Finite Group Databasebeta

← #21456615

Subgroups — #21456615

Order 7808.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D61C212yesmaximal, complemented
2#16840082C212yesmaximal, complemented
3#16840079C212yesmaximal, complemented
4#16840015C211yesmaximal, characteristic, complemented
5#16840013C212yesmaximal, complemented
6#16839897C212yesmaximal, complemented
7#16839894C212yesmaximal, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C61×#469C211yesmaximal, characteristic, complemented
10C2×D4×D61—22no—
11C2×D4×D61C2212yescomplemented
12C22×C4×D61C2211yescharacteristic
13C2×D488C2211yescharacteristic, complemented
14C2×#11758199C2212yescomplemented
15C2×#11758194C2211yescharacteristic, complemented
16#14519752C2212yes—
17#14519751C2212yescomplemented
18#14519750—22no—
19#14519749—22no—
20#14519748C2212yes—
21C4⋊C4×D61C2212yescomplemented
22C22⋊C4×D61—22no—
23#14519709C2211yescharacteristic, complemented
24#14519708C2212yescomplemented
25#14519699C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yescomplemented
28#14519689C2212yescomplemented
29#14519689C2212yescomplemented
30C2×D8×C61C2211yescharacteristic, complemented
31C2×M16×C61C2211yescharacteristic, complemented
32#121×C61C2212yescomplemented
33#106×C61C2211yescharacteristic, complemented
34#102×C61C2212yescomplemented
35C23×D61—22no—
36C23×D61D411yescharacteristic
37C2×D4×C61—22no—
38C2×D4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43C22×Dic61D411yescharacteristic
44D4×D61—42no—
45D4×D61—42no—
46D4×D61—48no—
47C2×D244—22no—
48C2×D244C2312yes—
49C2×C4×D61—22no—
50C2×C4×D61—41no—
51C2×C4×D61—41no—
52C2×C4×D61D412yes—
53C2×C4×D61C2312yes—
54D8×C61—41no—
55M16×C61—41no—
56C2×C8×C61C2311yescharacteristic
57C2×C8×C61C2311yescharacteristic
58C4⋊C4×C61C2312yes—
59C22⋊C4×C61—22no—
60C22⋊Dic61—22no—
61#11758199—42no—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61C2312yes—
65#11758196—22no—
66#11758194—41no—
67C2×#92418C2312yes—
68D488—41no—
69C23×C61—22no—
70C23×C61C2×D411yescharacteristic
71C22×D61—24no—
72C22×D61—22no—
73C22×D61—41no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—44no—
77C22×D61C2×D412yes—
78D4×C61—22no—
79D4×C61—22no—
80D4×C61—44no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—44no—
87C22⋊D61—44no—
88C22⋊D61—44no—
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61C2×D412yes—
92D244—22no—
93D244—22no—
94D244—44no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—42no—
98C4×D61—44no—
99C8×C61—21no—
100C8×C61—21no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61C22×D411yescharacteristic
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—44no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—88no—
115C2×D61AGL(1,ℤ/8)14yes—
116C4×C61—21no—
117C4×C61—42no—
118C4×C61H(5,𝔽2)11yescharacteristic
119C4×C61H(5,𝔽2)11yescharacteristic
120Dic61—22no—
121Dic61—42no—
122#3192—611nomaximal, Sylow
123C2×C61—41no—
124C2×C61—82no—
125C2×C61#53411yescharacteristic
126C2×C61C2×AGL(1,ℤ/8)12yes—
127D61—24no—
128D61—82no—
129C2×#121—612no—
130#481—612no—
131#481—612no—
132#469—611no—
133#469—612no—
134#469D6111yescharacteristic, complemented
135#447—612no—
136#447—612no—
137#407—611no—
138C61#319211yescharacteristic, complemented, Sylow
139C22×D4—612no—
140C22×D4—1222no—
141C23×C4—611no—
142C2×D8—612no—
143C2×D8—611no—
144C2×D8C2×D6111yescharacteristic, complemented
145C2×M16—611no—
146C2×M16C2×D6111yescharacteristic, complemented
147#121—612no—
148#121—612no—
149#121—612no—
150#121—1222no—
151#121—1222no—
152#121C2×D6112yescomplemented
153C2×C4⋊C4—612no—
154C2×C22⋊C4—1222no—
155#106—611no—
156#106—612no—
157#106C2×D6111yescharacteristic, complemented
158#102—612no—
159#102—612no—
160#102—612no—
161#102C2×D6112yescomplemented
162C22⋊C8—612no—
163C22⋊C8—612no—
164C24—611no—
165C24—1222no—
166C2×D4—22no—
167C2×D4—612no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—2442no—
173C2×D4—2442no—
174C2×D4—2448no—
175C2×D4C22×D6112yes—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—612no—
179C22×C4—1222no—
180C22×C4—2441no—
181C22×C4—2441no—
182C22×C4C22×D6111yescharacteristic
183D8—41no—
184D8—2441no—
185D8—2442no—
186M16—41no—
187M16—2441no—
188C2×C8—612no—
189C2×C8C22×D6111yescharacteristic
190C2×C8C22×D6111yescharacteristic
191C4⋊C4—612no—
192C4⋊C4—1222no—
193C4⋊C4C22×D6112yes—
194C22⋊C4—22no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C23—22no—
199C23—612no—
200C23—1224no—
201C23—1222no—
202C23—2441no—
203C23—2444no—
204C23—2444no—
205C23—2444no—
206C23D4×D6111yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—1222no—
211D4—1222no—
212D4—2444no—
213D4—2444no—
214D4—2444no—
215D4—2444no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—612no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—2442no—
224C2×C4—2444no—
225C2×C4—2441no—
226C2×C4D4×D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—21no—
229C8—21no—
230C8—1222no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—614no—
237C22—1222no—
238C22—1222no—
239C22—4888no—
240C22—2444no—
241C22—2442no—
242C22—2442no—
243C22—2442no—
244C22C2×D4×D6111yescharacteristic
245C4—21no—
246C4—42no—
247C4—1222no—
248C4—2442no—
249C4#1451982211yescharacteristic
250C4#1451982311yescharacteristic
251C2—41no—
252C2—82no—
253C2—1224no—
254C2—4882no—
255C2#1684032011yescharacteristic
256C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3192
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D61C2semidirect
2. #16840082C2semidirect
3. #16840079C2semidirect
4. #16840015C2semidirect
5. #16840013C2semidirect
6. #16839897C2semidirect
7. #16839894C2semidirect
8. #16839725C2semidirect
9. C61×#469C2semidirect
11. C2×D4×D61C22semidirect
13. C2×D488C22semidirect
14. C2×#11758199C22semidirect
15. C2×#11758194C22semidirect
17. #14519751C22semidirect
21. C4⋊C4×D61C22semidirect
23. #14519709C22semidirect
24. #14519708C22semidirect
25. #14519699C22semidirect
26. #14519698C22semidirect
27. #14519697C22semidirect
28. #14519689C22semidirect
29. #14519689C22semidirect
30. C2×D8×C61C22semidirect
31. C2×M16×C61C22semidirect
32. #121×C61C22semidirect
33. #106×C61C22semidirect
34. #102×C61C22semidirect
134. #469D61semidirect
138. C61#3192semidirect
144. C2×D8C2×D61semidirect
146. C2×M16C2×D61semidirect
152. #121C2×D61semidirect
157. #106C2×D61semidirect
161. #102C2×D61semidirect