Finite Group Databasebeta

← #20251401

Subgroups — #20251401

Order 6016.

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

normal subgroups only

This group has 478 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
1C2×#13094003C211yesmaximal, characteristic, complemented
2#15689056C212yesmaximal, complemented
3#15689053C211yesmaximal, characteristic, complemented
4#15689051C212yesmaximal, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689046C212yesmaximal, complemented
7#15689043C211yesmaximal, characteristic, complemented
8#15689037C212yesmaximal
9#15689035C211yesmaximal, characteristic, complemented
10#15688983C211yesmaximal, characteristic, complemented
11C2×#123×C47C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094003—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C22×D4×C47C2211yescharacteristic
30C23×C4×C47C2211yescharacteristic
31#123×C47—24no—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C24×C47C2311yescharacteristic
39C2×D4×C47—22no—
40C2×D4×C47—42no—
41C22×C4×C47—42no—
42C22×C4×C47D414yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C2×Dic94—22no—
53C2×Dic94—42no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—22no—
56C22⋊C4×C47—22no—
57C22⋊C4×C47—22no—
58C22⋊C4×C47—22no—
59C22⋊Dic47—24no—
60C22⋊Dic47—42no—
61C22⋊Dic47—42no—
62C22⋊Dic47—42no—
63C4⋊Dic47—22no—
64C4⋊Dic47—42no—
65Dic47⋊C4—24no—
66Dic47⋊C4—42no—
67Dic47⋊C4—42no—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—21no—
77C23×C47C2×D412yes—
78C23×C47C2411yescharacteristic
79D4×C47—44no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—44no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104Dic94—44no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47C22×D411yescharacteristic
116C22×C47H(5,𝔽2)12yes—
117C22×C47H(5,𝔽2)11yescharacteristic
118C22×C472−1+412yes—
119C22×C472−1+411yescharacteristic
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—41no—
123C4×C47—41no—
124C4×C47—41no—
125Dic47—42no—
126Dic47—42no—
127Dic47—42no—
128Dic47—42no—
129#2814—471nomaximal, Sylow
130C2×C47—42no—
131C2×C47—81no—
132C2×C47#53411yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#53711yescharacteristic
135C2×C47#56212yes—
136C2×C47#56312yes—
137C2×#123D4711yescharacteristic
138C2×C22⋊Q8—471no—
139#398—471no—
140#398—472no—
141#397—471no—
142#397—472no—
143#396—472no—
144#395—471no—
145#394—472no—
146#393—471no—
147#380—471no—
148C47#281411yescharacteristic, complemented, Sylow
149C22×Q8—471no—
150C22×D4C2×D4711yescharacteristic
151C23×C4C2×D4711yescharacteristic
152#123—24no—
153C22⋊Q8—944no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C4⋊C4C2×D4711yescharacteristic
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4C2×D4711yescharacteristic
167C2×C22⋊C4C2×D4711yescharacteristic
168#95—471no—
169#95—471no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95—472no—
174C24C22×D4711yescharacteristic
175C24C22×D4711yescharacteristic
176C2×Q8—942no—
177C2×Q8—1882no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—42no—
181C22×C4—472no—
182C22×C4—472no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4C22⋊D4714yes—
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4711yescharacteristic
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—1882no—
196C4⋊C4—1882no—
197C4⋊C4—1882no—
198C22⋊C4—22no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4—944no—
202C22⋊C4—1882no—
203C22⋊C4—1882no—
204C22⋊C4—1882no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—21no—
214C23C2×C22⋊D4712yes—
215C23C23×D4711yescharacteristic
216Q8—1884no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4C2×C22⋊D4712yes—
241C2×C4C2×C22⋊D4712yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22C22×C22⋊D4711yescharacteristic
253C22#1309406912yes—
254C22#1309407011yescharacteristic
255C22#1309407112yes—
256C22#1309407111yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—1882no—
263C4—1882no—
264C4—1882no—
265C4—1882no—
266C2—42no—
267C2—81no—
268C2#1568968211yescharacteristic
269C2#1568969411yescharacteristic
270C2#1568970111yescharacteristic
271C2#1568987012yes—
272C2#1568987612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2814
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13094003C2semidirect
2. #15689056C2semidirect
3. #15689053C2semidirect
4. #15689051C2semidirect
5. #15689048C2semidirect
6. #15689046C2semidirect
7. #15689043C2semidirect
9. #15689035C2semidirect
10. #15688983C2semidirect
148. C47#2814semidirect