Finite Group Databasebeta

← #20249349

Subgroups — #20249349

Order 6016.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#15689051C212yesmaximal, complemented
2#15689051C212yesmaximal, complemented
3#15689048C212yesmaximal, complemented
4#15689046C212yesmaximal, complemented
5#15689026C211yesmaximal, characteristic
6#15689026C211yesmaximal, characteristic
7#15689022C211yesmaximal, characteristic, complemented
8#15689021C211yesmaximal, characteristic, complemented
9#15689019C211yesmaximal, characteristic, complemented
10#15688969C211yesmaximal, characteristic, complemented
11C47×#390C211yesmaximal, characteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C22×D4×C47C2211yescharacteristic
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C22⋊C4×C47C2212yes—
33C2×C22⋊C4×C47C2212yes—
34C2×C42×C47C2211yescharacteristic
35C24×C47C2312yes—
36C2×D4×C47—22no—
37C2×D4×C47—22no—
38C2×D4×C47—22no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C4⋊C4×C47—22no—
50C22⋊C4×C47—42no—
51C22⋊C4×C47—42no—
52C42×C47—22no—
53C22⋊Dic47—42no—
54C22⋊Dic47—42no—
55C22⋊Dic47—42no—
56C22⋊Dic47—42no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—42no—
60Dic47⋊C4—42no—
61Dic47⋊C4—42no—
62C4×Dic47—22no—
63C4×Dic47—22no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47C2411yescharacteristic
72D4×C47—44no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47#4112yes—
83C2×C4×C47#4112yes—
84C2×C4×C47#4112yes—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47C2×#4111yescharacteristic
111C22×C47C2×#4111yescharacteristic
112C22×C47C2×#4111yescharacteristic
113C22×C47H(5,𝔽2)11yescharacteristic
114C22×C47H(5,𝔽2)11yescharacteristic
115C22×C47H(5,𝔽2)11yescharacteristic
116C22×C472−1+411yescharacteristic
117C4×C47—41no—
118C4×C47—42no—
119C4×C47—41no—
120C4×C47#12614yes—
121Dic47—41no—
122Dic47—42no—
123Dic47—42no—
124Dic47—41no—
125Dic47—41no—
126Dic47—41no—
127#2644—471nomaximal, Sylow
128C2×C47—82no—
129C2×C47C2×#12611yescharacteristic
130C2×C47#54011yescharacteristic
131C2×C47#54011yescharacteristic
132C2×C47#54011yescharacteristic
133C2×C47#54211yescharacteristic
134C2×C47#54211yescharacteristic
135C2×C47#54211yescharacteristic
136#397—472no—
137#397—472no—
138#397—472no—
139#396—472no—
140#390—471no—
141#390—471no—
142#390D4711yescharacteristic
143#389—471no—
144#389—471no—
145#389—471no—
146#376—471no—
147C47#264411yescharacteristic, complemented, Sylow
148C22×D4C2×D4711yescharacteristic
149C2×C4⋊C4—471no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4C2×D4711yescharacteristic
155C2×C22⋊C4—472no—
156C2×C22⋊C4—472no—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4C2×D4712yes—
160C2×C22⋊C4C2×D4712yes—
161C2×C42—471no—
162C2×C42—471no—
163C2×C42C2×D4711yescharacteristic
164#95—471no—
165#95—471no—
166#95—471no—
167#95—471no—
168#95—472no—
169#95—472no—
170#95—472no—
171C24C22×D4712yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—22no—
175C22×C4—471no—
176C22×C4—471no—
177C22×C4—471no—
178C22×C4—471no—
179C22×C4—472no—
180C22×C4—472no—
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C22×C4C22×D4712yes—
184C22×C4C22×D4711yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—1882no—
189C4⋊C4—1882no—
190C4⋊C4—1882no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C22⋊C4—1882no—
194C22⋊C4—1882no—
195C22⋊C4—1882no—
196C22⋊C4—1882no—
197C42—22no—
198C42—942no—
199C42—942no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23C23×D4711yescharacteristic
208D4—44no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—941no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—941no—
235C2×C4—941no—
236C2×C4#1062535012yes—
237C2×C4#1062535212yes—
238C2×C4#1062535212yes—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22C2×#1062535211yescharacteristic
247C22C2×#1062535211yescharacteristic
248C22C2×#1062535011yescharacteristic
249C22#1309406911yescharacteristic
250C22#1309406911yescharacteristic
251C22#1309407011yescharacteristic
252C22#1309407111yescharacteristic
253C4—41no—
254C4—41no—
255C4—42no—
256C4—1881no—
257C4—1881no—
258C4—1881no—
259C4—1882no—
260C4—1882no—
261C4—1881no—
262C4#1309401714yes—
263C2—82no—
264C2C2×#1309401711yescharacteristic
265C2#1568972411yescharacteristic
266C2#1568972611yescharacteristic
267C2#1568972711yescharacteristic
268C2#1568973811yescharacteristic
269C2#1568974011yescharacteristic
270C2#1568974211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2644
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #15689051C2semidirect
2. #15689051C2semidirect
3. #15689048C2semidirect
4. #15689046C2semidirect
7. #15689022C2semidirect
8. #15689021C2semidirect
9. #15689019C2semidirect
10. #15688969C2semidirect
147. C47#2644semidirect