Finite Group Databasebeta

← #20249608

Subgroups — #20249608

Order 6016.

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

normal subgroups only

This group has 796 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×#13094013C212yesmaximal, complemented
2C2×#13093994C212yesmaximal, complemented
3#15689041C212yesmaximal, complemented
4#15689033C212yesmaximal, complemented
5#15689032C211yesmaximal, characteristic, complemented
6#15689023C212yesmaximal, complemented
7#15689012C212yesmaximal, complemented
8#15688978C211yesmaximal, characteristic, complemented
9C47×#393C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C22×D188C2212yes—
12C22×D188C2212yes—
13C22×D188C2211yescharacteristic, complemented
14C22×C22⋊D47C2212yes—
15#13094013—28no—
16#13093994—28no—
17C2×Dic47⋊C4C2212yescomplemented
18C2×C22⋊Dic47C2211yescharacteristic
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yescomplemented
24C2×(C2×D47)⋊C4C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yescomplemented
26C2×C4×Dic47C2212yescomplemented
27C47⋊#95C2211yescharacteristic, complemented
28C22×Q8×C47C2211yescharacteristic, complemented
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2211yescharacteristic
31#95×C47C2212yescomplemented
32#95×C47C2211yescharacteristic, complemented
33C24×C47C2311yescharacteristic
34C23×D47—22no—
35C23×D47—24no—
36C23×D47—42no—
37C23×D47—41no—
38C23×D47—41no—
39C23×D47C2312yes—
40C23×D47C2312yes—
41C2×Q8×C47—24no—
42C2×Q8×C47—41no—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2312yes—
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—42no—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C2×D188—24no—
53C2×D188—24no—
54C2×D188—24no—
55C2×D188—42no—
56C2×D188—42no—
57C2×D188—42no—
58C2×D188—42no—
59C2×D188—41no—
60C22⋊C4×C47—24no—
61C22⋊C4×C47—41no—
62C22⋊Dic47—41no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—24no—
67(C2×D47)⋊C4—42no—
68(C2×D47)⋊C4—42no—
69(C2×D47)⋊C4D418yescomplemented
70Dic47⋊C4—42no—
71C4×Dic47—24no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—21no—
75C23×C47—22no—
76C23×C47#4112yes—
77C23×C47C2411yescharacteristic
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47—44no—
92C22×D47—48no—
93C22×D47—48no—
94C22×D47—44no—
95C22×D47—44no—
96C22×D47C2×D414yes—
97Q8×C47—44no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47C2×D414yes—
108C22⋊D47—48no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47C2×D414yes—
115D188—48no—
116D188—48no—
117D188—44no—
118C22×C47—22no—
119C22×C47—24no—
120C22×C47—42no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47C22×D412yes—
124C22×C47C2×#4111yescharacteristic
125C22×C47H(5,𝔽2)11yescharacteristic
126C22×C47H(5,𝔽2)11yescharacteristic
127C22×C47H(5,𝔽2)12yes—
128C2×D47—24no—
129C2×D47—24no—
130C2×D47—24no—
131C2×D47—416no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—42no—
141C2×D47—42no—
142C2×D47—42no—
143C4×C47—24no—
144C4×C47—42no—
145C4×C47—41no—
146C4×C47—41no—
147Dic47—24no—
148Dic47—42no—
149#2670—471nomaximal, Sylow
150C2×C47—42no—
151C2×C47#53512yes—
152C2×C47#53811yescharacteristic
153C2×C47D4211yescharacteristic
154C2×C47#54612yes—
155C2×C47H(3,𝔽4)11yescharacteristic
156D47—44no—
157D47—82no—
158C2×#124—472no—
159C2×#120—472no—
160#394—472no—
161#393D4711yescharacteristic, complemented
162#392—471no—
163#392—472no—
164#390—472no—
165#388—472no—
166#379—471no—
167C47#267011yescharacteristic, complemented, Sylow
168C25—471no—
169C22×Q8C2×D4711yescharacteristic, complemented
170C22×D4—472no—
171C22×D4—472no—
172C22×D4—472no—
173C22×D4—471no—
174#124—948no—
175#120—948no—
176C2×C4⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—471no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4C2×D4712yes—
186C2×C22⋊C4C2×D4711yescharacteristic
187C2×C42—472no—
188#95—471no—
189#95C2×D4712yescomplemented
190#95C2×D4711yescharacteristic, complemented
191C24—472no—
192C24—472no—
193C24—944no—
194C24—942no—
195C24—1881no—
196C24—1881no—
197C24—1882no—
198C24C22×D4711yescharacteristic
199C2×Q8—24no—
200C2×Q8—41no—
201C2×D4—944no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—944no—
205C2×D4—944no—
206C2×D4—1882no—
207C2×D4—1881no—
208C2×D4—1882no—
209C2×D4—1882no—
210C2×D4—1882no—
211C2×D4—1882no—
212C22×C4—472no—
213C22×C4—472no—
214C22×C4C22×D4711yescharacteristic
215C22×C4C22×D4712yes—
216C22×C4C22×D4711yescharacteristic
217C22×C4C22×D4712yes—
218C4⋊C4—1882no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—478no—
222C22⋊C4—944no—
223C22⋊C4—944no—
224C22⋊C4—944no—
225C22⋊C4—944no—
226C22⋊C4—1882no—
227C22⋊C4—1882no—
228C22⋊C4—1881no—
229C42—944no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—474no—
235C23—942no—
236C23—942no—
237C23—942no—
238C23—942no—
239C23—942no—
240C23—942no—
241C23—942no—
242C23—942no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—942no—
247C23—942no—
248C23—1888no—
249C23—1884no—
250C23—1884no—
251C23—1888no—
252C23—1884no—
253C23#1062535412yes—
254C23C23×D4711yescharacteristic
255Q8—44no—
256D4—1888no—
257D4—1888no—
258D4—1884no—
259D4—1888no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—474no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—942no—
275C2×C4D4×D4714yes—
276C22—24no—
277C22—22no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22—944no—
282C22—944no—
283C22—944no—
284C22—18816no—
285C22—1882no—
286C22—1882no—
287C22—1882no—
288C22—1882no—
289C22—1882no—
290C22—1882no—
291C22—1882no—
292C22—1882no—
293C22—1882no—
294C22—1882no—
295C22—1882no—
296C22C2×D4×D4712yes—
297C22C2×#1062535411yescharacteristic
298C22#1309406911yescharacteristic
299C22#1309407012yes—
300C22#1309407011yescharacteristic
301C4—24no—
302C4—41no—
303C4—41no—
304C4—42no—
305C4—944no—
306C4—1882no—
307C2—42no—
308C2—3762no—
309C2—1884no—
310C2#1568969112yes—
311C2#1568971311yescharacteristic
312C2#1568975511yescharacteristic
313C2#1568976412yes—
314C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2670
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094013C2semidirect
2. C2×#13093994C2semidirect
3. #15689041C2semidirect
4. #15689033C2semidirect
5. #15689032C2semidirect
6. #15689023C2semidirect
7. #15689012C2semidirect
8. #15688978C2semidirect
9. C47×#393C2semidirect
13. C22×D188C22semidirect
17. C2×Dic47⋊C4C22semidirect
23. C2×(C2×D47)⋊C4C22semidirect
24. C2×(C2×D47)⋊C4C22semidirect
25. C2×(C2×D47)⋊C4C22semidirect
26. C2×C4×Dic47C22semidirect
27. C47⋊#95C22semidirect
28. C22×Q8×C47C22semidirect
31. #95×C47C22semidirect
32. #95×C47C22semidirect
69. (C2×D47)⋊C4D4semidirect
161. #393D47semidirect
167. C47#2670semidirect
169. C22×Q8C2×D47semidirect
189. #95C2×D47semidirect
190. #95C2×D47semidirect