Finite Group Databasebeta

← #20250908

Subgroups — #20250908

Order 6016.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689062C212yesmaximal, complemented
2#15689061C212yesmaximal, complemented
3#15689048C211yesmaximal, characteristic
4#15689022C212yesmaximal, complemented
5#15689017C212yesmaximal
6#15689010C212yesmaximal, complemented
7#15688998C212yesmaximal
8#15688984C211yesmaximal, characteristic
9C47×#399C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
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×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic
31C24×C47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×Dic47—22no—
37C22×Dic47—41no—
38C22×Dic47—41no—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C4⋊C4×C47—24no—
44C4⋊C4×C47—41no—
45C22⋊C4×C47—24no—
46C22⋊C4×C47—41no—
47C22⋊Dic47—24no—
48C22⋊Dic47—41no—
49C4⋊Dic47—42no—
50C4⋊Dic47—41no—
51C4⋊Dic47—42no—
52Dic47⋊C4—24no—
53C4×Dic47—42no—
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—21no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47#4114yes—
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—22no—
82C2×Dic47—44no—
83C22×C47—22no—
84C22×C47—24no—
85C22×C47—42no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47C2×#4112yes—
89C22×C47C2×#4111yescharacteristic
90C22×C47H(5,𝔽2)11yescharacteristic
91C22×C47H(5,𝔽2)11yescharacteristic
92C22×C472−1+412yes—
93C4×C47—24no—
94C4×C47—42no—
95C4×C47—41no—
96C4×C47—41no—
97Dic47—42no—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101#2771—471nomaximal, Sylow
102C2×C47—42no—
103C2×C47#53811yescharacteristic
104C2×C47#53912yes—
105C2×C47#55212yes—
106C2×C47#55911yescharacteristic
107C2×C47#56311yescharacteristic
108#400—472no—
109#400—472no—
110#399D4711yescharacteristic
111#397—471no—
112#389—472no—
113#388—472no—
114#387—472no—
115#385—472no—
116#381—471no—
117C47#277111yescharacteristic, complemented, Sylow
118C23×C4—471no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4C2×D4712yes—
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
139C24C22×D4711yescharacteristic
140C22×C4—472no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4—472no—
144C22×C4—942no—
145C22×C4—1881no—
146C22×C4—1881no—
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4712yes—
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4712yes—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—944no—
154C4⋊C4—1882no—
155C4⋊C4—1881no—
156C4⋊C4—1882no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—944no—
160C22⋊C4—1881no—
161C42—1882no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#1062535412yes—
167C23C23×D4711yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
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—1884no—
190C2×C4#1062535214yes—
191C22—24no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—42no—
196C22C2×#1062535212yes—
197C22C2×#1062535411yescharacteristic
198C22#1309406911yescharacteristic
199C22#1309407011yescharacteristic
200C22#1309407112yes—
201C4—24no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—1882no—
206C4—1882no—
207C4—1882no—
208C4—1882no—
209C2—42no—
210C2#1568971311yescharacteristic
211C2#1568971712yes—
212C2#1568981512yes—
213C2#1568985911yescharacteristic
214C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2771
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #15689062C2semidirect
2. #15689061C2semidirect
4. #15689022C2semidirect
6. #15689010C2semidirect
117. C47#2771semidirect