Finite Group Databasebeta

← #20249079

Subgroups — #20249079

Order 6016.

476 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13093980C211yesmaximal, characteristic
3#15689061C211yesmaximal, characteristic, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic
6#15689019C212yesmaximal, complemented
7#15689011C212yesmaximal
8#15689009C212yesmaximal, complemented
9#15688998C212yesmaximal
10#15688968C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic
12C23×Dic47C2211yescharacteristic
13#13094015—24no—
14#13093980—24no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C4×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×Dic47—22no—
43C22×Dic47—22no—
44C22×Dic47—22no—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C4⋊C4×C47—22no—
52C4⋊C4×C47—24no—
53C22⋊C4×C47—22no—
54C22⋊C4×C47—24no—
55C22⋊Dic47—24no—
56C22⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—24no—
59C4⋊Dic47—24no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—24no—
63C4×Dic47—24no—
64C4×Dic47—22no—
65C4×Dic47D414yes—
66C23×C47—21no—
67C23×C47—22no—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47#4112yes—
71C23×C47C2411yescharacteristic
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47#4114yes—
82C2×Dic47—28no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47C2×D412yes—
97C2×Dic47C2×D412yes—
98C2×Dic47#4112yes—
99C22×C47—22no—
100C22×C47—24no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—42no—
104C22×C47C22×D411yescharacteristic
105C22×C47C2×#4111yescharacteristic
106C22×C47C2×#4112yes—
107C22×C47C2×#4111yescharacteristic
108C22×C472−1+412yes—
109C4×C47—22no—
110C4×C47—24no—
111C4×C47—41no—
112C4×C47—42no—
113Dic47—22no—
114Dic47—22no—
115Dic47—22no—
116Dic47—42no—
117Dic47—41no—
118Dic47—42no—
119#2611—471nomaximal, Sylow
120C2×C47—42no—
121C2×C47#52511yescharacteristic
122C2×C47#53211yescharacteristic
123C2×C47#53611yescharacteristic
124C2×C47#55212yes—
125C2×C47#55212yes—
126C2×#125—471no—
127C2×#117—471no—
128#400—471no—
129#399D4711yescharacteristic
130#398—471no—
131#397—471no—
132#389—472no—
133#388—472no—
134#387—472no—
135#385—472no—
136#376—471no—
137C47#261111yescharacteristic, complemented, Sylow
138C23×C4—471no—
139#125—944no—
140#117—944no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C4⋊C4C2×D4712yes—
149C2×C22⋊C4—471no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4C2×D4711yescharacteristic
152C2×C22⋊C4C2×D4712yes—
153C2×C42—471no—
154C2×C42—471no—
155C2×C42—472no—
156#95—472no—
157#95—471no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95—472no—
162#95C2×D4711yescharacteristic
163C24C22×D4711yescharacteristic
164C22×C4—471no—
165C22×C4—471no—
166C22×C4—471no—
167C22×C4—472no—
168C22×C4—471no—
169C22×C4—472no—
170C22×C4—942no—
171C22×C4—942no—
172C22×C4—942no—
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4712yes—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—942no—
180C4⋊C4—944no—
181C4⋊C4—944no—
182C4⋊C4—944no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C22⋊C4—22no—
186C22⋊C4—24no—
187C22⋊C4—942no—
188C22⋊C4—944no—
189C42—474no—
190C42—942no—
191C42—944no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23—22no—
196C23#1062535412yes—
197C23C23×D4711yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—472no—
207C2×C4—472no—
208C2×C4—472no—
209C2×C4—948no—
210C2×C4—941no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4D4×D4712yes—
224C2×C4#1062535214yes—
225C22—24no—
226C22—22no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22C2×D4×D4711yescharacteristic
231C22#41×D4711yescharacteristic
232C22C2×#1062535212yes—
233C22C2×#1062535411yescharacteristic
234C22#1309407112yes—
235C4—24no—
236C4—22no—
237C4—41no—
238C4—42no—
239C4—942no—
240C4—942no—
241C4—942no—
242C4—1882no—
243C4—1882no—
244C4—1881no—
245C2—42no—
246C2#1568963611yescharacteristic
247C2#1568967111yescharacteristic
248C2#1568969511yescharacteristic
249C2#1568981012yes—
250C2#1568981512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2611
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
3. #15689061C2semidirect
4. #15689055C2semidirect
6. #15689019C2semidirect
8. #15689009C2semidirect
10. #15688968C2semidirect
137. C47#2611semidirect