Finite Group Databasebeta

← #20254108

Subgroups — #20254108

Order 6016.

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

normal subgroups only

This group has 402 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#15689678C211yesmaximal, characteristic, complemented
2#15689674C211yesmaximal, characteristic
3#15689496C211yesmaximal, characteristic, complemented
4#15689475C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689370C214yesmaximal, complemented
7#15689222C214yesmaximal, complemented
8C4×#10625324C211yesmaximal, characteristic, complemented
9C47×#500C211yesmaximal, characteristic, complemented
10C2×#10625354—21no—
11C2×#10625325C2214yes—
12C2×#10625324C2212yes—
13#13094024C2211yescharacteristic
14#13094021C2211yescharacteristic
15#13094015—21no—
16#13094013—21no—
17#13094004C2212yes—
18#13094000—21no—
19#13093999—21no—
20#13093999C2212yes—
21Q8×Dic47—21no—
22#13093989C2212yes—
23#13093986—21no—
24#13093986C2212yes—
25#13093982—21no—
26C42×D47C2211yescharacteristic
27#13093947C2214yes—
28#13093944C2214yes—
29#13093934C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#107×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
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×Dic94C2312yes—
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47C2312yes—
51C4⋊C4×C47C2312yes—
52C42×C47C2311yescharacteristic
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—22no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C4×Dic47D411yescharacteristic
62C4×Dic47D411yescharacteristic
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2312yes—
65#10625325—28no—
66#10625324—24no—
67C22×D47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—42no—
70Q8×C47—42no—
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—24no—
89C8×C47#4114yescomplemented
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×C47AGL(1,ℤ/8)12yes—
101C4×C47#13712yes—
102C4×C47C2×#4112yes—
103Dic47—21no—
104Dic47—21no—
105Dic47—21no—
106Dic47—42no—
107#3182—471nomaximal, Sylow
108C2×C47#53211yescharacteristic
109C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C47C2×#13711yescharacteristic
111D47—41no—
112D47—82no—
113#533—471no—
114#532—471no—
115#500D4711yescharacteristic, complemented
116#492—471no—
117#487—471no—
118#486—471no—
119#468—474no—
120#440—474no—
121C4×M16—471no—
122C47#318211yescharacteristic, complemented, Sylow
123C2×#41—941no—
124C2×SD16—474no—
125C2×M16—472no—
126C4⋊Q8—471no—
127C4⋊Q8C2×D4711yescharacteristic
128C4⋊Q8C2×D4711yescharacteristic
129#127—471no—
130#125—941no—
131#124—941no—
132C22⋊Q8—472no—
133C22⋊Q8—941no—
134#121—472no—
135#121—941no—
136C4×Q8—472no—
137C4×Q8—941no—
138C4×D4—472no—
139C4×D4—941no—
140#117—941no—
141C2×C42—471no—
142#107C2×D4714yes—
143#103—474no—
144#102—474no—
145#97—472no—
146C4×C8—471no—
147C4×C8C2×D4711yescharacteristic
148#41—1884no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—472no—
152C2×D4—472no—
153C2×D4—942no—
154C2×D4—941no—
155C2×D4—941no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—942no—
160SD16—948no—
161M16—944no—
162C2×C8—472no—
163C2×C8C22×D4712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—941no—
169C4⋊C4—941no—
170C4⋊C4C22×D4712yes—
171C4⋊C4C22×D4712yes—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—471no—
176C42—471no—
177C42—471no—
178C42—942no—
179C42C22×D4711yescharacteristic
180C23—471no—
181C23—942no—
182Q8—42no—
183Q8—42no—
184Q8—944no—
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—942no—
203C8#1062535414yescomplemented
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#1309404812yes—
218C4#1309405612yes—
219C4C2×#1062535412yes—
220C2—3762no—
221C2—1881no—
222C2#1568967411yescharacteristic
223C2C2×#1309404811yescharacteristic
224C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#500C2
socleC22×C47C22×D4
hypercenter#500D47
hypocenterC47#3182
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689496C2semidirect
4. #15689475C2semidirect
5. #15689471C2semidirect
6. #15689370C2semidirect
7. #15689222C2semidirect
8. C4×#10625324C2semidirect
9. C47×#500C2semidirect
89. C8×C47#41semidirect
115. #500D47semidirect
122. C47#3182semidirect
203. C8#10625354semidirect