Finite Group Databasebeta

← #17992742

Subgroups — #17992742

Order 4736.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#14557700C211yesmaximal, characteristic
2#14557326C211yesmaximal, characteristic, complemented
3C37×#331C211yesmaximal, characteristic, complemented
4#11924581C411yescharacteristic, complemented
5#11924562—21no—
6#11924464—21no—
7#11924453C411yescharacteristic, complemented
8#11924451—21no—
9#127×C37C2211yescharacteristic
10C4⋊C8×C37—21no—
11C2×D4×C37—41no—
12C2×D4×C37C2×C411yescharacteristic
13C2×D4×C37D411yescharacteristic
14C2×C22⋊D37—41no—
15#10596964—41no—
16D4×D37—41no—
17#10596962—21no—
18C2×C8×C37—41no—
19C42×C37D411yescharacteristic
20C22⋊Dic37—41no—
21#10596940—41no—
22#10596939—41no—
23#10596934—21no—
24C23×C37—21no—
25C23×C37—21no—
26C22×D37—41no—
27D4×C37—41no—
28D4×C37—41no—
29D4×C37—81no—
30D4×C37—81no—
31C2×C4×C37—21no—
32C2×C4×C37C22⋊C411yescharacteristic
33C22⋊D37—42no—
34C22⋊D37—41no—
35C2×Dic37—41no—
36C2×Dic37—81no—
37D148—21no—
38C4×D37—41no—
39Dic74—21no—
40C8×C37—81no—
41#64436—41no—
42C22×C37—41no—
43C22×C37—41no—
44C22×C37—81no—
45C22×C37—81no—
46C22×C37#9911yescharacteristic
47C2×D37—41no—
48C2×D37—161no—
49C4×C37—21no—
50C4×C37—21no—
51C4×C37—21no—
52Dic37—41no—
53Dic37—161no—
54#1402—371nomaximal, Sylow
55C2×C37—21no—
56C2×C37—81no—
57C2×C37—81no—
58C2×C37AΣL(1,𝔽16)11yescharacteristic
59D37—81no—
60#453—371no—
61#353—371no—
62#331D3711yescharacteristic, complemented
63C37#140211yescharacteristic, complemented, Sylow
64H(5,𝔽2)—371no—
65AGL(1,ℤ/8)—741no—
66#127C2×D3711yescharacteristic
67C4⋊C8—21no—
68#104—741no—
69#100—371no—
70#99—741no—
71#41—741no—
72#41—1481no—
73C2×D4—41no—
74C2×D4—1481no—
75C2×D4—1481no—
76C2×D4C4×D3711yescharacteristic
77C2×D4D14811yescharacteristic
78SD16—1481no—
79D8—1481no—
80M16—741no—
81C2×C8—41no—
82C22⋊C4—1481no—
83C42C22⋊D3711yescharacteristic
84C23—21no—
85C23—21no—
86C23—1481no—
87Q8—741no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—741no—
93D4—1482no—
94D4—1481no—
95C2×C4—21no—
96C2×C4—2961no—
97C2×C4—1481no—
98C2×C4—1481no—
99C2×C4#1059693811yescharacteristic
100C8—81no—
101C8—1481no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—5921no—
107C22—1481no—
108C22#1192445011yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—5921no—
113C4—1481no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—2961no—
118C2#1455732111yescharacteristic
subgroupG/H
centerC2#14557321
commutatorC2×D4×C37C2×C4
Frattini#127C2×D37
FittingC37×#331C2
socleC2×C37AΣL(1,𝔽16)
prime radical#14557700C2
cosocle#127×C37C22
hypercenter#331D37
hypocenterC37#1402
LCSG ▷ C2×D4×C37 ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14557326C2semidirect
3. C37×#331C2semidirect
4. #11924581C4semidirect
7. #11924453C4semidirect
62. #331D37semidirect
63. C37#1402semidirect

Maximal subgroups

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

subgroupindex
#145577002
#145573262
C37×#3312
#140237