Finite Group Databasebeta

← #20249255

Subgroups — #20249255

Order 6016.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094014C211yesmaximal, characteristic, complemented
2C2×D4×Dic47C211yesmaximal, characteristic
3#15689059C212yesmaximal, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689053C211yesmaximal, characteristic, complemented
6#15689051C212yesmaximal, complemented
7#15689037C211yesmaximal, characteristic
8#15688998C212yesmaximal, complemented
9#15688995C212yesmaximal, complemented
10#15688990C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic
12C23×Dic47C2212yes—
13#13094014—24no—
14D4×Dic47—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C2×D4×C47—24no—
39C2×D4×C47—22no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×Dic47—24no—
45C22×Dic47—42no—
46C22×Dic47—42no—
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C4⋊C4×C47—22no—
54C22⋊C4×C47—24no—
55C22⋊C4×C47—42no—
56C22⋊Dic47—24no—
57C22⋊Dic47—24no—
58C22⋊Dic47—42no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—42no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—42no—
67C4×Dic47D414yes—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47#4114yes—
75C23×C47C2411yescharacteristic
76D4×C47—28no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D412yes—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—48no—
102C2×Dic47C2×D412yes—
103C2×Dic47C2×D412yes—
104C22×C47—24no—
105C22×C47—24no—
106C22×C47—24no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47C22×D411yescharacteristic
112C22×C47C2×#4112yes—
113C22×C47H(5,𝔽2)11yescharacteristic
114C22×C47H(5,𝔽2)11yescharacteristic
115C22×C472−1+412yes—
116C4×C47—22no—
117C4×C47—41no—
118C4×C47—41no—
119C4×C47—42no—
120Dic47—22no—
121Dic47—22no—
122Dic47—41no—
123Dic47—41no—
124Dic47—42no—
125Dic47—42no—
126#2633—471nomaximal, Sylow
127C2×C47—44no—
128C2×C47#52511yescharacteristic
129C2×C47#53511yescharacteristic
130C2×C47#53611yescharacteristic
131C2×C47#53912yes—
132C2×C47#53912yes—
133C2×#125—471no—
134C2×C4×D4—471no—
135#399—472no—
136#398—471no—
137#398—471no—
138#397—472no—
139#394—471no—
140#394D4711yescharacteristic
141#385—472no—
142#385—472no—
143#383—471no—
144C47#263311yescharacteristic, complemented, Sylow
145C22×D4C2×D4711yescharacteristic
146C23×C4—472no—
147#125—944no—
148C4×D4—944no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—471no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—471no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4C2×D4711yescharacteristic
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4C2×D4712yes—
162C2×C22⋊C4C2×D4712yes—
163C2×C42—471no—
164#95—472no—
165#95—471no—
166#95—472no—
167#95—472no—
168#95—472no—
169#95C2×D4711yescharacteristic
170C24C22×D4712yes—
171C2×D4—24no—
172C2×D4—22no—
173C22×C4—471no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—471no—
177C22×C4—472no—
178C22×C4—471no—
179C22×C4—944no—
180C22×C4—1882no—
181C22×C4—1882no—
182C22×C4C22×D4712yes—
183C22×C4C22×D4711yescharacteristic
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4711yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—944no—
198C22⋊C4—944no—
199C22⋊C4—1882no—
200C42—474no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#1062535214yes—
208C23C23×D4711yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—472no—
220C2×C4—472no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—941no—
226C2×C4—941no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—941no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—1888no—
236C2×C4D4×D4712yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D4711yescharacteristic
245C22C2×#1062535212yes—
246C22#1309406911yescharacteristic
247C22#1309407011yescharacteristic
248C22#1309407112yes—
249C4—22no—
250C4—41no—
251C4—41no—
252C4—42no—
253C4—942no—
254C4—942no—
255C4—1881no—
256C4—1882no—
257C4—1881no—
258C4—1882no—
259C2—44no—
260C2#1568962911yescharacteristic
261C2#1568968911yescharacteristic
262C2#1568969311yescharacteristic
263C2#1568971712yes—
264C2#1568971812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2633
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094014C2semidirect
3. #15689059C2semidirect
4. #15689055C2semidirect
5. #15689053C2semidirect
6. #15689051C2semidirect
8. #15688998C2semidirect
9. #15688995C2semidirect
10. #15688990C2semidirect
144. C47#2633semidirect