Finite Group Databasebeta

← #20249282

Subgroups — #20249282

Order 6016.

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

normal subgroups only

This group has 562 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×#13094017C211yesmaximal, characteristic, complemented
2C2×D4×Dic47C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689046C212yesmaximal, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689037C212yesmaximal, complemented
8#15689003C212yesmaximal, complemented
9#15688995C212yesmaximal, complemented
10#15688987C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic
12C23×Dic47C2212yes—
13#13094017—24no—
14D4×Dic47—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C22×D4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C24×C47C2312yes—
39C2×D4×C47—24no—
40C2×D4×C47—24no—
41C2×D4×C47—22no—
42C2×D4×C47—42no—
43C2×D4×C47—42no—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—24no—
48C22×Dic47—42no—
49C22×Dic47—42no—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22⋊C4×C47—22no—
57C22⋊C4×C47—42no—
58C22⋊Dic47—24no—
59C22⋊Dic47—24no—
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C22⋊Dic47—42no—
63C22⋊Dic47—42no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4—42no—
69Dic47⋊C4—42no—
70C4×Dic47D414yescomplemented
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—21no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—21no—
81C23×C47—21no—
82C23×C47#4114yes—
83C23×C47C2411yescharacteristic
84D4×C47—28no—
85D4×C47—48no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47C2×D412yes—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—48no—
108C2×Dic47C2×D412yes—
109C2×Dic47C2×D412yes—
110C22×C47—24no—
111C22×C47—24no—
112C22×C47—24no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—41no—
118C22×C47—41no—
119C22×C47—41no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47C22×D411yescharacteristic
123C22×C47C2×#4112yes—
124C22×C47H(5,𝔽2)12yes—
125C22×C47H(5,𝔽2)11yescharacteristic
126C22×C472−1+411yescharacteristic
127C4×C47—22no—
128C4×C47—41no—
129C4×C47—42no—
130Dic47—22no—
131Dic47—22no—
132Dic47—41no—
133Dic47—42no—
134Dic47—41no—
135Dic47—42no—
136#2636—471nomaximal, Sylow
137C2×C47—44no—
138C2×C47—81no—
139C2×C47#52511yescharacteristic
140C2×C47#53511yescharacteristic
141C2×C47#53711yescharacteristic
142C2×C47#53812yes—
143C2×C47#53912yes—
144C2×#126—471no—
145C2×C4×D4—471no—
146#400—471no—
147#399—471no—
148#396—472no—
149#394—471no—
150#394—472no—
151#392D4711yescharacteristic
152#386—472no—
153#385—472no—
154#382—471no—
155C47#263611yescharacteristic, complemented, Sylow
156C22×D4C2×D4711yescharacteristic
157C22×D4C2×D4712yes—
158C23×C4—472no—
159#126—944no—
160C4×D4—944no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—471no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—471no—
165C2×C4⋊C4—472no—
166C2×C4⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—471no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—472no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4C2×D4711yescharacteristic
174C2×C22⋊C4C2×D4712yes—
175C2×C42—471no—
176#95—472no—
177#95—471no—
178#95—472no—
179#95—472no—
180#95C2×D4711yescharacteristic
181C24C22×D4711yescharacteristic
182C24C22×D4712yes—
183C2×D4—24no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—472no—
193C22×C4—472no—
194C22×C4—944no—
195C22×C4—1882no—
196C22×C4—1882no—
197C22×C4C22×D4712yes—
198C22×C4C22×D4711yescharacteristic
199C22×C4C22×D4711yescharacteristic
200C4⋊C4—942no—
201C4⋊C4—942no—
202C4⋊C4—942no—
203C4⋊C4—942no—
204C4⋊C4—1882no—
205C4⋊C4—1882no—
206C22⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—944no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—944no—
212C22⋊C4—1882no—
213C22⋊C4—1882no—
214C42—474no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23#1062535214yes—
227C23C23×D4711yescharacteristic
228D4—28no—
229D4—48no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—472no—
237C2×C4—472no—
238C2×C4—941no—
239C2×C4—942no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—941no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—1888no—
253C2×C4D4×D4712yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22C2×D4×D4711yescharacteristic
267C22C2×#1062535212yes—
268C22#1309406912yes—
269C22#1309406911yescharacteristic
270C22#1309407111yescharacteristic
271C4—22no—
272C4—41no—
273C4—42no—
274C4—942no—
275C4—942no—
276C4—1881no—
277C4—1882no—
278C4—1881no—
279C4—1882no—
280C2—44no—
281C2—81no—
282C2#1568962911yescharacteristic
283C2#1568968611yescharacteristic
284C2#1568970211yescharacteristic
285C2#1568970812yes—
286C2#1568971812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2636
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13094017C2semidirect
2. C2×D4×Dic47C2semidirect
3. #15689063C2semidirect
4. #15689059C2semidirect
5. #15689046C2semidirect
6. #15689037C2semidirect
7. #15689037C2semidirect
8. #15689003C2semidirect
9. #15688995C2semidirect
10. #15688987C2semidirect
70. C4×Dic47D4semidirect
155. C47#2636semidirect