Finite Group Databasebeta

← #20249350

Subgroups — #20249350

Order 6016.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689051C213yesmaximal, complemented
2#15689049C213yesmaximal, complemented
3#15689047C211yesmaximal, characteristic, complemented
4#15689023C213yesmaximal
5#15689018C213yesmaximal, complemented
6#15688968C211yesmaximal, characteristic, complemented
7C47×#396C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C2×Dic47⋊C4C2213yes—
10C2×Dic47⋊C4C2213yes—
11C2×C22⋊Dic47C2213yes—
12C2×(C2×D47)⋊C4C2213yes—
13C2×(C2×D47)⋊C4C2213yes—
14C2×C4×Dic47C2213yes—
15C47⋊#95C2213yes—
16C47⋊#95C2216yes—
17C2×C4⋊C4×C47C2213yes—
18C2×C22⋊C4×C47C2213yes—
19#95×C47C2211yescharacteristic
20C24×C47C2311yescharacteristic
21C23×D47C2311yescharacteristic
22C22×C4×C47C2313yes—
23C22×C4×C47C2313yes—
24C2×C22⋊D47—26no—
25C22×Dic47C2313yes—
26C22×Dic47C2313yes—
27C22×Dic47C2311yescharacteristic
28C4⋊C4×C47—43no—
29C22⋊C4×C47—43no—
30C22⋊Dic47—43no—
31(C2×D47)⋊C4—43no—
32(C2×D47)⋊C4—43no—
33Dic47⋊C4—26no—
34Dic47⋊C4—43no—
35C4×Dic47—26no—
36C23×C47—23no—
37C23×C47—23no—
38C23×C47—21no—
39C23×C47C2411yescharacteristic
40C22×D47—23no—
41C22×D47—23no—
42C22×D47—21no—
43C2×C4×C47—23no—
44C2×C4×C47—23no—
45C2×C4×C47—23no—
46C2×C4×C47—23no—
47C2×C4×C47—23no—
48C2×C4×C47—23no—
49C22⋊D47—44no—
50C2×Dic47—23no—
51C2×Dic47—23no—
52C2×Dic47—23no—
53C2×Dic47—23no—
54C2×Dic47—23no—
55C2×Dic47—23no—
56C2×Dic47#4116yes—
57C22×C47—41no—
58C22×C47—43no—
59C22×C47—43no—
60C22×C47C2×#4113yes—
61C22×C47H(5,𝔽2)13yes—
62C22×C472−1+411yescharacteristic
63C2×D47—41no—
64C2×D47—43no—
65C2×D47—43no—
66C4×C47—43no—
67C4×C47—43no—
68Dic47—43no—
69Dic47—43no—
70Dic47#12614yes—
71#2644—471nomaximal, Sylow
72C2×C47—81no—
73C2×C47C2×#12611yescharacteristic
74C2×C47#54013yes—
75C2×C47#54213yes—
76D47—81no—
77#397—473no—
78#397—473no—
79#396—471no—
80#396D4711yescharacteristic, complemented
81#390—473no—
82#389—473no—
83#376—471no—
84C47#264411yescharacteristic, complemented, Sylow
85C22×D4—471no—
86C2×C4⋊C4—473no—
87C2×C4⋊C4—473no—
88C2×C4⋊C4C2×D4713yes—
89C2×C22⋊C4—473no—
90C2×C22⋊C4—473no—
91C2×C22⋊C4—473no—
92C2×C22⋊C4C2×D4713yes—
93C2×C42—473no—
94#95—473no—
95#95—476no—
96#95C2×D4711yescharacteristic
97C24—471no—
98C24C22×D4711yescharacteristic
99C2×D4—946no—
100C22×C4—471no—
101C22×C4—473no—
102C22×C4—473no—
103C22×C4C22×D4713yes—
104C22×C4C22×D4713yes—
105C4⋊C4—43no—
106C4⋊C4—946no—
107C4⋊C4—1883no—
108C22⋊C4—43no—
109C22⋊C4—1883no—
110C22⋊C4—1883no—
111C22⋊C4—1883no—
112C42—946no—
113C23—23no—
114C23—23no—
115C23—21no—
116C23—943no—
117C23—943no—
118C23—941no—
119C23C23×D4711yescharacteristic
120D4—1884no—
121C2×C4—23no—
122C2×C4—23no—
123C2×C4—23no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—476no—
128C2×C4—943no—
129C2×C4—943no—
130C2×C4—943no—
131C2×C4—943no—
132C2×C4—943no—
133C2×C4—943no—
134C22—43no—
135C22—41no—
136C22—43no—
137C22—1883no—
138C22—1881no—
139C22—1883no—
140C22#41×D4713yes—
141C22#1309406913yes—
142C22#1309407211yescharacteristic
143C4—43no—
144C4—43no—
145C4—474no—
146C4—1883no—
147C4—1883no—
148C2—81no—
149C2—3761no—
150C2#126×D4711yescharacteristic
151C2#1568972313yes—
152C2#1568974313yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2644
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #15689051C2semidirect
2. #15689049C2semidirect
3. #15689047C2semidirect
5. #15689018C2semidirect
6. #15688968C2semidirect
7. C47×#396C2semidirect
80. #396D47semidirect
84. C47#2644semidirect