Finite Group Databasebeta

← #20254339

Subgroups — #20254339

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#15689671C211yesmaximal, characteristic
3#15689502C211yesmaximal, characteristic, complemented
4#15689474C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689343C214yesmaximal, complemented
7#15689282C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#492C211yesmaximal, characteristic, complemented
10C2×#10625352C2212yes—
11C2×#10625337C2214yes—
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094015—21no—
15#13094011C2212yes—
16#13094004—21no—
17#13094000C2212yes—
18#13093995—21no—
19#13093995—21no—
20Q8×Dic47C2212yes—
21#13093989—21no—
22D4×Dic47—21no—
23D4×Dic47—21no—
24#13093982—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093949C2214yes—
28#13093945C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C2×SD16×C47C2214yes—
32C4⋊Q8×C47C2211yescharacteristic
33#127×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C2×C22⋊D47—22no—
40C22×Dic47—22no—
41#10625352—44no—
42C2×C4×D47D411yescharacteristic
43C2×C4×D47D411yescharacteristic
44C2×C4×D47C2311yescharacteristic
45C2×Dic94—21no—
46C2×Dic94C2312yes—
47SD16×C47—44no—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C42×C47C2311yescharacteristic
52C22⋊Dic47—22no—
53C22⋊Dic47—22no—
54#10625337—44no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47D411yescharacteristic
64C4×Dic47D411yescharacteristic
65C4×Dic47C2311yescharacteristic
66C2×C47⋊C8C2312yes—
67C23×C47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—24no—
70D4×C47—24no—
71D4×C47—42no—
72D4×C47—42no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—44no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—44no—
81C2×Dic47C2×D411yescharacteristic
82C2×Dic47C2×D411yescharacteristic
83C2×Dic47C2×D411yescharacteristic
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—22no—
87Dic94—24no—
88Dic94—42no—
89C8×C47—22no—
90C47⋊C8—22no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47C22×D411yescharacteristic
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—21no—
98C4×C47—42no—
99C4×C47#13512yes—
100C4×C47#13712yes—
101C4×C47H(5,𝔽2)12yes—
102Dic47—21no—
103Dic47—21no—
104Dic47—21no—
105Dic47—42no—
106Dic47—42no—
107#3210—471nomaximal, Sylow
108C2×C47—82no—
109C2×C47#53511yescharacteristic
110C2×C47C2×#13511yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—41no—
113#533—471no—
114#532—471no—
115#494—471no—
116#492D4711yescharacteristic, complemented
117#487—471no—
118#486—471no—
119#464—474no—
120#452—474no—
121#431—471no—
122C47#321011yescharacteristic, complemented, Sylow
123C2×#41—472no—
124C2×Q16—474no—
125C2×SD16C2×D4714yes—
126C4⋊Q8—471no—
127C4⋊Q8—471no—
128C4⋊Q8C2×D4711yescharacteristic
129#127C2×D4711yescharacteristic
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—472no—
150C2×Q8—941no—
151C2×Q8C22×D4712yes—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—942no—
155C2×D4C22×D4712yes—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—942no—
160Q16—1884no—
161SD16—44no—
162C2×C8—472no—
163C2×C8C22×D4712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—472no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—471no—
176C42—471no—
177C42—471no—
178C42—942no—
179C42C22×D4711yescharacteristic
180C23—22no—
181C23—471no—
182Q8—24no—
183Q8—944no—
184Q8—1882no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—1884no—
189C2×C4—22no—
190C2×C4—471no—
191C2×C4—471no—
192C2×C4—471no—
193C2×C4—942no—
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—42no—
205C22—42no—
206C22—42no—
207C22—941no—
208C22—941no—
209C22—941no—
210C22C2×D4×D4711yescharacteristic
211C4—42no—
212C4—941no—
213C4—941no—
214C4—941no—
215C4—1882no—
216C4—1882no—
217C4#1309404512yes—
218C4#1309405312yes—
219C4#1309406912yes—
220C2—82no—
221C2—1881no—
222C2#1568968611yescharacteristic
223C2C2×#1309404511yescharacteristic
224C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3210
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689502C2semidirect
4. #15689474C2semidirect
5. #15689469C2semidirect
6. #15689343C2semidirect
7. #15689282C2semidirect
8. #15689174C2semidirect
9. C47×#492C2semidirect
116. #492D47semidirect
122. C47#3210semidirect