Finite Group Databasebeta

← #20247034

Subgroups — #20247034

Order 6016.

1088 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 1088 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
1C22×D4×D47C211yesmaximal, characteristic
2C2×#13094010C212yesmaximal, complemented
3C2×#13094002C211yesmaximal, characteristic, complemented
4#15689041C211yesmaximal, characteristic, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689023C212yesmaximal, complemented
8#15688978C212yesmaximal, complemented
9#15688978C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C24×D47C2212yes—
13C22×Dic94C2211yescharacteristic, complemented
14C22×D188C2211yescharacteristic
15C22×C22⋊D47C2212yes—
16C2×D4×D47—28no—
17C2×D4×D47—24no—
18C22×C4×D47C2211yescharacteristic
19#13094010—28no—
20#13094002—24no—
21C2×Dic47⋊C4C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2211yescharacteristic, complemented
23C2×C22⋊Dic47C2212yescomplemented
24C2×C22⋊Dic47C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2212yescomplemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C2×(C2×D47)⋊C4C2212yescomplemented
31C2×(C2×D47)⋊C4C2212yescomplemented
32C2×C4×Dic47C2212yescomplemented
33C47⋊#95C2211yescharacteristic, complemented
34C22×D4×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2211yescharacteristic, complemented
36C2×C22⋊C4×C47C2212yescomplemented
37C2×C22⋊C4×C47C2212yescomplemented
38#95×C47C2211yescharacteristic, complemented
39C24×C47C2312yes—
40C23×D47—24no—
41C23×D47—24no—
42C23×D47—24no—
43C23×D47—24no—
44C23×D47—24no—
45C23×D47—42no—
46C23×D47—42no—
47C23×D47C2312yes—
48C23×D47C2311yescharacteristic
49C2×D4×C47—24no—
50C2×D4×C47—22no—
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2312yes—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—24no—
56C2×C22⋊D47—24no—
57C2×C22⋊D47D418yes—
58C22×Dic47C2312yes—
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62D4×D47—232no—
63C2×D188—24no—
64C2×D188—22no—
65C2×C4×D47—24no—
66C2×C4×D47D414yes—
67C2×Dic94—22no—
68C2×Dic94—24no—
69C4⋊C4×C47—22no—
70C22⋊C4×C47—24no—
71C22⋊C4×C47—42no—
72C22⋊Dic47—24no—
73C22⋊Dic47—42no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—24no—
77(C2×D47)⋊C4—24no—
78(C2×D47)⋊C4—24no—
79(C2×D47)⋊C4—42no—
80(C2×D47)⋊C4—42no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83C4×Dic47—24no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47C2×D414yes—
91C23×C47C2411yescharacteristic
92C22×D47—22no—
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—216no—
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—22no—
102C22×D47—48no—
103C22×D47—48no—
104C22×D47—48no—
105C22×D47—48no—
106C22×D47—48no—
107C22×D47—48no—
108C22×D47C2×D414yes—
109C22×D47C2×D412yes—
110C22×D47#4114yes—
111D4×C47—28no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—22no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—22no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D412yes—
122C22⋊D47—216no—
123C2×Dic47—22no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—21no—
129C2×Dic47—22no—
130C2×Dic47—21no—
131C2×Dic47C2×D414yes—
132C2×Dic47C2×D412yes—
133D188—28no—
134C4×D47—28no—
135Dic94—44no—
136C22×C47—24no—
137C22×C47—24no—
138C22×C47—24no—
139C22×C47—42no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47—42no—
143C22×C47C22×D411yescharacteristic
144C22×C47C22×D412yes—
145C22×C47C2×#4112yes—
146C22×C47H(5,𝔽2)11yescharacteristic
147C22×C47H(5,𝔽2)11yescharacteristic
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—24no—
151C2×D47—24no—
152C2×D47—24no—
153C2×D47—24no—
154C2×D47—24no—
155C2×D47—432no—
156C2×D47—42no—
157C2×D47—42no—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47#12414yescomplemented
161C4×C47—22no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—42no—
165Dic47—41no—
166Dic47—41no—
167Dic47—42no—
168Dic47#12014yes—
169#2435—471nomaximal, Sylow
170C2×C47—44no—
171C2×C47C2×#12011yescharacteristic
172C2×C47C2×#12411yescharacteristic
173C2×C47#53511yescharacteristic
174C2×C47#54612yes—
175C2×C47#54612yes—
176D47—24no—
177D47—44no—
178C23×D4—471no—
179C2×#124—472no—
180C2×C22⋊Q8—471no—
181#394—471no—
182#394—471no—
183#394—471no—
184#394D4711yescharacteristic, complemented
185#390—472no—
186#379—472no—
187#379—472no—
188C4×C22⋊C4—471no—
189C47#243511yescharacteristic, complemented, Sylow
190C25—472no—
191C22×Q8—471no—
192C22×D4—472no—
193C22×D4—471no—
194C22×D4—944no—
195C22×D4—948no—
196C22×D4C2×D4711yescharacteristic
197C23×C4—471no—
198#124—948no—
199C22⋊Q8—944no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4C2×D4711yescharacteristic, complemented
203C2×C22⋊C4—472no—
204C2×C22⋊C4—471no—
205C2×C22⋊C4—471no—
206C2×C22⋊C4—472no—
207C2×C22⋊C4—472no—
208C2×C22⋊C4—472no—
209C2×C22⋊C4—472no—
210C2×C22⋊C4—472no—
211C2×C22⋊C4—472no—
212C2×C22⋊C4C2×D4712yescomplemented
213C2×C22⋊C4C2×D4712yescomplemented
214C2×C42—472no—
215#95—471no—
216#95C2×D4711yescharacteristic, complemented
217C24—471no—
218C24—472no—
219C24—944no—
220C24—944no—
221C24—944no—
222C24—944no—
223C24—944no—
224C24—1882no—
225C24—1882no—
226C24C22×D4712yes—
227C2×Q8—942no—
228C2×Q8—944no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—478no—
232C2×D4—944no—
233C2×D4—944no—
234C2×D4—944no—
235C2×D4—9432no—
236C2×D4—942no—
237C22×C4—471no—
238C22×C4—474no—
239C22×C4—472no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—944no—
243C22×C4C22×D4712yes—
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—942no—
249C4⋊C4—942no—
250C22⋊C4—24no—
251C22⋊C4—42no—
252C22⋊C4—944no—
253C22⋊C4—942no—
254C22⋊C4—942no—
255C22⋊C4—944no—
256C22⋊C4—944no—
257C22⋊C4—944no—
258C22⋊C4—1882no—
259C22⋊C4—1882no—
260C22⋊C4—1882no—
261C42—944no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—472no—
269C23—474no—
270C23—474no—
271C23—9416no—
272C23—942no—
273C23—941no—
274C23—941no—
275C23—942no—
276C23—942no—
277C23—942no—
278C23—942no—
279C23—942no—
280C23—942no—
281C23—1888no—
282C23—1888no—
283C23—1888no—
284C23—1888no—
285C23—1888no—
286C23—1888no—
287C23D4×D4714yes—
288C23C23×D4711yescharacteristic
289Q8—1884no—
290D4—28no—
291D4—948no—
292D4—9416no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—474no—
303C2×C4—472no—
304C2×C4—948no—
305C2×C4—942no—
306C2×C4—942no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—942no—
310C2×C4—941no—
311C2×C4—942no—
312C2×C4—941no—
313C2×C4D4×D4712yes—
314C22—24no—
315C22—24no—
316C22—24no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—474no—
322C22—944no—
323C22—944no—
324C22—942no—
325C22—942no—
326C22—944no—
327C22—944no—
328C22—944no—
329C22—18832no—
330C22—1882no—
331C22—1882no—
332C22—1882no—
333C22—1882no—
334C22C2×D4×D4712yes—
335C22C2×D4×D4711yescharacteristic
336C22#41×D4712yes—
337C22#1309406911yescharacteristic
338C22#1309407011yescharacteristic
339C4—22no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—474no—
344C4—1882no—
345C4—1881no—
346C4—1881no—
347C2—44no—
348C2—944no—
349C2—1884no—
350C2#120×D4711yescharacteristic
351C2#124×D4711yescharacteristic
352C2#1568968911yescharacteristic
353C2#1568976212yes—
354C2#1568976512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2435
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13094010C2semidirect
3. C2×#13094002C2semidirect
4. #15689041C2semidirect
5. #15689040C2semidirect
6. #15689037C2semidirect
7. #15689023C2semidirect
8. #15688978C2semidirect
9. #15688978C2semidirect
10. #15688970C2semidirect
11. C47×#394C2semidirect
13. C22×Dic94C22semidirect
21. C2×Dic47⋊C4C22semidirect
22. C2×Dic47⋊C4C22semidirect
23. C2×C22⋊Dic47C22semidirect
24. C2×C22⋊Dic47C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
30. C2×(C2×D47)⋊C4C22semidirect
31. C2×(C2×D47)⋊C4C22semidirect
32. C2×C4×Dic47C22semidirect
33. C47⋊#95C22semidirect
35. C2×C4⋊C4×C47C22semidirect
36. C2×C22⋊C4×C47C22semidirect
37. C2×C22⋊C4×C47C22semidirect
38. #95×C47C22semidirect
160. C2×D47#124semidirect
184. #394D47semidirect
189. C47#2435semidirect
202. C2×C4⋊C4C2×D47semidirect
212. C2×C22⋊C4C2×D47semidirect
213. C2×C22⋊C4C2×D47semidirect
216. #95C2×D47semidirect