Finite Group Databasebeta

← #20249544

Subgroups — #20249544

Order 6016.

498 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13094006C211yesmaximal, characteristic
2C2×#13094000C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689052C212yesmaximal, complemented
6#15689042C211yesmaximal, characteristic, complemented
7#15689038C212yesmaximal
8#15689020C212yesmaximal, complemented
9#15689011C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14#13094006—24no—
15#13094000—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×C4×Dic47C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—42no—
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2312yes—
52C2×C4×D47—42no—
53C2×C4×D47D414yes—
54C22⋊C4×C47—22no—
55C22⋊C4×C47—42no—
56C22⋊Dic47—22no—
57C22⋊Dic47—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—24no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—24no—
65Dic47⋊C4—24no—
66Dic47⋊C4—42no—
67C4×Dic47—42no—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47C2411yescharacteristic
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—21no—
77C22×D47—21no—
78C22×D47C2×D412yes—
79Q8×C47—44no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D412yes—
90C22⋊D47—44no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47C2×D412yes—
103C2×Dic47#4114yes—
104C4×D47—44no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47C22×D411yescharacteristic
111C22×C47C2×#4112yes—
112C22×C47H(5,𝔽2)12yes—
113C22×C472−1+411yescharacteristic
114C22×C472−1+411yescharacteristic
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—22no—
118C2×D47—42no—
119C2×D47—42no—
120C4×C47—22no—
121C4×C47—41no—
122C4×C47—42no—
123C4×C47—42no—
124Dic47—22no—
125Dic47—24no—
126Dic47—42no—
127Dic47—41no—
128Dic47—41no—
129#2663—471nomaximal, Sylow
130C2×C47—81no—
131C2×C47#53211yescharacteristic
132C2×C47#53411yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#53912yes—
135C2×C47#54212yes—
136D47—42no—
137C2×#123—471no—
138C2×C22⋊Q8—471no—
139#400—471no—
140#399—471no—
141#397—472no—
142#395—471no—
143#394—472no—
144#393D4711yescharacteristic, complemented
145#389—472no—
146#388—472no—
147C4×C22⋊C4—471no—
148C47#266311yescharacteristic, complemented, Sylow
149C22×Q8C2×D4711yescharacteristic
150C22×D4—471no—
151C23×C4—471no—
152#123—944no—
153C22⋊Q8—944no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4—471no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—472no—
160C2×C22⋊C4—471no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—471no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4C2×D4712yes—
167C2×C42—472no—
168#95—471no—
169#95—472no—
170#95—472no—
171#95—472no—
172#95C2×D4711yescharacteristic
173#95C2×D4712yes—
174C24—471no—
175C24C22×D4711yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—942no—
179C2×D4—1882no—
180C22×C4—472no—
181C22×C4—471no—
182C22×C4—474no—
183C22×C4—471no—
184C22×C4—472no—
185C22×C4—471no—
186C22×C4—1882no—
187C22×C4C22×D4712yes—
188C22×C4C22×D4712yes—
189C22×C4C22×D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—944no—
192C4⋊C4—944no—
193C4⋊C4—942no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—1882no—
197C22⋊C4—22no—
198C22⋊C4—42no—
199C22⋊C4—944no—
200C22⋊C4—944no—
201C22⋊C4—942no—
202C22⋊C4—944no—
203C22⋊C4—942no—
204C42—1882no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—472no—
211C23—942no—
212C23—942no—
213C23—941no—
214C23—941no—
215C23C23×D4711yescharacteristic
216Q8—44no—
217D4—1884no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—472no—
228C2×C4—474no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—941no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—1884no—
241C2×C4D4×D4712yes—
242C22—42no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—942no—
248C22—942no—
249C22—942no—
250C22—1882no—
251C22—1882no—
252C22C2×D4×D4711yescharacteristic
253C22#41×D4712yes—
254C22#1309406912yes—
255C22#1309407111yescharacteristic
256C22#1309407211yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—942no—
262C4—944no—
263C4—1882no—
264C4—1881no—
265C4—1881no—
266C2—81no—
267C2—1882no—
268C2#1568967211yescharacteristic
269C2#1568968311yescharacteristic
270C2#1568969611yescharacteristic
271C2#1568971912yes—
272C2#1568973712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2663
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×#13094000C2semidirect
3. #15689063C2semidirect
4. #15689059C2semidirect
5. #15689052C2semidirect
6. #15689042C2semidirect
8. #15689020C2semidirect
9. #15689011C2semidirect
10. #15688970C2semidirect
11. C47×#393C2semidirect
144. #393D47semidirect
148. C47#2663semidirect