Finite Group Databasebeta

← #20251559

Subgroups — #20251559

Order 6016.

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

normal subgroups only

This group has 416 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#15689065C212yesmaximal, complemented
2#15689048C212yesmaximal, complemented
3#15689043C211yesmaximal, characteristic, complemented
4#15689037C212yesmaximal
5#15689035C212yesmaximal, complemented
6#15689035C212yesmaximal, complemented
7#15689028C211yesmaximal, characteristic, complemented
8#15689016C212yesmaximal, complemented
9C47×#394C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C4×Dic47C2211yescharacteristic
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
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—
42C2×Dic94—22no—
43C2×Dic94—41no—
44C2×Dic94—41no—
45C2×Dic94—42no—
46C2×Dic94—41no—
47C4⋊C4×C47—41no—
48C22⋊C4×C47—24no—
49C22⋊C4×C47—42no—
50C22⋊Dic47—42no—
51C22⋊Dic47—42no—
52C22⋊Dic47—42no—
53C22⋊Dic47—42no—
54C4⋊Dic47—42no—
55Dic47⋊C4—42no—
56C4×Dic47—41no—
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—22no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
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—
89Dic94—44no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47C2×#4111yescharacteristic
98C22×C47H(5,𝔽2)11yescharacteristic
99C22×C47H(5,𝔽2)12yes—
100C22×C47H(5,𝔽2)11yescharacteristic
101C22×C472−1+412yes—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47—41no—
106Dic47—42no—
107Dic47—42no—
108Dic47—42no—
109Dic47—42no—
110#2832—471nomaximal, Sylow
111C2×C47—82no—
112C2×C47#53811yescharacteristic
113C2×C47#54212yes—
114C2×C47H(3,𝔽4)11yescharacteristic
115C2×C47#56212yes—
116C2×C47#56311yescharacteristic
117#400—472no—
118#397—472no—
119#395—471no—
120#394—472no—
121#394D4711yescharacteristic
122#393—472no—
123#393—472no—
124#391—471no—
125#388—472no—
126C47#283211yescharacteristic, complemented, Sylow
127C22×Q8—471no—
128C22×Q8—471no—
129C22×D4C2×D4711yescharacteristic
130C2×C4⋊C4—472no—
131C2×C4⋊C4—472no—
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×C42—471no—
140#95—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95—472no—
145#95—472no—
146#95—471no—
147#95C2×D4711yescharacteristic
148C24C22×D4712yes—
149C2×Q8—942no—
150C2×Q8—1881no—
151C2×Q8—1881no—
152C2×Q8—1882no—
153C2×Q8—1881no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—472no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4C22×D4712yes—
161C22×C4C22×D4711yescharacteristic
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4711yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—1882no—
166C4⋊C4—1882no—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—1882no—
170C22⋊C4—1882no—
171C22⋊C4—1882no—
172C22⋊C4—1882no—
173C42—1881no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C23×D4711yescharacteristic
182Q8—1884no—
183Q8—1884no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
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—942no—
205C2×C4—942no—
206C2×C4#1062535212yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#1062535211yescharacteristic
215C22#1309406912yes—
216C22#1309406911yescharacteristic
217C22#1309407011yescharacteristic
218C22#1309407112yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—1882no—
224C4—1882no—
225C4—1882no—
226C4—1882no—
227C2—82no—
228C2#1568971011yescharacteristic
229C2#1568974012yes—
230C2#1568986611yescharacteristic
231C2#1568987012yes—
232C2#1568987311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2832
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
2. #15689048C2semidirect
3. #15689043C2semidirect
5. #15689035C2semidirect
6. #15689035C2semidirect
7. #15689028C2semidirect
8. #15689016C2semidirect
126. C47#2832semidirect