Finite Group Databasebeta

← #20247662

Subgroups — #20247662

Order 6016.

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

normal subgroups only

This group has 672 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×#13093983C211yesmaximal, characteristic, complemented
2#15689059C212yesmaximal, complemented
3#15689048C212yesmaximal, complemented
4#15689011C214yesmaximal, complemented
5#15688996C212yesmaximal, complemented
6#15688986C211yesmaximal, characteristic, complemented
7#15688979C212yesmaximal
8C22×C22⋊C4×C47C211yesmaximal, characteristic
9#13093983—24no—
10C2×C4⋊Dic47C2211yescharacteristic, complemented
11C2×C4⋊Dic47C2211yescharacteristic, complemented
12C2×Dic47⋊C4C2214yescomplemented
13C2×C22⋊Dic47C2212yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2214yes—
16C2×C22⋊Dic47C2214yes—
17C2×C4×Dic47C2212yescomplemented
18C47⋊#95C2212yescomplemented
19C47⋊#95C2212yescomplemented
20C47⋊#95C2214yescomplemented
21C25×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—24no—
25C2×C22⋊C4×C47C2212yes—
26C2×C22⋊C4×C47C2212yes—
27C24×C47—22no—
28C24×C47—24no—
29C24×C47—24no—
30C24×C47—42no—
31C24×C47C2312yes—
32C24×C47C2311yescharacteristic
33C22×C4×C47—24no—
34C22×C4×C47—22no—
35C22×C4×C47—42no—
36C22×C4×C47D414yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×Dic47C2314yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22⋊C4×C47—24no—
44C22⋊C4×C47—24no—
45C22⋊Dic47—24no—
46C22⋊Dic47—28no—
47C22⋊Dic47—24no—
48C22⋊Dic47—44no—
49C4⋊Dic47—22no—
50C4⋊Dic47—22no—
51Dic47⋊C4—44no—
52C4×Dic47—24no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—28no—
56C23×C47—22no—
57C23×C47—24no—
58C23×C47—22no—
59C23×C47—24no—
60C23×C47—416no—
61C23×C47—44no—
62C23×C47—44no—
63C23×C47C2×D412yes—
64C23×C47#4114yes—
65C23×C47#4114yes—
66C23×C47C2411yescharacteristic
67C2×C4×C47—28no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—24no—
72C2×C4×C47—44no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81C2×Dic47—24no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—28no—
85C22×C47—24no—
86C22×C47—28no—
87C22×C47—416no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47—44no—
91C22×C47#12314yes—
92C22×C47C22×D411yescharacteristic
93C22×C47C2×#4112yes—
94C22×C47C2×#4112yes—
95C22×C47H(5,𝔽2)12yes—
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—42no—
99Dic47—42no—
100Dic47—42no—
101Dic47—44no—
102#2482—471nomaximal, Sylow
103C2×C47—24no—
104C2×C47—44no—
105C2×C47C2×#12311yescharacteristic
106C2×C47#52511yescharacteristic
107C2×C47#53511yescharacteristic
108C2×C47#55114yes—
109C2×#117—471no—
110C22×C22⋊C4D4711yescharacteristic
111#399—472no—
112#397—472no—
113#388—474no—
114#385—472no—
115#381—471no—
116#379—472no—
117C47#248211yescharacteristic, complemented, Sylow
118C25C2×D4711yescharacteristic
119C23×C4C2×D4711yescharacteristic
120C23×C4C2×D4711yescharacteristic
121#117—944no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—474no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4—472no—
127C2×C22⋊C4—472no—
128C2×C22⋊C4—474no—
129C2×C22⋊C4—474no—
130C2×C22⋊C4C2×D4712yes—
131C2×C22⋊C4C2×D4712yes—
132C2×C42—472no—
133#95—472no—
134#95—472no—
135#95—474no—
136C24—24no—
137C24—22no—
138C24—24no—
139C24—42no—
140C24C22×D4712yes—
141C24C22×D4711yescharacteristic
142C22×C4—24no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—474no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4C22⋊D4714yes—
149C22×C4C22×D4712yes—
150C22×C4C22×D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—1884no—
155C22⋊C4—24no—
156C22⋊C4—24no—
157C22⋊C4—948no—
158C22⋊C4—944no—
159C22⋊C4—944no—
160C22⋊C4—1884no—
161C42—944no—
162C23—22no—
163C23—22no—
164C23—28no—
165C23—22no—
166C23—24no—
167C23—22no—
168C23—24no—
169C23—416no—
170C23—44no—
171C23—44no—
172C23#1062535014yes—
173C23#1062535214yes—
174C23C2×C22⋊D4712yes—
175C23C23×D4711yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—44no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—944no—
185C2×C4—944no—
186C2×C4—944no—
187C2×C4—944no—
188C2×C4—944no—
189C2×C4C2×C22⋊D4712yes—
190C2×C4C2×C22⋊D4712yes—
191C22—28no—
192C22—22no—
193C22—22no—
194C22—28no—
195C22—24no—
196C22—416no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22#1309400514yes—
201C22C22×C22⋊D4711yescharacteristic
202C22C2×#1062535212yes—
203C22C2×#1062535012yes—
204C22#1309406912yes—
205C4—22no—
206C4—22no—
207C4—42no—
208C4—1884no—
209C4—1882no—
210C4—1882no—
211C2—24no—
212C2—44no—
213C2C2×#1309400511yescharacteristic
214C2#1568963411yescharacteristic
215C2#1568969011yescharacteristic
216C2#1568979914yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2482
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13093983C2semidirect
2. #15689059C2semidirect
3. #15689048C2semidirect
4. #15689011C2semidirect
5. #15688996C2semidirect
6. #15688986C2semidirect
10. C2×C4⋊Dic47C22semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×Dic47⋊C4C22semidirect
17. C2×C4×Dic47C22semidirect
18. C47⋊#95C22semidirect
19. C47⋊#95C22semidirect
20. C47⋊#95C22semidirect
117. C47#2482semidirect