Finite Group Databasebeta

← #20248277

Subgroups — #20248277

Order 6016.

800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13093992C211yesmaximal, characteristic
2C2×D4×Dic47C211yesmaximal, characteristic, complemented
3C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
4#15689045C212yesmaximal, complemented
5#15689038C212yesmaximal, complemented
6#15689013C212yesmaximal, complemented
7#15689000C212yesmaximal, complemented
8#15688986C211yesmaximal, characteristic, complemented
9#15688981C211yesmaximal, characteristic, complemented
10#15688978C211yesmaximal, characteristic, complemented
11C2×#123×C47C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C23×Dic47C2211yescharacteristic
15C23×Dic47C2211yescharacteristic, complemented
16#13093992—24no—
17D4×Dic47—24no—
18C2×C4⋊Dic47C2211yescharacteristic, complemented
19C2×Dic47⋊C4C2212yescomplemented
20C2×C22⋊Dic47C2211yescharacteristic
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic, complemented
23C2×(C2×D47)⋊C4—24no—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×C4×Dic47C2211yescharacteristic, complemented
30C47⋊#95C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C22×D4×C47C2211yescharacteristic
34C23×C4×C47C2211yescharacteristic
35#123×C47—24no—
36C2×C4⋊C4×C47C2212yescomplemented
37C2×C22⋊C4×C47C2211yescharacteristic
38C2×C22⋊C4×C47C2212yescomplemented
39C24×C47C2311yescharacteristic
40C24×C47C2311yescharacteristic
41C23×D47—22no—
42C23×D47—24no—
43C23×D47—22no—
44C23×D47—22no—
45C23×D47—42no—
46C23×D47C2312yes—
47C2×D4×C47—22no—
48C2×D4×C47—22no—
49C2×D4×C47D414yes—
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—22no—
53C22×C4×C47C2312yes—
54C22×C4×C47C2312yes—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—24no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—42no—
59C22×Dic47—22no—
60C22×Dic47—42no—
61C22×Dic47—42no—
62C22×Dic47D414yescomplemented
63C22×Dic47C2312yes—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C4⋊C4×C47—24no—
69C22⋊C4×C47—22no—
70C22⋊C4×C47—24no—
71C22⋊Dic47—22no—
72C22⋊Dic47—22no—
73C22⋊Dic47—22no—
74(C2×D47)⋊C4—24no—
75(C2×D47)⋊C4—24no—
76(C2×D47)⋊C4—24no—
77(C2×D47)⋊C4—24no—
78(C2×D47)⋊C4—42no—
79C4⋊Dic47—22no—
80Dic47⋊C4—42no—
81C4×Dic47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—21no—
85C23×C47—22no—
86C23×C47—21no—
87C23×C47—22no—
88C23×C47C2×D412yes—
89C23×C47C2×D412yes—
90C23×C47C2×D412yes—
91C23×C47#4112yes—
92C23×C47C2411yescharacteristic
93C22×D47—28no—
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—48no—
101C22×D47—48no—
102C22×D47—44no—
103C22×D47—44no—
104C22×D47#4114yes—
105D4×C47—28no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—44no—
115C2×C4×C47C2×D412yes—
116C22⋊D47—48no—
117C2×Dic47—22no—
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—44no—
127C2×Dic47—44no—
128C2×Dic47C2×D412yes—
129C2×Dic47C2×D412yes—
130C22×C47—22no—
131C22×C47—22no—
132C22×C47—24no—
133C22×C47—24no—
134C22×C47—22no—
135C22×C47—24no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47—42no—
139C22×C47#12114yes—
140C22×C47C22×D411yescharacteristic
141C22×C47C22×D411yescharacteristic
142C22×C47C2×#4112yes—
143C22×C47C2×#4111yescharacteristic
144C22×C47H(5,𝔽2)12yes—
145C2×D47—24no—
146C2×D47—24no—
147C2×D47—24no—
148C2×D47—416no—
149C2×D47—42no—
150C2×D47—42no—
151C2×D47—42no—
152C2×D47—42no—
153C4×C47—22no—
154C4×C47—42no—
155C4×C47—42no—
156Dic47—22no—
157Dic47—22no—
158Dic47—41no—
159Dic47—41no—
160Dic47—42no—
161#2534—471nomaximal, Sylow
162C2×C47—24no—
163C2×C47—42no—
164C2×C47C2×#12111yescharacteristic
165C2×C47#52511yescharacteristic
166C2×C47#53411yescharacteristic
167C2×C47#54612yes—
168C2×C47#55112yes—
169D47—44no—
170C2×#123D4711yescharacteristic, complemented
171C2×#120—471no—
172C2×C4×D4—471no—
173C22×C22⋊C4—471no—
174#396—472no—
175#394—472no—
176#388—472no—
177#386—472no—
178#381—471no—
179#380—471no—
180#379—471no—
181C47#253411yescharacteristic, complemented, Sylow
182C25—471no—
183C22×D4—472no—
184C22×D4C2×D4711yescharacteristic
185C23×C4—471no—
186C23×C4—471no—
187C23×C4C2×D4711yescharacteristic
188#123—24no—
189#120—944no—
190C4×D4—944no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—472no—
193C2×C4⋊C4C2×D4712yescomplemented
194C2×C22⋊C4—471no—
195C2×C22⋊C4—471no—
196C2×C22⋊C4—471no—
197C2×C22⋊C4—472no—
198C2×C22⋊C4—472no—
199C2×C22⋊C4—472no—
200C2×C22⋊C4—472no—
201C2×C22⋊C4—472no—
202C2×C22⋊C4—944no—
203C2×C22⋊C4C2×D4711yescharacteristic
204C2×C22⋊C4C2×D4712yescomplemented
205C2×C42—471no—
206#95—472no—
207#95—472no—
208#95—472no—
209C24—472no—
210C24—944no—
211C24—942no—
212C24—942no—
213C24—942no—
214C24—1882no—
215C24C22×D4711yescharacteristic
216C24C22×D4711yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—944no—
220C2×D4—944no—
221C2×D4—1882no—
222C2×D4C22⋊D4714yes—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—474no—
229C22×C4—472no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—942no—
233C22×C4—1882no—
234C22×C4—1882no—
235C22×C4C22×D4712yes—
236C22×C4C22×D4712yes—
237C22×C4C22×D4711yescharacteristic
238C4⋊C4—24no—
239C4⋊C4—942no—
240C4⋊C4—1882no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—944no—
244C22⋊C4—944no—
245C22⋊C4—944no—
246C22⋊C4—942no—
247C22⋊C4—942no—
248C22⋊C4—942no—
249C22⋊C4—944no—
250C22⋊C4—1882no—
251C42—942no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—474no—
259C23—948no—
260C23—942no—
261C23—942no—
262C23—942no—
263C23—942no—
264C23—942no—
265C23—942no—
266C23—1888no—
267C23—1888no—
268C23—1884no—
269C23—1884no—
270C23D4×D4712yes—
271C23#1062535212yes—
272C23C2×C22⋊D4712yes—
273C23C2×C22⋊D4712yes—
274C23C23×D4711yescharacteristic
275D4—28no—
276D4—1888no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—472no—
287C2×C4—472no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—942no—
297C2×C4—1884no—
298C2×C4—1884no—
299C2×C4C2×C22⋊D4712yes—
300C22—24no—
301C22—24no—
302C22—22no—
303C22—22no—
304C22—24no—
305C22—22no—
306C22—42no—
307C22—41no—
308C22—41no—
309C22—944no—
310C22—944no—
311C22—944no—
312C22—18816no—
313C22—1882no—
314C22—1882no—
315C22—1882no—
316C22—1882no—
317C22#1309399614yes—
318C22C2×D4×D4711yescharacteristic
319C22C22×C22⋊D4711yescharacteristic
320C22#41×D4712yes—
321C22C2×#1062535211yescharacteristic
322C22#1309407012yes—
323C4—22no—
324C4—42no—
325C4—42no—
326C4—942no—
327C4—942no—
328C4—1882no—
329C4—1881no—
330C4—1881no—
331C2—24no—
332C2—42no—
333C2—1884no—
334C2C2×#1309399611yescharacteristic
335C2#1568963111yescharacteristic
336C2#1568968411yescharacteristic
337C2#1568976112yes—
338C2#1568979612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2534
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic47C2semidirect
3. C22×(C2×D47)⋊C4C2semidirect
4. #15689045C2semidirect
5. #15689038C2semidirect
6. #15689013C2semidirect
7. #15689000C2semidirect
8. #15688986C2semidirect
9. #15688981C2semidirect
10. #15688978C2semidirect
11. C2×#123×C47C2semidirect
15. C23×Dic47C22semidirect
18. C2×C4⋊Dic47C22semidirect
19. C2×Dic47⋊C4C22semidirect
22. C2×C22⋊Dic47C22semidirect
29. C2×C4×Dic47C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
36. C2×C4⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
62. C22×Dic47D4semidirect
170. C2×#123D47semidirect
181. C47#2534semidirect
193. C2×C4⋊C4C2×D47semidirect
204. C2×C22⋊C4C2×D47semidirect