Finite Group Databasebeta

← #20250348

Subgroups — #20250348

Order 6016.

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

normal subgroups only

This group has 476 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×#13094019C212yesmaximal, complemented
2#15689058C212yesmaximal, complemented
3#15689045C212yesmaximal, complemented
4#15689041C212yesmaximal
5#15689025C211yesmaximal, characteristic
6#15689021C211yesmaximal, characteristic, complemented
7#15689020C212yesmaximal, complemented
8#15689013C212yesmaximal, complemented
9C47×#389C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094019—28no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31#95×C47C2212yes—
32C23×D47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×D188—22no—
42C2×D188—41no—
43C2×D188—41no—
44C4⋊C4×C47—24no—
45C4⋊C4×C47—22no—
46C4⋊C4×C47—41no—
47C42×C47—41no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4—24no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—42no—
53(C2×D47)⋊C4—42no—
54C4⋊Dic47—41no—
55C4⋊Dic47—41no—
56C4⋊Dic47D414yescomplemented
57Dic47⋊C4—24no—
58Dic47⋊C4—24no—
59Dic47⋊C4—42no—
60C4×Dic47—24no—
61C23×C47C2411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D412yes—
82C2×C4×C47#4112yes—
83C2×C4×C47#4112yes—
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×Dic47C2×D414yes—
93D188—44no—
94C22×C47C22×D411yescharacteristic
95C22×C47C2×#4111yescharacteristic
96C22×C47C2×#4111yescharacteristic
97C22×C47H(5,𝔽2)11yescharacteristic
98C22×C47H(5,𝔽2)11yescharacteristic
99C22×C472−1+411yescharacteristic
100C22×C472−1+411yescharacteristic
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—22no—
111C4×C47—42no—
112C4×C47—42no—
113Dic47—24no—
114Dic47—42no—
115Dic47—42no—
116#2727—471nomaximal, Sylow
117C2×C47#53711yescharacteristic
118C2×C47#53811yescharacteristic
119C2×C47#53911yescharacteristic
120C2×C47#54711yescharacteristic
121C2×C47#55011yescharacteristic
122C2×C47#55611yescharacteristic
123C2×C47#56311yescharacteristic
124D47—82no—
125C2×#126—472no—
126#399—472no—
127#396—472no—
128#394—472no—
129#390—471no—
130#389—471no—
131#389—472no—
132#389D4711yescharacteristic, complemented
133#388—472no—
134C47#272711yescharacteristic, complemented, Sylow
135C22×D4—471no—
136#126—948no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4C2×D4712yes—
144C2×C4⋊C4C2×D4711yescharacteristic
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C22⋊C4—472no—
147C2×C22⋊C4—472no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C42—472no—
153C2×C42C2×D4711yescharacteristic
154#95—472no—
155#95—472no—
156#95C2×D4712yes—
157C24—472no—
158C2×D4—942no—
159C2×D4—1881no—
160C2×D4—1881no—
161C22×C4—472no—
162C22×C4—472no—
163C22×C4—472no—
164C22×C4C22×D4712yes—
165C22×C4C22×D4712yes—
166C22×C4C22×D4711yescharacteristic
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4711yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—41no—
172C4⋊C4—474no—
173C4⋊C4—944no—
174C4⋊C4—944no—
175C4⋊C4—1882no—
176C4⋊C4—1881no—
177C4⋊C4—1881no—
178C22⋊C4—944no—
179C22⋊C4—944no—
180C22⋊C4—944no—
181C22⋊C4—944no—
182C22⋊C4—1882no—
183C22⋊C4—1882no—
184C42—41no—
185C42—944no—
186C23—942no—
187C23—942no—
188C23—942no—
189C23—942no—
190C23—942no—
191C23—942no—
192C23—942no—
193C23C23×D4711yescharacteristic
194D4—1884no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—474no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4#1062535012yes—
217C2×C4D4×D4712yes—
218C2×C4#1062535412yes—
219C22—1882no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22—1882no—
225C22—1882no—
226C22C2×D4×D4711yescharacteristic
227C22C2×#1062535011yescharacteristic
228C22C2×#1062535411yescharacteristic
229C22#1309406911yescharacteristic
230C22#1309407011yescharacteristic
231C22#1309407111yescharacteristic
232C22#1309407211yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—944no—
239C4—1882no—
240C4—1882no—
241C2—3762no—
242C2#1568970011yescharacteristic
243C2#1568971311yescharacteristic
244C2#1568972011yescharacteristic
245C2#1568977611yescharacteristic
246C2#1568979411yescharacteristic
247C2#1568984611yescharacteristic
248C2#1568987711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2727
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. #15689058C2semidirect
3. #15689045C2semidirect
6. #15689021C2semidirect
7. #15689020C2semidirect
8. #15689013C2semidirect
9. C47×#389C2semidirect
56. C4⋊Dic47D4semidirect
132. #389D47semidirect
134. C47#2727semidirect