Finite Group Databasebeta

← #20251297

Subgroups — #20251297

Order 6016.

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

normal subgroups only

This group has 420 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
1C47⋊#401C211yesmaximal, characteristic, complemented
2#15689060C211yesmaximal, characteristic, complemented
3#15689039C213yesmaximal
4#15689022C213yesmaximal, complemented
5#15689016C213yesmaximal, complemented
6#15689013C213yesmaximal, complemented
7C47×#396C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C2×C4⋊Dic47C2213yes—
10C2×C4⋊Dic47C2213yes—
11C2×C22⋊Dic47C2213yes—
12C2×(C2×D47)⋊C4C2213yes—
13C2×(C2×D47)⋊C4C2213yes—
14C2×C4×Dic47C2213yes—
15C47⋊#95C2213yes—
16C47⋊#95C2213yes—
17C47⋊#95C2213yes—
18C2×C4⋊C4×C47C2213yes—
19C2×C22⋊C4×C47C2213yes—
20#95×C47C2211yescharacteristic
21C24×C47C2311yescharacteristic
22C23×D47C2311yescharacteristic
23C22×C4×C47C2313yes—
24C22×C4×C47C2313yes—
25C2×C22⋊D47—43no—
26C22×Dic47C2313yes—
27C22×Dic47C2311yescharacteristic
28C22×Dic47C2313yes—
29C4⋊C4×C47—26no—
30C22⋊C4×C47—26no—
31C22⋊Dic47—43no—
32(C2×D47)⋊C4—26no—
33(C2×D47)⋊C4—43no—
34C4⋊Dic47—43no—
35C4⋊Dic47—43no—
36C4×Dic47—43no—
37C23×C47—23no—
38C23×C47—23no—
39C23×C47—21no—
40C23×C47C2411yescharacteristic
41C22×D47—23no—
42C22×D47—23no—
43C22×D47—21no—
44C2×C4×C47—23no—
45C2×C4×C47—23no—
46C2×C4×C47—23no—
47C2×C4×C47—23no—
48C2×C4×C47—23no—
49C2×C4×C47#4116yes—
50C22⋊D47—44no—
51C2×Dic47—23no—
52C2×Dic47—23no—
53C2×Dic47—23no—
54C2×Dic47—23no—
55C2×Dic47—23no—
56C2×Dic47—23no—
57C2×Dic47—23no—
58C22×C47—43no—
59C22×C47—43no—
60C22×C47—41no—
61C22×C47C2×#4113yes—
62C22×C47H(5,𝔽2)13yes—
63C22×C472−1+411yescharacteristic
64C2×D47—43no—
65C2×D47—43no—
66C2×D47—41no—
67C4×C47—26no—
68C4×C47—43no—
69Dic47—43no—
70Dic47—43no—
71Dic47—41no—
72#2801—471nomaximal, Sylow
73C2×C47—81no—
74C2×C47#54213yes—
75C2×C47#55313yes—
76C2×C47#56011yescharacteristic
77D47—81no—
78#401—471no—
79#399—471no—
80#396D4711yescharacteristic, complemented
81#394—473no—
82#389—473no—
83#388—473no—
84#388—473no—
85C47#280111yescharacteristic, complemented, Sylow
86C22×D4—471no—
87C2×C4⋊C4—473no—
88C2×C4⋊C4—473no—
89C2×C4⋊C4C2×D4713yes—
90C2×C22⋊C4—473no—
91C2×C22⋊C4—473no—
92C2×C22⋊C4—473no—
93C2×C22⋊C4C2×D4713yes—
94C2×C42—473no—
95#95—473no—
96#95—473no—
97#95—473no—
98#95C2×D4711yescharacteristic
99C24—471no—
100C24C22×D4711yescharacteristic
101C2×D4—1883no—
102C22×C4—473no—
103C22×C4—471no—
104C22×C4—473no—
105C22×C4C22×D4713yes—
106C22×C4C22×D4713yes—
107C4⋊C4—26no—
108C4⋊C4—1883no—
109C4⋊C4—1883no—
110C22⋊C4—26no—
111C22⋊C4—946no—
112C22⋊C4—1883no—
113C22⋊C4—1883no—
114C42—1883no—
115C23—23no—
116C23—23no—
117C23—21no—
118C23—943no—
119C23—943no—
120C23—941no—
121C23C23×D4711yescharacteristic
122D4—1884no—
123C2×C4—23no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—943no—
129C2×C4—943no—
130C2×C4—943no—
131C2×C4—943no—
132C2×C4—943no—
133C2×C4—943no—
134C2×C4—943no—
135C2×C4#1062535216yes—
136C22—43no—
137C22—43no—
138C22—41no—
139C22—1883no—
140C22—1883no—
141C22—1881no—
142C22C2×#1062535213yes—
143C22#1309407013yes—
144C22#1309407211yescharacteristic
145C4—26no—
146C4—43no—
147C4—1883no—
148C4—1881no—
149C4—1883no—
150C2—81no—
151C2—3761no—
152C2#1568974613yes—
153C2#1568982513yes—
154C2#1568986411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2801
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
2. #15689060C2semidirect
4. #15689022C2semidirect
5. #15689016C2semidirect
6. #15689013C2semidirect
7. C47×#396C2semidirect
80. #396D47semidirect
85. C47#2801semidirect