Finite Group Databasebeta

← #18010875

Subgroups — #18010875

Order 4736.

270 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558512C212yesmaximal, complemented
2#14558437C214yesmaximal, complemented
3#14558100C211yesmaximal, characteristic
4#11924615—22no—
5#11924595C2214yescomplemented
6#11924594—22no—
7C2×#10596962C2211yescharacteristic
8#11924532C2212yes—
9#11924523C412yescomplemented
10#11924507—22no—
11#11924505—22no—
12#11924495C411yescharacteristic, complemented
13C22×D4×C37C411yescharacteristic, complemented
14C24×C37—21no—
15C2×D4×C37—21no—
16C2×D4×C37—42no—
17C2×D4×C37C2×C412yes—
18C22×C4×C37C2×C411yescharacteristic
19C2×C22⋊D37—24no—
20C2×C22⋊D37D412yes—
21#10596962—42no—
22C2×D148C2311yescharacteristic
23C2×C4×D37D412yes—
24C2×Dic74C2×C411yescharacteristic
25C22⋊#3866—24no—
26C4⋊#3866—42no—
27C4×#3866—42no—
28C22⋊Dic37—21no—
29C22⋊Dic37—24no—
30C4⋊Dic37—21no—
31C4×Dic37C2×C412yes—
32C23×C37—22no—
33C23×C37—42no—
34C23×C37—82no—
35C23×C37C22⋊C411yescharacteristic
36C22×D37C2×D412yes—
37C2×#3866—44no—
38D4×C37—42no—
39D4×C37—42no—
40C2×C4×C37—22no—
41C2×C4×C37C22⋊C411yescharacteristic
42C2×C4×C37C22×C411yescharacteristic
43C22⋊D37—42no—
44C22⋊D37—84no—
45C2×Dic37—22no—
46C2×Dic37C22⋊C412yes—
47D148—41no—
48C4×D37—22no—
49C4×D37—22no—
50Dic74—41no—
51C22×C37—21no—
52C22×C37—41no—
53C22×C37—44no—
54C22×C37—42no—
55C22×C37—84no—
56C22×C37C2×C22⋊C411yescharacteristic
57C2×D37—22no—
58C2×D37—42no—
59#3866—84no—
60C4×C37—21no—
61C4×C37#9912yes—
62Dic37—22no—
63Dic37—42no—
64#2128—371nomaximal, Sylow
65C2×C37—21no—
66C2×C37—41no—
67C2×C37—82no—
68C2×C37C2×#9911yescharacteristic
69D37—42no—
70#535—371no—
71#410—372no—
72#353—374no—
73C37#212811yescharacteristic, complemented, Sylow
74C2×#41—371no—
75C22×D4#386611yescharacteristic, complemented
76#127—372no—
77#124—372no—
78#121—742no—
79#120—742no—
80#117—371no—
81#117—742no—
82#99—374no—
83#99—742no—
84C24—21no—
85#41—1482no—
86C2×Q8—371no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4—372no—
90C2×D4—371no—
91C2×D4—744no—
92C2×D4C2×#386612yes—
93C22×C4—372no—
94C22×C4C2×#386611yescharacteristic
95C4⋊C4—741no—
96C4⋊C4—1482no—
97C22⋊C4—744no—
98C22⋊C4—741no—
99C22⋊C4—744no—
100C42—372no—
101C42—1482no—
102C23—22no—
103C23—42no—
104C23—82no—
105C23—372no—
106C23C22⋊#386611yescharacteristic
107Q8—1481no—
108D4—42no—
109D4—42no—
110D4—2964no—
111D4—1481no—
112D4—1482no—
113C2×C4—22no—
114C2×C4—372no—
115C2×C4—742no—
116C2×C4—742no—
117C2×C4—742no—
118C2×C4—1484no—
119C2×C4C22⋊#386611yescharacteristic
120C2×C4C22×#386611yescharacteristic
121C22—21no—
122C22—41no—
123C22—44no—
124C22—42no—
125C22—84no—
126C22—742no—
127C22—1482no—
128C22C2×C22⋊#386611yescharacteristic
129C4—21no—
130C4—2964no—
131C4—742no—
132C4—1482no—
133C4#1192459412yes—
134C2—21no—
135C2—41no—
136C2—82no—
137C2—1482no—
138C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×D4×C37C4
socleC2×C37C2×#99
prime radical#14558100C2
cosocleC2×D148C23
hypercenterC22×D4#3866
hypocenterC37#2128
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558512C2semidirect
2. #14558437C2semidirect
5. #11924595C22semidirect
9. #11924523C4semidirect
12. #11924495C4semidirect
13. C22×D4×C37C4semidirect
73. C37#2128semidirect
75. C22×D4#3866semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145585122
#145584372
#145581002
#212837