Finite Group Databasebeta

← #20246531

Subgroups — #20246531

Order 6016.

512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13094005C211yesmaximal, characteristic
2#15689026C211yesmaximal, characteristic
3#15689020C212yesmaximal, complemented
4#15689017C212yesmaximal, complemented
5#15689011C212yesmaximal, complemented
6#15689005C212yesmaximal, complemented
7#15688996C212yesmaximal, complemented
8#15688981C212yesmaximal, complemented
9C47×#386C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic
11#13094005C418yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2211yescharacteristic
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C22×D4×C47C2211yescharacteristic
28C23×C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2211yescharacteristic
31#95×C47C2212yes—
32C24×C47C2311yescharacteristic
33C24×C47C2311yescharacteristic
34C2×D4×C47—41no—
35C2×D4×C47—41no—
36C2×D4×C47C2×C414yes—
37C22×C4×C47—41no—
38C22×C4×C47—42no—
39C22×C4×C47C2312yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—41no—
43C22×Dic47—41no—
44C22×Dic47C2×C414yescomplemented
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C22⋊C4×C47—42no—
50C22⋊C4×C47—41no—
51C22⋊Dic47—42no—
52C22⋊Dic47—42no—
53C22⋊Dic47C2×C418yes—
54C22⋊Dic47C2×C414yescomplemented
55C4⋊Dic47—41no—
56Dic47⋊C4—42no—
57Dic47⋊C4—42no—
58Dic47⋊C4—42no—
59Dic47⋊C4C2×C418yescomplemented
60C4×Dic47—42no—
61C4×Dic47—41no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—21no—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47—21no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47C22×C412yes—
71C23×C47C22×C412yes—
72C23×C47C2411yescharacteristic
73D4×C47—44no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—44no—
83C2×C4×C47C22×C412yes—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—44no—
95C2×Dic47C22×C414yes—
96C2×Dic47C22×C414yes—
97C22×C47—22no—
98C22×C47—22no—
99C22×C47—24no—
100C22×C47—24no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47C23×C411yescharacteristic
108C22×C47H(5,𝔽2)11yescharacteristic
109C22×C47H(5,𝔽2)11yescharacteristic
110C22×C47H(5,𝔽2)12yes—
111C22×C472−1+412yes—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47—42no—
115Dic47—24no—
116Dic47—24no—
117Dic47—42no—
118Dic47—42no—
119#2376—471nomaximal, Sylow
120C2×C47—42no—
121C2×C47—42no—
122C2×C47#51811yescharacteristic
123C2×C47#52012yes—
124C2×C47#56011yescharacteristic
125C2×C47#56212yes—
126C2×C47#56311yescharacteristic
127C2×#123—471no—
128#390—471no—
129#389—472no—
130#388—472no—
131#388—472no—
132#387—472no—
133#386D4711yescharacteristic
134#385—472no—
135#380—472no—
136C47#237611yescharacteristic, complemented, Sylow
137C22×D4C2×D4711yescharacteristic
138C23×C4—471no—
139C23×C4C2×D4711yescharacteristic
140#123—478no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4—471no—
146C2×C22⋊C4—472no—
147C2×C22⋊C4—471no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4C2×D4712yes—
151C2×C22⋊C4C2×D4711yescharacteristic
152C2×C42—471no—
153C2×C42—472no—
154#95—472no—
155#95—472no—
156#95—472no—
157#95—472no—
158#95C2×D4712yes—
159C24C22×D4711yescharacteristic
160C24C22×D4711yescharacteristic
161C2×D4—41no—
162C2×D4—41no—
163C2×D4C4×D4714yes—
164C22×C4—42no—
165C22×C4—41no—
166C22×C4—472no—
167C22×C4—472no—
168C22×C4—474no—
169C22×C4—472no—
170C22×C4—472no—
171C22×C4—1881no—
172C22×C4—1881no—
173C22×C4C22×D4712yes—
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C4⋊C4—478no—
177C4⋊C4—1882no—
178C4⋊C4—1882no—
179C4⋊C4—1882no—
180C4⋊C4—1881no—
181C22⋊C4—42no—
182C22⋊C4—41no—
183C22⋊C4—478no—
184C22⋊C4—474no—
185C22⋊C4—1882no—
186C22⋊C4—1882no—
187C42—1881no—
188C42—1882no—
189C23—22no—
190C23—21no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23C2×C4×D4712yes—
198C23C2×C4×D4712yes—
199C23C23×D4711yescharacteristic
200D4—44no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—44no—
210C2×C4—474no—
211C2×C4—474no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—1884no—
223C2×C4C2×C4×D4712yes—
224C22—22no—
225C22—22no—
226C22—24no—
227C22—24no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22C22×C4×D4711yescharacteristic
235C22#1309406911yescharacteristic
236C22#1309406911yescharacteristic
237C22#1309406912yes—
238C22#1309407112yes—
239C4—22no—
240C4—42no—
241C4—42no—
242C4—944no—
243C4—944no—
244C4—1882no—
245C4—1882no—
246C2—42no—
247C2—42no—
248C2#1568959611yescharacteristic
249C2#1568960212yes—
250C2#1568986211yescharacteristic
251C2#1568986812yes—
252C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#386C2
socleC23×C47C24
hypercenter#386D47
hypocenterC47#2376
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #15689020C2semidirect
4. #15689017C2semidirect
5. #15689011C2semidirect
6. #15689005C2semidirect
7. #15688996C2semidirect
8. #15688981C2semidirect
11. #13094005C4semidirect
44. C22×Dic47C2×C4semidirect
54. C22⋊Dic47C2×C4semidirect
59. Dic47⋊C4C2×C4semidirect
136. C47#2376semidirect