Finite Group Databasebeta

← #20251221

Subgroups — #20251221

Order 6016.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689046C212yesmaximal, complemented
3#15689037C212yesmaximal
4#15689016C212yesmaximal, complemented
5#15689011C212yesmaximal, complemented
6#15689011C212yesmaximal, complemented
7#15689005C212yesmaximal, complemented
8#15688992C211yesmaximal, characteristic, complemented
9C47×#394C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C4×Dic47C2211yescharacteristic
20C2×C4×Dic47C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C22×D4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2212yes—
30#95×C47C2211yescharacteristic
31C24×C47C2312yes—
32C2×D4×C47—42no—
33C2×D4×C47—41no—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C4⋊C4×C47—41no—
43C22⋊C4×C47—24no—
44C22⋊C4×C47—42no—
45C22⋊Dic47—24no—
46C22⋊Dic47—24no—
47C22⋊Dic47—42no—
48C22⋊Dic47—42no—
49C4⋊Dic47—41no—
50C4⋊Dic47—41no—
51Dic47⋊C4—24no—
52Dic47⋊C4—42no—
53Dic47⋊C4—42no—
54C4×Dic47—22no—
55C4×Dic47—42no—
56C23×C47—22no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47C2411yescharacteristic
64D4×C47—44no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47#4112yes—
75C2×Dic47—22no—
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#4114yes—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47C2×#4112yes—
95C22×C47C2×#4111yescharacteristic
96C22×C47H(5,𝔽2)11yescharacteristic
97C22×C47H(5,𝔽2)12yes—
98C22×C472−1+411yescharacteristic
99C4×C47—22no—
100C4×C47—42no—
101C4×C47—41no—
102C4×C47—41no—
103Dic47—24no—
104Dic47—42no—
105Dic47—42no—
106Dic47—42no—
107#2795—471nomaximal, Sylow
108C2×C47—82no—
109C2×C47#53911yescharacteristic
110C2×C47#54212yes—
111C2×C47#55312yes—
112C2×C47#55511yescharacteristic
113C2×C47#56011yescharacteristic
114#400—471no—
115#396—472no—
116#394—472no—
117#394D4711yescharacteristic
118#388—472no—
119#388—472no—
120#388—472no—
121#387—472no—
122#384—471no—
123C47#279511yescharacteristic, complemented, Sylow
124C22×D4C2×D4711yescharacteristic
125C2×C4⋊C4—472no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C22⋊C4—472no—
132C2×C22⋊C4—472no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4C2×D4712yes—
136C2×C22⋊C4C2×D4712yes—
137C2×C42—471no—
138C2×C42—472no—
139#95—472no—
140#95—472no—
141#95—472no—
142#95—471no—
143#95—472no—
144#95C2×D4711yescharacteristic
145C24C22×D4712yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C22×C4C22×D4711yescharacteristic
155C22×C4C22×D4711yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—944no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1881no—
161C4⋊C4—1881no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—944no—
165C22⋊C4—944no—
166C22⋊C4—1882no—
167C22⋊C4—1882no—
168C42—942no—
169C42—1882no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D4711yescharacteristic
178D4—44no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—474no—
189C2×C4—942no—
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—942no—
200C2×C4#1062535212yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D4712yes—
209C22C2×#1062535211yescharacteristic
210C22#1309406912yes—
211C22#1309406911yescharacteristic
212C22#1309407111yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—944no—
218C4—1882no—
219C4—1882no—
220C4—1882no—
221C2—82no—
222C2#1568971811yescharacteristic
223C2#1568974112yes—
224C2#1568982012yes—
225C2#1568983511yescharacteristic
226C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2795
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #15689062C2semidirect
2. #15689046C2semidirect
4. #15689016C2semidirect
5. #15689011C2semidirect
6. #15689011C2semidirect
7. #15689005C2semidirect
8. #15688992C2semidirect
123. C47#2795semidirect