Finite Group Databasebeta

← #20249021

Subgroups — #20249021

Order 6016.

470 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13094017C211yesmaximal, characteristic
2C2×Q8×Dic47C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic
5#15689042C211yesmaximal, characteristic, complemented
6#15689020C212yesmaximal, complemented
7#15689017C212yesmaximal
8#15689016C212yesmaximal
9#15689010C212yesmaximal, complemented
10#15688968C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic
12#13094017—24no—
13Q8×Dic47—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C4×Dic47C2212yes—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—24no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22⋊C4×C47—22no—
51C22⋊C4×C47—24no—
52C22⋊Dic47—22no—
53C22⋊Dic47—22no—
54C22⋊Dic47—24no—
55C4⋊Dic47—22no—
56C4⋊Dic47—24no—
57C4⋊Dic47—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—24no—
60Dic47⋊C4—22no—
61Dic47⋊C4—24no—
62C4×Dic47—24no—
63C4×Dic47—24no—
64C4×Dic47D414yes—
65C23×C47—21no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—21no—
69C23×C47—21no—
70C23×C47C2411yescharacteristic
71Q8×C47—28no—
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—22no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47C2×D412yes—
96C2×Dic47C2×D412yes—
97C2×Dic47#4114yes—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47C22×D411yescharacteristic
104C22×C47C2×#4112yes—
105C22×C47C2×#4112yes—
106C22×C472−1+411yescharacteristic
107C22×C472−1+411yescharacteristic
108C4×C47—22no—
109C4×C47—24no—
110C4×C47—41no—
111C4×C47—42no—
112Dic47—22no—
113Dic47—22no—
114Dic47—24no—
115Dic47—41no—
116Dic47—42no—
117Dic47—41no—
118#2604—471nomaximal, Sylow
119C2×C47—81no—
120C2×C47#52511yescharacteristic
121C2×C47#53211yescharacteristic
122C2×C47#53611yescharacteristic
123C2×C47#55212yes—
124C2×C47#55612yes—
125C2×#126—471no—
126C2×C4×Q8—471no—
127#400—471no—
128#399—471no—
129#395—471no—
130#393D4711yescharacteristic
131#389—472no—
132#388—472no—
133#388—472no—
134#387—472no—
135#376—471no—
136C47#260411yescharacteristic, complemented, Sylow
137C22×Q8C2×D4711yescharacteristic
138#126—944no—
139C4×Q8—944no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C22⋊C4—471no—
148C2×C22⋊C4—471no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4C2×D4711yescharacteristic
151C2×C22⋊C4C2×D4712yes—
152C2×C42—471no—
153C2×C42—472no—
154C2×C42—472no—
155#95—472no—
156#95—471no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95C2×D4711yescharacteristic
161#95C2×D4712yes—
162C24C22×D4711yescharacteristic
163C2×Q8—22no—
164C2×Q8—24no—
165C22×C4—472no—
166C22×C4—471no—
167C22×C4—471no—
168C22×C4—471no—
169C22×C4—472no—
170C22×C4—471no—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4712yes—
175C4⋊C4—944no—
176C4⋊C4—942no—
177C4⋊C4—944no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—944no—
182C22⋊C4—22no—
183C22⋊C4—24no—
184C22⋊C4—944no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C42—474no—
188C42—944no—
189C42—944no—
190C23—21no—
191C23—22no—
192C23—22no—
193C23—21no—
194C23—21no—
195C23C23×D4711yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—472no—
206C2×C4—472no—
207C2×C4—474no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—941no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4D4×D4712yes—
222C2×C4#1062535214yes—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22C2×D4×D4711yescharacteristic
229C22#41×D4712yes—
230C22C2×#1062535212yes—
231C22#1309407111yescharacteristic
232C22#1309407211yescharacteristic
233C4—22no—
234C4—24no—
235C4—42no—
236C4—41no—
237C4—944no—
238C4—942no—
239C4—942no—
240C4—1881no—
241C4—1882no—
242C4—1881no—
243C2—81no—
244C2#1568962911yescharacteristic
245C2#1568967211yescharacteristic
246C2#1568969611yescharacteristic
247C2#1568980712yes—
248C2#1568984212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2604
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic47C2semidirect
3. #15689063C2semidirect
5. #15689042C2semidirect
6. #15689020C2semidirect
9. #15689010C2semidirect
10. #15688968C2semidirect
136. C47#2604semidirect