Finite Group Databasebeta

← #20246713

Subgroups — #20246713

Order 6016.

1116 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1116 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×#13094006C212yesmaximal, complemented
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689039C212yesmaximal, complemented
5#15689038C212yesmaximal, complemented
6#15688999C212yesmaximal, complemented
7#15688998C211yesmaximal, characteristic, complemented
8#15688995C211yesmaximal, characteristic, complemented
9#15688979C211yesmaximal, characteristic, complemented
10#15688978C211yesmaximal, characteristic, complemented
11C47×#379C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×C22⋊D47—24no—
14C22×C22⋊D47—28no—
15C22×C22⋊D47C2212yes—
16C22×C22⋊D47C2212yes—
17C23×Dic47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic, complemented
19C22×C4×D47C2211yescharacteristic, complemented
20#13094006—28no—
21C2×C4⋊Dic47C2212yescomplemented
22C2×Dic47⋊C4C2212yescomplemented
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2212yescomplemented
26C2×C22⋊Dic47C2212yescomplemented
27C2×(C2×D47)⋊C4C2212yescomplemented
28C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
29C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
30C2×(C2×D47)⋊C4C2212yescomplemented
31C22⋊C4×D47—24no—
32C47⋊#95C2212yescomplemented
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—22no—
48C23×D47—24no—
49C23×D47—42no—
50C23×D47D414yes—
51C23×D47C2311yescharacteristic
52C23×D47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2312yes—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—232no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—24no—
61C2×C22⋊D47—24no—
62C2×C22⋊D47D418yes—
63C22×Dic47—22no—
64C22×Dic47—24no—
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2312yes—
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2312yes—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—24no—
72C2×C4×D47—42no—
73C22⋊C4×C47—22no—
74C22⋊C4×C47—24no—
75C22⋊C4×C47—22no—
76C22⋊C4×C47—42no—
77C22⋊Dic47—22no—
78C22⋊Dic47—24no—
79C22⋊Dic47—22no—
80C22⋊Dic47—42no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—24no—
84(C2×D47)⋊C4—42no—
85C4⋊Dic47—24no—
86Dic47⋊C4—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—21no—
106C22×D47—21no—
107C22×D47—22no—
108C22×D47—28no—
109C22×D47—22no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—22no—
113C22×D47—28no—
114C22×D47—44no—
115C22×D47—48no—
116C22×D47—48no—
117C22×D47C2×D412yes—
118C22×D47C2×D414yes—
119C22×D47C2×D412yes—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—22no—
127C22⋊D47—216no—
128C22⋊D47—216no—
129C2×Dic47—28no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—22no—
137C2×Dic47—22no—
138C2×Dic47—22no—
139C2×Dic47C2×D414yes—
140C4×D47—44no—
141C4×D47—44no—
142C22×C47—22no—
143C22×C47—22no—
144C22×C47—24no—
145C22×C47—24no—
146C22×C47—24no—
147C22×C47—24no—
148C22×C47—24no—
149C22×C47—416no—
150C22×C47—42no—
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47#12314yescomplemented
155C22×C47C22×D411yescharacteristic
156C22×C47C22×D412yes—
157C22×C47C2×#4111yescharacteristic
158C22×C47C2×#4111yescharacteristic
159C22×C47H(5,𝔽2)12yes—
160C2×D47—22no—
161C2×D47—22no—
162C2×D47—24no—
163C2×D47—24no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—416no—
168C2×D47—42no—
169C2×D47—42no—
170C2×D47#12014yes—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—42no—
174Dic47—24no—
175Dic47—41no—
176Dic47—41no—
177Dic47—42no—
178#2405—471nomaximal, Sylow
179C2×C47—24no—
180C2×C47—44no—
181C2×C47C2×#12011yescharacteristic
182C2×C47C2×#12311yescharacteristic
183C2×C47#53411yescharacteristic
184C2×C47#54612yes—
185C2×C47#54612yes—
186D47—24no—
187D47—42no—
188C23×D4—471no—
189C2×#123—472no—
190C22×C22⋊C4—471no—
191#394—472no—
192#394—472no—
193#386—472no—
194#385—471no—
195#385—471no—
196#379—471no—
197#379—471no—
198#379D4711yescharacteristic, complemented
199C47#240511yescharacteristic, complemented, Sylow
200C25—471no—
201C25C2×D4711yescharacteristic
202C22×D4—472no—
203C22×D4—472no—
204C22×D4—948no—
205C22×D4—944no—
206C23×C4—471no—
207C23×C4—471no—
208C23×C4—471no—
209#123—948no—
210C2×C4⋊C4—472no—
211C2×C4⋊C4—472no—
212C2×C22⋊C4—471no—
213C2×C22⋊C4—472no—
214C2×C22⋊C4—471no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—471no—
217C2×C22⋊C4—472no—
218C2×C22⋊C4—472no—
219C2×C22⋊C4—472no—
220C2×C22⋊C4—944no—
221C2×C22⋊C4C2×D4711yescharacteristic
222C2×C22⋊C4C2×D4711yescharacteristic
223C2×C22⋊C4C2×D4712yescomplemented
224C2×C22⋊C4C2×D4712yescomplemented
225#95—472no—
226#95—472no—
227C24—24no—
228C24—22no—
229C24—22no—
230C24—22no—
231C24—42no—
232C24—471no—
233C24—471no—
234C24—474no—
235C24—944no—
236C24—942no—
237C24—942no—
238C24—1882no—
239C24C22×D4712yes—
240C24C22×D4711yescharacteristic
241C2×D4—478no—
242C2×D4—944no—
243C2×D4—944no—
244C2×D4—944no—
245C2×D4—944no—
246C2×D4—9432no—
247C2×D4—944no—
248C22×C4—472no—
249C22×C4—471no—
250C22×C4—472no—
251C22×C4—471no—
252C22×C4—942no—
253C22×C4—942no—
254C22×C4—944no—
255C22×C4—944no—
256C22×C4—942no—
257C22×C4—1882no—
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4712yes—
260C22×C4C22×D4711yescharacteristic
261C4⋊C4—944no—
262C4⋊C4—944no—
263C22⋊C4—22no—
264C22⋊C4—24no—
265C22⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—942no—
268C22⋊C4—942no—
269C22⋊C4—944no—
270C22⋊C4—942no—
271C22⋊C4—942no—
272C22⋊C4—944no—
273C22⋊C4—1882no—
274C22⋊C4—1882no—
275C23—22no—
276C23—22no—
277C23—28no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—48no—
285C23—48no—
286C23—44no—
287C23—44no—
288C23—474no—
289C23—472no—
290C23—472no—
291C23—948no—
292C23—941no—
293C23—941no—
294C23—942no—
295C23—948no—
296C23—942no—
297C23—941no—
298C23—941no—
299C23—942no—
300C23—1884no—
301C23—1888no—
302C23—1888no—
303C23#1062535012yes—
304C23D4×D4714yes—
305C23D4×D4712yes—
306C23#1062535212yes—
307C23C23×D4711yescharacteristic
308D4—9416no—
309D4—9416no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—474no—
318C2×C4—948no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—942no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—1884no—
329C2×C4—1884no—
330C22—24no—
331C22—24no—
332C22—22no—
333C22—22no—
334C22—24no—
335C22—24no—
336C22—24no—
337C22—416no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—474no—
343C22—944no—
344C22—944no—
345C22—942no—
346C22—942no—
347C22—942no—
348C22—942no—
349C22—942no—
350C22—18816no—
351C22—1882no—
352C22—1882no—
353C22#1309400614yescomplemented
354C22C2×D4×D4712yes—
355C22C2×D4×D4711yescharacteristic
356C22C2×#1062535211yescharacteristic
357C22C2×#1062535011yescharacteristic
358C22#1309406912yes—
359C4—42no—
360C4—41no—
361C4—41no—
362C4—944no—
363C4—1882no—
364C4—1881no—
365C4—1881no—
366C2—24no—
367C2—44no—
368C2—944no—
369C2—1882no—
370C2#120×D4711yescharacteristic
371C2C2×#1309400611yescharacteristic
372C2#1568968311yescharacteristic
373C2#1568976012yes—
374C2#1568976312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2405
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#13094006C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689039C2semidirect
5. #15689038C2semidirect
6. #15688999C2semidirect
7. #15688998C2semidirect
8. #15688995C2semidirect
9. #15688979C2semidirect
10. #15688978C2semidirect
11. C47×#379C2semidirect
18. C22×C4×D47C22semidirect
19. C22×C4×D47C22semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×Dic47⋊C4C22semidirect
25. C2×C22⋊Dic47C22semidirect
26. C2×C22⋊Dic47C22semidirect
27. C2×(C2×D47)⋊C4C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
30. C2×(C2×D47)⋊C4C22semidirect
32. C47⋊#95C22semidirect
33. C47⋊#95C22semidirect
37. C2×C22⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
154. C22×C47#123semidirect
198. #379D47semidirect
199. C47#2405semidirect
223. C2×C22⋊C4C2×D47semidirect
224. C2×C22⋊C4C2×D47semidirect
353. C22#13094006semidirect