Finite Group Databasebeta

← #20249721

Subgroups — #20249721

Order 6016.

1000 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13093994C212yesmaximal, complemented
2C2×#13093994C212yesmaximal, complemented
3C2×#13093992C212yesmaximal, complemented
4#15689041C212yesmaximal, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689038C212yesmaximal, complemented
7#15689024C211yesmaximal, characteristic, complemented
8#15689023C212yesmaximal, complemented
9C47×#394C211yesmaximal, characteristic, complemented
10C24×D47C2212yescomplemented
11C22×D188C2211yescharacteristic
12C22×D188C2212yes—
13C22×D188C2211yescharacteristic
14C22×C22⋊D47C2212yes—
15C22×C22⋊D47C2212yes—
16#13093994—28no—
17#13093994—28no—
18#13093992—28no—
19C2×Dic47⋊C4C2212yescomplemented
20C2×C22⋊Dic47C2212yescomplemented
21C2×(C2×D47)⋊C4C2212yescomplemented
22C2×(C2×D47)⋊C4C2212yescomplemented
23C2×(C2×D47)⋊C4C2212yescomplemented
24C2×(C2×D47)⋊C4C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yescomplemented
26C2×(C2×D47)⋊C4C2212yescomplemented
27C2×C4×Dic47C2211yescharacteristic, complemented
28C47⋊#95C2211yescharacteristic, complemented
29C22×D4×C47C2211yescharacteristic
30C2×C4⋊C4×C47C2211yescharacteristic, complemented
31C2×C22⋊C4×C47C2212yescomplemented
32C2×C22⋊C4×C47C2212yescomplemented
33#95×C47C2211yescharacteristic, complemented
34C24×C47C2312yes—
35C23×D47—24no—
36C23×D47—24no—
37C23×D47—24no—
38C23×D47—42no—
39C23×D47—42no—
40C23×D47—42no—
41C23×D47—42no—
42C23×D47C2312yes—
43C23×D47C2312yes—
44C2×D4×C47—24no—
45C2×D4×C47—41no—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—24no—
51C2×C22⋊D47—24no—
52C2×C22⋊D47—42no—
53C2×C22⋊D47—42no—
54C2×C22⋊D47—42no—
55C2×C22⋊D47D418yescomplemented
56C22×Dic47C2312yes—
57C22×Dic47C2312yes—
58C2×D188—24no—
59C2×D188—24no—
60C2×D188—24no—
61C2×D188—41no—
62C2×D188—41no—
63C2×D188—42no—
64C2×D188—41no—
65C2×D188D414yescomplemented
66C4⋊C4×C47—41no—
67C22⋊C4×C47—24no—
68C22⋊C4×C47—24no—
69C22⋊Dic47—24no—
70(C2×D47)⋊C4—24no—
71(C2×D47)⋊C4—24no—
72(C2×D47)⋊C4—24no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—24no—
75(C2×D47)⋊C4—24no—
76Dic47⋊C4—42no—
77C4×Dic47—41no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47C2×D414yes—
85C23×C47C2411yescharacteristic
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47—22no—
92C22×D47—22no—
93C22×D47—22no—
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—48no—
99C22×D47—48no—
100C22×D47—48no—
101C22×D47—48no—
102C22×D47—48no—
103C22×D47—48no—
104C22×D47—48no—
105C22×D47C2×D414yes—
106C22×D47C2×D414yes—
107D4×C47—44no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D412yes—
118C22⋊D47—48no—
119C22⋊D47—48no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—22no—
125C2×Dic47C2×D414yes—
126D188—44no—
127D188—44no—
128D188—48no—
129C22×C47—24no—
130C22×C47—24no—
131C22×C47—24no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47—42no—
135C22×C47—42no—
136C22×C47C22×D411yescharacteristic
137C22×C47C22×D412yes—
138C22×C47H(5,𝔽2)11yescharacteristic
139C22×C47H(5,𝔽2)11yescharacteristic
140C22×C47H(5,𝔽2)12yes—
141C2×D47—24no—
142C2×D47—24no—
143C2×D47—24no—
144C2×D47—24no—
145C2×D47—24no—
146C2×D47—24no—
147C2×D47—432no—
148C2×D47—42no—
149C2×D47—42no—
150C2×D47—42no—
151C2×D47—42no—
152C2×D47—42no—
153C2×D47—42no—
154C2×D47—42no—
155C2×D47—42no—
156C4×C47—22no—
157C4×C47—41no—
158C4×C47—42no—
159C4×C47—41no—
160Dic47—24no—
161Dic47—42no—
162#2679—471nomaximal, Sylow
163C2×C47—44no—
164C2×C47#53411yescharacteristic
165C2×C47#53412yes—
166C2×C47D4211yescharacteristic
167C2×C47D4212yes—
168C2×C47H(3,𝔽4)11yescharacteristic
169D47—44no—
170D47—44no—
171C2×#120—472no—
172C2×#120—472no—
173C2×#120—472no—
174#394—471no—
175#394—472no—
176#394—472no—
177#394D4711yescharacteristic, complemented
178#390—471no—
179#390—472no—
180C47#267911yescharacteristic, complemented, Sylow
181C25—472no—
182C22×D4—472no—
183C22×D4—472no—
184C22×D4—471no—
185C22×D4—471no—
186C22×D4—472no—
187C22×D4C2×D4711yescharacteristic
188#120—948no—
189#120—948no—
190#120—948no—
191C2×C4⋊C4—472no—
192C2×C4⋊C4C2×D4711yescharacteristic, complemented
193C2×C22⋊C4—472no—
194C2×C22⋊C4—472no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—472no—
197C2×C22⋊C4—472no—
198C2×C22⋊C4—472no—
199C2×C22⋊C4—472no—
200C2×C22⋊C4C2×D4712yescomplemented
201C2×C22⋊C4C2×D4712yescomplemented
202C2×C42—471no—
203#95—471no—
204#95C2×D4711yescharacteristic, complemented
205C24—472no—
206C24—472no—
207C24—944no—
208C24—944no—
209C24—944no—
210C24—1882no—
211C24—1882no—
212C24—1882no—
213C24—1882no—
214C24C22×D4712yes—
215C2×D4—24no—
216C2×D4—41no—
217C2×D4—478no—
218C2×D4—474no—
219C2×D4—944no—
220C2×D4—944no—
221C2×D4—944no—
222C2×D4—944no—
223C2×D4—944no—
224C2×D4—1881no—
225C2×D4—1881no—
226C2×D4—1881no—
227C2×D4—1882no—
228C2×D4—1882no—
229C2×D4—1882no—
230C2×D4—1882no—
231C22×C4—472no—
232C22×C4—472no—
233C22×C4C22×D4711yescharacteristic
234C22×C4C22×D4711yescharacteristic
235C22×C4C22×D4712yes—
236C22×C4C22×D4711yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—1882no—
239C22⋊C4—24no—
240C22⋊C4—24no—
241C22⋊C4—944no—
242C22⋊C4—944no—
243C22⋊C4—944no—
244C22⋊C4—944no—
245C22⋊C4—944no—
246C22⋊C4—944no—
247C22⋊C4—944no—
248C42—1881no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—474no—
256C23—474no—
257C23—942no—
258C23—942no—
259C23—942no—
260C23—942no—
261C23—942no—
262C23—942no—
263C23—942no—
264C23—942no—
265C23—942no—
266C23—942no—
267C23—942no—
268C23—942no—
269C23—1888no—
270C23—1888no—
271C23—1888no—
272C23—1888no—
273C23—1888no—
274C23—1888no—
275C23—1888no—
276C23D4×D4714yes—
277C23C23×D4711yescharacteristic
278D4—44no—
279D4—1884no—
280D4—1884no—
281D4—1888no—
282D4—1888no—
283D4—1888no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—474no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4D4×D4712yes—
300C22—24no—
301C22—24no—
302C22—24no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—944no—
308C22—944no—
309C22—944no—
310C22—944no—
311C22—944no—
312C22—944no—
313C22—18832no—
314C22—1882no—
315C22—1882no—
316C22—1882no—
317C22—1882no—
318C22—1882no—
319C22—1882no—
320C22—1882no—
321C22—1882no—
322C22C2×D4×D4712yes—
323C22C2×D4×D4711yescharacteristic
324C22#1309406911yescharacteristic
325C22#1309407012yes—
326C22#1309407011yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—42no—
331C4—944no—
332C4—1882no—
333C2—44no—
334C2—1884no—
335C2—1884no—
336C2#1568968111yescharacteristic
337C2#1568968412yes—
338C2#1568975511yescharacteristic
339C2#1568975712yes—
340C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2679
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13093994C2semidirect
2. C2×#13093994C2semidirect
3. C2×#13093992C2semidirect
4. #15689041C2semidirect
5. #15689040C2semidirect
6. #15689038C2semidirect
7. #15689024C2semidirect
8. #15689023C2semidirect
9. C47×#394C2semidirect
10. C24×D47C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×C22⋊Dic47C22semidirect
21. C2×(C2×D47)⋊C4C22semidirect
22. C2×(C2×D47)⋊C4C22semidirect
23. C2×(C2×D47)⋊C4C22semidirect
24. C2×(C2×D47)⋊C4C22semidirect
25. C2×(C2×D47)⋊C4C22semidirect
26. C2×(C2×D47)⋊C4C22semidirect
27. C2×C4×Dic47C22semidirect
28. C47⋊#95C22semidirect
30. C2×C4⋊C4×C47C22semidirect
31. C2×C22⋊C4×C47C22semidirect
32. C2×C22⋊C4×C47C22semidirect
33. #95×C47C22semidirect
55. C2×C22⋊D47D4semidirect
65. C2×D188D4semidirect
177. #394D47semidirect
180. C47#2679semidirect
192. C2×C4⋊C4C2×D47semidirect
200. C2×C22⋊C4C2×D47semidirect
201. C2×C22⋊C4C2×D47semidirect
204. #95C2×D47semidirect