Finite Group Databasebeta

← #20247664

Subgroups — #20247664

Order 6016.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic
3#15689060C212yesmaximal, complemented
4#15689050C212yesmaximal, complemented
5#15689015C214yesmaximal, complemented
6#15688998C212yesmaximal, complemented
7#15688978C212yesmaximal
8C47×#381C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11#13093983—24no—
12C2×C4⋊Dic47C2211yescharacteristic, complemented
13C2×C4⋊Dic47C2211yescharacteristic, complemented
14C2×C4⋊Dic47C2214yescomplemented
15C2×C22⋊Dic47C2212yes—
16C2×(C2×D47)⋊C4—24no—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×C4×Dic47C2212yescomplemented
22C47⋊#95C2214yescomplemented
23C23×C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47C2212yes—
25#95×C47C2212yescomplemented
26#95×C47C2212yescomplemented
27C24×C47C2311yescharacteristic
28C23×D47—22no—
29C23×D47—24no—
30C23×D47—24no—
31C23×D47—42no—
32C23×D47C2312yes—
33C22×C4×C47—24no—
34C22×C4×C47D414yes—
35C22×C4×C47C2314yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—22no—
39C22×Dic47—42no—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22⋊C4×C47—24no—
44C22⋊Dic47—24no—
45(C2×D47)⋊C4—28no—
46(C2×D47)⋊C4—24no—
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—22no—
50C4⋊Dic47—22no—
51C4⋊Dic47—44no—
52C4×Dic47—24no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47C2×D412yes—
56C23×C47#4114yes—
57C23×C47C2411yescharacteristic
58C22×D47—28no—
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—24no—
62C22×D47—24no—
63C22×D47—416no—
64C22×D47—44no—
65C22×D47—44no—
66C22×D47#4114yes—
67C2×C4×C47—28no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47—24no—
72C2×C4×C47—24no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81C2×Dic47—44no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—28no—
85C22×C47#12314yes—
86C22×C47C22×D411yescharacteristic
87C22×C47C2×#4112yes—
88C22×C47C2×#4112yes—
89C22×C47H(5,𝔽2)12yes—
90C2×D47—24no—
91C2×D47—28no—
92C2×D47—416no—
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—44no—
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—44no—
99Dic47—42no—
100Dic47—42no—
101Dic47—42no—
102#2482—471nomaximal, Sylow
103C2×C47—24no—
104C2×C47C2×#12311yescharacteristic
105C2×C47#52511yescharacteristic
106C2×C47#53511yescharacteristic
107C2×C47#55114yes—
108D47—44no—
109C2×#117—471no—
110C22×C22⋊C4—471no—
111#399—472no—
112#397—472no—
113#388—474no—
114#385—472no—
115#381D4711yescharacteristic, complemented
116#379—472no—
117C47#248211yescharacteristic, complemented, Sylow
118C25—471no—
119C23×C4—471no—
120C23×C4C2×D4711yescharacteristic
121#117—944no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—474no—
125C2×C22⋊C4—472no—
126C2×C22⋊C4—472no—
127C2×C22⋊C4—472no—
128C2×C22⋊C4—474no—
129C2×C22⋊C4—474no—
130C2×C22⋊C4—944no—
131C2×C22⋊C4C2×D4712yes—
132C2×C42—472no—
133#95—474no—
134#95C2×D4712yescomplemented
135#95C2×D4712yescomplemented
136C24—472no—
137C24—944no—
138C24—942no—
139C24—944no—
140C24—1882no—
141C24C22×D4711yescharacteristic
142C22×C4—24no—
143C22×C4—472no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—942no—
147C22×C4—1882no—
148C22×C4D18814yes—
149C22×C4C22×D4714yes—
150C22×C4C22×D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—1884no—
155C22⋊C4—24no—
156C22⋊C4—948no—
157C22⋊C4—944no—
158C22⋊C4—944no—
159C22⋊C4—944no—
160C22⋊C4—1884no—
161C42—944no—
162C23—22no—
163C23—22no—
164C23—474no—
165C23—948no—
166C23—942no—
167C23—942no—
168C23—944no—
169C23—944no—
170C23—18816no—
171C23—1884no—
172C23—1884no—
173C23C2×D18812yes—
174C23#1062535214yes—
175C23C23×D4711yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—944no—
186C2×C4—944no—
187C2×C4—944no—
188C2×C4—1884no—
189C2×C4C2×D18812yes—
190C2×C4C2×D18812yes—
191C22—28no—
192C22—22no—
193C22—22no—
194C22—948no—
195C22—944no—
196C22—18816no—
197C22—1884no—
198C22—1882no—
199C22—1882no—
200C22#1309400814yes—
201C22C22×D18811yescharacteristic
202C22#41×D4712yes—
203C22C2×#1062535212yes—
204C22#1309407012yes—
205C4—22no—
206C4—22no—
207C4—44no—
208C4—1882no—
209C4—1882no—
210C4—1882no—
211C2—24no—
212C2—1884no—
213C2C2×#1309400811yescharacteristic
214C2#1568963511yescharacteristic
215C2#1568969211yescharacteristic
216C2#1568979614yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2482
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#13093983C2semidirect
3. #15689060C2semidirect
4. #15689050C2semidirect
5. #15689015C2semidirect
6. #15688998C2semidirect
8. C47×#381C2semidirect
12. C2×C4⋊Dic47C22semidirect
13. C2×C4⋊Dic47C22semidirect
14. C2×C4⋊Dic47C22semidirect
21. C2×C4×Dic47C22semidirect
22. C47⋊#95C22semidirect
25. #95×C47C22semidirect
26. #95×C47C22semidirect
115. #381D47semidirect
117. C47#2482semidirect
134. #95C2×D47semidirect
135. #95C2×D47semidirect