Finite Group Databasebeta

← #20254307

Subgroups — #20254307

Order 6016.

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#15689674C211yesmaximal, characteristic, complemented
2#127×D47C211yesmaximal, characteristic, complemented
3#15689500C211yesmaximal, characteristic, complemented
4#15689499C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689317C214yesmaximal, complemented
7#15689258C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#486C211yesmaximal, characteristic, complemented
10C2×#10625354—21no—
11C2×D4×D47—21no—
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×D376C2214yescomplemented
15C2×#10625334C2214yescomplemented
16#13094021C2211yescharacteristic
17#13094021C2211yescharacteristic, complemented
18#13094020—21no—
19#13094020—21no—
20#13094020C2212yes—
21#13094013—21no—
22#13093999—21no—
23#13093999C2212yes—
24#13093986—21no—
25#13093986C2212yescomplemented
26C42×D47C2211yescharacteristic
27Dic47⋊C8C2212yescomplemented
28#13093944C2214yescomplemented
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C47C2211yescharacteristic, complemented
32#127×C47C2211yescharacteristic
33#102×C47C2214yescomplemented
34C4×C8×C47C2211yescharacteristic, complemented
35C23×D47—22no—
36C2×Q8×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47C2312yes—
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43#10625354—44no—
44D4×D47—44no—
45D4×D47—44no—
46D4×D47—44no—
47C2×D188—22no—
48C2×D188—21no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—21no—
52C2×D188C2312yes—
53C2×D188C2312yes—
54C2×C4×D47—22no—
55C2×C4×D47D411yescharacteristic
56C2×C4×D47D411yescharacteristic
57C2×C4×D47C2311yescharacteristic
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C42×C47C2311yescharacteristic
62#10625334—44no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65C4×Dic47D411yescharacteristic
66C4×Dic47D411yescharacteristic
67C4×Dic47C2311yescharacteristic
68C2×C47⋊C8C2312yes—
69D376—44no—
70C23×C47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—44no—
74C22×D47—44no—
75C22×D47—44no—
76C22×D47C2×D411yescharacteristic
77Q8×C47—42no—
78D4×C47—24no—
79D4×C47—42no—
80D4×C47—42no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—44no—
86C22⋊D47—44no—
87C22⋊D47—44no—
88C2×Dic47C2×D411yescharacteristic
89C2×Dic47C2×D411yescharacteristic
90C2×Dic47C2×D411yescharacteristic
91D188—24no—
92D188—24no—
93D188—44no—
94D188—42no—
95D188—42no—
96D188—42no—
97D188—42no—
98C4×D47—22no—
99C4×D47—22no—
100C4×D47—44no—
101C4×D47D814yescomplemented
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47C22×D411yescharacteristic
108C2×D47—21no—
109C2×D47—21no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—42no—
116C2×D47—88no—
117C2×D47C2×D812yes—
118C4×C47—42no—
119C4×C47C2×D812yes—
120C4×C47AGL(1,ℤ/8)12yes—
121C4×C47H(5,𝔽2)12yes—
122Dic47—21no—
123Dic47—21no—
124Dic47C2×D812yes—
125#3205—471nomaximal, Sylow
126C2×C47—82no—
127C2×C47#53511yescharacteristic
128C2×C47C22×D811yescharacteristic
129C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
130D47—22no—
131D47—82no—
132D47—82no—
133#532—471no—
134C2×#127—471no—
135#493—471no—
136#493—471no—
137#486—471no—
138#486D4711yescharacteristic, complemented
139#459—474no—
140#447—474no—
141#431—471no—
142C47#320511yescharacteristic, complemented, Sylow
143C2×#41—941no—
144C22×D4—472no—
145C22×D4—941no—
146C22×D4—941no—
147C2×D8—474no—
148C2×D8—474no—
149C4⋊Q8C2×D4711yescharacteristic, complemented
150#127—472no—
151#127—471no—
152#127—471no—
153#127—941no—
154#127—941no—
155#127C2×D4711yescharacteristic
156#124—941no—
157#121—472no—
158#121—941no—
159C4×D4—472no—
160C4×D4—941no—
161C2×C42—471no—
162C4⋊C8—472no—
163#102—474no—
164#102C2×D4714yescomplemented
165C22⋊C8—472no—
166C4×C8—471no—
167C4×C8C2×D4711yescharacteristic, complemented
168C24—942no—
169#41—1884no—
170C2×Q8—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—472no—
174C2×D4—472no—
175C2×D4—942no—
176C2×D4—942no—
177C2×D4—942no—
178C2×D4—942no—
179C2×D4—941no—
180C2×D4—941no—
181C2×D4—941no—
182C2×D4—941no—
183C2×D4—1884no—
184C2×D4—1884no—
185C2×D4—1884no—
186C2×D4C22×D4712yes—
187C22×C4—471no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—942no—
191D8—1884no—
192D8—1884no—
193C2×C8—472no—
194C2×C8C22×D4712yes—
195C4⋊C4—21no—
196C4⋊C4C22×D4712yes—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C42—471no—
200C42—471no—
201C42—471no—
202C42C22×D4711yescharacteristic
203C23—22no—
204C23—471no—
205C23—942no—
206C23—942no—
207C23—1884no—
208C23—1884no—
209C23—1884no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—944no—
215D4—944no—
216D4—1884no—
217D4—1884no—
218D4—1884no—
219D4—1884no—
220D4—1882no—
221D4—1882no—
222D4—1882no—
223D4—1882no—
224C2×C4—22no—
225C2×C4—471no—
226C2×C4—474no—
227C2×C4—471no—
228C2×C4—471no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—1884no—
232C2×C4D4×D4711yescharacteristic
233C2×C4D4×D4711yescharacteristic
234C2×C4C23×D4711yescharacteristic
235C8—22no—
236C8—942no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—472no—
241C22—941no—
242C22—941no—
243C22—3768no—
244C22—1882no—
245C22—1882no—
246C22—1882no—
247C22—1882no—
248C22—1882no—
249C22—1882no—
250C22C2×D4×D4711yescharacteristic
251C4—42no—
252C4—472no—
253C4—941no—
254C4—941no—
255C4D8×D4712yes—
256C4#1309405112yes—
257C4#1309407012yes—
258C2—82no—
259C2—942no—
260C2—3762no—
261C2—3762no—
262C2#1568969111yescharacteristic
263C2C2×D8×D4711yescharacteristic
264C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3205
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689674C2semidirect
2. #127×D47C2semidirect
3. #15689500C2semidirect
4. #15689499C2semidirect
5. #15689471C2semidirect
6. #15689317C2semidirect
7. #15689258C2semidirect
8. #15689174C2semidirect
9. C47×#486C2semidirect
14. C2×D376C22semidirect
15. C2×#10625334C22semidirect
17. #13094021C22semidirect
25. #13093986C22semidirect
27. Dic47⋊C8C22semidirect
28. #13093944C22semidirect
30. C4×C47⋊C8C22semidirect
31. C4⋊Q8×C47C22semidirect
33. #102×C47C22semidirect
34. C4×C8×C47C22semidirect
101. C4×D47D8semidirect
138. #486D47semidirect
142. C47#3205semidirect
149. C4⋊Q8C2×D47semidirect
164. #102C2×D47semidirect
167. C4×C8C2×D47semidirect