Finite Group Databasebeta

← #21450121

Subgroups — #21450121

Order 7808.

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

normal subgroups only

This group has 624 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×#14519760C212yesmaximal
2C2×C4×C22⋊D61C211yesmaximal, characteristic
3#16839693C212yesmaximal, complemented
4#16839688C212yesmaximal, complemented
5#16839658C212yesmaximal, complemented
6#16839625C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8#16839619C212yesmaximal, complemented
9C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2211yescharacteristic
11C22×C4×D61C2211yescharacteristic
12#14519760—28no—
13C4×C22⋊D61—24no—
14C2×C4⋊Dic61C2212yes—
15C2×#11758196C2211yescharacteristic
16C2×#11758196C2214yes—
17C2×C22⋊Dic61C2211yescharacteristic
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2211yescharacteristic
20C2×#11758198C2214yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2214yes—
24#14519684C2214yes—
25C23×C4×C61C2212yes—
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61—24no—
28C2×C4⋊C4×C61C2212yes—
29C2×C4⋊C4×C61C2212yes—
30C24×C61C2311yescharacteristic
31C23×D61C2311yescharacteristic
32C22×C4×C61—24no—
33C22×C4×C61—24no—
34C22×C4×C61—24no—
35C22×C4×C61—24no—
36C22×C4×C61D414yes—
37C22×C4×C61C2314yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61D414yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2314yes—
46C22×Dic61C2311yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61—24no—
49C4⋊C4×C61—24no—
50C4⋊C4×C61—24no—
51C22⋊Dic61—22no—
52C22⋊Dic61—24no—
53#11758198—28no—
54#11758198—22no—
55C4⋊Dic61—24no—
56#11758196—22no—
57#11758196—28no—
58C4×Dic61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61C2×D412yes—
62C23×C61C2×D412yes—
63C23×C61#4112yes—
64C23×C61C2411yescharacteristic
65C22×D61—21no—
66C22×D61—22no—
67C22×D61—21no—
68C22×D61—22no—
69C22×D61C2×D412yes—
70C2×C4×C61—22no—
71C2×C4×C61—28no—
72C2×C4×C61—24no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—48no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61#4114yes—
79C22⋊D61—28no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—24no—
84C2×Dic61—21no—
85C2×Dic61—24no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—24no—
89C2×Dic61C2×D412yes—
90C4×D61—44no—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—24no—
94C22×C61—24no—
95C22×C61#12114yes—
96C22×C61C22×D411yescharacteristic
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4111yescharacteristic
99C22×C61C2×#4112yes—
100C22×C612−1+412yes—
101C2×D61—22no—
102C2×D61—24no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61—44no—
108C4×C61#12314yescomplemented
109Dic61—22no—
110Dic61—41no—
111Dic61—41no—
112Dic61—44no—
113#2486—611nomaximal, Sylow
114C2×C61—24no—
115C2×C61C2×#12111yescharacteristic
116C2×C61C2×#12311yescharacteristic
117C2×C61#53611yescharacteristic
118C2×C61#54712yes—
119C2×C61#55212yes—
120D61—42no—
121C2×#123—612no—
122C2×C4×D4—611no—
123C22×C4⋊C4D6111yescharacteristic, complemented
124#398—612no—
125#397—612no—
126#389—612no—
127#381—612no—
128#380—611no—
129#380—612no—
130C61#248611yescharacteristic, complemented, Sylow
131C22×D4—611no—
132C23×C4—611no—
133C23×C4C2×D6112yes—
134C23×C4C2×D6111yescharacteristic
135#123—1228no—
136C4×D4—1224no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—614no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4C2×D6112yes—
142C2×C4⋊C4C2×D6112yes—
143C2×C22⋊C4—611no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—611no—
146C2×C22⋊C4—614no—
147C2×C42—611no—
148#95—614no—
149#95—612no—
150#95—614no—
151C24—611no—
152C24C22×D6111yescharacteristic
153C2×D4—614no—
154C2×D4—1222no—
155C2×D4—1222no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—614no—
164C22×C4—1224no—
165C22×C4—1222no—
166C22×C4C22⋊D6114yes—
167C22×C4C22×D6114yes—
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6111yescharacteristic
170C4⋊C4—24no—
171C4⋊C4—24no—
172C4⋊C4—1228no—
173C4⋊C4—1224no—
174C4⋊C4—1222no—
175C22⋊C4—1228no—
176C22⋊C4—1224no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C42—1222no—
180C23—22no—
181C23—22no—
182C23—612no—
183C23—1221no—
184C23—1221no—
185C23—1222no—
186C23—1222no—
187C23D4×D6112yes—
188C23#1175822412yes—
189C23C2×C22⋊D6112yes—
190C23C23×D6111yescharacteristic
191D4—1228no—
192C2×C4—22no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—48no—
198C2×C4—612no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1224no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1224no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1224no—
208C2×C4—2444no—
209C2×C4#1175822214yes—
210C2×C4C2×C22⋊D6112yes—
211C2×C4C2×C22⋊D6112yes—
212C22—22no—
213C22—22no—
214C22—24no—
215C22—24no—
216C22—1222no—
217C22—1224no—
218C22—2441no—
219C22—2441no—
220C22—2442no—
221C22#1451974814yes—
222C22C2×D4×D6111yescharacteristic
223C22C22×C22⋊D6111yescharacteristic
224C22C2×#1175822411yescharacteristic
225C22C2×#1175822212yes—
226C22#1451982512yes—
227C4—22no—
228C4—44no—
229C4—1222no—
230C4—2441no—
231C4—2441no—
232C4—2444no—
233C4#1451976014yescomplemented
234C2—24no—
235C2—2442no—
236C2C2×#1451974811yescharacteristic
237C2C2×#1451976011yescharacteristic
238C2#1684033611yescharacteristic
239C2#1684041312yes—
240C2#1684044712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16839693C2semidirect
4. #16839688C2semidirect
5. #16839658C2semidirect
6. #16839625C2semidirect
7. #16839622C2semidirect
8. #16839619C2semidirect
9. C22×C4⋊C4×C61C2semidirect
108. C4×C61#123semidirect
123. C22×C4⋊C4D61semidirect
130. C61#2486semidirect
233. C4#14519760semidirect