Finite Group Databasebeta

← #20249172

Subgroups — #20249172

Order 6016.

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

normal subgroups only

This group has 526 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×#13094005C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
3#15689064C212yesmaximal, complemented
4#15689059C212yesmaximal, complemented
5#15689057C212yesmaximal, complemented
6#15689051C212yesmaximal, complemented
7#15689003C211yesmaximal, characteristic
8#15688998C211yesmaximal, characteristic, complemented
9#15688996C211yesmaximal, characteristic, complemented
10#15688984C211yesmaximal, characteristic, complemented
11C47×#386C211yesmaximal, characteristic
12C23×Dic47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14#13094005—24no—
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4—24no—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C23×C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C24×C47C2311yescharacteristic
39C2×D4×C47—22no—
40C2×D4×C47—22no—
41C2×D4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—42no—
44C22×C4×C47C2312yes—
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—22no—
48C22×Dic47—22no—
49C22×Dic47—22no—
50C22×Dic47—42no—
51C22×Dic47D414yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2312yes—
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2311yescharacteristic
58C22⋊C4×C47—22no—
59C22⋊C4×C47—42no—
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C22⋊Dic47—22no—
63C22⋊Dic47—22no—
64C22⋊Dic47—42no—
65C4⋊Dic47—42no—
66Dic47⋊C4—24no—
67Dic47⋊C4—24no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—42no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2×D412yes—
79C23×C47#4112yes—
80C23×C47#4112yes—
81C23×C47C2411yescharacteristic
82D4×C47—44no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—44no—
93C2×Dic47—28no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—44no—
109C2×Dic47C2×D412yes—
110C2×Dic47C2×D412yes—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—24no—
114C22×C47—24no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47—41no—
118C22×C47—42no—
119C22×C47—42no—
120C22×C47#12314yes—
121C22×C47C22×D411yescharacteristic
122C22×C47C2×#4111yescharacteristic
123C22×C47C2×#4111yescharacteristic
124C22×C47H(5,𝔽2)12yes—
125C22×C472−1+412yes—
126C4×C47—41no—
127C4×C47—42no—
128C4×C47—42no—
129Dic47—22no—
130Dic47—22no—
131Dic47—41no—
132Dic47—42no—
133Dic47—41no—
134Dic47—42no—
135#2623—471nomaximal, Sylow
136C2×C47—24no—
137C2×C47—81no—
138C2×C47C2×#12311yescharacteristic
139C2×C47#53511yescharacteristic
140C2×C47#53611yescharacteristic
141C2×C47#53912yes—
142C2×C47#53912yes—
143C2×#123—471no—
144C22×C4⋊C4—471no—
145#400—472no—
146#399—472no—
147#398—472no—
148#397—472no—
149#386—471no—
150#386D4711yescharacteristic
151#385—471no—
152#385—471no—
153#381—471no—
154C47#262311yescharacteristic, complemented, Sylow
155C22×D4C2×D4711yescharacteristic
156C23×C4—471no—
157C23×C4—471no—
158C23×C4C2×D4711yescharacteristic
159#123—944no—
160C2×C4⋊C4—472no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—471no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—472no—
165C2×C4⋊C4—472no—
166C2×C4⋊C4—944no—
167C2×C22⋊C4—471no—
168C2×C22⋊C4—471no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4C2×D4711yescharacteristic
173C2×C22⋊C4C2×D4712yes—
174#95—472no—
175#95—472no—
176#95—472no—
177#95—472no—
178#95—472no—
179#95C2×D4712yes—
180C24C22×D4711yescharacteristic
181C24C22×D4711yescharacteristic
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—474no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—471no—
191C22×C4—472no—
192C22×C4—472no—
193C22×C4—471no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4—942no—
197C22×C4—1882no—
198C22×C4C22×D4712yes—
199C22×C4C22×D4711yescharacteristic
200C22×C4C22×D4712yes—
201C4⋊C4—944no—
202C4⋊C4—944no—
203C4⋊C4—942no—
204C4⋊C4—942no—
205C4⋊C4—1882no—
206C4⋊C4—1882no—
207C22⋊C4—22no—
208C22⋊C4—42no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—942no—
213C22⋊C4—1882no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—22no—
220C23—22no—
221C23#1062535012yes—
222C23D4×D4712yes—
223C23#1062535212yes—
224C23C23×D4711yescharacteristic
225D4—44no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—472no—
237C2×C4—472no—
238C2×C4—948no—
239C2×C4—941no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—941no—
244C2×C4—941no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—1884no—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22#1309400614yes—
264C22C2×D4×D4711yescharacteristic
265C22C2×#1062535211yescharacteristic
266C22C2×#1062535011yescharacteristic
267C22#1309406912yes—
268C22#1309407112yes—
269C4—41no—
270C4—42no—
271C4—42no—
272C4—942no—
273C4—942no—
274C4—1882no—
275C4—1881no—
276C4—1881no—
277C4—1882no—
278C2—24no—
279C2—81no—
280C2C2×#1309400611yescharacteristic
281C2#1568968811yescharacteristic
282C2#1568969511yescharacteristic
283C2#1568971512yes—
284C2#1568971812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2623
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×Dic47⋊C4C2semidirect
3. #15689064C2semidirect
4. #15689059C2semidirect
5. #15689057C2semidirect
6. #15689051C2semidirect
8. #15688998C2semidirect
9. #15688996C2semidirect
10. #15688984C2semidirect
154. C47#2623semidirect