Finite Group Databasebeta

← #20248959

Subgroups — #20248959

Order 6016.

492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#13093981C211yesmaximal, characteristic
2#15689054C211yesmaximal, characteristic, complemented
3#15689049C211yesmaximal, characteristic
4#15689042C211yesmaximal, characteristic, complemented
5#15689034C211yesmaximal, characteristic
6#15689014C212yesmaximal
7#15689007C212yesmaximal, complemented
8#15689004C212yesmaximal, complemented
9#15688994C212yesmaximal
10#15688991C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C47C211yesmaximal, characteristic, complemented
12C22×C4×D47C2211yescharacteristic
13#13093981—24no—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2211yescharacteristic
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×Q8×C47C2211yescharacteristic
32C4×Q8×C47—24no—
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C42×C47C2212yes—
36C2×C42×C47C2211yescharacteristic
37C23×D47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—24no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×C4×D47—22no—
51C2×C4×D47—22no—
52C2×C4×D47—22no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—22no—
55C42×C47—24no—
56C42×C47D414yes—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—24no—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—24no—
65C4×Dic47—22no—
66C23×C47C2411yescharacteristic
67C22×D47—21no—
68C22×D47—22no—
69C22×D47—21no—
70C22×D47—22no—
71C22×D47#4112yes—
72Q8×C47—28no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47#4114yes—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47#4112yes—
99C4×D47—28no—
100C22×C47C22×D411yescharacteristic
101C22×C47C2×#4111yescharacteristic
102C22×C47C2×#4111yescharacteristic
103C22×C47C2×#4112yes—
104C22×C472−1+412yes—
105C2×D47—22no—
106C2×D47—24no—
107C2×D47—41no—
108C2×D47—41no—
109C2×D47—42no—
110C4×C47—22no—
111C4×C47—22no—
112C4×C47—24no—
113C4×C47—22no—
114C4×C47—42no—
115Dic47—22no—
116Dic47—41no—
117Dic47—41no—
118Dic47—42no—
119Dic47—42no—
120#2599—471nomaximal, Sylow
121C2×C47#52511yescharacteristic
122C2×C47#52511yescharacteristic
123C2×C47#53611yescharacteristic
124C2×C47#55212yes—
125C2×C47#55612yes—
126D47—42no—
127C2×C4×Q8D4711yescharacteristic, complemented
128C2×#117—471no—
129#398—471no—
130#397—471no—
131#395—471no—
132#393—471no—
133#388—472no—
134#387—472no—
135#387—472no—
136#385—472no—
137#383—471no—
138C47#259911yescharacteristic, complemented, Sylow
139C22×Q8C2×D4711yescharacteristic
140C23×C4—471no—
141C4×Q8—24no—
142#117—944no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4712yes—
148C2×C4⋊C4C2×D4711yescharacteristic
149C2×C22⋊C4—471no—
150C2×C22⋊C4—471no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C42—471no—
154C2×C42C2×D4712yes—
155C2×C42C2×D4711yescharacteristic
156#95—472no—
157#95—472no—
158#95—471no—
159#95—471no—
160#95—472no—
161#95—472no—
162#95—472no—
163#95—472no—
164C24—471no—
165C2×Q8—24no—
166C2×Q8—22no—
167C22×C4—471no—
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—471no—
171C22×C4—471no—
172C22×C4—942no—
173C22×C4—942no—
174C22×C4—942no—
175C22×C4C22×D4712yes—
176C22×C4C22×D4712yes—
177C22×C4C22×D4711yescharacteristic
178C22×C4C22×D4711yescharacteristic
179C22×C4C22×D4711yescharacteristic
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—944no—
183C4⋊C4—944no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C22⋊C4—944no—
187C22⋊C4—944no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C42—24no—
191C42—942no—
192C42C22⋊D4714yes—
193C23—472no—
194C23—941no—
195C23—941no—
196C23—942no—
197C23—942no—
198C23C23×D4711yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—472no—
210C2×C4—948no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4#1062535014yes—
224C2×C4C2×C22⋊D4712yes—
225C2×C4C2×C22⋊D4712yes—
226C2×C4C2×C22⋊D4712yes—
227C22—944no—
228C22—942no—
229C22—1882no—
230C22—1881no—
231C22—1881no—
232C22C22×C22⋊D4711yescharacteristic
233C22#41×D4711yescharacteristic
234C22#41×D4711yescharacteristic
235C22C2×#1062535012yes—
236C22#1309407212yes—
237C4—22no—
238C4—24no—
239C4—22no—
240C4—22no—
241C4—42no—
242C4—942no—
243C4—1882no—
244C4—1882no—
245C4—1881no—
246C4—1881no—
247C2—1882no—
248C2#1568963011yescharacteristic
249C2#1568963411yescharacteristic
250C2#1568969711yescharacteristic
251C2#1568981412yes—
252C2#1568984512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×Q8×C47C2
hypercenterC2×C4×Q8D47
hypocenterC47#2599
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #15689054C2semidirect
4. #15689042C2semidirect
7. #15689007C2semidirect
8. #15689004C2semidirect
10. #15688991C2semidirect
11. C2×C4×Q8×C47C2semidirect
127. C2×C4×Q8D47semidirect
138. C47#2599semidirect