Finite Group Databasebeta

← #20246769

Subgroups — #20246769

Order 6016.

786 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094005C211yesmaximal, characteristic, complemented
2C2×#13093980C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
4#15689046C212yesmaximal, complemented
5#15689037C212yesmaximal, complemented
6#15689026C212yesmaximal, complemented
7#15689011C212yesmaximal, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15688998C211yesmaximal, characteristic, complemented
10#15688979C211yesmaximal, characteristic, complemented
11C2×#120×C47C211yesmaximal, characteristic
12C23×Dic47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14#13094005—24no—
15#13093980—24no—
16C2×C4⋊Dic47C2212yescomplemented
17C2×Dic47⋊C4C2211yescharacteristic, complemented
18C2×Dic47⋊C4C2212yescomplemented
19C2×Dic47⋊C4C2211yescharacteristic, complemented
20C2×C22⋊Dic47—24no—
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×C22⋊Dic47C2211yescharacteristic, complemented
28C2×C22⋊Dic47C2211yescharacteristic, complemented
29C2×C22⋊Dic47C2212yescomplemented
30C2×C4×Dic47C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C25×C47C2211yescharacteristic
34C22×D4×C47C2211yescharacteristic
35C22×D4×C47C2212yes—
36#120×C47—24no—
37C2×C22⋊C4×C47C2212yes—
38C2×C22⋊C4×C47C2211yescharacteristic
39C24×C47—22no—
40C24×C47—24no—
41C24×C47—22no—
42C24×C47—22no—
43C24×C47—42no—
44C24×C47C2311yescharacteristic
45C24×C47C2312yes—
46C24×C47C2311yescharacteristic
47C2×D4×C47—22no—
48C2×D4×C47—22no—
49C2×D4×C47—24no—
50C2×D4×C47—22no—
51C2×D4×C47—24no—
52C2×D4×C47—42no—
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2312yes—
55C22×Dic47—22no—
56C22×Dic47—22no—
57C22×Dic47—22no—
58C22×Dic47—42no—
59C22×Dic47D414yescomplemented
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2312yes—
62C22×Dic47C2312yes—
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22⋊C4×C47—24no—
67C22⋊C4×C47D414yes—
68C22⋊Dic47—22no—
69C22⋊Dic47—22no—
70C22⋊Dic47—24no—
71C22⋊Dic47—24no—
72C22⋊Dic47—24no—
73C22⋊Dic47—22no—
74C22⋊Dic47—22no—
75C22⋊Dic47—42no—
76C22⋊Dic47—42no—
77C4⋊Dic47—42no—
78Dic47⋊C4—24no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81C4×Dic47—24no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—28no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—21no—
94C23×C47—22no—
95C23×C47—22no—
96C23×C47—48no—
97C23×C47—48no—
98C23×C47—44no—
99C23×C47—44no—
100C23×C47C2×D412yes—
101C23×C47C2×D412yes—
102C23×C47#4114yes—
103C23×C47#4112yes—
104C23×C47C2411yescharacteristic
105D4×C47—48no—
106D4×C47—44no—
107C2×C4×C47—22no—
108C2×C4×C47—22no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D414yes—
113C2×Dic47—28no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—22no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—44no—
129C2×Dic47C2×D412yes—
130C2×Dic47C2×D412yes—
131C22×C47—22no—
132C22×C47—22no—
133C22×C47—24no—
134C22×C47—24no—
135C22×C47—24no—
136C22×C47—24no—
137C22×C47—24no—
138C22×C47—416no—
139C22×C47—42no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47—42no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47#12114yes—
149C22×C47C22×D411yescharacteristic
150C22×C47C22×D411yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47C2×#4112yes—
153C22×C47H(5,𝔽2)12yes—
154C4×C47—24no—
155C4×C47—41no—
156Dic47—22no—
157Dic47—22no—
158Dic47—41no—
159Dic47—41no—
160Dic47—42no—
161Dic47—42no—
162#2411—471nomaximal, Sylow
163C2×C47—24no—
164C2×C47—44no—
165C2×C47—81no—
166C2×C47C2×#12111yescharacteristic
167C2×C47#52511yescharacteristic
168C2×C47#53511yescharacteristic
169C2×C47#54612yes—
170C2×C47#55112yes—
171C2×#123—471no—
172C2×#120D4711yescharacteristic
173C2×#117—471no—
174C22×C22⋊C4—471no—
175#396—472no—
176#394—472no—
177#390—472no—
178#388—472no—
179#386—471no—
180#385—471no—
181#379—471no—
182C47#241111yescharacteristic, complemented, Sylow
183C25C2×D4711yescharacteristic
184C22×D4C2×D4711yescharacteristic
185C22×D4C2×D4712yes—
186C23×C4—471no—
187C23×C4—471no—
188#123—944no—
189#120—24no—
190#117—944no—
191C2×C4⋊C4—472no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—472no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—472no—
197C2×C22⋊C4—471no—
198C2×C22⋊C4—471no—
199C2×C22⋊C4—471no—
200C2×C22⋊C4—471no—
201C2×C22⋊C4—472no—
202C2×C22⋊C4—472no—
203C2×C22⋊C4—472no—
204C2×C22⋊C4—944no—
205C2×C22⋊C4C2×D4712yes—
206C2×C22⋊C4C2×D4711yescharacteristic
207C2×C42—472no—
208#95—472no—
209#95—472no—
210C24—22no—
211C24—24no—
212C24—22no—
213C24—22no—
214C24—42no—
215C24C22×D4711yescharacteristic
216C24C22×D4712yes—
217C24C22×D4711yescharacteristic
218C2×D4—22no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—24no—
223C2×D4—42no—
224C22×C4—474no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—472no—
229C22×C4—472no—
230C22×C4—471no—
231C22×C4—942no—
232C22×C4—942no—
233C22×C4—942no—
234C22×C4—1882no—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4712yes—
237C4⋊C4—942no—
238C4⋊C4—942no—
239C4⋊C4—944no—
240C4⋊C4—1882no—
241C22⋊C4—24no—
242C22⋊C4—944no—
243C22⋊C4—944no—
244C22⋊C4—942no—
245C22⋊C4—942no—
246C22⋊C4—942no—
247C22⋊C4—944no—
248C22⋊C4—942no—
249C22⋊C4—1882no—
250C22⋊C4—1882no—
251C22⋊C4C22⋊D4714yes—
252C42—944no—
253C23—22no—
254C23—22no—
255C23—28no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—21no—
263C23—21no—
264C23—22no—
265C23—21no—
266C23—22no—
267C23—48no—
268C23—48no—
269C23—44no—
270C23—44no—
271C23D4×D4712yes—
272C23#1062535214yes—
273C23#1062535212yes—
274C23C2×C22⋊D4712yes—
275C23C23×D4711yescharacteristic
276D4—48no—
277D4—44no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—472no—
284C2×C4—472no—
285C2×C4—948no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4—942no—
300C2×C4—1884no—
301C2×C4C2×C22⋊D4714yes—
302C22—24no—
303C22—24no—
304C22—22no—
305C22—22no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—416no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22#1309399514yes—
320C22C2×D4×D4711yescharacteristic
321C22C22×C22⋊D4711yescharacteristic
322C22C2×#1062535212yes—
323C22C2×#1062535211yescharacteristic
324C22#1309406912yes—
325C4—24no—
326C4—41no—
327C4—942no—
328C4—942no—
329C4—1882no—
330C4—1881no—
331C4—1882no—
332C4—1881no—
333C2—24no—
334C2—44no—
335C2—81no—
336C2C2×#1309399511yescharacteristic
337C2#1568962911yescharacteristic
338C2#1568968811yescharacteristic
339C2#1568976712yes—
340C2#1568980412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2411
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. C2×#13093980C2semidirect
3. C22×C22⋊Dic47C2semidirect
4. #15689046C2semidirect
5. #15689037C2semidirect
6. #15689026C2semidirect
7. #15689011C2semidirect
8. #15689003C2semidirect
9. #15688998C2semidirect
10. #15688979C2semidirect
16. C2×C4⋊Dic47C22semidirect
17. C2×Dic47⋊C4C22semidirect
18. C2×Dic47⋊C4C22semidirect
19. C2×Dic47⋊C4C22semidirect
27. C2×C22⋊Dic47C22semidirect
28. C2×C22⋊Dic47C22semidirect
29. C2×C22⋊Dic47C22semidirect
30. C2×C4×Dic47C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
59. C22×Dic47D4semidirect
182. C47#2411semidirect