Finite Group Databasebeta

← #20249723

Subgroups — #20249723

Order 6016.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13093994C214yesmaximal, complemented
2C2×#13093992C212yesmaximal, complemented
3#15689040C212yesmaximal, complemented
4#15689039C214yesmaximal, complemented
5#15689025C212yesmaximal, complemented
6C47×#390C211yesmaximal, characteristic, complemented
7C24×D47C2212yescomplemented
8C22×D188C2212yes—
9C22×D188C2212yes—
10C22×C22⋊D47C2214yes—
11#13093994—216no—
12#13093992—28no—
13C2×C4⋊Dic47C2212yescomplemented
14C2×C22⋊Dic47C2212yescomplemented
15C2×(C2×D47)⋊C4C2214yescomplemented
16C2×(C2×D47)⋊C4C2214yescomplemented
17C2×(C2×D47)⋊C4C2214yescomplemented
18C47⋊#95C2212yescomplemented
19C22×D4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic, complemented
21C2×C22⋊C4×C47C2214yescomplemented
22C2×C42×C47C2211yescharacteristic, complemented
23C24×C47C2312yes—
24C23×D47—24no—
25C23×D47—28no—
26C23×D47—42no—
27C23×D47—42no—
28C23×D47—44no—
29C23×D47C2314yes—
30C2×D4×C47—41no—
31C2×D4×C47—41no—
32C2×D4×C47D414yescomplemented
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—28no—
37C2×C22⋊D47—28no—
38C2×C22⋊D47—44no—
39C22×Dic47C2314yes—
40C2×D188—28no—
41C2×D188—42no—
42C2×D188—42no—
43C2×D188—42no—
44C2×D188D418yescomplemented
45C4⋊C4×C47—41no—
46C22⋊C4×C47—28no—
47C42×C47—41no—
48C22⋊Dic47—24no—
49(C2×D47)⋊C4—28no—
50(C2×D47)⋊C4—28no—
51(C2×D47)⋊C4—28no—
52C4⋊Dic47—42no—
53C23×C47—24no—
54C23×C47—24no—
55C23×C47—22no—
56C23×C47—22no—
57C23×C47C2×D414yes—
58C23×C47C2411yescharacteristic
59C22×D47—24no—
60C22×D47—24no—
61C22×D47—24no—
62C22×D47—24no—
63C22×D47—24no—
64C22×D47—24no—
65C22×D47—48no—
66C22×D47—416no—
67C22×D47—416no—
68C22×D47—48no—
69C22×D47—48no—
70C22×D47C2×D418yes—
71D4×C47—44no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—24no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D414yes—
80C22⋊D47—416no—
81C2×Dic47—24no—
82C2×Dic47—24no—
83C2×Dic47—24no—
84D188—48no—
85D188—48no—
86C22×C47—24no—
87C22×C47—28no—
88C22×C47—44no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47C22×D412yes—
92C22×C47C22×D411yescharacteristic
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C47H(5,𝔽2)11yescharacteristic
95C22×C47H(5,𝔽2)12yes—
96C2×D47—28no—
97C2×D47—28no—
98C2×D47—28no—
99C2×D47—432no—
100C2×D47—44no—
101C2×D47—44no—
102C2×D47—44no—
103C2×D47—44no—
104C4×C47—24no—
105C4×C47—22no—
106C4×C47—42no—
107Dic47—44no—
108#2679—471nomaximal, Sylow
109C2×C47—44no—
110C2×C47#53412yes—
111C2×C47#53411yescharacteristic
112C2×C47D4211yescharacteristic
113C2×C47D4212yes—
114C2×C47H(3,𝔽4)11yescharacteristic
115D47—48no—
116C2×#120—472no—
117C2×#120—474no—
118#394—472no—
119#394—474no—
120#390—472no—
121#390D4711yescharacteristic, complemented
122C47#267911yescharacteristic, complemented, Sylow
123C25—472no—
124C22×D4—474no—
125C22×D4—472no—
126C22×D4—472no—
127C22×D4C2×D4711yescharacteristic
128#120—9416no—
129#120—948no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4C2×D4711yescharacteristic, complemented
132C2×C22⋊C4—472no—
133C2×C22⋊C4—474no—
134C2×C22⋊C4—474no—
135C2×C22⋊C4—474no—
136C2×C22⋊C4C2×D4714yescomplemented
137C2×C42C2×D4711yescharacteristic, complemented
138#95—472no—
139C24—474no—
140C24—948no—
141C24—944no—
142C24—1882no—
143C24—1882no—
144C24—1884no—
145C24C22×D4712yes—
146C2×D4—41no—
147C2×D4—41no—
148C2×D4—478no—
149C2×D4—948no—
150C2×D4—948no—
151C2×D4—948no—
152C2×D4—1882no—
153C2×D4—1882no—
154C2×D4—1882no—
155C2×D4—1884no—
156C2×D4D18814yescomplemented
157C22×C4—474no—
158C22×C4C22×D4712yes—
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4712yes—
161C4⋊C4—41no—
162C4⋊C4—1882no—
163C22⋊C4—28no—
164C22⋊C4—948no—
165C22⋊C4—944no—
166C22⋊C4—948no—
167C22⋊C4—948no—
168C42—41no—
169C23—24no—
170C23—22no—
171C23—22no—
172C23—24no—
173C23—478no—
174C23—944no—
175C23—944no—
176C23—944no—
177C23—944no—
178C23—944no—
179C23—944no—
180C23—18816no—
181C23—1888no—
182C23—1888no—
183C23—18816no—
184C23—1888no—
185C23C2×D18814yes—
186C23C23×D4711yescharacteristic
187D4—44no—
188D4—1888no—
189D4—1888no—
190D4—18816no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—944no—
198C2×C4—944no—
199C2×C4—944no—
200C2×C4C2×D18812yes—
201C2×C4D4×D4714yes—
202C22—28no—
203C22—24no—
204C22—42no—
205C22—42no—
206C22—44no—
207C22—948no—
208C22—948no—
209C22—948no—
210C22—18832no—
211C22—1884no—
212C22—1884no—
213C22—1884no—
214C22—1884no—
215C22C2×D4×D4712yes—
216C22C22×D18811yescharacteristic
217C22#1309406911yescharacteristic
218C22#1309406911yescharacteristic
219C22#1309407012yes—
220C4—24no—
221C4—22no—
222C4—42no—
223C4—1884no—
224C2—44no—
225C2—1888no—
226C2#1568968112yes—
227C2#1568968511yescharacteristic
228C2#1568975811yescharacteristic
229C2D4×D18812yes—
230C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2679
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13093994C2semidirect
2. C2×#13093992C2semidirect
3. #15689040C2semidirect
4. #15689039C2semidirect
5. #15689025C2semidirect
6. C47×#390C2semidirect
7. C24×D47C22semidirect
13. C2×C4⋊Dic47C22semidirect
14. C2×C22⋊Dic47C22semidirect
15. C2×(C2×D47)⋊C4C22semidirect
16. C2×(C2×D47)⋊C4C22semidirect
17. C2×(C2×D47)⋊C4C22semidirect
18. C47⋊#95C22semidirect
20. C2×C4⋊C4×C47C22semidirect
21. C2×C22⋊C4×C47C22semidirect
22. C2×C42×C47C22semidirect
32. C2×D4×C47D4semidirect
44. C2×D188D4semidirect
121. #390D47semidirect
122. C47#2679semidirect
131. C2×C4⋊C4C2×D47semidirect
136. C2×C22⋊C4C2×D47semidirect
137. C2×C42C2×D47semidirect
156. C2×D4D188semidirect