Finite Group Databasebeta

← #20247022

Subgroups — #20247022

Order 6016.

1348 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 193 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, complemented
2C2×#13094020C211yesmaximal, characteristic, complemented
3C2×#13093995C211yesmaximal, characteristic, complemented
4C2×#13093992C214yesmaximal, complemented
5#15689031C214yesmaximal, complemented
6#15689026C211yesmaximal, characteristic, complemented
7#15689025C211yesmaximal, characteristic, complemented
8C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
9C2×#127×C47C211yesmaximal, characteristic, complemented
10C24×D47C2212yes—
11C22×D188C2211yescharacteristic
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2214yescomplemented
15C2×D4×D47—24no—
16C2×D4×D47—24no—
17C2×D4×D47—24no—
18C22×C4×D47C2211yescharacteristic
19#13094020—24no—
20#13093995—24no—
21#13093992—216no—
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×C22⋊Dic47C2214yescomplemented
24C2×C22⋊Dic47C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2214yescomplemented
27C2×C4×Dic47C2211yescharacteristic, complemented
28C47⋊#95C2212yescomplemented
29C22×D4×C47C2211yescharacteristic
30C22×D4×C47C2211yescharacteristic, complemented
31C22×D4×C47C2214yescomplemented
32#127×C47—24no—
33C2×C42×C47C2211yescharacteristic, complemented
34C24×C47C2312yes—
35C24×C47C2312yes—
36C23×D47—24no—
37C23×D47—24no—
38C23×D47—24no—
39C23×D47—28no—
40C23×D47—44no—
41C23×D47C2312yes—
42C23×D47C2311yescharacteristic
43C2×D4×C47—28no—
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—22no—
47C2×D4×C47—22no—
48C2×D4×C47—22no—
49C2×D4×C47—28no—
50C2×D4×C47—44no—
51C2×D4×C47D414yescomplemented
52C22×C4×C47C2312yes—
53C22×C4×C47C2311yescharacteristic
54C2×C22⋊D47—24no—
55C2×C22⋊D47—24no—
56C2×C22⋊D47—28no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—28no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—28no—
61C2×C22⋊D47—44no—
62C22×Dic47C2312yes—
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2312yes—
65D4×D47—232no—
66C2×D188—22no—
67C2×D188—22no—
68C2×D188D414yescomplemented
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47D414yescomplemented
72C42×C47—22no—
73C22⋊Dic47—24no—
74C22⋊Dic47—28no—
75(C2×D47)⋊C4—28no—
76(C2×D47)⋊C4D418yescomplemented
77C4⋊Dic47—22no—
78C4×Dic47—22no—
79C23×C47—24no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—24no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—24no—
86C23×C47—22no—
87C23×C47—24no—
88C23×C47C2×D414yes—
89C23×C47C2411yescharacteristic
90C22×D47—21no—
91C22×D47—21no—
92C22×D47—22no—
93C22×D47—216no—
94C22×D47—24no—
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—24no—
98C22×D47—416no—
99C22×D47—416no—
100C22×D47—48no—
101C22×D47—48no—
102C22×D47C2×D414yes—
103C22×D47C2×D414yes—
104C22×D47C2×D412yes—
105D4×C47—28no—
106D4×C47—416no—
107D4×C47—44no—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47C2×D412yes—
111C2×C4×C47C2×D412yes—
112C2×C4×C47C2×D412yes—
113C2×C4×C47C2×D414yescomplemented
114C22⋊D47—216no—
115C22⋊D47—416no—
116C22⋊D47—48no—
117C2×Dic47—22no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—24no—
123C2×Dic47C2×D412yes—
124C2×Dic47C2×D414yescomplemented
125D188—28no—
126C4×D47—28no—
127C22×C47—24no—
128C22×C47—28no—
129C22×C47—42no—
130C22×C47—42no—
131C22×C47—44no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47—42no—
135C22×C47—44no—
136C22×C47—44no—
137C22×C47C22×D411yescharacteristic
138C22×C47C22×D411yescharacteristic
139C22×C47C22×D412yes—
140C22×C47C22×D411yescharacteristic
141C22×C47H(5,𝔽2)12yes—
142C2×D47—22no—
143C2×D47—22no—
144C2×D47—24no—
145C2×D47—24no—
146C2×D47—24no—
147C2×D47—28no—
148C2×D47—432no—
149C2×D47—42no—
150C2×D47—42no—
151C2×D47—44no—
152C2×D47#12714yescomplemented
153C4×C47—24no—
154C4×C47#12014yescomplemented
155Dic47—22no—
156Dic47—24no—
157Dic47—42no—
158#2433—471nomaximal, Sylow
159C2×C47—44no—
160C2×C47—82no—
161C2×C47C2×#12011yescharacteristic
162C2×C47C2×#12711yescharacteristic
163C2×C47#53511yescharacteristic
164C2×C47D4212yes—
165C2×C47D4212yes—
166D47—24no—
167D47—44no—
168C23×D4—471no—
169C2×#127—471no—
170C2×#127D4711yescharacteristic, complemented
171C2×#121—471no—
172C2×#120—474no—
173#392—474no—
174#390—471no—
175#390—471no—
176C4×C22⋊C4—471no—
177C47#243311yescharacteristic, complemented, Sylow
178C25—472no—
179C22×D4—472no—
180C22×D4—472no—
181C22×D4—474no—
182C22×D4—471no—
183C22×D4—944no—
184C22×D4—944no—
185C22×D4—944no—
186C22×D4C2×D4711yescharacteristic
187C22×D4C2×D4711yescharacteristic, complemented
188C22×D4C2×D4714yescomplemented
189C23×C4—471no—
190#127—24no—
191#127—944no—
192#121—944no—
193#120—9416no—
194C2×C4⋊C4—471no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—474no—
197C2×C22⋊C4—472no—
198C2×C22⋊C4—474no—
199C2×C42—471no—
200C2×C42C2×D4711yescharacteristic, complemented
201#95—472no—
202C24—471no—
203C24—472no—
204C24—944no—
205C24—944no—
206C24—948no—
207C24—944no—
208C24—1884no—
209C24C22×D4712yes—
210C24C22×D4712yes—
211C2×D4—28no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—28no—
217C2×D4—22no—
218C2×D4—44no—
219C2×D4—474no—
220C2×D4—944no—
221C2×D4—948no—
222C2×D4—9432no—
223C2×D4—944no—
224C2×D4—944no—
225C2×D4—948no—
226C2×D4—944no—
227C2×D4—948no—
228C2×D4—942no—
229C2×D4—942no—
230C2×D4—1884no—
231C2×D4C22⋊D4714yescomplemented
232C22×C4—471no—
233C22×C4—472no—
234C22×C4—474no—
235C22×C4—472no—
236C22×C4—942no—
237C22×C4—942no—
238C22×C4C22×D4712yes—
239C22×C4C22×D4711yescharacteristic
240C4⋊C4—942no—
241C22⋊C4—478no—
242C22⋊C4—948no—
243C22⋊C4—944no—
244C22⋊C4—948no—
245C42—22no—
246C42—942no—
247C23—24no—
248C23—22no—
249C23—22no—
250C23—24no—
251C23—22no—
252C23—24no—
253C23—22no—
254C23—22no—
255C23—24no—
256C23—474no—
257C23—472no—
258C23—474no—
259C23—9416no—
260C23—941no—
261C23—941no—
262C23—942no—
263C23—944no—
264C23—942no—
265C23—942no—
266C23—944no—
267C23—18816no—
268C23—1888no—
269C23—18816no—
270C23—1888no—
271C23C2×C22⋊D4714yes—
272C23C23×D4711yescharacteristic
273D4—28no—
274D4—416no—
275D4—44no—
276D4—9416no—
277D4—948no—
278D4—18816no—
279D4—1888no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—472no—
283C2×C4—474no—
284C2×C4—942no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—942no—
288C2×C4—948no—
289C2×C4—944no—
290C2×C4—942no—
291C2×C4D4×D4712yes—
292C2×C4D4×D4712yes—
293C2×C4D4×D4714yescomplemented
294C2×C4C2×C22⋊D4712yes—
295C22—28no—
296C22—24no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—44no—
301C22—44no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—474no—
306C22—944no—
307C22—944no—
308C22—942no—
309C22—942no—
310C22—948no—
311C22—944no—
312C22—18832no—
313C22—1884no—
314C22—1882no—
315C22—1882no—
316C22C2×D4×D4712yes—
317C22C2×D4×D4711yescharacteristic
318C22C2×D4×D4711yescharacteristic
319C22C22×C22⋊D4711yescharacteristic
320C22#1309406912yes—
321C4—24no—
322C4—944no—
323C4—942no—
324C4—1882no—
325C4#1309399214yescomplemented
326C2—44no—
327C2—82no—
328C2—944no—
329C2—1884no—
330C2C2×#1309399211yescharacteristic
331C2#127×D4711yescharacteristic
332C2#1568968611yescharacteristic
333C2D4×C22⋊D4712yes—
334C2#1568975812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#127×C47C2
hypercenterC2×#127D47
hypocenterC47#2433
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13094020C2semidirect
3. C2×#13093995C2semidirect
4. C2×#13093992C2semidirect
5. #15689031C2semidirect
6. #15689026C2semidirect
7. #15689025C2semidirect
8. C4×(C2×D47)⋊C4C2semidirect
9. C2×#127×C47C2semidirect
14. C22×C22⋊D47C22semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×C22⋊Dic47C22semidirect
24. C2×C22⋊Dic47C22semidirect
26. C2×(C2×D47)⋊C4C22semidirect
27. C2×C4×Dic47C22semidirect
28. C47⋊#95C22semidirect
30. C22×D4×C47C22semidirect
31. C22×D4×C47C22semidirect
33. C2×C42×C47C22semidirect
51. C2×D4×C47D4semidirect
68. C2×D188D4semidirect
71. C2×C4×D47D4semidirect
76. (C2×D47)⋊C4D4semidirect
113. C2×C4×C47C2×D4semidirect
124. C2×Dic47C2×D4semidirect
152. C2×D47#127semidirect
154. C4×C47#120semidirect
170. C2×#127D47semidirect
177. C47#2433semidirect
187. C22×D4C2×D47semidirect
188. C22×D4C2×D47semidirect
200. C2×C42C2×D47semidirect
231. C2×D4C22⋊D47semidirect
293. C2×C4D4×D47semidirect
325. C4#13093992semidirect