Finite Group Databasebeta

← #20253042

Subgroups — #20253042

Order 6016.

460 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×#10625337C211yesmaximal, characteristic, complemented
2C2×#13094032C211yesmaximal, characteristic
3#15689699C211yesmaximal, characteristic
4#15689697C211yesmaximal, characteristic
5#15689380C214yesmaximal, complemented
6#15689363C214yesmaximal, complemented
7#15689159C211yesmaximal, characteristic, complemented
8#15689133C211yesmaximal, characteristic, complemented
9C47×#419C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12C2×#10625337—24no—
13C2×#10625337C2212yes—
14C2×#10625337C2212yes—
15#13094032—24no—
16C2×#10625324C2212yes—
17C22×C47⋊C8C2211yescharacteristic
18C2×C8×D47C2212yes—
19#13094024—21no—
20#13094022—21no—
21#13094013—21no—
22#13094012—21no—
23#13094008—22no—
24#13094007—22no—
25#13094004C2214yes—
26#13094000C2214yes—
27#13093983C2211yescharacteristic
28#13093957C2212yes—
29#13093955C2212yes—
30#13093949C2214yes—
31C22×Q8×C47C2211yescharacteristic
32C2×M16×C47C2211yescharacteristic
33#117×C47C2211yescharacteristic
34#103×C47C2214yes—
35C2×Q8×C47—21no—
36C2×Q8×C47—22no—
37C2×Q8×C47—22no—
38C2×Q8×C47C2312yes—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47D412yes—
42C22×Dic47—21no—
43#10625350—22no—
44#10625350—22no—
45C2×D188D411yescharacteristic
46C2×C4×D47C2312yes—
47C2×Dic94—22no—
48C2×Dic94—22no—
49C2×Dic94—21no—
50C2×Dic94D411yescharacteristic
51C2×Dic94C2312yes—
52M16×C47—22no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—21no—
56C42×C47—21no—
57C22⋊Dic47—21no—
58#10625337—24no—
59#10625337—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—24no—
62C4⋊Dic47—24no—
63C4⋊Dic47C2312yes—
64Dic47⋊C4—24no—
65C4×Dic47—21no—
66C2×C47⋊C8D414yes—
67C2×C47⋊C8C2311yescharacteristic
68C2×C47⋊C8C2311yescharacteristic
69#10625324—24no—
70C8×D47—24no—
71C23×C47C2×D411yescharacteristic
72C22×D47C2×D412yes—
73Q8×C47—22no—
74Q8×C47—22no—
75Q8×C47—42no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—42no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D412yes—
81C2×C4×C47#4112yes—
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—24no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—42no—
87C2×Dic47C2×D412yes—
88D188—22no—
89C4×D47—22no—
90C4×D47—22no—
91Dic94—22no—
92Dic94—22no—
93Dic94—22no—
94Dic94—42no—
95C8×C47—22no—
96C47⋊C8C2×D412yes—
97C47⋊C8C2×D412yes—
98C22×C47—22no—
99C22×C47#12112yes—
100C22×C47C22×D411yescharacteristic
101C2×D47—22no—
102C2×D47—24no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47#12112yes—
106C4×C47C22×D411yescharacteristic
107C4×C47C2×#4111yescharacteristic
108Dic47—22no—
109Dic47—42no—
110Dic47—42no—
111#3059—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47C2×#12111yescharacteristic
114C2×C47#57812yes—
115D47—42no—
116C22×Q16—471no—
117C2×#131—471no—
118#536—471no—
119#536—471no—
120#470—474no—
121#467—474no—
122#427—471no—
123#419—471no—
124#419D4711yescharacteristic, complemented
125C47#305911yescharacteristic, complemented, Sylow
126C2×#41—471no—
127C22×Q8—471no—
128C22×Q8C2×D4711yescharacteristic
129C2×Q16—472no—
130C2×Q16—472no—
131C2×Q16—944no—
132#131—944no—
133C2×M16—472no—
134C2×M16C2×D4711yescharacteristic
135C22×C8—471no—
136C22×C8—472no—
137C4⋊Q8—941no—
138C4⋊Q8—941no—
139#124—941no—
140#124—941no—
141#123—942no—
142#123—942no—
143C22⋊Q8—474no—
144C22⋊Q8—474no—
145#117—471no—
146#117C2×D4711yescharacteristic
147#107—472no—
148#106—472no—
149#103—474no—
150#103C2×D4714yes—
151#41—942no—
152#41—942no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—471no—
157C2×Q8—472no—
158C2×Q8—941no—
159C2×Q8—942no—
160C2×Q8—942no—
161C2×Q8C22×D4712yes—
162C2×D4—472no—
163C2×D4—471no—
164C22×C4—21no—
165C22×C4—472no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169Q16—944no—
170M16—22no—
171M16—944no—
172C2×C8—474no—
173C2×C8—471no—
174C2×C8—471no—
175C2×C8—944no—
176C2×C8C22×D4712yes—
177C4⋊C4—472no—
178C4⋊C4—944no—
179C4⋊C4—944no—
180C4⋊C4C22×D4712yes—
181C22⋊C4—21no—
182C22⋊C4—944no—
183C22⋊C4—944no—
184C22⋊C4—941no—
185C42—21no—
186C42—941no—
187C23—472no—
188C23D4×D4711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—942no—
193Q8—942no—
194Q8—942no—
195Q8—1882no—
196D4—944no—
197D4—942no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—472no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—1882no—
207C2×C4#1062535012yes—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—472no—
213C8—472no—
214C22—22no—
215C22—942no—
216C22—944no—
217C22#1309399712yes—
218C22C2×D4×D4711yescharacteristic
219C4—42no—
220C4—42no—
221C4—942no—
222C4—1882no—
223C4—1882no—
224C4#1309399712yes—
225C4C2×D4×D4711yescharacteristic
226C4C2×#1062535011yescharacteristic
227C2—22no—
228C2—1882no—
229C2C2×#1309399711yescharacteristic
230C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3059
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#10625337C2semidirect
5. #15689380C2semidirect
6. #15689363C2semidirect
7. #15689159C2semidirect
8. #15689133C2semidirect
9. C47×#419C2semidirect
124. #419D47semidirect
125. C47#3059semidirect