Finite Group Databasebeta

← #20251379

Subgroups — #20251379

Order 6016.

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

normal subgroups only

This group has 344 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#15689063C212yesmaximal
2#15689062C212yesmaximal
3#15689061C212yesmaximal
4#15689021C211yesmaximal, characteristic
5#15689021C211yesmaximal, characteristic
6#15689010C212yesmaximal
7#15689009C212yesmaximal
8#15689004C212yesmaximal
9C47×#389C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×C4×Dic47C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2212yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C4⋊C4×C47—22no—
41C4⋊C4×C47—24no—
42C4⋊C4×C47—41no—
43C42×C47—41no—
44C4⋊Dic47—22no—
45C4⋊Dic47—22no—
46C4⋊Dic47—41no—
47C4⋊Dic47—41no—
48Dic47⋊C4—24no—
49Dic47⋊C4—24no—
50C4×Dic47—42no—
51C23×C47C2411yescharacteristic
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47#4112yes—
65C2×C4×C47#4112yes—
66C2×C4×C47#4112yes—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—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—
79C22×C47C2×#4111yescharacteristic
80C22×C47C2×#4111yescharacteristic
81C22×C47C2×#4111yescharacteristic
82C22×C47H(5,𝔽2)11yescharacteristic
83C22×C472−1+411yescharacteristic
84C22×C472−1+411yescharacteristic
85C22×C472−1+411yescharacteristic
86C4×C47—22no—
87C4×C47—22no—
88C4×C47—22no—
89C4×C47—42no—
90C4×C47—42no—
91Dic47—42no—
92Dic47—42no—
93Dic47—42no—
94Dic47—42no—
95#2810—471nomaximal, Sylow
96C2×C47#53911yescharacteristic
97C2×C47#53911yescharacteristic
98C2×C47#53911yescharacteristic
99C2×C47#55611yescharacteristic
100C2×C47#55611yescharacteristic
101C2×C47#55611yescharacteristic
102C2×C47#56411yescharacteristic
103#400—472no—
104#400—472no—
105#400—472no—
106#389—471no—
107#389—471no—
108#389D4711yescharacteristic
109#387—472no—
110#387—472no—
111#387—472no—
112C47#281011yescharacteristic, complemented, Sylow
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4C2×D4712yes—
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C42—472no—
123C2×C42C2×D4711yescharacteristic
124#95—472no—
125#95—472no—
126#95—472no—
127#95—472no—
128#95—472no—
129#95—472no—
130#95—472no—
131#95—472no—
132#95—472no—
133#95C2×D4712yes—
134C22×C4—472no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4C22×D4712yes—
139C22×C4C22×D4712yes—
140C22×C4C22×D4711yescharacteristic
141C22×C4C22×D4711yescharacteristic
142C22×C4C22×D4711yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—24no—
145C4⋊C4—41no—
146C4⋊C4—944no—
147C4⋊C4—942no—
148C4⋊C4—944no—
149C4⋊C4—942no—
150C4⋊C4—1881no—
151C4⋊C4—1881no—
152C42—41no—
153C42—1882no—
154C23C23×D4711yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4#1062535012yes—
180C2×C4#1062535212yes—
181C2×C4#1062535412yes—
182C22C2×#1062535211yescharacteristic
183C22C2×#1062535011yescharacteristic
184C22C2×#1062535411yescharacteristic
185C22#1309406911yescharacteristic
186C22#1309407111yescharacteristic
187C22#1309407111yescharacteristic
188C22#1309407211yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—1882no—
195C4—1882no—
196C4—1882no—
197C4—1882no—
198C2#1568971811yescharacteristic
199C2#1568972011yescharacteristic
200C2#1568972211yescharacteristic
201C2#1568984311yescharacteristic
202C2#1568984611yescharacteristic
203C2#1568984711yescharacteristic
204C2C47⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2810
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
112. C47#2810semidirect