Finite Group Databasebeta

← #20248969

Subgroups — #20248969

Order 6016.

604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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×D4×Dic47C212yesmaximal, complemented
2#15689048C211yesmaximal, characteristic, complemented
3#15689037C212yesmaximal, complemented
4#15689017C212yesmaximal, complemented
5#15689010C212yesmaximal, complemented
6#15689003C212yesmaximal, complemented
7#15688998C212yesmaximal, complemented
8#15688984C211yesmaximal, characteristic, complemented
9C47×#392C211yesmaximal, characteristic
10C23×Dic47C2212yes—
11C23×Dic47C2211yescharacteristic
12D4×Dic47—28no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2212yes—
21C2×C4×Dic47C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C22×D4×C47C2212yes—
28C22×D4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2211yescharacteristic
31#95×C47C2211yescharacteristic
32C24×C47C2311yescharacteristic
33C24×C47C2312yes—
34C2×D4×C47—24no—
35C2×D4×C47—24no—
36C2×D4×C47—24no—
37C2×D4×C47—24no—
38C2×D4×C47—41no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×Dic47—24no—
43C22×Dic47—41no—
44C22×Dic47—41no—
45C22×Dic47—42no—
46C22×Dic47—42no—
47C22×Dic47D414yescomplemented
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C22⋊C4×C47—24no—
53C22⋊C4×C47—41no—
54C22⋊Dic47—24no—
55C22⋊Dic47—24no—
56C22⋊Dic47—24no—
57C22⋊Dic47—41no—
58C22⋊Dic47—42no—
59C4⋊Dic47—24no—
60C4⋊Dic47—41no—
61Dic47⋊C4—24no—
62C4×Dic47—24no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—21no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47C2×D412yes—
74C23×C47#4114yes—
75C23×C47C2411yescharacteristic
76D4×C47—216no—
77D4×C47—44no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47#4114yes—
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—22no—
95C2×Dic47—22no—
96C2×Dic47—44no—
97C2×Dic47—48no—
98C2×Dic47C2×D414yes—
99C22×C47—24no—
100C22×C47—24no—
101C22×C47—22no—
102C22×C47—24no—
103C22×C47—24no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—41no—
111C22×C47C22×D411yescharacteristic
112C22×C47C2×#4112yes—
113C22×C47C2×#4112yes—
114C22×C47H(5,𝔽2)11yescharacteristic
115C22×C47H(5,𝔽2)11yescharacteristic
116C4×C47—24no—
117C4×C47—41no—
118C4×C47—41no—
119Dic47—24no—
120Dic47—42no—
121Dic47—42no—
122Dic47—42no—
123#2600—471nomaximal, Sylow
124C2×C47—42no—
125C2×C47—44no—
126C2×C47#52512yes—
127C2×C47#53411yescharacteristic
128C2×C47#55111yescharacteristic
129C2×C47#55312yes—
130C2×C47#55911yescharacteristic
131C2×C4×D4—472no—
132#397—471no—
133#394—472no—
134#392D4711yescharacteristic
135#388—472no—
136#387—472no—
137#386—472no—
138#385—472no—
139#381—471no—
140C47#260011yescharacteristic, complemented, Sylow
141C22×D4C2×D4712yes—
142C22×D4C2×D4711yescharacteristic
143C23×C4—471no—
144C23×C4—472no—
145C4×D4—948no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—471no—
153C2×C22⋊C4—472no—
154C2×C22⋊C4C2×D4712yes—
155C2×C22⋊C4C2×D4711yescharacteristic
156C2×C42—472no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95—471no—
162#95C2×D4711yescharacteristic
163C24C22×D4711yescharacteristic
164C24C22×D4712yes—
165C2×D4—24no—
166C2×D4—24no—
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—41no—
170C22×C4—472no—
171C22×C4—474no—
172C22×C4—472no—
173C22×C4—472no—
174C22×C4—472no—
175C22×C4—944no—
176C22×C4—1881no—
177C22×C4—1882no—
178C22×C4—1881no—
179C22×C4—1882no—
180C22×C4C22×D4711yescharacteristic
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4712yes—
183C4⋊C4—944no—
184C4⋊C4—944no—
185C4⋊C4—1881no—
186C22⋊C4—24no—
187C22⋊C4—41no—
188C22⋊C4—944no—
189C22⋊C4—944no—
190C22⋊C4—944no—
191C22⋊C4—1881no—
192C22⋊C4—1882no—
193C42—944no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23D4×D4712yes—
205C23#1062535214yes—
206C23C23×D4711yescharacteristic
207D4—216no—
208D4—44no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—474no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—1884no—
228C2×C4—1888no—
229C2×C4#1062535214yes—
230C22—24no—
231C22—24no—
232C22—24no—
233C22—24no—
234C22—22no—
235C22—41no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22C2×D4×D4711yescharacteristic
243C22C2×#1062535212yes—
244C22C2×#1062535212yes—
245C22#1309406911yescharacteristic
246C22#1309407011yescharacteristic
247C4—24no—
248C4—41no—
249C4—41no—
250C4—944no—
251C4—1882no—
252C4—1882no—
253C4—1882no—
254C2—44no—
255C2—42no—
256C2#1568962912yes—
257C2#1568968111yescharacteristic
258C2#1568980411yescharacteristic
259C2#1568982512yes—
260C2#1568985911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2600
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic47C2semidirect
2. #15689048C2semidirect
3. #15689037C2semidirect
4. #15689017C2semidirect
5. #15689010C2semidirect
6. #15689003C2semidirect
7. #15688998C2semidirect
8. #15688984C2semidirect
47. C22×Dic47D4semidirect
140. C47#2600semidirect