Finite Group Databasebeta

← #20247035

Subgroups — #20247035

Order 6016.

1088 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13094011C212yesmaximal, complemented
2C2×#13094003C211yesmaximal, characteristic, complemented
3#15689037C214yesmaximal, complemented
4#15689026C212yesmaximal, complemented
5#15688979C214yesmaximal, complemented
6C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
7C23×D4×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic, complemented
9#13094011—28no—
10#13094003—24no—
11C2×C4⋊Dic47C2211yescharacteristic, complemented
12C2×Dic47⋊C4C2212yescomplemented
13C2×C22⋊Dic47C2212yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2218yescomplemented
16C2×C22⋊Dic47C2218yescomplemented
17C2×C4×Dic47C2212yescomplemented
18C47⋊#95C2212yescomplemented
19C25×C47C2212yes—
20C22×D4×C47—28no—
21C22×D4×C47—24no—
22C22×D4×C47C2212yes—
23C22×D4×C47C2212yes—
24C23×C4×C47C2211yescharacteristic
25C24×C47—28no—
26C24×C47—24no—
27C24×C47—28no—
28C24×C47—44no—
29C24×C47C2314yes—
30C24×C47C2311yescharacteristic
31C2×D4×C47—232no—
32C2×D4×C47—28no—
33C2×D4×C47—24no—
34C2×D4×C47—24no—
35C2×D4×C47—24no—
36C2×D4×C47D418yes—
37C22×C4×C47—24no—
38C22×C4×C47D414yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×Dic47C2314yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C2×Dic94—22no—
45C2×Dic94—24no—
46C22⋊Dic47—24no—
47C22⋊Dic47—216no—
48C22⋊Dic47—24no—
49C22⋊Dic47—48no—
50C4⋊Dic47—22no—
51Dic47⋊C4—24no—
52C4×Dic47—24no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—216no—
56C23×C47—24no—
57C23×C47—24no—
58C23×C47—28no—
59C23×C47—28no—
60C23×C47—432no—
61C23×C47—48no—
62C23×C47—48no—
63C23×C47C2×D418yes—
64C23×C47C2×D412yes—
65C23×C47#4114yes—
66C23×C47C2411yescharacteristic
67D4×C47—216no—
68D4×C47—216no—
69C2×C4×C47—22no—
70C2×C4×C47—28no—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×D414yes—
73C2×C4×C47C2×D412yes—
74C2×Dic47—24no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81Dic94—44no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—28no—
85C22×C47—28no—
86C22×C47—216no—
87C22×C47—432no—
88C22×C47—44no—
89C22×C47—44no—
90C22×C47—48no—
91C22×C47#12414yescomplemented
92C22×C47C22×D411yescharacteristic
93C22×C47C22×D412yes—
94C22×C47C2×#4112yes—
95C22×C47H(5,𝔽2)12yes—
96C4×C47—22no—
97C4×C47#12014yes—
98Dic47—42no—
99Dic47—42no—
100Dic47—44no—
101#2435—471nomaximal, Sylow
102C2×C47—24no—
103C2×C47—48no—
104C2×C47C2×#12011yescharacteristic
105C2×C47C2×#12411yescharacteristic
106C2×C47#53511yescharacteristic
107C2×C47#54614yes—
108C23×D4D4711yescharacteristic
109C2×#124—472no—
110C2×C22⋊Q8—471no—
111#394—474no—
112#390—472no—
113#379—474no—
114C4×C22⋊C4—471no—
115C47#243511yescharacteristic, complemented, Sylow
116C25C2×D4712yes—
117C22×Q8—471no—
118C22×D4—28no—
119C22×D4—24no—
120C22×D4C2×D4712yes—
121C22×D4C2×D4712yes—
122C23×C4C2×D4711yescharacteristic
123#124—948no—
124C22⋊Q8—944no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—471no—
127C2×C22⋊C4—472no—
128C2×C22⋊C4—478no—
129C2×C22⋊C4—472no—
130C2×C22⋊C4—478no—
131C2×C42—472no—
132#95—472no—
133C24—28no—
134C24—24no—
135C24—28no—
136C24—44no—
137C24C22×D4714yes—
138C24C22×D4711yescharacteristic
139C2×Q8—942no—
140C2×Q8—944no—
141C2×D4—232no—
142C2×D4—28no—
143C2×D4—24no—
144C2×D4—24no—
145C2×D4—24no—
146C2×D4C22⋊D4718yes—
147C22×C4—24no—
148C22×C4—474no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4C22⋊D4714yes—
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4711yescharacteristic
154C4⋊C4—944no—
155C4⋊C4—942no—
156C22⋊C4—944no—
157C22⋊C4—944no—
158C22⋊C4—9416no—
159C22⋊C4—1888no—
160C42—944no—
161C23—22no—
162C23—22no—
163C23—216no—
164C23—24no—
165C23—24no—
166C23—28no—
167C23—28no—
168C23—432no—
169C23—48no—
170C23—48no—
171C23#1062535214yes—
172C23C2×C22⋊D4718yes—
173C23C2×C22⋊D4712yes—
174C23C23×D4711yescharacteristic
175Q8—1884no—
176D4—216no—
177D4—216no—
178C2×C4—22no—
179C2×C4—28no—
180C2×C4—944no—
181C2×C4—944no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—944no—
185C2×C4—944no—
186C2×C4—944no—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C2×C22⋊D4714yes—
189C2×C4C2×C22⋊D4712yes—
190C22—28no—
191C22—22no—
192C22—22no—
193C22—216no—
194C22—28no—
195C22—432no—
196C22—48no—
197C22—44no—
198C22—44no—
199C22#1309401114yescomplemented
200C22C22×C22⋊D4712yes—
201C22C22×C22⋊D4711yescharacteristic
202C22C2×#1062535212yes—
203C22#1309406912yes—
204C4—22no—
205C4—1884no—
206C4—1882no—
207C4—1882no—
208C4#1309399314yes—
209C2—24no—
210C2—48no—
211C2C2×#1309399311yescharacteristic
212C2C2×#1309401111yescharacteristic
213C2#1568969011yescharacteristic
214C2#1568976714yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC23×D4×C47C2
hypercenterC23×D4D47
hypocenterC47#2435
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094011C2semidirect
2. C2×#13094003C2semidirect
3. #15689037C2semidirect
4. #15689026C2semidirect
5. #15688979C2semidirect
6. C4×C22⋊Dic47C2semidirect
8. C22×Dic94C22semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×Dic47⋊C4C22semidirect
15. C2×C22⋊Dic47C22semidirect
16. C2×C22⋊Dic47C22semidirect
17. C2×C4×Dic47C22semidirect
18. C47⋊#95C22semidirect
91. C22×C47#124semidirect
115. C47#2435semidirect
199. C22#13094011semidirect