Finite Group Databasebeta

← #20251208

Subgroups — #20251208

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#15689062C211yesmaximal, characteristic
2#15689061C212yesmaximal
3#15689061C212yesmaximal
4#15689053C211yesmaximal, characteristic
5#15689009C212yesmaximal
6#15689009C212yesmaximal
7#15689007C212yesmaximal
8#15689004C212yesmaximal
9C47×#384C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×C4×Dic47C2212yes—
15C47⋊#95C2212yes—
16C47⋊#95C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C4⋊C4×C47—24no—
41C4⋊C4×C47—24no—
42C4⋊C4×C47—41no—
43C4⋊C4×C47—41no—
44C42×C47—22no—
45C4⋊Dic47—41no—
46C4⋊Dic47—41no—
47Dic47⋊C4—24no—
48Dic47⋊C4—24no—
49C4×Dic47—42no—
50C23×C47C2411yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47#4112yes—
63C2×C4×C47#4114yes—
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—24no—
75C22×C47C2×#4112yes—
76C22×C47C2×#4111yescharacteristic
77C22×C47H(5,𝔽2)11yescharacteristic
78C22×C472−1+411yescharacteristic
79C22×C472−1+412yes—
80C4×C47—22no—
81C4×C47—24no—
82C4×C47—42no—
83C4×C47—41no—
84C4×C47—41no—
85Dic47—42no—
86Dic47—42no—
87Dic47—42no—
88Dic47—42no—
89#2794—471nomaximal, Sylow
90C2×C47#53911yescharacteristic
91C2×C47#54112yes—
92C2×C47#55212yes—
93C2×C47#55911yescharacteristic
94C2×C47#56311yescharacteristic
95#400—472no—
96#400—472no—
97#400—471no—
98#398—471no—
99#387—472no—
100#387—472no—
101#387—472no—
102#387—472no—
103#384D4711yescharacteristic
104C47#279411yescharacteristic, complemented, Sylow
105C2×C4⋊C4—472no—
106C2×C4⋊C4—472no—
107C2×C4⋊C4—471no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4C2×D4712yes—
110C2×C4⋊C4C2×D4712yes—
111C2×C4⋊C4C2×D4711yescharacteristic
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C42—472no—
114C2×C42C2×D4711yescharacteristic
115#95—472no—
116#95—472no—
117#95—472no—
118#95—472no—
119#95—472no—
120#95—472no—
121#95—472no—
122#95—472no—
123#95—472no—
124#95—471no—
125#95—471no—
126C22×C4—472no—
127C22×C4—472no—
128C22×C4—472no—
129C22×C4—472no—
130C22×C4C22×D4712yes—
131C22×C4C22×D4711yescharacteristic
132C22×C4C22×D4711yescharacteristic
133C22×C4C22×D4711yescharacteristic
134C22×C4C22×D4712yes—
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—944no—
140C4⋊C4—944no—
141C4⋊C4—1881no—
142C4⋊C4—1881no—
143C42—22no—
144C42—1882no—
145C23C23×D4711yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—942no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—942no—
161C2×C4—942no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—944no—
167C2×C4—942no—
168C2×C4#1062535012yes—
169C2×C4#1062535214yes—
170C22C2×#1062535212yes—
171C22C2×#1062535011yescharacteristic
172C22#1309406911yescharacteristic
173C22#1309407211yescharacteristic
174C22#1309407212yes—
175C4—24no—
176C4—22no—
177C4—42no—
178C4—41no—
179C4—41no—
180C4—1882no—
181C4—1882no—
182C4—1882no—
183C4—1882no—
184C2#1568972011yescharacteristic
185C2#1568973412yes—
186C2#1568980812yes—
187C2#1568985911yescharacteristic
188C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#384C2
hypercenter#384D47
hypocenterC47#2794
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
104. C47#2794semidirect