Finite Group Databasebeta

← #20254341

Subgroups — #20254341

Order 6016.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689678C211yesmaximal, characteristic, complemented
2#15689674C211yesmaximal, characteristic
3#15689497C211yesmaximal, characteristic, complemented
4#15689473C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689347C214yesmaximal, complemented
7#15689284C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#494C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×#10625336C2214yes—
12#13094024C2211yescharacteristic
13#13094021C2211yescharacteristic
14#13094015—21no—
15#13094013C2212yes—
16#13094004—21no—
17#13094000C2212yes—
18#13093999—21no—
19#13093999—21no—
20Q8×Dic47C2212yes—
21#13093989—21no—
22#13093986—21no—
23#13093986—21no—
24#13093982—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093948C2214yes—
28#13093946C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C2×Q16×C47C2214yes—
32C4⋊Q8×C47C2211yescharacteristic
33C4⋊Q8×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×Q8×C47C2312yes—
37#10625354—44no—
38C2×D188—22no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188C2312yes—
42C2×C4×D47—22no—
43C2×C4×D47D411yescharacteristic
44C2×C4×D47D411yescharacteristic
45C2×C4×D47C2311yescharacteristic
46C2×Dic94—21no—
47Q16×C47—44no—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C42×C47C2311yescharacteristic
54#10625336—44no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47D411yescharacteristic
64C4×Dic47D411yescharacteristic
65C4×Dic47C2311yescharacteristic
66C2×C47⋊C8C2312yes—
67C22×D47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—24no—
70Q8×C47—24no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D411yescharacteristic
80D188—24no—
81D188—44no—
82D188—42no—
83D188—42no—
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—22no—
87C4×D47—44no—
88Dic94—42no—
89C8×C47—22no—
90C47⋊C8—22no—
91C22×C47C22×D411yescharacteristic
92C2×D47—21no—
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47#13512yes—
101C4×C47#13712yes—
102C4×C47H(5,𝔽2)12yes—
103Dic47—21no—
104Dic47—21no—
105Dic47—21no—
106Dic47—42no—
107#3210—471nomaximal, Sylow
108C2×C47#53511yescharacteristic
109C2×C47C2×#13511yescharacteristic
110C2×C47C2×#13711yescharacteristic
111D47—41no—
112D47—82no—
113#533—471no—
114#532—471no—
115#494D4711yescharacteristic, complemented
116#492—471no—
117#487—471no—
118#486—471no—
119#464—474no—
120#452—474no—
121#431—471no—
122C47#321011yescharacteristic, complemented, Sylow
123C2×#41—472no—
124C2×Q16C2×D4714yes—
125C2×SD16—474no—
126C4⋊Q8—471no—
127C4⋊Q8C2×D4711yescharacteristic
128C4⋊Q8C2×D4711yescharacteristic
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×C42—471no—
142C4⋊C8—472no—
143#103—474no—
144#102—474no—
145C22⋊C8—472no—
146C4×C8—471no—
147C4×C8C2×D4711yescharacteristic
148#41—1884no—
149C2×Q8—941no—
150C2×Q8C22×D4712yes—
151C2×Q8C22×D4712yes—
152C2×D4—472no—
153C2×D4—942no—
154C2×D4—941no—
155C2×D4—941no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—942no—
160Q16—44no—
161SD16—1884no—
162C2×C8—472no—
163C2×C8C22×D4712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—472no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—941no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—471no—
176C42—471no—
177C42—471no—
178C42—942no—
179C42C22×D4711yescharacteristic
180C23—471no—
181C23—942no—
182Q8—24no—
183Q8—24no—
184Q8—1882no—
185D4—944no—
186D4—1884no—
187D4—1882no—
188D4—1882no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—471no—
192C2×C4—471no—
193C2×C4—471no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—1884no—
199C2×C4D4×D4711yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—22no—
203C8—942no—
204C22—941no—
205C22—941no—
206C22—941no—
207C22—1882no—
208C22—1882no—
209C22—1882no—
210C22C2×D4×D4711yescharacteristic
211C4—42no—
212C4—42no—
213C4—941no—
214C4—941no—
215C4—941no—
216C4—1882no—
217C4#1309404712yes—
218C4#1309405612yes—
219C4#1309406912yes—
220C2—3762no—
221C2—1881no—
222C2#1568968611yescharacteristic
223C2C2×#1309404711yescharacteristic
224C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#494C2
socleC22×C47C22×D4
hypercenter#494D47
hypocenterC47#3210
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689497C2semidirect
4. #15689473C2semidirect
5. #15689470C2semidirect
6. #15689347C2semidirect
7. #15689284C2semidirect
8. #15689174C2semidirect
9. C47×#494C2semidirect
115. #494D47semidirect
122. C47#3210semidirect