Finite Group Databasebeta

← #20249949

Subgroups — #20249949

Order 6016.

680 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094005C211yesmaximal, characteristic, complemented
2#15689051C212yesmaximal, complemented
3#15689046C212yesmaximal, complemented
4#15689037C212yesmaximal, complemented
5#15689026C211yesmaximal, characteristic, complemented
6#15689017C212yesmaximal, complemented
7#15689003C212yesmaximal, complemented
8#15688979C212yesmaximal, complemented
9C2×#120×C47C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic, complemented
11#13094005—24no—
12C2×C4⋊Dic47C2211yescharacteristic, complemented
13C2×Dic47⋊C4C2212yescomplemented
14C2×Dic47⋊C4C2212yescomplemented
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2211yescharacteristic, complemented
22C2×C22⋊Dic47C2212yescomplemented
23C2×C4×Dic47C2211yescharacteristic, complemented
24C47⋊#95C2212yescomplemented
25C47⋊#95C2212yescomplemented
26C47⋊#95C2212yescomplemented
27C25×C47C2211yescharacteristic
28C22×D4×C47C2212yes—
29C22×D4×C47C2211yescharacteristic
30#120×C47—24no—
31C2×C22⋊C4×C47C2212yes—
32C2×C22⋊C4×C47C2211yescharacteristic
33C24×C47—22no—
34C24×C47—24no—
35C24×C47—42no—
36C24×C47—41no—
37C24×C47—41no—
38C24×C47C2311yescharacteristic
39C24×C47C2311yescharacteristic
40C24×C47C2312yes—
41C2×D4×C47—24no—
42C2×D4×C47—24no—
43C2×D4×C47—41no—
44C2×D4×C47—41no—
45C2×D4×C47—42no—
46C2×D4×C47D414yes—
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×Dic47—22no—
50C22×Dic47—41no—
51C22×Dic47—41no—
52C22×Dic47C2312yes—
53C22×Dic47C2312yes—
54C22×Dic47C2312yes—
55C22×Dic47C2312yes—
56C22⋊C4×C47—22no—
57C22⋊C4×C47—24no—
58C22⋊Dic47—24no—
59C22⋊Dic47—22no—
60C22⋊Dic47—24no—
61C22⋊Dic47—42no—
62C22⋊Dic47—42no—
63C22⋊Dic47—42no—
64C22⋊Dic47—42no—
65C22⋊Dic47—42no—
66C4⋊Dic47—41no—
67Dic47⋊C4—24no—
68Dic47⋊C4—42no—
69C4×Dic47—41no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—21no—
80C23×C47—21no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—22no—
84C23×C47—48no—
85C23×C47—44no—
86C23×C47—44no—
87C23×C47—48no—
88C23×C47—44no—
89C23×C47C2×D412yes—
90C23×C47C2×D412yes—
91C23×C47#4114yes—
92C23×C47C2411yescharacteristic
93D4×C47—44no—
94D4×C47—48no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47C2×D412yes—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—44no—
114C22×C47—22no—
115C22×C47—22no—
116C22×C47—24no—
117C22×C47—24no—
118C22×C47—24no—
119C22×C47—24no—
120C22×C47—24no—
121C22×C47—416no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—41no—
128C22×C47—41no—
129C22×C47—41no—
130C22×C47—41no—
131C22×C47—42no—
132C22×C47C22×D411yescharacteristic
133C22×C47C2×#4112yes—
134C22×C47H(5,𝔽2)11yescharacteristic
135C22×C47H(5,𝔽2)11yescharacteristic
136C22×C47H(5,𝔽2)12yes—
137C4×C47—22no—
138C4×C47—42no—
139Dic47—42no—
140Dic47—42no—
141Dic47—42no—
142Dic47—42no—
143#2697—471nomaximal, Sylow
144C2×C47—42no—
145C2×C47—42no—
146C2×C47—44no—
147C2×C47#53411yescharacteristic
148C2×C47#53812yes—
149C2×C47#54612yes—
150C2×C47#55111yescharacteristic
151C2×C47#56011yescharacteristic
152C2×#123—471no—
153C2×#120D4711yescharacteristic
154#397—472no—
155#396—472no—
156#394—472no—
157#390—471no—
158#388—472no—
159#386—472no—
160#379—472no—
161C47#269711yescharacteristic, complemented, Sylow
162C25C2×D4711yescharacteristic
163C22×D4C2×D4712yes—
164C22×D4C2×D4711yescharacteristic
165C23×C4—471no—
166#123—944no—
167#120—24no—
168C2×C4⋊C4—472no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—471no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4—471no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4C2×D4712yes—
180C2×C22⋊C4C2×D4711yescharacteristic
181C2×C42—471no—
182#95—472no—
183#95—472no—
184#95—472no—
185C24—24no—
186C24—22no—
187C24—42no—
188C24—41no—
189C24—41no—
190C24C22×D4712yes—
191C24C22×D4711yescharacteristic
192C24C22×D4711yescharacteristic
193C2×D4—24no—
194C2×D4—24no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—42no—
198C2×D4C22⋊D4714yes—
199C22×C4—472no—
200C22×C4—472no—
201C22×C4—472no—
202C22×C4—472no—
203C22×C4—942no—
204C22×C4—1881no—
205C22×C4—1881no—
206C22×C4C22×D4712yes—
207C22×C4C22×D4711yescharacteristic
208C4⋊C4—944no—
209C4⋊C4—1882no—
210C4⋊C4—1881no—
211C22⋊C4—22no—
212C22⋊C4—24no—
213C22⋊C4—944no—
214C22⋊C4—942no—
215C22⋊C4—944no—
216C22⋊C4—1882no—
217C22⋊C4—1882no—
218C22⋊C4—1882no—
219C22⋊C4—1882no—
220C22⋊C4—1882no—
221C42—1881no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23—48no—
237C23—44no—
238C23—44no—
239C23—48no—
240C23—44no—
241C23#1062535214yes—
242C23C2×C22⋊D4712yes—
243C23C2×C22⋊D4712yes—
244C23C23×D4711yescharacteristic
245D4—44no—
246D4—48no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—1884no—
265C2×C4C2×C22⋊D4712yes—
266C22—24no—
267C22—24no—
268C22—24no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—24no—
273C22—416no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22C22×C22⋊D4711yescharacteristic
285C22C2×#1062535212yes—
286C22#1309406912yes—
287C22#1309406911yescharacteristic
288C22#1309406911yescharacteristic
289C4—22no—
290C4—42no—
291C4—1882no—
292C4—1882no—
293C4—1882no—
294C4—1882no—
295C2—44no—
296C2—42no—
297C2—42no—
298C2#1568968211yescharacteristic
299C2#1568970812yes—
300C2#1568976712yes—
301C2#1568980411yescharacteristic
302C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2697
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. #15689051C2semidirect
3. #15689046C2semidirect
4. #15689037C2semidirect
5. #15689026C2semidirect
6. #15689017C2semidirect
7. #15689003C2semidirect
8. #15688979C2semidirect
10. C23×Dic47C22semidirect
12. C2×C4⋊Dic47C22semidirect
13. C2×Dic47⋊C4C22semidirect
14. C2×Dic47⋊C4C22semidirect
21. C2×C22⋊Dic47C22semidirect
22. C2×C22⋊Dic47C22semidirect
23. C2×C4×Dic47C22semidirect
24. C47⋊#95C22semidirect
25. C47⋊#95C22semidirect
26. C47⋊#95C22semidirect
161. C47#2697semidirect