Finite Group Databasebeta

← #20249751

Subgroups — #20249751

Order 6016.

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

normal subgroups only

This group has 668 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×#13094006C212yesmaximal, complemented
2C2×#13093997C212yesmaximal, complemented
3#15689046C212yesmaximal, complemented
4#15689039C212yesmaximal, complemented
5#15689031C212yesmaximal, complemented
6#15689025C211yesmaximal, characteristic, complemented
7#15689021C211yesmaximal, characteristic, complemented
8#15688994C212yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C22×C22⋊D47C2212yes—
13C22×C4×D47C2212yes—
14#13094006—28no—
15#13093997—28no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C22×D4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2212yes—
31C2×C22⋊C4×C47C2212yes—
32C2×C42×C47C2211yescharacteristic
33C24×C47C2312yes—
34C23×D47C2312yes—
35C2×D4×C47—22no—
36C2×D4×C47—41no—
37C2×D4×C47—41no—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—24no—
43C2×C22⋊D47—24no—
44C2×C22⋊D47—24no—
45C2×C22⋊D47—42no—
46C2×C22⋊D47—42no—
47C2×C22⋊D47—42no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C2×D188—41no—
52C2×D188—41no—
53C2×D188D414yescomplemented
54C2×C4×D47—24no—
55C2×C4×D47—24no—
56C2×C4×D47—42no—
57C4⋊C4×C47—41no—
58C22⋊C4×C47—24no—
59C22⋊C4×C47—24no—
60C42×C47—41no—
61C22⋊Dic47—24no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66C4⋊Dic47—41no—
67C4⋊Dic47—41no—
68C4⋊Dic47D414yescomplemented
69Dic47⋊C4—24no—
70Dic47⋊C4—24no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2411yescharacteristic
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47C2×D414yes—
86D4×C47—44no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C2×C4×C47#4112yes—
99C22⋊D47—48no—
100C22⋊D47—48no—
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×Dic47C2×D414yes—
110D188—44no—
111C4×D47—48no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47C22×D411yescharacteristic
120C22×C47C22×D411yescharacteristic
121C22×C47C2×#4111yescharacteristic
122C22×C47H(5,𝔽2)11yescharacteristic
123C22×C47H(5,𝔽2)11yescharacteristic
124C22×C47H(5,𝔽2)11yescharacteristic
125C22×C472−1+411yescharacteristic
126C2×D47—24no—
127C2×D47—24no—
128C2×D47—24no—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—42no—
133C4×C47—22no—
134C4×C47—22no—
135C4×C47—22no—
136C4×C47—42no—
137Dic47—24no—
138Dic47—42no—
139Dic47—42no—
140#2682—471nomaximal, Sylow
141C2×C47—82no—
142C2×C47#53411yescharacteristic
143C2×C47#53711yescharacteristic
144C2×C47#53811yescharacteristic
145C2×C47D4211yescharacteristic
146C2×C47#54711yescharacteristic
147C2×C47#55011yescharacteristic
148C2×C47#56211yescharacteristic
149D47—44no—
150C2×#123—472no—
151C2×#121—472no—
152#396—472no—
153#394—472no—
154#392—472no—
155#390—471no—
156#390D4711yescharacteristic, complemented
157#389—471no—
158#385—472no—
159C47#268211yescharacteristic, complemented, Sylow
160C22×D4—472no—
161C22×D4—472no—
162C22×D4—471no—
163C22×D4C2×D4711yescharacteristic
164C23×C4—472no—
165#123—948no—
166#121—948no—
167C2×C4⋊C4—471no—
168C2×C4⋊C4—472no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—471no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4C2×D4711yescharacteristic
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4C2×D4712yes—
179C2×C22⋊C4C2×D4712yes—
180C2×C42C2×D4711yescharacteristic
181#95—472no—
182#95—472no—
183C24—472no—
184C24C22×D4712yes—
185C2×D4—22no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—474no—
189C2×D4—944no—
190C2×D4—944no—
191C2×D4—944no—
192C2×D4—1881no—
193C2×D4—1881no—
194C2×D4—1882no—
195C2×D4—1882no—
196C2×D4—1882no—
197C22×C4—472no—
198C22×C4—472no—
199C22×C4—472no—
200C22×C4—944no—
201C22×C4—944no—
202C22×C4—1882no—
203C22×C4C22×D4712yes—
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4711yescharacteristic
206C22×C4C22×D4711yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—474no—
209C4⋊C4—944no—
210C4⋊C4—944no—
211C4⋊C4—1881no—
212C4⋊C4—1881no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—944no—
216C22⋊C4—944no—
217C22⋊C4—944no—
218C22⋊C4—944no—
219C22⋊C4—1882no—
220C42—41no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—474no—
229C23—942no—
230C23—942no—
231C23—942no—
232C23—942no—
233C23—942no—
234C23—942no—
235C23C23×D4711yescharacteristic
236D4—44no—
237D4—1884no—
238D4—1888no—
239D4—1888no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—474no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—1888no—
259C2×C4#1062535012yes—
260C2×C4D4×D4712yes—
261C2×C4D4×D4712yes—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—944no—
270C22—944no—
271C22—944no—
272C22—1882no—
273C22—1882no—
274C22—1882no—
275C22—1882no—
276C22C2×D4×D4711yescharacteristic
277C22C2×D4×D4711yescharacteristic
278C22C2×#1062535011yescharacteristic
279C22#1309406911yescharacteristic
280C22#1309406911yescharacteristic
281C22#1309407011yescharacteristic
282C22#1309407111yescharacteristic
283C4—22no—
284C4—22no—
285C4—22no—
286C4—42no—
287C4—944no—
288C4—1882no—
289C4—1882no—
290C2—82no—
291C2—1884no—
292C2#1568968111yescharacteristic
293C2#1568970011yescharacteristic
294C2#1568971111yescharacteristic
295C2#1568975811yescharacteristic
296C2#1568977811yescharacteristic
297C2#1568979411yescharacteristic
298C2#1568986711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2682
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094006C2semidirect
2. C2×#13093997C2semidirect
3. #15689046C2semidirect
4. #15689039C2semidirect
5. #15689031C2semidirect
6. #15689025C2semidirect
7. #15689021C2semidirect
8. #15688994C2semidirect
9. C47×#390C2semidirect
53. C2×D188D4semidirect
68. C4⋊Dic47D4semidirect
156. #390D47semidirect
159. C47#2682semidirect