Finite Group Databasebeta

← #20249341

Subgroups — #20249341

Order 6016.

462 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689064C213yesmaximal, complemented
3#15689052C213yesmaximal, complemented
4#15689047C211yesmaximal, characteristic, complemented
5#15689002C213yesmaximal
6#15688996C213yesmaximal, complemented
7C2×#95×C47C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C2×Dic47⋊C4C2213yes—
10C2×Dic47⋊C4C2213yes—
11C2×C22⋊Dic47C2213yes—
12C2×(C2×D47)⋊C4C2213yes—
13C2×(C2×D47)⋊C4C2213yes—
14C47⋊#95C2213yes—
15C47⋊#95C2213yes—
16C47⋊#95C2213yes—
17C47⋊#95C2213yes—
18C23×C4×C47C2213yes—
19#95×C47C2211yescharacteristic
20#95×C47C2213yes—
21C24×C47C2311yescharacteristic
22C23×D47C2311yescharacteristic
23C22×C4×C47—26no—
24C22×C4×C47—43no—
25C22×C4×C47—43no—
26C22×C4×C47C2313yes—
27C22×C4×C47C2313yes—
28C2×C22⋊D47—26no—
29C22×Dic47C2311yescharacteristic
30C22×Dic47C2313yes—
31C22×Dic47C2313yes—
32C22⋊Dic47—26no—
33(C2×D47)⋊C4—43no—
34(C2×D47)⋊C4—43no—
35Dic47⋊C4—43no—
36Dic47⋊C4—43no—
37C23×C47—23no—
38C23×C47—21no—
39C23×C47#4116yes—
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—23no—
50C2×C4×C47—412no—
51C22⋊D47—44no—
52C2×Dic47—23no—
53C2×Dic47—23no—
54C2×Dic47—23no—
55C2×Dic47—23no—
56C2×Dic47—23no—
57C2×Dic47—23no—
58C2×Dic47—23no—
59C22×C47—26no—
60C22×C47—26no—
61C22×C47#12614yes—
62C22×C47C2×#4113yes—
63C22×C47H(5,𝔽2)13yes—
64C22×C472−1+411yescharacteristic
65C2×D47—41no—
66C2×D47—43no—
67C2×D47—43no—
68C4×C47—43no—
69C4×C47—43no—
70Dic47—41no—
71Dic47—43no—
72Dic47—43no—
73#2643—471nomaximal, Sylow
74C2×C47—24no—
75C2×C47C2×#12611yescharacteristic
76C2×C47#53813yes—
77C2×C47#53913yes—
78D47—81no—
79#401—471no—
80#400—473no—
81#397—473no—
82#396—471no—
83#386—473no—
84#385—473no—
85C2×#95D4711yescharacteristic, complemented
86C47#264311yescharacteristic, complemented, Sylow
87C22×D4—471no—
88C23×C4C2×D4713yes—
89C2×C4⋊C4—473no—
90C2×C4⋊C4—473no—
91C2×C22⋊C4—473no—
92C2×C22⋊C4—473no—
93C2×C22⋊C4—473no—
94#95—473no—
95#95—473no—
96#95—473no—
97#95—473no—
98#95C2×D4711yescharacteristic
99#95C2×D4713yes—
100C24—471no—
101C24C22×D4711yescharacteristic
102C2×D4—946no—
103C22×C4—26no—
104C22×C4—43no—
105C22×C4—43no—
106C22×C4—471no—
107C22×C4—473no—
108C22×C4—473no—
109C22×C4C22×D4713yes—
110C22×C4C22×D4713yes—
111C4⋊C4—1883no—
112C4⋊C4—1883no—
113C22⋊C4—946no—
114C22⋊C4—1883no—
115C22⋊C4—1883no—
116C23—23no—
117C23—21no—
118C23—943no—
119C23—943no—
120C23—941no—
121C23#1062535016yes—
122C23C23×D4711yescharacteristic
123D4—1884no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—23no—
129C2×C4—23no—
130C2×C4—412no—
131C2×C4—943no—
132C2×C4—943no—
133C2×C4—943no—
134C2×C4—943no—
135C2×C4—943no—
136C2×C4—943no—
137C2×C4—943no—
138C22—26no—
139C22—26no—
140C22—1881no—
141C22—1883no—
142C22—1883no—
143C22#1309401814yes—
144C22C2×#1062535013yes—
145C22#1309406913yes—
146C22#1309407211yescharacteristic
147C4—43no—
148C4—43no—
149C4—1881no—
150C4—1883no—
151C4—1883no—
152C2—24no—
153C2—3761no—
154C2C2×#1309401811yescharacteristic
155C2#1568971113yes—
156C2#1568972013yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#95×C47C2
hypercenterC2×#95D47
hypocenterC47#2643
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
2. #15689064C2semidirect
3. #15689052C2semidirect
4. #15689047C2semidirect
6. #15688996C2semidirect
7. C2×#95×C47C2semidirect
85. C2×#95D47semidirect
86. C47#2643semidirect