Finite Group Databasebeta

← #20247378

Subgroups — #20247378

Order 6016.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094001C212yesmaximal, complemented
2C2×D4×Dic47C212yesmaximal, complemented
3#15689037C212yesmaximal, complemented
4#15689035C211yesmaximal, characteristic, complemented
5#15689011C212yesmaximal, complemented
6#15689008C212yesmaximal, complemented
7#15689003C212yesmaximal, complemented
8#15688995C211yesmaximal, characteristic, complemented
9C47×#392C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C23×Dic47C2212yes—
13#13094001—28no—
14D4×Dic47—28no—
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2211yescharacteristic
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C4×Dic47C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C22×D4×C47C2212yes—
29C22×D4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2212yes—
31C2×C22⋊C4×C47C2211yescharacteristic
32#95×C47C2211yescharacteristic
33C24×C47C2312yes—
34C24×C47C2311yescharacteristic
35C2×D4×C47—24no—
36C2×D4×C47—24no—
37C2×D4×C47—24no—
38C2×D4×C47—24no—
39C2×D4×C47—41no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×Dic47—24no—
44C22×Dic47—24no—
45C22×Dic47—24no—
46C22×Dic47—42no—
47C22×Dic47—41no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C2×Dic94—24no—
53C2×Dic94—41no—
54C22⋊C4×C47—24no—
55C22⋊C4×C47—41no—
56C22⋊Dic47—22no—
57C22⋊Dic47—24no—
58C22⋊Dic47—24no—
59C22⋊Dic47—24no—
60C22⋊Dic47—24no—
61C4⋊Dic47D418yescomplemented
62Dic47⋊C4—24no—
63Dic47⋊C4—24no—
64C4×Dic47—24no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47#4112yes—
76C23×C47#4114yes—
77C23×C47C2411yescharacteristic
78D4×C47—216no—
79D4×C47—44no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47C2×D414yes—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—48no—
98C2×Dic47—44no—
99C2×Dic47C2×D414yes—
100C2×Dic47C2×D414yes—
101Dic94—44no—
102C22×C47—24no—
103C22×C47—24no—
104C22×C47—22no—
105C22×C47—24no—
106C22×C47—24no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—41no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47—41no—
114C22×C47C22×D412yes—
115C22×C47C2×#4111yescharacteristic
116C22×C47C2×#4112yes—
117C22×C47H(5,𝔽2)11yescharacteristic
118C22×C472−1+411yescharacteristic
119C4×C47—24no—
120C4×C47—41no—
121C4×C47—41no—
122Dic47—24no—
123Dic47—24no—
124Dic47—42no—
125Dic47—42no—
126#2463—471nomaximal, Sylow
127C2×C47—42no—
128C2×C47—44no—
129C2×C47#52512yes—
130C2×C47#53911yescharacteristic
131C2×C47D4211yescharacteristic
132C2×C47#54812yes—
133C2×C47#55111yescharacteristic
134C2×C22⋊Q8—472no—
135C2×C4×D4—472no—
136#394—472no—
137#393—471no—
138#392D4711yescharacteristic
139#388—472no—
140#387—472no—
141#386—472no—
142#385—471no—
143C47#246311yescharacteristic, complemented, Sylow
144C22×Q8—471no—
145C22×D4C2×D4712yes—
146C22×D4C2×D4711yescharacteristic
147C23×C4—471no—
148C23×C4—472no—
149C22⋊Q8—948no—
150C4×D4—948no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C22⋊C4—472no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—472no—
157C2×C22⋊C4—471no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4C2×D4712yes—
160C2×C22⋊C4C2×D4711yescharacteristic
161C2×C42—472no—
162#95—472no—
163#95—472no—
164#95—472no—
165#95—471no—
166#95C2×D4711yescharacteristic
167C24C22×D4712yes—
168C24C22×D4711yescharacteristic
169C2×Q8—944no—
170C2×Q8—1881no—
171C2×D4—24no—
172C2×D4—24no—
173C2×D4—24no—
174C2×D4—24no—
175C2×D4—41no—
176C22×C4—472no—
177C22×C4—472no—
178C22×C4—472no—
179C22×C4—472no—
180C22×C4—944no—
181C22×C4—944no—
182C22×C4—944no—
183C22×C4—1881no—
184C22×C4—1882no—
185C22×C4C22×D4711yescharacteristic
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4712yes—
188C4⋊C4—478no—
189C4⋊C4—944no—
190C4⋊C4—944no—
191C22⋊C4—24no—
192C22⋊C4—41no—
193C22⋊C4—944no—
194C22⋊C4—944no—
195C22⋊C4—944no—
196C22⋊C4—942no—
197C22⋊C4—944no—
198C42—944no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23#1062535214yes—
210C23#1062535212yes—
211C23C23×D4711yescharacteristic
212Q8—1884no—
213D4—216no—
214D4—44no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—474no—
222C2×C4—474no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—1884no—
234C2×C4—1888no—
235C2×C4D4×D4714yes—
236C22—24no—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—42no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22C2×D4×D4712yes—
249C22C2×#1062535212yes—
250C22C2×#1062535211yescharacteristic
251C22#1309406911yescharacteristic
252C22#1309407111yescharacteristic
253C4—24no—
254C4—41no—
255C4—41no—
256C4—944no—
257C4—944no—
258C4—1882no—
259C4—1882no—
260C2—44no—
261C2—42no—
262C2#1568962912yes—
263C2#1568971811yescharacteristic
264C2#1568975811yescharacteristic
265C2#1568977912yes—
266C2#1568980411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2463
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13094001C2semidirect
2. C2×D4×Dic47C2semidirect
3. #15689037C2semidirect
4. #15689035C2semidirect
5. #15689011C2semidirect
6. #15689008C2semidirect
7. #15689003C2semidirect
8. #15688995C2semidirect
61. C4⋊Dic47D4semidirect
143. C47#2463semidirect