Finite Group Databasebeta

← #20250423

Subgroups — #20250423

Order 6016.

552 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689059C211yesmaximal, characteristic, complemented
2#15689050C212yesmaximal, complemented
3#15689045C212yesmaximal, complemented
4#15689016C212yesmaximal, complemented
5#15689015C212yesmaximal, complemented
6#15689012C212yesmaximal, complemented
7#15688978C212yesmaximal
8#15688978C211yesmaximal, characteristic
9C47×#397C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic, complemented
12C2×C4⋊Dic47C2212yescomplemented
13C2×Dic47⋊C4C2212yescomplemented
14C2×C22⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×C4×Dic47C2212yescomplemented
23C47⋊#95C2212yescomplemented
24C47⋊#95C2212yescomplemented
25C47⋊#95C2211yescharacteristic, complemented
26C2×C4⋊C4×C47C2211yescharacteristic, complemented
27C2×C22⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2211yescharacteristic
29#95×C47C2211yescharacteristic, complemented
30#95×C47C2212yescomplemented
31C24×C47C2311yescharacteristic
32C23×D47—22no—
33C23×D47—24no—
34C23×D47—41no—
35C23×D47—42no—
36C23×D47—41no—
37C23×D47C2312yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C4⋊C4×C47—41no—
46C22⋊C4×C47—24no—
47C22⋊C4×C47—41no—
48C22⋊Dic47—42no—
49C22⋊Dic47—41no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—42no—
53(C2×D47)⋊C4—42no—
54(C2×D47)⋊C4—42no—
55(C2×D47)⋊C4—42no—
56C4⋊Dic47—41no—
57C4⋊Dic47—42no—
58Dic47⋊C4—42no—
59C4×Dic47—42no—
60C23×C47—22no—
61C23×C47—21no—
62C23×C47—22no—
63C23×C47—21no—
64C23×C47#4112yes—
65C23×C47C2411yescharacteristic
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—44no—
73C22×D47—48no—
74C22×D47—48no—
75C22×D47—44no—
76C22×D47—44no—
77C22×D47#4114yes—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
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—
97C22×C47—22no—
98C22×C47—24no—
99C22×C47—42no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47C2×#4112yes—
103C22×C47C2×#4111yescharacteristic
104C22×C47H(5,𝔽2)11yescharacteristic
105C22×C47H(5,𝔽2)11yescharacteristic
106C22×C47H(5,𝔽2)12yes—
107C2×D47—24no—
108C2×D47—24no—
109C2×D47—24no—
110C2×D47—416no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C4×C47—42no—
116C4×C47—42no—
117C4×C47—41no—
118C4×C47—41no—
119Dic47—42no—
120Dic47—42no—
121Dic47—42no—
122#2735—471nomaximal, Sylow
123C2×C47—42no—
124C2×C47#53811yescharacteristic
125C2×C47#53812yes—
126C2×C47#55112yes—
127C2×C47#55111yescharacteristic
128C2×C47#56011yescharacteristic
129D47—44no—
130#399—471no—
131#397—472no—
132#397D4711yescharacteristic, complemented
133#396—472no—
134#388—472no—
135#388—472no—
136#388—472no—
137#379—471no—
138#379—472no—
139C47#273511yescharacteristic, complemented, Sylow
140C25—471no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4C2×D4711yescharacteristic, complemented
145C2×C22⋊C4—472no—
146C2×C22⋊C4—472no—
147C2×C22⋊C4—471no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4C2×D4712yes—
154C2×C22⋊C4C2×D4711yescharacteristic
155C2×C42—472no—
156#95—472no—
157#95—472no—
158#95—471no—
159#95C2×D4711yescharacteristic, complemented
160#95C2×D4712yescomplemented
161C24—472no—
162C24—944no—
163C24—942no—
164C24—1881no—
165C24—1882no—
166C24—1881no—
167C24C22×D4711yescharacteristic
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—472no—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C22×C4C22×D4712yes—
174C22×C4C22×D4711yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—1882no—
177C4⋊C4—1881no—
178C4⋊C4—1882no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—944no—
182C22⋊C4—944no—
183C22⋊C4—1882no—
184C22⋊C4—1882no—
185C22⋊C4—1882no—
186C22⋊C4—1882no—
187C22⋊C4—1882no—
188C22⋊C4—1881no—
189C42—1882no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—474no—
195C23—942no—
196C23—942no—
197C23—942no—
198C23—942no—
199C23—942no—
200C23—942no—
201C23—1888no—
202C23—1884no—
203C23—1884no—
204C23—1888no—
205C23—1884no—
206C23#1062535212yes—
207C23C23×D4711yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
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—
227C22—24no—
228C22—22no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—944no—
233C22—944no—
234C22—944no—
235C22—18816no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22—1882no—
240C22#41×D4712yes—
241C22C2×#1062535211yescharacteristic
242C22#1309406911yescharacteristic
243C22#1309407012yes—
244C22#1309407011yescharacteristic
245C4—42no—
246C4—41no—
247C4—41no—
248C4—42no—
249C4—1882no—
250C4—1882no—
251C4—1882no—
252C2—42no—
253C2—1884no—
254C2#1568971011yescharacteristic
255C2#1568971212yes—
256C2#1568979612yes—
257C2#1568980311yescharacteristic
258C2#1568986311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2735
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #15689059C2semidirect
2. #15689050C2semidirect
3. #15689045C2semidirect
4. #15689016C2semidirect
5. #15689015C2semidirect
6. #15689012C2semidirect
9. C47×#397C2semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×C4⋊Dic47C22semidirect
13. C2×Dic47⋊C4C22semidirect
22. C2×C4×Dic47C22semidirect
23. C47⋊#95C22semidirect
24. C47⋊#95C22semidirect
25. C47⋊#95C22semidirect
26. C2×C4⋊C4×C47C22semidirect
29. #95×C47C22semidirect
30. #95×C47C22semidirect
132. #397D47semidirect
139. C47#2735semidirect
144. C2×C4⋊C4C2×D47semidirect
159. #95C2×D47semidirect
160. #95C2×D47semidirect