Finite Group Databasebeta

← #20251531

Subgroups — #20251531

Order 6016.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689053C211yesmaximal, characteristic, complemented
2#15689051C212yesmaximal, complemented
3#15689051C212yesmaximal, complemented
4#15689046C212yesmaximal, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689037C212yesmaximal
7#15689035C212yesmaximal, complemented
8#15689007C212yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C22×D4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2212yes—
30C2×C42×C47C2211yescharacteristic
31C24×C47C2312yes—
32C2×D4×C47—22no—
33C2×D4×C47—41no—
34C2×D4×C47—41no—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C2×Dic94—42no—
44C2×Dic94—41no—
45C4⋊C4×C47—41no—
46C22⋊C4×C47—42no—
47C22⋊C4×C47—42no—
48C42×C47—41no—
49C22⋊Dic47—42no—
50C22⋊Dic47—42no—
51C22⋊Dic47—42no—
52C22⋊Dic47—42no—
53C4⋊Dic47—41no—
54Dic47⋊C4—24no—
55Dic47⋊C4—42no—
56Dic47⋊C4—42no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47C2411yescharacteristic
65D4×C47—44no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47#4112yes—
76C2×Dic47—22no—
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—
86C2×Dic47—22no—
87C2×Dic47—22no—
88Dic94—44no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47C2×#4111yescharacteristic
97C22×C47H(5,𝔽2)11yescharacteristic
98C22×C47H(5,𝔽2)11yescharacteristic
99C22×C47H(5,𝔽2)12yes—
100C22×C472−1+412yes—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—41no—
104C4×C47—42no—
105Dic47—42no—
106Dic47—42no—
107Dic47—42no—
108Dic47—42no—
109#2830—471nomaximal, Sylow
110C2×C47—82no—
111C2×C47#53811yescharacteristic
112C2×C47#54212yes—
113C2×C47#56011yescharacteristic
114C2×C47#56212yes—
115C2×C47#56311yescharacteristic
116#398—471no—
117#397—472no—
118#397—472no—
119#396—472no—
120#395—471no—
121#394—472no—
122#393—472no—
123#390D4711yescharacteristic
124#387—472no—
125C47#283011yescharacteristic, complemented, Sylow
126C22×Q8—471no—
127C22×D4C2×D4711yescharacteristic
128C2×C4⋊C4—472no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C22⋊C4—472no—
137C2×C22⋊C4C2×D4712yes—
138C2×C22⋊C4C2×D4712yes—
139C2×C42C2×D4711yescharacteristic
140#95—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95—472no—
145#95—471no—
146#95—471no—
147C24C22×D4712yes—
148C2×Q8—1882no—
149C2×Q8—1881no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4—472no—
154C22×C4—472no—
155C22×C4—472no—
156C22×C4—472no—
157C22×C4C22×D4712yes—
158C22×C4C22×D4711yescharacteristic
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4711yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—944no—
163C4⋊C4—1882no—
164C4⋊C4—1882no—
165C4⋊C4—1881no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C22⋊C4—1882no—
169C22⋊C4—1882no—
170C22⋊C4—1882no—
171C22⋊C4—1882no—
172C42—41no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23C23×D4711yescharacteristic
181Q8—1884no—
182D4—44no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4#1062535012yes—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22C2×#1062535011yescharacteristic
213C22#1309406912yes—
214C22#1309406911yescharacteristic
215C22#1309406911yescharacteristic
216C22#1309407112yes—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—42no—
221C4—1882no—
222C4—1882no—
223C4—1882no—
224C4—1882no—
225C2—82no—
226C2#1568971111yescharacteristic
227C2#1568973812yes—
228C2#1568986011yescharacteristic
229C2#1568986812yes—
230C2#1568987311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2830
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #15689053C2semidirect
2. #15689051C2semidirect
3. #15689051C2semidirect
4. #15689046C2semidirect
5. #15689043C2semidirect
7. #15689035C2semidirect
8. #15689007C2semidirect
125. C47#2830semidirect