C2×D4—1222no—
161C2×D4—1221no—
162C2×D4C22⋊D6118yescomplemented
163C2×D4C22×D6114yes—
164C22×C4—24no—
165C22×C4—1221no—
166C22×C4C22⋊D6112yes—
167C22×C4C22⋊D6111yescharacteristic
168C22×C4C22×D6112yes—
169C22×C4C22×D6111yescharacteristic
170SD16—1228no—
171D8—1228no—
172M16—1224no—
173C2×C8—614no—
174C4⋊C4—612no—
175C4⋊C4—1222no—
176C22⋊C4—1221no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C42—1221no—
180C23—22no—
181C23—24no—
182C23—216no—
183C23—24no—
184C23—28no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—1221no—
190C23C2×C22⋊D6111yescharacteristic
191C23C2×C22⋊D6112yes—
192Q8—1222no—
193D4—216no—
194D4—24no—
195D4—28no—
196D4—1222no—
197D4—2442no—
198D4—2444no—
199D4C2×C22⋊D6118yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6114yes—
208C2×C4C2×C22⋊D6111yescharacteristic
209C2×C4C23×D6111yescharacteristic
210C8—1224no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—416no—
217C22—432no—
218C22—48no—
219C22—2441no—
220C22—2442no—
221C22#1451974612yes—
222C22#1451980314yescomplemented
223C22C22×C22⋊D6111yescharacteristic
224C4—22no—
225C4—2441no—
226C4—2442no—
227C4#1451974612yes—
228C4C22×C22⋊D6112yes—
229C2—22no—
230C2—24no—
231C2—48no—
232C2—4881no—
233C2C2×#1451974611yescharacteristic
234C2C2×#1451980312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC23×D4×C61C2
socleC22×C61C22×D4
hypercenterC23×D4D61
hypocenterC61#3003
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. #16840273C2semidirect
3. #16839913C2semidirect
4. #16839896C2semidirect
5. #16839767C2semidirect
6. #16839726C2semidirect
7. C23×D4×C61C2semidirect
8. C2×#11758222C22semidirect
10. C2×#11758200C22semidirect
11. C2×#11758199C22semidirect
12. C2×#11758194C22semidirect
14. #14519756C22semidirect
15. #14519751C22semidirect
18. #14519736C22semidirect
19. #14519698C22semidirect
20. C22⋊#92418C22semidirect
39. C2×D4×C61D4semidirect
49. C2×D244C23semidirect
51. C2×Dic122C23semidirect
57. C4⋊Dic61C23semidirect
61. C2×#92418C23semidirect
102. C22×C61AGL(1,ℤ/8)semidirect
118. C23×D4D61semidirect
125. C61#3003semidirect
162. C2×D4C22⋊D61semidirect
222. C22#14519803semidirect