Finite Group Databasebeta

← #21444320

Subgroups — #21444320

Order 7808.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#16840272C211yesmaximal, characteristic
2#16839724C211yesmaximal, characteristic, complemented
3#95×D61C211yesmaximal, characteristic, complemented
4#16839500C211yesmaximal, characteristic, complemented
5#16839498C211yesmaximal, characteristic, complemented
6#16839496C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C2×#11758224C411yescharacteristic, complemented
9C22×C4×D61—21no—
10C22×C4×D61C2211yescharacteristic
11C2×#11758189—21no—
12#14519759—21no—
13#14519757C411yescharacteristic, complemented
14#14519756C2211yescharacteristic
15#14519748C411yescharacteristic, complemented
16#14519745—21no—
17D4×Dic61—21no—
18#14519737—21no—
19#14519735C411yescharacteristic, complemented
20C22⋊#92418C2211yescharacteristic
21#14519689—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×D4×C61—21no—
29C2×D4×C61C2×C411yescharacteristic, complemented
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37#11758224—42no—
38C2×C4×D61—24no—
39C2×C4×D61—42no—
40C2×C4×D61—42no—
41C2×C4×D61—42no—
42C2×C4×D61C2×C411yescharacteristic
43C2×C4×D61C2×C411yescharacteristic
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×Dic122C2×C411yescharacteristic, complemented
47C2×C8×C61—21no—
48C4⋊C4×C61C2×C411yescharacteristic, complemented
49C22⋊C4×C61—21no—
50C22⋊Dic61—21no—
51C22⋊Dic61—21no—
52#11758198—21no—
53#11758198—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61C2×C411yescharacteristic, complemented
56#11758196—21no—
57C4×Dic61—21no—
58C2×#92418—21no—
59#11758189—42no—
60C23×C61—21no—
61C23×C61C2×D411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61C22⋊C411yescharacteristic
67C22×D61C22⋊C411yescharacteristic
68D4×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C22×C411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C22⋊D61—42no—
79C22⋊D61—42no—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—41no—
84C2×Dic61—42no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61C22⋊C411yescharacteristic
88C2×Dic61C22⋊C411yescharacteristic
89C4×D61—22no—
90C4×D61—22no—
91C4×D61—41no—
92C4×D61—41no—
93C4×D61—48no—
94Dic122—41no—
95C8×C61—41no—
96#92418—41no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61C2×C22⋊C411yescharacteristic
103C22×C61AGL(1,ℤ/8)11yescharacteristic
104C22×C61#13711yescharacteristic
105C2×D61—24no—
106C2×D61—24no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—21no—
111C2×D61#9912yes—
112C2×D61#10412yes—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—42no—
116C4×C61—41no—
117Dic61—21no—
118Dic61—21no—
119Dic61—42no—
120Dic61—41no—
121Dic61—41no—
122#1504—611nomaximal, Sylow
123C2×C61—21no—
124C2×C61—21no—
125C2×C61—81no—
126C2×C61C2×#9911yescharacteristic
127C2×C61#41711yescharacteristic
128C2×C61C2×#10411yescharacteristic
129D61—22no—
130D61—22no—
131#525—611no—
132#407—611no—
133C2×#95—611no—
134#328—611no—
135#328—611no—
136#327—611no—
137#327D6111yescharacteristic, complemented
138C61#150411yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C23×C4—611no—
141C23×C4—1221no—
142C2×M16—1221no—
143#123—1221no—
144C22⋊Q8—611no—
145C22⋊Q8—611no—
146#121—611no—
147#121C2×D6111yescharacteristic
148#120—1221no—
149C4×D4—1221no—
150C4×D4—1221no—
151#117—611no—
152C22⋊C8—611no—
153C22⋊C8—1221no—
154C22⋊C8C2×D6111yescharacteristic
155#95—611no—
156#95—1221no—
157#95C2×D6111yescharacteristic
158C24—611no—
159#41—2442no—
160C2×Q8—611no—
161C2×D4—21no—
162C2×D4—1221no—
163C2×D4—1221no—
164C2×D4C4×D6111yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1224no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—2442no—
175C22×C4—2442no—
176C22×C4—2442no—
177C22×C4C22×D6111yescharacteristic
178M16—2442no—
179C2×C8—21no—
180C2×C8—1221no—
181C4⋊C4—611no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4C4×D6111yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C22⋊C4—1221no—
189C22⋊C4—1221no—
190C42—1221no—
191C23—21no—
192C23—611no—
193C23—611no—
194C23—1222no—
195C23—1222no—
196C23—1221no—
197C23—1221no—
198C23D4×D6111yescharacteristic
199Q8—2441no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—2442no—
204D4—2442no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2448no—
220C2×C4—2441no—
221C2×C4—2442no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4C2×C4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C8—41no—
227C8—2441no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—612no—
234C22—612no—
235C22—1224no—
236C22—1224no—
237C22—1221no—
238C22—1221no—
239C22—1221no—
240C22—1221no—
241C22C22⋊C4×D6111yescharacteristic
242C22#1451980111yescharacteristic
243C22#1451980611yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—1221no—
249C4—1221no—
250C4—2442no—
251C4—2441no—
252C4—2441no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—1222no—
257C2—1222no—
258C2#99×D6111yescharacteristic
259C2#1683976011yescharacteristic
260C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61C2×C22⋊C4
hypercenter#327D61
hypocenterC61#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16839724C2semidirect
3. #95×D61C2semidirect
4. #16839500C2semidirect
5. #16839498C2semidirect
6. #16839496C2semidirect
7. C61×#327C2semidirect
8. C2×#11758224C4semidirect
13. #14519757C4semidirect
15. #14519748C4semidirect
19. #14519735C4semidirect
29. C2×D4×C61C2×C4semidirect
46. C2×Dic122C2×C4semidirect
48. C4⋊C4×C61C2×C4semidirect
55. C4⋊Dic61C2×C4semidirect
137. #327D61semidirect
138. C61#1504semidirect
164. C2×D4C4×D61semidirect
184. C4⋊C4C4×D61semidirect