Finite Group Databasebeta

← #20247037

Subgroups — #20247037

Order 6016.

1088 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 169 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
2C2×#13094010C212yesmaximal, complemented
3C2×#13094001C211yesmaximal, characteristic, complemented
4#15689039C212yesmaximal, complemented
5#15689038C212yesmaximal, complemented
6#15689023C212yesmaximal, complemented
7#15688979C211yesmaximal, characteristic, complemented
8#15688978C211yesmaximal, characteristic, complemented
9#15688978C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C47×#379C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×Dic94C2211yescharacteristic, complemented
14C22×C22⋊D47—28no—
15C22×C22⋊D47—24no—
16C22×C22⋊D47C2212yes—
17C22×C22⋊D47C2212yes—
18C23×Dic47C2211yescharacteristic
19#13094010—28no—
20#13094001—24no—
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2212yescomplemented
27C2×C22⋊Dic47C2212yescomplemented
28C2×(C2×D47)⋊C4C2212yescomplemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C2×(C2×D47)⋊C4C2212yescomplemented
31C2×(C2×D47)⋊C4C2212yescomplemented
32C2×C4×Dic47C2212yescomplemented
33C47⋊#95C2212yescomplemented
34C25×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2211yescharacteristic
37C2×C22⋊C4×C47C2212yescomplemented
38C2×C22⋊C4×C47C2212yescomplemented
39C24×C47—24no—
40C24×C47—22no—
41C24×C47—22no—
42C24×C47—22no—
43C24×C47—42no—
44C24×C47C2312yes—
45C24×C47C2311yescharacteristic
46C23×D47—22no—
47C23×D47—24no—
48C23×D47—22no—
49C23×D47—22no—
50C23×D47—42no—
51C23×D47C2312yes—
52C22×C4×C47C2312yes—
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—232no—
56C2×C22⋊D47—24no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—24no—
61C2×C22⋊D47D418yes—
62C22×Dic47—24no—
63C22×Dic47D414yes—
64C22×Dic47C2312yes—
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C2×Dic94—22no—
70C2×Dic94—24no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47—24no—
73C22⋊C4×C47—22no—
74C22⋊C4×C47—42no—
75C22⋊Dic47—22no—
76C22⋊Dic47—24no—
77C22⋊Dic47—22no—
78C22⋊Dic47—42no—
79(C2×D47)⋊C4—24no—
80(C2×D47)⋊C4—24no—
81(C2×D47)⋊C4—42no—
82(C2×D47)⋊C4—42no—
83C4⋊Dic47—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86C4×Dic47—24no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—28no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47—22no—
93C23×C47—22no—
94C23×C47—22no—
95C23×C47—22no—
96C23×C47—48no—
97C23×C47—48no—
98C23×C47—44no—
99C23×C47—44no—
100C23×C47C2×D414yes—
101C23×C47C2×D412yes—
102C23×C47#4112yes—
103C23×C47#4112yes—
104C23×C47C2411yescharacteristic
105C22×D47—28no—
106C22×D47—22no—
107C22×D47—22no—
108C22×D47—22no—
109C22×D47—22no—
110C22×D47—22no—
111C22×D47—22no—
112C22×D47—48no—
113C22×D47—48no—
114C22×D47—44no—
115C22×D47—44no—
116C22×D47C2×D414yes—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C22⋊D47—216no—
125C22⋊D47—216no—
126C2×Dic47—22no—
127C2×Dic47—28no—
128C2×Dic47—22no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47C2×D412yes—
136C2×Dic47C2×D414yes—
137C2×Dic47C2×D412yes—
138Dic94—44no—
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—24no—
142C22×C47—24no—
143C22×C47—24no—
144C22×C47—24no—
145C22×C47—24no—
146C22×C47—416no—
147C22×C47—42no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47—42no—
151C22×C47#12414yescomplemented
152C22×C47C22×D411yescharacteristic
153C22×C47C22×D412yes—
154C22×C47C2×#4111yescharacteristic
155C22×C47C2×#4111yescharacteristic
156C22×C47H(5,𝔽2)12yes—
157C2×D47—24no—
158C2×D47—24no—
159C2×D47—24no—
160C2×D47—416no—
161C2×D47—42no—
162C2×D47—42no—
163C2×D47—42no—
164C2×D47—42no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—42no—
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171Dic47—42no—
172Dic47#12014yes—
173#2435—471nomaximal, Sylow
174C2×C47—24no—
175C2×C47—44no—
176C2×C47C2×#12011yescharacteristic
177C2×C47C2×#12411yescharacteristic
178C2×C47#53511yescharacteristic
179C2×C47#54612yes—
180C2×C47#54612yes—
181D47—44no—
182C23×D4—471no—
183C2×#124—472no—
184C2×C22⋊Q8—471no—
185#394—472no—
186#394—472no—
187#390—472no—
188#379—471no—
189#379—471no—
190#379—471no—
191#379D4711yescharacteristic, complemented
192C4×C22⋊C4—471no—
193C47#243511yescharacteristic, complemented, Sylow
194C25—471no—
195C25C2×D4711yescharacteristic
196C22×Q8—471no—
197C22×D4—472no—
198C22×D4—472no—
199C22×D4—944no—
200C22×D4—948no—
201C23×C4—471no—
202#124—948no—
203C22⋊Q8—944no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C22⋊C4—471no—
208C2×C22⋊C4—472no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—472no—
211C2×C22⋊C4—472no—
212C2×C22⋊C4—472no—
213C2×C22⋊C4—472no—
214C2×C22⋊C4—472no—
215C2×C22⋊C4C2×D4711yescharacteristic
216C2×C22⋊C4C2×D4711yescharacteristic
217C2×C22⋊C4C2×D4712yescomplemented
218C2×C22⋊C4C2×D4712yescomplemented
219C2×C42—472no—
220#95—472no—
221C24—24no—
222C24—22no—
223C24—22no—
224C24—22no—
225C24—42no—
226C24—472no—
227C24—944no—
228C24—942no—
229C24—942no—
230C24—942no—
231C24—1882no—
232C24C22×D4712yes—
233C24C22×D4711yescharacteristic
234C2×Q8—942no—
235C2×Q8—944no—
236C2×D4—478no—
237C2×D4—944no—
238C2×D4—944no—
239C2×D4—944no—
240C2×D4—944no—
241C2×D4—9432no—
242C2×D4—944no—
243C22×C4—471no—
244C22×C4—474no—
245C22×C4—471no—
246C22×C4—472no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—944no—
250C22×C4C22×D4712yes—
251C22×C4C22×D4711yescharacteristic
252C22×C4C22×D4711yescharacteristic
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C22⋊C4—22no—
257C22⋊C4—24no—
258C22⋊C4—22no—
259C22⋊C4—42no—
260C22⋊C4—944no—
261C22⋊C4—944no—
262C22⋊C4—942no—
263C22⋊C4—942no—
264C22⋊C4—944no—
265C22⋊C4—1882no—
266C22⋊C4—1882no—
267C22⋊C4—1882no—
268C42—944no—
269C23—22no—
270C23—22no—
271C23—28no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—48no—
279C23—48no—
280C23—44no—
281C23—44no—
282C23—474no—
283C23—948no—
284C23—942no—
285C23—942no—
286C23—942no—
287C23—942no—
288C23—942no—
289C23—942no—
290C23—1888no—
291C23—1888no—
292C23—1884no—
293C23—1884no—
294C23#1062535012yes—
295C23D4×D4714yes—
296C23D4×D4712yes—
297C23#1062535212yes—
298C23C23×D4711yescharacteristic
299Q8—1884no—
300D4—9416no—
301D4—9416no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—474no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—948no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—942no—
321C22—24no—
322C22—24no—
323C22—22no—
324C22—22no—
325C22—24no—
326C22—24no—
327C22—24no—
328C22—416no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—944no—
334C22—944no—
335C22—944no—
336C22—18816no—
337C22—1882no—
338C22—1882no—
339C22—1882no—
340C22—1882no—
341C22#1309401014yescomplemented
342C22C2×D4×D4712yes—
343C22C2×D4×D4711yescharacteristic
344C22C2×#1062535211yescharacteristic
345C22C2×#1062535011yescharacteristic
346C22#1309406912yes—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—474no—
351C4—942no—
352C4—1882no—
353C4—1881no—
354C4—1881no—
355C2—24no—
356C2—44no—
357C2—1884no—
358C2#120×D4711yescharacteristic
359C2C2×#1309401011yescharacteristic
360C2#1568968811yescharacteristic
361C2#1568976012yes—
362C2#1568976312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2435
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#13094010C2semidirect
3. C2×#13094001C2semidirect
4. #15689039C2semidirect
5. #15689038C2semidirect
6. #15689023C2semidirect
7. #15688979C2semidirect
8. #15688978C2semidirect
9. #15688978C2semidirect
10. C22⋊C4×Dic47C2semidirect
11. C47×#379C2semidirect
13. C22×Dic94C22semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×Dic47⋊C4C22semidirect
23. C2×Dic47⋊C4C22semidirect
26. C2×C22⋊Dic47C22semidirect
27. 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
37. C2×C22⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
151. C22×C47#124semidirect
191. #379D47semidirect
193. C47#2435semidirect
217. C2×C22⋊C4C2×D47semidirect
218. C2×C22⋊C4C2×D47semidirect
341. C22#13094010semidirect