Finite Group Databasebeta

← #20251713

Subgroups — #20251713

Order 6016.

582 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094008C211yesmaximal, characteristic
2C22×C4×Dic47C211yesmaximal, characteristic, complemented
3#15689013C212yesmaximal, complemented
4#15689012C212yesmaximal, complemented
5#15689010C212yesmaximal, complemented
6#15689009C212yesmaximal, complemented
7#15689002C211yesmaximal, characteristic
8#15689000C211yesmaximal, characteristic
9#15688995C211yesmaximal, characteristic, complemented
10#15688984C211yesmaximal, characteristic, complemented
11C47×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15#13094008—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×C4×Dic47—24no—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C23×C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47—22no—
40C22×C4×C47—24no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C22×Dic47—22no—
49C22×Dic47—22no—
50C22×Dic47—22no—
51C22×Dic47—24no—
52C22×Dic47D414yes—
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2312yes—
58C4⋊C4×C47—24no—
59C22⋊C4×C47—22no—
60C22⋊C4×C47—22no—
61C22⋊Dic47—22no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—24no—
66C4⋊Dic47—22no—
67C4⋊Dic47—22no—
68Dic47⋊C4—24no—
69C4×Dic47—24no—
70C4×Dic47—24no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47C2×D412yes—
74C23×C47#4112yes—
75C23×C47#4112yes—
76C23×C47C2411yescharacteristic
77C22×D47—21no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—21no—
82C2×C4×C47—28no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47#4114yes—
93C22⋊D47—44no—
94C2×Dic47—28no—
95C2×Dic47—28no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47C2×D412yes—
109C2×Dic47C2×D412yes—
110C2×Dic47#4114yes—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—24no—
114C22×C47—24no—
115C22×C47#12314yes—
116C22×C47C22×D411yescharacteristic
117C22×C47C2×#4112yes—
118C22×C47C2×#4112yes—
119C22×C47C2×#4111yescharacteristic
120C22×C47C2×#4111yescharacteristic
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—42no—
125C2×D47—42no—
126C4×C47—24no—
127C4×C47—41no—
128C4×C47—41no—
129C4×C47—42no—
130Dic47—22no—
131Dic47—22no—
132Dic47—24no—
133Dic47—41no—
134Dic47—42no—
135#2853—471nomaximal, Sylow
136C2×C47—24no—
137C2×C47C2×#12311yescharacteristic
138C2×C47#52511yescharacteristic
139C2×C47#52511yescharacteristic
140C2×C47#52912yes—
141C2×C47#52912yes—
142D47—81no—
143C2×#123—471no—
144C22×C42—471no—
145#388—472no—
146#388—472no—
147#387—472no—
148#387—472no—
149#386—471no—
150#386—471no—
151#385—471no—
152#385D4711yescharacteristic, complemented
153#381—471no—
154C47#285311yescharacteristic, complemented, Sylow
155C22×D4—471no—
156C23×C4—471no—
157C23×C4—471no—
158C23×C4C2×D4711yescharacteristic
159#123—944no—
160C2×C4⋊C4—471no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4C2×D4712yes—
164C2×C22⋊C4—471no—
165C2×C22⋊C4—471no—
166C2×C22⋊C4—471no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4C2×D4711yescharacteristic
170C2×C22⋊C4C2×D4711yescharacteristic
171C2×C42—472no—
172C2×C42—472no—
173C2×C42—944no—
174#95—472no—
175#95—472no—
176#95—472no—
177#95—472no—
178#95—472no—
179#95C2×D4712yes—
180C24—471no—
181C24C22×D4711yescharacteristic
182C2×D4—942no—
183C2×D4—942no—
184C2×D4—942no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—474no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—472no—
191C22×C4—472no—
192C22×C4—471no—
193C22×C4—944no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4—942no—
197C22×C4C22×D4712yes—
198C22×C4C22×D4711yescharacteristic
199C22×C4C22×D4711yescharacteristic
200C22×C4C22×D4712yes—
201C4⋊C4—24no—
202C4⋊C4—944no—
203C4⋊C4—942no—
204C4⋊C4—942no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—944no—
208C22⋊C4—942no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—944no—
212C42—944no—
213C42—944no—
214C23—22no—
215C23—22no—
216C23—941no—
217C23—942no—
218C23—942no—
219C23—941no—
220C23—941no—
221C23#1062535012yes—
222C23D4×D4712yes—
223C23#1062535412yes—
224C23C23×D4711yescharacteristic
225D4—1884no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—472no—
237C2×C4—472no—
238C2×C4—474no—
239C2×C4—948no—
240C2×C4—948no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—941no—
244C2×C4—941no—
245C2×C4—941no—
246C2×C4—941no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4—942no—
252C2×C4—941no—
253C2×C4#1062535214yes—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—1881no—
259C22—1881no—
260C22—1881no—
261C22—1882no—
262C22—1882no—
263C22#1309400914yes—
264C22C2×D4×D4711yescharacteristic
265C22#41×D4712yes—
266C22C2×#1062535212yes—
267C22C2×#1062535011yescharacteristic
268C22C2×#1062535411yescharacteristic
269C4—24no—
270C4—41no—
271C4—41no—
272C4—42no—
273C4—942no—
274C4—942no—
275C4—944no—
276C4—1881no—
277C4—1882no—
278C2—24no—
279C2—3761no—
280C2C2×#1309400911yescharacteristic
281C2#1568962911yescharacteristic
282C2#1568963111yescharacteristic
283C2#1568965312yes—
284C2#1568965912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2853
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic47C2semidirect
3. #15689013C2semidirect
4. #15689012C2semidirect
5. #15689010C2semidirect
6. #15689009C2semidirect
9. #15688995C2semidirect
10. #15688984C2semidirect
11. C47×#385C2semidirect
152. #385D47semidirect
154. C47#2853semidirect