Finite Group Databasebeta

← #20249361

Subgroups — #20249361

Order 6016.

436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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#15689065C212yesmaximal, complemented
2#15689062C212yesmaximal, complemented
3#15689056C212yesmaximal, complemented
4#15689055C212yesmaximal, complemented
5#15688998C212yesmaximal
6#15688995C212yesmaximal
7#15688983C211yesmaximal, characteristic
8C2×C47⋊#95C211yesmaximal, characteristic
9C47×#380C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C23×C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30#95×C47C2212yes—
31C24×C47C2311yescharacteristic
32C22×C4×C47—41no—
33C22×C4×C47—41no—
34C22×C4×C47Q814yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—22no—
40C22×Dic47—22no—
41C22×Dic47—41no—
42C22×Dic47—41no—
43C22×Dic47—41no—
44C22×Dic47—41no—
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C4⋊C4×C47—41no—
50C4⋊C4×C47—41no—
51C22⋊C4×C47—24no—
52C22⋊Dic47—24no—
53C4⋊Dic47—41no—
54C4⋊Dic47—42no—
55C4⋊Dic47—41no—
56C4⋊Dic47—42no—
57Dic47⋊C4—42no—
58Dic47⋊C4—42no—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—21no—
63C23×C47C2×Q812yes—
64C23×C47#4112yes—
65C23×C47#4112yes—
66C23×C47C2411yescharacteristic
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—44no—
78C2×C4×C47C2×Q812yes—
79C2×C4×C47C2×Q812yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—44no—
93C2×Dic47—44no—
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—22no—
97C22×C47—22no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47#12514yes—
101C22×C47C22×Q811yescharacteristic
102C22×C47C2×#4111yescharacteristic
103C22×C47C2×#4111yescharacteristic
104C22×C47H(5,𝔽2)11yescharacteristic
105C22×C47H(5,𝔽2)11yescharacteristic
106C22×C47H(5,𝔽2)11yescharacteristic
107C22×C472−1+411yescharacteristic
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—42no—
111C4×C47—42no—
112Dic47—42no—
113Dic47—42no—
114Dic47—42no—
115Dic47—42no—
116#2646—471nomaximal, Sylow
117C2×C47—24no—
118C2×C47C2×#12511yescharacteristic
119C2×C47#53811yescharacteristic
120C2×C47#53811yescharacteristic
121C2×C47#53911yescharacteristic
122C2×C47#53911yescharacteristic
123C2×C47#54311yescharacteristic
124C2×C47#54411yescharacteristic
125#400—472no—
126#400—472no—
127#398—472no—
128#398—472no—
129#385—472no—
130#385—472no—
131#380—471no—
132#380D4711yescharacteristic
133C2×#95—471no—
134C47#264611yescharacteristic, complemented, Sylow
135C23×C4—471no—
136C23×C4—471no—
137C23×C4C2×D4711yescharacteristic
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4C2×D4711yescharacteristic
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C22⋊C4—472no—
147C2×C22⋊C4C2×D4712yes—
148#95—472no—
149#95—472no—
150#95—472no—
151#95—472no—
152#95—472no—
153#95—472no—
154#95—472no—
155#95C2×D4712yes—
156C24C22×D4711yescharacteristic
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4—472no—
162C22×C4—472no—
163C22×C4—942no—
164C22×C4—942no—
165C22×C4—1881no—
166C22×C4—1881no—
167C22×C4—1881no—
168C22×C4—1881no—
169C22×C4Dic9414yes—
170C22×C4C22×D4712yes—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—1882no—
177C4⋊C4—1882no—
178C4⋊C4—1881no—
179C4⋊C4—1881no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C22⋊C4—24no—
183C22⋊C4—944no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23C2×Dic9412yes—
189C23#1062535212yes—
190C23#1062535412yes—
191C23C23×D4711yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—1884no—
216C2×C4—1884no—
217C2×C4C2×Dic9412yes—
218C2×C4C2×Dic9412yes—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#1309401514yes—
226C22C22×Dic9411yescharacteristic
227C22C2×#1062535211yescharacteristic
228C22C2×#1062535411yescharacteristic
229C22#1309406911yescharacteristic
230C22#1309406911yescharacteristic
231C22#1309407011yescharacteristic
232C22#1309407111yescharacteristic
233C4—22no—
234C4—22no—
235C4—42no—
236C4—42no—
237C4—1882no—
238C4—1882no—
239C4—1882no—
240C4—1882no—
241C2—24no—
242C2C2×#1309401511yescharacteristic
243C2#1568971011yescharacteristic
244C2#1568971311yescharacteristic
245C2#1568971811yescharacteristic
246C2#1568972211yescharacteristic
247C2#1568974911yescharacteristic
248C2#1568975111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#380C2
hypercenter#380D47
hypocenterC47#2646
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
2. #15689062C2semidirect
3. #15689056C2semidirect
4. #15689055C2semidirect
134. C47#2646semidirect