Finite Group Databasebeta

← #21445805

Subgroups — #21445805

Order 7808.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic61C211yesmaximal, characteristic
2C2×#14519692C211yesmaximal, characteristic
3#16839620C212yesmaximal, complemented
4#16839528C212yesmaximal, complemented
5C2×#99×C61C211yesmaximal, characteristic
6C23×Dic61C411yescharacteristic, complemented
7C23×Dic61C2211yescharacteristic
8D4×Dic61—22no—
9D4×Dic61—22no—
10C2×C4⋊Dic61C411yescharacteristic, complemented
11C2×#11758196—22no—
12C2×C22⋊Dic61C411yescharacteristic, complemented
13C2×C22⋊Dic61C2212yes—
14C2×C22⋊Dic61C2211yescharacteristic
15C2×C4×Dic61C411yescharacteristic, complemented
16#14519692—22no—
17#14519684—22no—
18C22×D4×C61C2211yescharacteristic
19C2×C22⋊C4×C61C2212yes—
20#99×C61—22no—
21C24×C61C2×C411yescharacteristic
22C24×C61C2311yescharacteristic
23C2×D4×C61—22no—
24C2×D4×C61—22no—
25C2×D4×C61D412yes—
26C2×D4×C61Q812yes—
27C22×C4×C61—22no—
28C22×C4×C61C2×C411yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C22×Dic61—22no—
32C22×Dic61—42no—
33C22×Dic61—42no—
34C22×Dic61C2×C411yescharacteristic
35C22×Dic61C2×C411yescharacteristic
36C22×Dic61C2×C411yescharacteristic
37C22×Dic61C2×C411yescharacteristic
38C22×Dic61D412yes—
39C22×Dic61D412yes—
40C22⋊C4×C61—22no—
41C22⋊C4×C61—22no—
42C22⋊Dic61—22no—
43C22⋊Dic61—22no—
44C22⋊Dic61—22no—
45C22⋊Dic61—22no—
46C4⋊Dic61—22no—
47#11758196—44no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C23×C61—21no—
51C23×C61—21no—
52C23×C61—41no—
53C23×C61—41no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C4⋊C412yescomplemented
57C23×C61C22×C411yescharacteristic
58C23×C61C2×D412yes—
59C23×C61C2×D411yescharacteristic
60C23×C61C2×Q811yescharacteristic
61C23×C61#4112yes—
62D4×C61—24no—
63D4×C61—24no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61C4⋊C412yescomplemented
70C2×Dic61—24no—
71C2×Dic61—22no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C22⋊C412yes—
85C2×Dic61C22⋊C411yescharacteristic
86C22×C61—22no—
87C22×C61—21no—
88C22×C61—22no—
89C22×C61—21no—
90C22×C61—22no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61C2×C22⋊C411yescharacteristic
99C22×C61C2×C4⋊C411yescharacteristic
100C22×C61#11711yescharacteristic
101C22×C61#12112yes—
102C22×C61C22⋊Q812yes—
103C4×C61—22no—
104C4×C61—82no—
105Dic61—21no—
106Dic61—22no—
107Dic61—41no—
108Dic61—41no—
109Dic61—82no—
110Dic61#9912yescomplemented
111#1799—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—22no—
116C2×C61—42no—
117C2×C61#38011yescharacteristic
118C2×C61C2×#9911yescharacteristic
119C2×C61#41011yescharacteristic
120C2×C4×D4—611no—
121C2×#99—611no—
122C2×#99D6111yescharacteristic
123#380—612no—
124#342—612no—
125C61#179911yescharacteristic, complemented, Sylow
126C22×D4C2×D6111yescharacteristic
127C23×C4—611no—
128C23×C4—611no—
129C4×D4—1222no—
130C4×D4—1222no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—1222no—
133C2×C22⋊C4—611no—
134C2×C22⋊C4—611no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4C2×D6112yes—
137C2×C42—611no—
138#99—22no—
139#99—1222no—
140#95—1222no—
141C24C4×D6111yescharacteristic
142C24C22×D6111yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4Dic12212yes—
146C2×D4C22⋊D6112yes—
147C22×C4—22no—
148C22×C4—611no—
149C22×C4—612no—
150C22×C4—611no—
151C22×C4—612no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—1222no—
157C22×C4—2442no—
158C22×C4—2442no—
159C22×C4C4×D6111yescharacteristic
160C4⋊C4—1222no—
161C4⋊C4—2444no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—1222no—
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C42—1221no—
169C42—1221no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23#1175819612yescomplemented
177C23C2×Dic12211yescharacteristic
178C23C2×C4×D6111yescharacteristic
179C23D4×D6112yes—
180C23#1175822412yes—
181C23C2×C22⋊D6111yescharacteristic
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—612no—
192C2×C4—1224no—
193C2×C4—1222no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—2442no—
197C2×C4—2441no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4#1175819612yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—42no—
213C22—41no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D6111yescharacteristic
219C22C2×#1175819611yescharacteristic
220C22#1451973311yescharacteristic
221C22#1451974912yes—
222C22#1451975412yes—
223C4—22no—
224C4—82no—
225C4—612no—
226C4—1222no—
227C4—1221no—
228C4—4882no—
229C4—2441no—
230C4—2441no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#1683962011yescharacteristic
237C2#99×D6111yescharacteristic
238C2#1683973411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×#99×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#99D61
hypocenterC61#1799
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #16839620C2semidirect
4. #16839528C2semidirect
6. C23×Dic61C4semidirect
10. C2×C4⋊Dic61C4semidirect
12. C2×C22⋊Dic61C4semidirect
15. C2×C4×Dic61C4semidirect
56. C23×C61C4⋊C4semidirect
69. C2×C4×C61C4⋊C4semidirect
110. Dic61#99semidirect
125. C61#1799semidirect
176. C23#11758196semidirect
205. C2×C4#11758196semidirect