Finite Group Databasebeta

← #21456738

Subgroups — #21456738

Order 7808.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840313C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic, complemented
3#16840139C211yesmaximal, characteristic, complemented
4#16840138C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16839956C214yesmaximal, complemented
7#16839897C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11C2×D4×D61—21no—
12C2×D4×D61—21no—
13C2×D4×D61C2212yes—
14C2×D488C2214yescomplemented
15C2×#11758199C2214yescomplemented
16#14519774C2211yescharacteristic
17#14519774C2211yescharacteristic, complemented
18#14519773—21no—
19#14519773—21no—
20#14519773C2212yes—
21#14519766—21no—
22#14519752—21no—
23#14519752C2212yes—
24#14519739—21no—
25#14519739C2212yescomplemented
26C42×D61C2211yescharacteristic
27#14519706C2212yescomplemented
28#14519697C2214yescomplemented
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic, complemented
31C4⋊Q8×C61C2211yescharacteristic, complemented
32#127×C61C2211yescharacteristic
33#102×C61C2214yescomplemented
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—22no—
36C2×Q8×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61C2312yes—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43#11758226—44no—
44D4×D61—44no—
45D4×D61—44no—
46D4×D61—44no—
47C2×D244—22no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244C2312yes—
53C2×D244C2312yes—
54C2×C4×D61—22no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C42×C61C2311yescharacteristic
62#11758199—44no—
63#11758198—22no—
64#11758198—22no—
65C4×Dic61D411yescharacteristic
66C4×Dic61D411yescharacteristic
67C4×Dic61C2311yescharacteristic
68C2×#92418C2312yes—
69D488—44no—
70C23×C61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61C2×D411yescharacteristic
77Q8×C61—42no—
78D4×C61—24no—
79D4×C61—42no—
80D4×C61—42no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C22⋊D61—44no—
87C22⋊D61—44no—
88C2×Dic61C2×D411yescharacteristic
89C2×Dic61C2×D411yescharacteristic
90C2×Dic61C2×D411yescharacteristic
91D244—24no—
92D244—24no—
93D244—44no—
94D244—42no—
95D244—42no—
96D244—42no—
97D244—42no—
98C4×D61—22no—
99C4×D61—22no—
100C4×D61—44no—
101C4×D61D814yescomplemented
102C8×C61—22no—
103#92418—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61C22×D411yescharacteristic
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—88no—
117C2×D61C2×D812yes—
118C4×C61—42no—
119C4×C61C2×D812yes—
120C4×C61AGL(1,ℤ/8)12yes—
121C4×C61H(5,𝔽2)12yes—
122Dic61—21no—
123Dic61—21no—
124Dic61C2×D812yes—
125#3205—611nomaximal, Sylow
126C2×C61—82no—
127C2×C61#53511yescharacteristic
128C2×C61C22×D811yescharacteristic
129C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
130D61—22no—
131D61—82no—
132D61—82no—
133#532—611no—
134C2×#127—611no—
135#493—611no—
136#493—611no—
137#486—611no—
138#486D6111yescharacteristic, complemented
139#459—614no—
140#447—614no—
141#431—611no—
142C61#320511yescharacteristic, complemented, Sylow
143C2×#41—1221no—
144C22×D4—612no—
145C22×D4—1221no—
146C22×D4—1221no—
147C2×D8—614no—
148C2×D8—614no—
149C4⋊Q8C2×D6111yescharacteristic, complemented
150#127—612no—
151#127—611no—
152#127—611no—
153#127—1221no—
154#127—1221no—
155#127C2×D6111yescharacteristic
156#124—1221no—
157#121—612no—
158#121—1221no—
159C4×D4—612no—
160C4×D4—1221no—
161C2×C42—611no—
162C4⋊C8—612no—
163#102—614no—
164#102C2×D6114yescomplemented
165C22⋊C8—612no—
166C4×C8—611no—
167C4×C8C2×D6111yescharacteristic, complemented
168C24—1222no—
169#41—2444no—
170C2×Q8—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—612no—
174C2×D4—612no—
175C2×D4—1222no—
176C2×D4—1222no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4—1221no—
180C2×D4—1221no—
181C2×D4—1221no—
182C2×D4—1221no—
183C2×D4—2444no—
184C2×D4—2444no—
185C2×D4—2444no—
186C2×D4C22×D6112yes—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1222no—
191D8—2444no—
192D8—2444no—
193C2×C8—612no—
194C2×C8C22×D6112yes—
195C4⋊C4—21no—
196C4⋊C4C22×D6112yes—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42C22×D6111yescharacteristic
203C23—22no—
204C23—611no—
205C23—1222no—
206C23—1222no—
207C23—2444no—
208C23—2444no—
209C23—2444no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—1224no—
215D4—1224no—
216D4—2444no—
217D4—2444no—
218D4—2444no—
219D4—2444no—
220D4—2442no—
221D4—2442no—
222D4—2442no—
223D4—2442no—
224C2×C4—22no—
225C2×C4—611no—
226C2×C4—614no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4C23×D6111yescharacteristic
235C8—22no—
236C8—1222no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—612no—
241C22—1221no—
242C22—1221no—
243C22—4888no—
244C22—2442no—
245C22—2442no—
246C22—2442no—
247C22—2442no—
248C22—2442no—
249C22—2442no—
250C22C2×D4×D6111yescharacteristic
251C4—42no—
252C4—612no—
253C4—1221no—
254C4—1221no—
255C4D8×D6112yes—
256C4#1451980412yes—
257C4#1451982312yes—
258C2—82no—
259C2—1222no—
260C2—4882no—
261C2—4882no—
262C2#1684033011yescharacteristic
263C2C2×D8×D6111yescharacteristic
264C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3205
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #127×D61C2semidirect
3. #16840139C2semidirect
4. #16840138C2semidirect
5. #16840110C2semidirect
6. #16839956C2semidirect
7. #16839897C2semidirect
8. #16839813C2semidirect
9. C61×#486C2semidirect
14. C2×D488C22semidirect
15. C2×#11758199C22semidirect
17. #14519774C22semidirect
25. #14519739C22semidirect
27. #14519706C22semidirect
28. #14519697C22semidirect
30. C4×#92418C22semidirect
31. C4⋊Q8×C61C22semidirect
33. #102×C61C22semidirect
34. C4×C8×C61C22semidirect
101. C4×D61D8semidirect
138. #486D61semidirect
142. C61#3205semidirect
149. C4⋊Q8C2×D61semidirect
164. #102C2×D61semidirect
167. C4×C8C2×D61semidirect