Finite Group Databasebeta

← #20254393

Subgroups — #20254393

Order 6016.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689680C211yesmaximal, characteristic, complemented
2C2×#13094012C211yesmaximal, characteristic
3#15689517C212yesmaximal, complemented
4#15689483C212yesmaximal, complemented
5#15689346C214yesmaximal, complemented
6#15689281C212yesmaximal, complemented
7#15689276C212yesmaximal
8C47×#432C211yesmaximal, characteristic, complemented
9C22×Dic94C2211yescharacteristic
10C22×D188C2211yescharacteristic
11C2×Dic188C2214yescomplemented
12C2×#10625325C2214yes—
13#13094024C2211yescharacteristic, complemented
14#13094024C2211yescharacteristic, complemented
15#13094016—21no—
16#13094012—21no—
17#13094012—21no—
18#13094012C2212yes—
19#13094012C2212yes—
20#13094003—21no—
21#13094003C2212yes—
22C4×Dic94—21no—
23C4×Dic94C2212yescomplemented
24#13093983—21no—
25C2×(C2×D47)⋊C4—21no—
26C2×(C2×D47)⋊C4—21no—
27#13093949C2214yescomplemented
28#13093946C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yescomplemented
31C22⋊C8×C47C2212yes—
32#97×C47C2212yescomplemented
33C23×D47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C2×D188—21no—
39C2×D188—42no—
40C2×D188C2312yes—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—42no—
44C2×Dic94C2312yes—
45C2×Dic94C2312yes—
46C2×C8×C47C2314yes—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51C22⋊Dic47—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63Dic188—44no—
64#10625325—44no—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67C22×D47—42no—
68C22×D47—42no—
69C22×D47—42no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—41no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2411yescharacteristic
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—42no—
83D188—24no—
84D188—42no—
85Dic94—24no—
86Dic94—24no—
87Dic94—42no—
88Dic94—42no—
89C8×C47—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#13712yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—84no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47H(5,𝔽2)12yes—
104Dic47—42no—
105Dic47—42no—
106Dic47—42no—
107#3215—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#53511yescharacteristic
110C2×C47C2×#13711yescharacteristic
111C2×C47#57511yescharacteristic
112D47—82no—
113#533—471no—
114C2×#124—471no—
115#497—472no—
116#489—472no—
117#464—474no—
118#451—472no—
119#450—472no—
120#432D4711yescharacteristic, complemented
121C47#321511yescharacteristic, complemented, Sylow
122C22×Q8—471no—
123C22×D4—471no—
124C2×Q16—474no—
125C2×SD16—474no—
126C4⋊Q8—471no—
127C4⋊Q8—471no—
128#125—941no—
129#124—472no—
130#124—472no—
131#124—941no—
132#124—941no—
133C22⋊Q8—472no—
134C22⋊Q8—941no—
135C4×Q8—472no—
136C4×Q8—941no—
137#117—941no—
138C2×C22⋊C4—941no—
139C2×C22⋊C4—941no—
140C2×C42C2×D4711yescharacteristic
141C4⋊C8C2×D4712yescomplemented
142#103—474no—
143#102—474no—
144C22⋊C8C2×D4712yes—
145#97C2×D4712yescomplemented
146C24—941no—
147C2×Q8—472no—
148C2×Q8—472no—
149C2×Q8—941no—
150C2×Q8—941no—
151C2×Q8—1882no—
152C2×D4—472no—
153C2×D4—941no—
154C2×D4—1882no—
155C22×C4—941no—
156C22×C4D18811yescharacteristic
157C22×C4D18811yescharacteristic
158C22×C4C22×D4711yescharacteristic
159Q16—1884no—
160SD16—1884no—
161C2×C8C22×D4714yes—
162C4⋊C4—472no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C22⋊C4—942no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C42—942no—
174C42D18811yescharacteristic
175C42D18811yescharacteristic
176C42C22×D4711yescharacteristic
177C42C22×D4711yescharacteristic
178C23—942no—
179C23—1882no—
180C23—1882no—
181C23—1882no—
182C23C2×D18811yescharacteristic
183Q8—944no—
184Q8—944no—
185Q8—1882no—
186Q8—1882no—
187D4—944no—
188D4—1882no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—1882no—
196C2×C4C2×D18811yescharacteristic
197C2×C4C2×D18811yescharacteristic
198C2×C4C2×D18811yescharacteristic
199C2×C4C2×D18811yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—3764no—
206C22—1882no—
207C22—1882no—
208C22—1882no—
209C22#1309405712yes—
210C22C22×D18811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—1882no—
217C4—1882no—
218C4—1882no—
219C4#1309407012yes—
220C2—22no—
221C2—3762no—
222C2#1568969211yescharacteristic
223C2C2×#1309405711yescharacteristic
224C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3215
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689517C2semidirect
4. #15689483C2semidirect
5. #15689346C2semidirect
6. #15689281C2semidirect
8. C47×#432C2semidirect
11. C2×Dic188C22semidirect
13. #13094024C22semidirect
14. #13094024C22semidirect
23. C4×Dic94C22semidirect
27. #13093949C22semidirect
30. C4⋊C8×C47C22semidirect
32. #97×C47C22semidirect
120. #432D47semidirect
121. C47#3215semidirect
141. C4⋊C8C2×D47semidirect
145. #97C2×D47semidirect