Finite Group Databasebeta

← #20250815

Subgroups — #20250815

Order 6016.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689063C212yesmaximal, complemented
2#15689056C212yesmaximal, complemented
3#15689035C211yesmaximal, characteristic
4#15689027C212yesmaximal, complemented
5#15689016C212yesmaximal
6#15688995C212yesmaximal
7#15688990C212yesmaximal, complemented
8#15688984C211yesmaximal, characteristic
9C47×#397C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2211yescharacteristic
17C2×C4×Dic47C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2211yescharacteristic
29#95×C47C2211yescharacteristic
30#95×C47C2212yes—
31C24×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C22×Dic47—41no—
38C22×Dic47—41no—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C2×Dic94—24no—
44C2×Dic94—41no—
45C4⋊C4×C47—41no—
46C22⋊C4×C47—24no—
47C22⋊C4×C47—41no—
48C22⋊Dic47—24no—
49C22⋊Dic47—41no—
50C4⋊Dic47—42no—
51Dic47⋊C4—42no—
52Dic47⋊C4—42no—
53C4×Dic47—24no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47—21no—
57C23×C47—22no—
58C23×C47#4112yes—
59C23×C47C2411yescharacteristic
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—44no—
82C2×Dic47#4114yes—
83Dic94—44no—
84C22×C47—22no—
85C22×C47—24no—
86C22×C47—42no—
87C22×C47—41no—
88C22×C47—41no—
89C22×C47C2×#4112yes—
90C22×C47C2×#4111yescharacteristic
91C22×C47H(5,𝔽2)11yescharacteristic
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C472−1+412yes—
94C4×C47—42no—
95C4×C47—41no—
96C4×C47—42no—
97C4×C47—41no—
98Dic47—24no—
99Dic47—42no—
100Dic47—42no—
101Dic47—42no—
102#2764—471nomaximal, Sylow
103C2×C47—42no—
104C2×C47#53811yescharacteristic
105C2×C47#54212yes—
106C2×C47#55111yescharacteristic
107C2×C47#55212yes—
108C2×C47#56311yescharacteristic
109#400—472no—
110#398—472no—
111#397D4711yescharacteristic
112#393—471no—
113#391—472no—
114#388—472no—
115#385—472no—
116#383—472no—
117#381—471no—
118C47#276411yescharacteristic, complemented, Sylow
119C22×Q8—471no—
120C23×C4—471no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4C2×D4711yescharacteristic
125C2×C22⋊C4—472no—
126C2×C22⋊C4—471no—
127C2×C22⋊C4C2×D4712yes—
128C2×C22⋊C4C2×D4711yescharacteristic
129C2×C42—472no—
130#95—472no—
131#95—472no—
132#95—472no—
133#95—472no—
134#95—472no—
135#95—472no—
136#95—472no—
137#95—471no—
138#95C2×D4711yescharacteristic
139#95C2×D4712yes—
140C24C22×D4711yescharacteristic
141C2×Q8—944no—
142C2×Q8—1881no—
143C22×C4—472no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—942no—
148C22×C4—1881no—
149C22×C4—1881no—
150C22×C4C22×D4711yescharacteristic
151C22×C4C22×D4712yes—
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4712yes—
154C4⋊C4—41no—
155C4⋊C4—1882no—
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C22⋊C4—24no—
159C22⋊C4—41no—
160C22⋊C4—944no—
161C22⋊C4—1881no—
162C42—944no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—22no—
167C23#1062535212yes—
168C23C23×D4711yescharacteristic
169Q8—1884no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—474no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—1884no—
193C22—24no—
194C22—22no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22#41×D4712yes—
199C22C2×#1062535211yescharacteristic
200C22#1309406911yescharacteristic
201C22#1309407011yescharacteristic
202C22#1309407112yes—
203C4—41no—
204C4—42no—
205C4—41no—
206C4—42no—
207C4—944no—
208C4—1882no—
209C4—1882no—
210C4—1882no—
211C2—42no—
212C2#1568971011yescharacteristic
213C2#1568973912yes—
214C2#1568980311yescharacteristic
215C2#1568981012yes—
216C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2764
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #15689063C2semidirect
2. #15689056C2semidirect
4. #15689027C2semidirect
7. #15688990C2semidirect
118. C47#2764semidirect