Finite Group Databasebeta

← #20251217

Subgroups — #20251217

Order 6016.

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

normal subgroups only

This group has 420 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#15689062C211yesmaximal, characteristic, complemented
2#15689045C212yesmaximal, complemented
3#15689040C212yesmaximal
4#15689040C211yesmaximal, characteristic
5#15689014C212yesmaximal, complemented
6#15689013C212yesmaximal, complemented
7#15689013C212yesmaximal, complemented
8#15689004C212yesmaximal, complemented
9C47×#384C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×(C2×D47)⋊C4C2212yes—
14C2×(C2×D47)⋊C4C2212yes—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×C4×Dic47C2212yes—
20C47⋊#95C2211yescharacteristic
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2212yes—
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31C23×D47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×D188—41no—
41C2×D188—42no—
42C4⋊C4×C47—42no—
43C4⋊C4×C47—41no—
44C4⋊C4×C47—41no—
45C4⋊C4×C47—42no—
46C42×C47—22no—
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4—24no—
50(C2×D47)⋊C4—42no—
51(C2×D47)⋊C4—42no—
52(C2×D47)⋊C4—42no—
53C4⋊Dic47—41no—
54Dic47⋊C4—24no—
55C4×Dic47—42no—
56C23×C47C2411yescharacteristic
57C22×D47—22no—
58C22×D47—22no—
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47#4112yes—
76C2×C4×C47#4114yes—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86D188—44no—
87C22×C47C2×#4111yescharacteristic
88C22×C47C2×#4112yes—
89C22×C47H(5,𝔽2)11yescharacteristic
90C22×C47H(5,𝔽2)12yes—
91C22×C472−1+411yescharacteristic
92C2×D47—42no—
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C4×C47—22no—
100C4×C47—24no—
101C4×C47—41no—
102C4×C47—42no—
103C4×C47—41no—
104Dic47—42no—
105Dic47—42no—
106Dic47—42no—
107#2795—471nomaximal, Sylow
108C2×C47#53911yescharacteristic
109C2×C47#54212yes—
110C2×C47#55312yes—
111C2×C47#55511yescharacteristic
112C2×C47#56011yescharacteristic
113D47—82no—
114#400—471no—
115#396—472no—
116#394—471no—
117#394—472no—
118#388—472no—
119#388—472no—
120#388—472no—
121#387—472no—
122#384D4711yescharacteristic, complemented
123C47#279511yescharacteristic, complemented, Sylow
124C22×D4—471no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4C2×D4712yes—
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C4⋊C4C2×D4712yes—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C22⋊C4—472no—
132C2×C22⋊C4—472no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C22⋊C4—472no—
137C2×C42—472no—
138C2×C42C2×D4711yescharacteristic
139#95—471no—
140#95—472no—
141#95—472no—
142#95—472no—
143#95—471no—
144#95—472no—
145C24—472no—
146C2×D4—1882no—
147C2×D4—1881no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4C22×D4711yescharacteristic
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C22×C4C22×D4711yescharacteristic
155C22×C4C22×D4712yes—
156C4⋊C4—42no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—944no—
161C4⋊C4—1881no—
162C22⋊C4—944no—
163C22⋊C4—944no—
164C22⋊C4—944no—
165C22⋊C4—1882no—
166C22⋊C4—1882no—
167C22⋊C4—1882no—
168C42—22no—
169C42—1882no—
170C23—942no—
171C23—942no—
172C23—942no—
173C23—942no—
174C23—942no—
175C23—942no—
176C23—942no—
177C23C23×D4711yescharacteristic
178D4—1884no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4#1062535012yes—
200C2×C4#1062535414yes—
201C22—1882no—
202C22—1882no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22—1882no—
207C22—1882no—
208C22C2×#1062535011yescharacteristic
209C22C2×#1062535412yes—
210C22#1309406912yes—
211C22#1309406911yescharacteristic
212C22#1309407211yescharacteristic
213C4—24no—
214C4—22no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—1882no—
219C4—1882no—
220C4—1882no—
221C2—3762no—
222C2#1568972011yescharacteristic
223C2#1568974712yes—
224C2#1568982112yes—
225C2#1568983911yescharacteristic
226C2#1568986011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#384C2
hypercenter#384D47
hypocenterC47#2795
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #15689062C2semidirect
2. #15689045C2semidirect
5. #15689014C2semidirect
6. #15689013C2semidirect
7. #15689013C2semidirect
8. #15689004C2semidirect
9. C47×#384C2semidirect
122. #384D47semidirect
123. C47#2795semidirect