Finite Group Databasebeta

← #20249124

Subgroups — #20249124

Order 6016.

824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13093992C212yesmaximal, complemented
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
3#15689049C212yesmaximal, complemented
4#15689039C214yesmaximal, complemented
5#15689031C212yesmaximal, complemented
6#15689003C212yesmaximal, complemented
7#15688983C211yesmaximal, characteristic, complemented
8C2×#121×C47C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic
10C22×C22⋊D47C2214yes—
11C23×Dic47C2211yescharacteristic
12#13093992—28no—
13C2×C4⋊Dic47C2212yescomplemented
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2214yescomplemented
16C2×(C2×D47)⋊C4—24no—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2214yes—
20C47⋊#95C2212yescomplemented
21C47⋊#95C2214yescomplemented
22C22×D4×C47C2212yes—
23C22×D4×C47C2211yescharacteristic, complemented
24C23×C4×C47C2211yescharacteristic
25#121×C47—24no—
26C2×C4⋊C4×C47C2211yescharacteristic, complemented
27C2×C22⋊C4×C47C2212yescomplemented
28C24×C47C2312yes—
29C24×C47C2311yescharacteristic
30C23×D47—22no—
31C23×D47—22no—
32C23×D47—42no—
33C23×D47—42no—
34C23×D47D414yescomplemented
35C23×D47C2312yes—
36C2×D4×C47—24no—
37C2×D4×C47—24no—
38C2×D4×C47—24no—
39C2×D4×C47—22no—
40C2×D4×C47—42no—
41C22×C4×C47—42no—
42C22×C4×C47D414yescomplemented
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—28no—
47C2×C22⋊D47—44no—
48C2×C22⋊D47—44no—
49C22×Dic47—22no—
50C22×Dic47—42no—
51C22×Dic47C2312yes—
52C22×Dic47C2314yes—
53C4⋊C4×C47—22no—
54C22⋊C4×C47—24no—
55C22⋊Dic47—24no—
56C22⋊Dic47—44no—
57(C2×D47)⋊C4—28no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—24no—
60C4⋊Dic47—42no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—24no—
67C23×C47—24no—
68C23×C47C2×D412yes—
69C23×C47C2×D412yes—
70C23×C47#4112yes—
71C23×C47C2411yescharacteristic
72C22×D47—28no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—24no—
76C22×D47—24no—
77C22×D47—48no—
78C22×D47—44no—
79C22×D47—44no—
80C22×D47—48no—
81C22×D47C2×D414yes—
82D4×C47—44no—
83D4×C47—48no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—44no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C22⋊D47—416no—
93C2×Dic47—22no—
94C2×Dic47—24no—
95C2×Dic47—24no—
96C2×Dic47—24no—
97C2×Dic47—24no—
98C2×Dic47—44no—
99C22×C47—22no—
100C22×C47—24no—
101C22×C47—22no—
102C22×C47—24no—
103C22×C47—42no—
104C22×C47—44no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—44no—
108C22×C47#12114yes—
109C22×C47C22×D411yescharacteristic
110C22×C47C22×D411yescharacteristic
111C22×C47C2×#4111yescharacteristic
112C22×C47H(5,𝔽2)12yes—
113C22×C47H(5,𝔽2)12yes—
114C2×D47—24no—
115C2×D47—28no—
116C2×D47—416no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—44no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—42no—
123Dic47—44no—
124Dic47—42no—
125#2617—471nomaximal, Sylow
126C2×C47—24no—
127C2×C47—82no—
128C2×C47C2×#12111yescharacteristic
129C2×C47#53412yes—
130C2×C47#53411yescharacteristic
131C2×C47#53511yescharacteristic
132C2×C47#53812yes—
133D47—44no—
134C2×#121D4711yescharacteristic, complemented
135C2×#120—472no—
136C22×C22⋊C4—471no—
137#397—472no—
138#394—474no—
139#392—472no—
140#386—472no—
141#380—471no—
142C47#261711yescharacteristic, complemented, Sylow
143C25—471no—
144C22×D4—474no—
145C22×D4C2×D4712yes—
146C22×D4C2×D4711yescharacteristic, complemented
147C23×C4—471no—
148C23×C4C2×D4711yescharacteristic
149#121—24no—
150#120—948no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4C2×D4711yescharacteristic, complemented
153C2×C22⋊C4—472no—
154C2×C22⋊C4—472no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—474no—
157C2×C22⋊C4—474no—
158C2×C22⋊C4—944no—
159C2×C22⋊C4C2×D4712yescomplemented
160#95—472no—
161#95—474no—
162C24—472no—
163C24—474no—
164C24—942no—
165C24—942no—
166C24—1882no—
167C24—1882no—
168C24C22×D4712yes—
169C24C22×D4711yescharacteristic
170C2×D4—24no—
171C2×D4—24no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—948no—
176C2×D4—1884no—
177C2×D4—1884no—
178C22×C4—42no—
179C22×C4—472no—
180C22×C4—474no—
181C22×C4—942no—
182C22×C4—1882no—
183C22×C4C22⋊D4714yescomplemented
184C22×C4C22×D4712yes—
185C22×C4C22×D4711yescharacteristic
186C22×C4C22×D4711yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—1882no—
189C22⋊C4—24no—
190C22⋊C4—948no—
191C22⋊C4—944no—
192C22⋊C4—944no—
193C22⋊C4—944no—
194C22⋊C4—1884no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—24no—
201C23—24no—
202C23—474no—
203C23—948no—
204C23—942no—
205C23—942no—
206C23—944no—
207C23—944no—
208C23—1888no—
209C23—1884no—
210C23—1884no—
211C23—1888no—
212C23D4×D4712yes—
213C23#1062535212yes—
214C23C2×C22⋊D4712yes—
215C23C23×D4711yescharacteristic
216D4—44no—
217D4—48no—
218D4—18816no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—44no—
225C2×C4—944no—
226C2×C4—942no—
227C2×C4—944no—
228C2×C4—944no—
229C2×C4—944no—
230C2×C4—1884no—
231C2×C4C2×C22⋊D4712yes—
232C2×C4C2×C22⋊D4712yes—
233C22—24no—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—42no—
238C22—44no—
239C22—42no—
240C22—42no—
241C22—44no—
242C22—944no—
243C22—948no—
244C22—18816no—
245C22—1882no—
246C22—1882no—
247C22—1884no—
248C22#1309399514yes—
249C22C2×D4×D4711yescharacteristic
250C22C22×C22⋊D4711yescharacteristic
251C22C2×#1062535211yescharacteristic
252C22#1309406912yes—
253C22#1309407012yes—
254C4—22no—
255C4—22no—
256C4—42no—
257C4—1884no—
258C4—1882no—
259C2—24no—
260C2—82no—
261C2—1884no—
262C2C2×#1309399511yescharacteristic
263C2#1568968112yes—
264C2#1568968211yescharacteristic
265C2#1568968711yescharacteristic
266C2#1568971012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2617
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13093992C2semidirect
2. C22×(C2×D47)⋊C4C2semidirect
3. #15689049C2semidirect
4. #15689039C2semidirect
5. #15689031C2semidirect
6. #15689003C2semidirect
7. #15688983C2semidirect
8. C2×#121×C47C2semidirect
13. C2×C4⋊Dic47C22semidirect
15. C2×C22⋊Dic47C22semidirect
20. C47⋊#95C22semidirect
21. C47⋊#95C22semidirect
23. C22×D4×C47C22semidirect
26. C2×C4⋊C4×C47C22semidirect
27. C2×C22⋊C4×C47C22semidirect
34. C23×D47D4semidirect
42. C22×C4×C47D4semidirect
134. C2×#121D47semidirect
142. C47#2617semidirect
146. C22×D4C2×D47semidirect
152. C2×C4⋊C4C2×D47semidirect
159. C2×C22⋊C4C2×D47semidirect
183. C22×C4C22⋊D47semidirect