Finite Group Databasebeta

← #18009715

Subgroups — #18009715

Order 4736.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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#14558437C211yesmaximal, characteristic, complemented
2#14558391C211yesmaximal, characteristic, complemented
3#14557701C211yesmaximal, characteristic
4#11924603—21no—
5#11924595—21no—
6#11924561—21no—
7#11924532C2211yescharacteristic
8#11924463—21no—
9#11924453C411yescharacteristic, complemented
10H(5,𝔽2)×C37C411yescharacteristic, complemented
11#41×C37—21no—
12#41×C37—41no—
13C2×D4×C37—41no—
14C2×D4×C37—41no—
15C2×D4×C37C2×C411yescharacteristic
16C2×C22⋊D37—41no—
17C2×D148D411yescharacteristic
18C22⋊#3866—41no—
19C2×#64438—41no—
20#10596941—41no—
21#10596939—41no—
22C4×Dic37D411yescharacteristic
23#10596934—21no—
24C23×C37—21no—
25C23×C37—41no—
26C22×D37—21no—
27C2×#3866—81no—
28Q8×C37—21no—
29D4×C37—21no—
30D4×C37—41no—
31D4×C37—42no—
32D4×C37—41no—
33C2×C4×C37—41no—
34C2×C4×C37—41no—
35C2×C4×C37C22⋊C411yescharacteristic
36C22⋊D37—81no—
37C22⋊D37—81no—
38C2×Dic37—21no—
39D148—41no—
40#64438—81no—
41#64436—41no—
42C22×C37—41no—
43C22×C37—41no—
44C22×C37—81no—
45C22×C37—161no—
46C22×C37#9911yescharacteristic
47C2×D37—41no—
48C2×D37—81no—
49#3866—161no—
50C4×C37—21no—
51C4×C37—41no—
52Dic37—21no—
53Dic37—21no—
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#331—371no—
63C37#140211yescharacteristic, complemented, Sylow
64H(5,𝔽2)#386611yescharacteristic, complemented
65AGL(1,ℤ/8)—741no—
66#127—371no—
67C4⋊C8—741no—
68#104—741no—
69#100—371no—
70#99—741no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—371no—
76C2×D4—1481no—
77C2×D4C2×#386611yescharacteristic
78SD16—1481no—
79D8—1481no—
80M16—741no—
81C2×C8—1481no—
82C22⋊C4—1481no—
83C42—371no—
84C23—21no—
85C23—41no—
86C23—741no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—2961no—
93D4—2961no—
94D4—1481no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2961no—
98C2×C4—741no—
99C2×C4C22⋊#386611yescharacteristic
100C8—2961no—
101C8—1481no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—2961no—
107C22—1481no—
108C22#1192459411yescharacteristic
109C4—21no—
110C4—41no—
111C4—741no—
112C4—741no—
113C4—5921no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—2961no—
118C2#1455843311yescharacteristic
subgroupG/H
centerC2#14558433
commutatorC2×D4×C37C2×C4
FrattiniC2×D4C2×#3866
FittingH(5,𝔽2)×C37C4
socleC2×C37AΣL(1,𝔽16)
prime radical#14557701C2
cosocle#11924532C22
hypercenterH(5,𝔽2)#3866
hypocenterC37#1402
LCSG ▷ C2×D4×C37 ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14558437C2semidirect
2. #14558391C2semidirect
9. #11924453C4semidirect
10. H(5,𝔽2)×C37C4semidirect
63. C37#1402semidirect
64. H(5,𝔽2)#3866semidirect

Maximal subgroups

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

subgroupindex
#145584372
#145583912
#145577012
#140237