Finite Group Databasebeta

← #20246698

Subgroups — #20246698

Order 6016.

1564 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 213 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
1C23×C22⋊D47C211yesmaximal, characteristic, complemented
2C2×#13093993C212yesmaximal, complemented
3C2×#13093992C212yesmaximal, complemented
4#15689031C214yesmaximal, complemented
5#15689003C212yesmaximal, complemented
6#15689002C212yesmaximal, complemented
7#15688979C211yesmaximal, characteristic, complemented
8C23×D4×C47C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic, complemented
10C22×C22⋊D47—24no—
11C22×C22⋊D47—28no—
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2212yescomplemented
14C22×C22⋊D47C2214yescomplemented
15C23×Dic47C2211yescharacteristic, complemented
16#13093993—28no—
17#13093992—28no—
18C2×C22⋊Dic47C2212yescomplemented
19C2×C22⋊Dic47C2212yescomplemented
20C2×C22⋊Dic47C2214yescomplemented
21C2×C22⋊Dic47C2212yescomplemented
22C2×(C2×D47)⋊C4C2214yescomplemented
23C47⋊#95C2214yescomplemented
24C25×C47C2211yescharacteristic
25C25×C47C2211yescharacteristic, complemented
26C22×D4×C47—24no—
27C22×D4×C47—28no—
28C22×D4×C47C2212yes—
29C22×D4×C47C2212yescomplemented
30C23×C4×C47C2211yescharacteristic, complemented
31C24×C47—24no—
32C24×C47—22no—
33C24×C47—24no—
34C24×C47—24no—
35C24×C47—24no—
36C24×C47—42no—
37C24×C47—42no—
38C24×C47D414yescomplemented
39C24×C47C2311yescharacteristic
40C24×C47C2312yes—
41C24×C47C2311yescharacteristic
42C24×C47C2311yescharacteristic
43C23×D47—22no—
44C23×D47—24no—
45C23×D47—24no—
46C23×D47—42no—
47C23×D47C2312yes—
48C2×D4×C47—232no—
49C2×D4×C47—24no—
50C2×D4×C47—24no—
51C2×D4×C47—24no—
52C2×D4×C47—24no—
53C2×D4×C47—24no—
54C2×D4×C47D418yescomplemented
55C22×C4×C47—22no—
56C22×C4×C47—24no—
57C22×C4×C47C2312yes—
58C2×C22⋊D47—232no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—24no—
61C2×C22⋊D47—24no—
62C2×C22⋊D47—24no—
63C2×C22⋊D47—28no—
64C2×C22⋊D47—28no—
65C2×C22⋊D47—24no—
66C2×C22⋊D47—44no—
67C2×C22⋊D47D418yescomplemented
68C22×Dic47—22no—
69C22×Dic47—24no—
70C22×Dic47C2314yes—
71C22×Dic47C2312yes—
72C22⋊Dic47—24no—
73C22⋊Dic47—24no—
74C22⋊Dic47—28no—
75C22⋊Dic47—42no—
76(C2×D47)⋊C4—28no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—28no—
82C23×C47—28no—
83C23×C47—28no—
84C23×C47—24no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—24no—
91C23×C47—44no—
92C23×C47—416no—
93C23×C47—416no—
94C23×C47—44no—
95C23×C47—44no—
96C23×C47C2×D414yes—
97C23×C47C2×D412yes—
98C23×C47C2×D414yes—
99C23×C47C2×D412yes—
100C23×C47C2×D412yes—
101C23×C47C2×D414yescomplemented
102C23×C47C2411yescharacteristic
103C22×D47—28no—
104C22×D47—24no—
105C22×D47—22no—
106C22×D47—22no—
107C22×D47—24no—
108C22×D47—416no—
109C22×D47—44no—
110C22×D47—44no—
111C22×D47C2×D414yescomplemented
112D4×C47—216no—
113D4×C47—216no—
114C2×C4×C47—28no—
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47C2×D414yescomplemented
118C22⋊D47—216no—
119C22⋊D47—216no—
120C22⋊D47—416no—
121C2×Dic47—28no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—24no—
125C2×Dic47—24no—
126C2×Dic47—24no—
127C2×Dic47C2×D414yescomplemented
128C22×C47—22no—
129C22×C47—22no—
130C22×C47—22no—
131C22×C47—22no—
132C22×C47—28no—
133C22×C47—28no—
134C22×C47—22no—
135C22×C47—22no—
136C22×C47—24no—
137C22×C47—22no—
138C22×C47—28no—
139C22×C47—416no—
140C22×C47—416no—
141C22×C47—42no—
142C22×C47—42no—
143C22×C47—44no—
144C22×C47—44no—
145C22×C47#12014yescomplemented
146C22×C47#12014yescomplemented
147C22×C47C22×D412yes—
148C22×C47C22×D411yescharacteristic
149C22×C47C22×D412yes—
150C22×C47H(5,𝔽2)12yes—
151C2×D47—24no—
152C2×D47—28no—
153C2×D47—416no—
154C2×D47—42no—
155C2×D47—42no—
156C2×D47—44no—
157C4×C47—24no—
158Dic47—24no—
159Dic47—44no—
160#2403—471nomaximal, Sylow
161C2×C47—24no—
162C2×C47—24no—
163C2×C47—42no—
164C2×C47—44no—
165C2×C47C2×#12011yescharacteristic
166C2×C47C2×#12011yescharacteristic
167C2×C47#53411yescharacteristic
168C2×C47D4214yes—
169D47—44no—
170C23×D4—471no—
171C23×D4D4711yescharacteristic, complemented
172C2×#120—472no—
173C2×#120—472no—
174#392—474no—
175#386—472no—
176#386—472no—
177#379—471no—
178C47#240311yescharacteristic, complemented, Sylow
179C25—471no—
180C25C2×D4711yescharacteristic
181C25C2×D4711yescharacteristic, complemented
182C22×D4—24no—
183C22×D4—28no—
184C22×D4—472no—
185C22×D4—472no—
186C22×D4—474no—
187C22×D4—948no—
188C22×D4—944no—
189C22×D4C2×D4712yes—
190C22×D4C2×D4712yescomplemented
191C23×C4—471no—
192C23×C4C2×D4711yescharacteristic, complemented
193#120—948no—
194#120—948no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—472no—
197C2×C22⋊C4—474no—
198C2×C22⋊C4—474no—
199C2×C22⋊C4—472no—
200#95—474no—
201C24—24no—
202C24—24no—
203C24—22no—
204C24—24no—
205C24—24no—
206C24—42no—
207C24—42no—
208C24—472no—
209C24—944no—
210C24—942no—
211C24—944no—
212C24—1882no—
213C24C22⋊D4714yescomplemented
214C24C22×D4711yescharacteristic
215C24C22×D4712yes—
216C24C22×D4711yescharacteristic
217C24C22×D4711yescharacteristic
218C2×D4—232no—
219C2×D4—24no—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—24no—
223C2×D4—24no—
224C2×D4—478no—
225C2×D4—944no—
226C2×D4—944no—
227C2×D4—9432no—
228C2×D4—944no—
229C2×D4—944no—
230C2×D4—944no—
231C2×D4—948no—
232C2×D4—948no—
233C2×D4—1884no—
234C2×D4C22⋊D4718yescomplemented
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—472no—
238C22×C4—474no—
239C22×C4—944no—
240C22×C4—942no—
241C22×C4C22×D4712yes—
242C22⋊C4—948no—
243C22⋊C4—944no—
244C22⋊C4—944no—
245C22⋊C4—948no—
246C22⋊C4—1882no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—28no—
252C23—28no—
253C23—28no—
254C23—24no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—24no—
261C23—44no—
262C23—416no—
263C23—416no—
264C23—44no—
265C23—44no—
266C23—474no—
267C23—948no—
268C23—942no—
269C23—944no—
270C23—942no—
271C23—944no—
272C23—18816no—
273C23—1884no—
274C23—1884no—
275C23D4×D4714yes—
276C23C2×C22⋊D4712yes—
277C23C2×C22⋊D4712yes—
278C23C2×C22⋊D4714yes—
279C23C2×C22⋊D4712yes—
280C23C2×C22⋊D4714yescomplemented
281C23C23×D4711yescharacteristic
282D4—216no—
283D4—216no—
284D4—9416no—
285D4—9416no—
286D4—18816no—
287C2×C4—28no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—474no—
291C2×C4—948no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—944no—
295C2×C4—944no—
296C2×C4—944no—
297C2×C4C2×C22⋊D4714yescomplemented
298C22—28no—
299C22—28no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—28no—
305C22—22no—
306C22—22no—
307C22—24no—
308C22—22no—
309C22—416no—
310C22—416no—
311C22—44no—
312C22—44no—
313C22—42no—
314C22—42no—
315C22—948no—
316C22—944no—
317C22—18816no—
318C22—1884no—
319C22—1882no—
320C22—1882no—
321C22#1309399214yescomplemented
322C22#1309399314yescomplemented
323C22C2×D4×D4712yes—
324C22C22×C22⋊D4712yes—
325C22C22×C22⋊D4711yescharacteristic
326C22#1309406912yes—
327C4—24no—
328C4—944no—
329C4—1884no—
330C2—24no—
331C2—24no—
332C2—44no—
333C2—42no—
334C2—1884no—
335C2C2×#1309399211yescharacteristic
336C2C2×#1309399311yescharacteristic
337C2#1568968211yescharacteristic
338C2D4×C22⋊D4714yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC23×D4×C47C2
hypercenterC23×D4D47
hypocenterC47#2403
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D47C2semidirect
2. C2×#13093993C2semidirect
3. C2×#13093992C2semidirect
4. #15689031C2semidirect
5. #15689003C2semidirect
6. #15689002C2semidirect
7. #15688979C2semidirect
8. C23×D4×C47C2semidirect
9. C24×D47C22semidirect
13. C22×C22⋊D47C22semidirect
14. C22×C22⋊D47C22semidirect
15. C23×Dic47C22semidirect
18. C2×C22⋊Dic47C22semidirect
19. C2×C22⋊Dic47C22semidirect
20. C2×C22⋊Dic47C22semidirect
21. C2×C22⋊Dic47C22semidirect
22. C2×(C2×D47)⋊C4C22semidirect
23. C47⋊#95C22semidirect
25. C25×C47C22semidirect
29. C22×D4×C47C22semidirect
30. C23×C4×C47C22semidirect
38. C24×C47D4semidirect
54. C2×D4×C47D4semidirect
67. C2×C22⋊D47D4semidirect
101. C23×C47C2×D4semidirect
111. C22×D47C2×D4semidirect
117. C2×C4×C47C2×D4semidirect
127. C2×Dic47C2×D4semidirect
145. C22×C47#120semidirect
146. C22×C47#120semidirect
171. C23×D4D47semidirect
178. C47#2403semidirect
181. C25C2×D47semidirect
190. C22×D4C2×D47semidirect
192. C23×C4C2×D47semidirect
213. C24C22⋊D47semidirect
234. C2×D4C22⋊D47semidirect
280. C23C2×C22⋊D47semidirect
297. C2×C4C2×C22⋊D47semidirect
321. C22#13093992semidirect
322. C22#13093993semidirect