Finite Group Databasebeta

← #20249761

Subgroups — #20249761

Order 6016.

592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094003C212yesmaximal, complemented
2C2×#13094001C212yesmaximal, complemented
3#15689046C212yesmaximal, complemented
4#15689046C212yesmaximal, complemented
5#15689044C212yesmaximal, complemented
6#15689026C211yesmaximal, characteristic
7#15689020C212yesmaximal, complemented
8#15689003C211yesmaximal, characteristic
9C47×#386C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11C23×Dic47C2211yescharacteristic
12#13094003—28no—
13#13094001—28no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C22×D4×C47C2211yescharacteristic
29C23×C4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2212yes—
31C2×C22⋊C4×C47C2211yescharacteristic
32#95×C47C2212yes—
33C24×C47C2311yescharacteristic
34C24×C47C2311yescharacteristic
35C2×D4×C47—41no—
36C2×D4×C47—41no—
37C2×D4×C47Q814yescomplemented
38C22×C4×C47—24no—
39C22×C4×C47—41no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47—24no—
44C22×Dic47—41no—
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C2×Dic94—24no—
50C2×Dic94—24no—
51C2×Dic94—42no—
52C22⋊C4×C47—24no—
53C22⋊C4×C47—41no—
54C22⋊Dic47—24no—
55C22⋊Dic47—24no—
56C22⋊Dic47—24no—
57C22⋊Dic47—41no—
58C4⋊Dic47—24no—
59C4⋊Dic47—24no—
60C4⋊Dic47—41no—
61Dic47⋊C4—24no—
62Dic47⋊C4—24no—
63Dic47⋊C4—42no—
64Dic47⋊C4D418yescomplemented
65C4×Dic47—41no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—21no—
69C23×C47—21no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47C2×Q812yes—
75C23×C47C2×Q812yes—
76C23×C47C2411yescharacteristic
77D4×C47—44no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—44no—
86C2×C4×C47C2×D414yes—
87C2×C4×C47C2×Q812yes—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—44no—
99C2×Dic47C2×D414yes—
100C2×Dic47C2×D414yes—
101Dic94—48no—
102C22×C47—22no—
103C22×C47—22no—
104C22×C47—24no—
105C22×C47—24no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47C22×D412yes—
113C22×C47C22×Q811yescharacteristic
114C22×C47H(5,𝔽2)11yescharacteristic
115C22×C47H(5,𝔽2)11yescharacteristic
116C22×C472−1+412yes—
117C4×C47—22no—
118C4×C47—24no—
119C4×C47—42no—
120Dic47—24no—
121Dic47—24no—
122Dic47—42no—
123Dic47—42no—
124#2683—471nomaximal, Sylow
125C2×C47—42no—
126C2×C47—42no—
127C2×C47#53712yes—
128C2×C47#54311yescharacteristic
129C2×C47D4211yescharacteristic
130C2×C47D4×Q812yes—
131C2×C47#56311yescharacteristic
132C2×C22⋊Q8—472no—
133C2×C22⋊Q8—472no—
134#396—472no—
135#396—472no—
136#395—472no—
137#390—471no—
138#389—472no—
139#386—471no—
140#386D4711yescharacteristic
141C47#268311yescharacteristic, complemented, Sylow
142C22×Q8—472no—
143C22×D4C2×D4711yescharacteristic
144C23×C4—471no—
145C23×C4C2×D4711yescharacteristic
146C22⋊Q8—948no—
147C22⋊Q8—948no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—472no—
150C2×C4⋊C4—472no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—471no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—472no—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—471no—
159C2×C22⋊C4C2×D4712yes—
160C2×C22⋊C4C2×D4711yescharacteristic
161C2×C42—471no—
162#95—472no—
163#95—472no—
164#95C2×D4712yes—
165C24C22×D4711yescharacteristic
166C24C22×D4711yescharacteristic
167C2×Q8—944no—
168C2×Q8—944no—
169C2×Q8—1882no—
170C2×D4—41no—
171C2×D4—41no—
172C2×D4Dic9414yescomplemented
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—472no—
176C22×C4—472no—
177C22×C4—472no—
178C22×C4—472no—
179C22×C4—944no—
180C22×C4—1881no—
181C22×C4C22×D4712yes—
182C22×C4C22×D4711yescharacteristic
183C22×C4C22×D4712yes—
184C4⋊C4—478no—
185C4⋊C4—944no—
186C4⋊C4—944no—
187C4⋊C4—944no—
188C4⋊C4—944no—
189C4⋊C4—1882no—
190C4⋊C4—1881no—
191C22⋊C4—24no—
192C22⋊C4—41no—
193C22⋊C4—944no—
194C22⋊C4—944no—
195C22⋊C4—944no—
196C22⋊C4—1881no—
197C42—1881no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—22no—
205C23—22no—
206C23C2×Dic9412yes—
207C23C2×Dic9412yes—
208C23C23×D4711yescharacteristic
209Q8—1888no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—474no—
220C2×C4—474no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—1884no—
232C2×C4C2×Dic9412yes—
233C2×C4D4×D4714yes—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—24no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—42no—
244C22C2×D4×D4712yes—
245C22C22×Dic9411yescharacteristic
246C22#1309406911yescharacteristic
247C22#1309406911yescharacteristic
248C22#1309407112yes—
249C4—22no—
250C4—24no—
251C4—42no—
252C4—944no—
253C4—944no—
254C4—1882no—
255C4—1882no—
256C2—42no—
257C2—42no—
258C2#1568970212yes—
259C2#1568974911yescharacteristic
260C2#1568975511yescharacteristic
261C2D4×Dic9412yes—
262C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2683
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13094003C2semidirect
2. C2×#13094001C2semidirect
3. #15689046C2semidirect
4. #15689046C2semidirect
5. #15689044C2semidirect
7. #15689020C2semidirect
37. C2×D4×C47Q8semidirect
64. Dic47⋊C4D4semidirect
141. C47#2683semidirect
172. C2×D4Dic94semidirect