Finite Group Databasebeta

← #20254346

Subgroups — #20254346

Order 6016.

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

normal subgroups only

This group has 394 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#15689680C211yesmaximal, characteristic, complemented
2#15689673C211yesmaximal, characteristic
3#15689503C211yesmaximal, characteristic, complemented
4#15689496C211yesmaximal, characteristic, complemented
5#15689474C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689346C214yesmaximal, complemented
8#15689287C214yesmaximal, complemented
9C47×#431C211yesmaximal, characteristic, complemented
10C2×#10625350C2212yes—
11C2×Dic188C2214yes—
12C2×#10625325C2214yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094024C2211yescharacteristic
16#13094021C2211yescharacteristic
17#13094016—21no—
18#13094012C2212yes—
19#13094003—21no—
20#13094003C2212yes—
21#13093998—21no—
22#13093998—21no—
23C4×Dic94—21no—
24C4×Dic94C2212yes—
25C4×D188—21no—
26C4×D188—21no—
27#13093983—21no—
28#13093949C2214yes—
29#13093946C2214yes—
30C2×C42×C47C2211yescharacteristic
31C4⋊C8×C47C2212yes—
32C22⋊C8×C47C2212yes—
33C4×C8×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—22no—
39#10625350—44no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94—21no—
45C2×Dic94C2312yes—
46C2×Dic94C2312yes—
47C2×C8×C47C2312yes—
48C2×C8×C47C2312yes—
49C42×C47D411yescharacteristic
50C42×C47D411yescharacteristic
51C42×C47C2311yescharacteristic
52C42×C47C2311yescharacteristic
53C22⋊Dic47—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65Dic188—44no—
66#10625325—44no—
67C23×C47C2×D411yescharacteristic
68C22×D47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—44no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82D188—24no—
83D188—42no—
84D188—42no—
85C4×D47—44no—
86Dic94—24no—
87Dic94—24no—
88Dic94—42no—
89C8×C47—22no—
90C8×C47—22no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47C22×D411yescharacteristic
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47#13512yes—
102C4×C47#13712yes—
103C4×C47H(5,𝔽2)12yes—
104Dic47—42no—
105Dic47—42no—
106Dic47—42no—
107#3210—471nomaximal, Sylow
108C2×C47—41no—
109C2×C47#53511yescharacteristic
110C2×C47C2×#13511yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—82no—
113#533—471no—
114#532—471no—
115#494—471no—
116#492—471no—
117#487—471no—
118#486—471no—
119#464—474no—
120#452—474no—
121#431D4711yescharacteristic, complemented
122C47#321011yescharacteristic, complemented, Sylow
123C2×#41—472no—
124C2×Q16—474no—
125C2×SD16—474no—
126C4⋊Q8—471no—
127C4⋊Q8—471no—
128C4⋊Q8—471no—
129#127—471no—
130#125—941no—
131#124—472no—
132C22⋊Q8—472no—
133C22⋊Q8—941no—
134#121—941no—
135#121—941no—
136C4×Q8—472no—
137C4×Q8—941no—
138C4×D4—941no—
139C4×D4—941no—
140#117—941no—
141C2×C42C2×D4711yescharacteristic
142C4⋊C8C2×D4712yes—
143#103—474no—
144#102—474no—
145C22⋊C8C2×D4712yes—
146C4×C8C2×D4711yescharacteristic
147C4×C8C2×D4711yescharacteristic
148#41—1884no—
149C2×Q8—472no—
150C2×Q8—472no—
151C2×Q8—941no—
152C2×D4—472no—
153C2×D4—942no—
154C2×D4—941no—
155C2×D4—941no—
156C22×C4—942no—
157C22×C4D18811yescharacteristic
158C22×C4D18811yescharacteristic
159C22×C4C22×D4711yescharacteristic
160Q16—1884no—
161SD16—1884no—
162C2×C8C22×D4712yes—
163C2×C8C22×D4712yes—
164C4⋊C4—472no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—942no—
176C42D18811yescharacteristic
177C42D18811yescharacteristic
178C42C22×D4711yescharacteristic
179C42C22×D4711yescharacteristic
180C23—942no—
181C23C2×D18811yescharacteristic
182Q8—944no—
183Q8—944no—
184Q8—1882no—
185D4—944no—
186D4—1884no—
187D4—1882no—
188D4—1882no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—1884no—
196C2×C4C2×D18811yescharacteristic
197C2×C4C2×D18811yescharacteristic
198C2×C4C2×D18811yescharacteristic
199C2×C4C2×D18811yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—22no—
203C8—22no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—1882no—
208C22—1882no—
209C22—1882no—
210C22C22×D18811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—1882no—
215C4—1882no—
216C4—1882no—
217C4#1309404612yes—
218C4#1309405712yes—
219C4#1309407012yes—
220C2—41no—
221C2—3762no—
222C2#1568969211yescharacteristic
223C2C2×#1309404611yescharacteristic
224C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3210
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689503C2semidirect
4. #15689496C2semidirect
5. #15689474C2semidirect
6. #15689470C2semidirect
7. #15689346C2semidirect
8. #15689287C2semidirect
9. C47×#431C2semidirect
121. #431D47semidirect
122. C47#3210semidirect