Finite Group Databasebeta

← #21445606

Subgroups — #21445606

Order 7808.

412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14519737C211yesmaximal, characteristic
2C2×#14519691C212yesmaximal
3C22⋊C4×Dic61C212yesmaximal, complemented
4#16839529C211yesmaximal, characteristic, complemented
5C61×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D61C2211yescharacteristic
7C23×Dic61C2211yescharacteristic
8C22×C4×D61C411yescharacteristic, complemented
9#14519737—22no—
10#14519737—22no—
11C2×#11758196C411yescharacteristic, complemented
12C2×C22⋊Dic61C2212yes—
13C2×#11758198C411yescharacteristic, complemented
14C2×C4×Dic61—22no—
15C2×C4×Dic61C411yescharacteristic, complemented
16#14519691C418yescomplemented
17#14519684—22no—
18C2×C22⋊C4×C61C2211yescharacteristic
19C2×C22⋊C4×C61C2212yes—
20C24×C61C2311yescharacteristic
21C23×D61C2×C411yescharacteristic
22C22×C4×C61—22no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61—22no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61C2×C414yes—
29C22×Dic61—22no—
30C22×Dic61—42no—
31C22×Dic61C2×C411yescharacteristic
32C22×Dic61C2×C411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C22×Dic61D412yes—
35C22×Dic61D412yes—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61—42no—
39C22⋊C4×C61—22no—
40C22⋊C4×C61—22no—
41C22⋊C4×C61C2×C414yescomplemented
42C22⋊Dic61—22no—
43C22⋊Dic61C2×C414yescomplemented
44#11758198—22no—
45#11758196—22no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61—44no—
49C23×C61—41no—
50C23×C61—41no—
51C23×C61C22×C411yescharacteristic
52C23×C61C22×C412yes—
53C23×C61C2×D412yes—
54C23×C61#4111yescharacteristic
55C23×C61#4111yescharacteristic
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61C4212yescomplemented
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—24no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C22⋊D61—24no—
69C22⋊D61—24no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—24no—
73C2×Dic61—22no—
74C2×Dic61—24no—
75C2×Dic61—41no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61C4212yescomplemented
80C2×Dic61C22⋊C411yescharacteristic
81C2×Dic61C22⋊C412yes—
82C2×Dic61C22⋊C411yescharacteristic
83C4×D61—42no—
84C4×D61—42no—
85C22×C61—22no—
86C22×C61—21no—
87C22×C61—22no—
88C22×C61—21no—
89C22×C61—42no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C2×C4211yescharacteristic
93C22×C61C2×C22⋊C411yescharacteristic
94C22×C61#11711yescharacteristic
95C22×C61C4×D412yes—
96C22×C61C4×D412yes—
97C2×D61—22no—
98C2×D61—42no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—42no—
102C4×C61—44no—
103C4×C61—41no—
104C4×C61—41no—
105Dic61—22no—
106Dic61—21no—
107Dic61—22no—
108Dic61—44no—
109Dic61#9912yescomplemented
110C4×#99—611nomaximal, Sylow
111C2×C61—22no—
112C2×C61—22no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61C4×C22⋊C411yescharacteristic
116C2×C61C2×#9911yescharacteristic
117C2×C61#41011yescharacteristic
118D61—42no—
119C2×C4×D4—611no—
120C2×#99—612no—
121C4×C22⋊C4—612no—
122#342—611no—
123#342D6111yescharacteristic, complemented
124C61C4×#9911yescharacteristic, complemented, Sylow
125C22×D4—611no—
126C23×C4—611no—
127C23×C4—611no—
128C4×D4—1222no—
129C4×D4—1222no—
130C2×C4⋊C4—611no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4C2×D6112yes—
135C2×C42—611no—
136C2×C42—1222no—
137#99—618no—
138#95—1222no—
139C24—611no—
140C24C22×D6111yescharacteristic
141C2×D4—614no—
142C2×D4—1222no—
143C2×D4—1221no—
144C2×D4—1221no—
145C22×C4—22no—
146C22×C4—611no—
147C22×C4—611no—
148C22×C4—612no—
149C22×C4—611no—
150C22×C4—612no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4—1222no—
154C22×C4—2442no—
155C22×C4—2442no—
156C22×C4C4×D6111yescharacteristic
157C22×C4C4×D6111yescharacteristic
158C4⋊C4—1222no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—614no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C22⋊C4C4×D6114yescomplemented
165C42—1221no—
166C42—1221no—
167C42—2444no—
168C23—41no—
169C23—41no—
170C23—612no—
171C23—1221no—
172C23—1221no—
173C23—2441no—
174C23—2441no—
175C23C2×C4×D6111yescharacteristic
176C23C2×C4×D6112yes—
177C23D4×D6112yes—
178C23#1175822411yescharacteristic
179C23#1175822611yescharacteristic
180D4—1224no—
181D4—1224no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—24no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—611no—
190C2×C4—612no—
191C2×C4—611no—
192C2×C4—612no—
193C2×C4—1224no—
194C2×C4—1222no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1224no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2441no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2442no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—42no—
209C22—41no—
210C22—41no—
211C22—1222no—
212C22—2442no—
213C22—2442no—
214C22—2441no—
215C22—2441no—
216C22C42×D6111yescharacteristic
217C22C22⋊C4×D6111yescharacteristic
218C22#1451973511yescharacteristic
219C22#1451973712yes—
220C22#1451973912yes—
221C4—44no—
222C4—41no—
223C4—41no—
224C4—612no—
225C4—1222no—
226C4—1221no—
227C4—1222no—
228C4—2444no—
229C2—22no—
230C2—22no—
231C2—21no—
232C2—21no—
233C2—2442no—
234C2#1683960911yescharacteristic
235C2#99×D6111yescharacteristic
236C2#1683973411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC22×C61C2×C42
FrattiniC24C22×D61
FittingC61×#342C2
socleC22×C61C2×C22⋊C4
hypercenter#342D61
hypocenterC61C4×#99
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic61C2semidirect
4. #16839529C2semidirect
5. C61×#342C2semidirect
8. C22×C4×D61C4semidirect
11. C2×#11758196C4semidirect
13. C2×#11758198C4semidirect
15. C2×C4×Dic61C4semidirect
16. #14519691C4semidirect
41. C22⋊C4×C61C2×C4semidirect
43. C22⋊Dic61C2×C4semidirect
60. C22×D61C42semidirect
79. C2×Dic61C42semidirect
109. Dic61#99semidirect
123. #342D61semidirect
124. C61C4×#99semidirect
164. C22⋊C4C4×D61semidirect