Finite Group Databasebeta

← #17994094

Subgroups — #17994094

Order 4736.

160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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#14557929C211yesmaximal, characteristic, complemented
2#14557824C211yesmaximal, characteristic
3#14557735C211yesmaximal, characteristic
4#14557610C211yesmaximal, characteristic
5#14557285C211yesmaximal, characteristic, complemented
6#14557281C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9C2×#10596929—21no—
10#11924536C2211yescharacteristic
11C4×D148C2211yescharacteristic
12#11924468—21no—
13#11924467—21no—
14#11924467—21no—
15C4⋊#64436C2211yescharacteristic
16#11924460—21no—
17#11924458—21no—
18#11924448—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4⋊C8×C37C2211yescharacteristic
22C4⋊C8×C37C2211yescharacteristic
23C2×Q8×C37—21no—
24C2×D148D411yescharacteristic
25C2×C4×D37—21no—
26C2×Dic74—21no—
27C2×C8×C37—21no—
28C2×C8×C37—21no—
29C4⋊C4×C37—21no—
30C4⋊C4×C37—21no—
31C42×C37C2311yescharacteristic
32#10596941—42no—
33#10596938—21no—
34C4⋊Dic37—21no—
35C4⋊Dic37—21no—
36C4⋊Dic37D411yescharacteristic
37C2×#64436—21no—
38C2×#64436D411yescharacteristic
39C2×#64436D411yescharacteristic
40#10596929—42no—
41C22×D37—21no—
42Q8×C37—41no—
43Q8×C37—41no—
44C2×C4×C37—41no—
45C2×C4×C37C2×D411yescharacteristic
46C2×C4×C37C2×D411yescharacteristic
47C2×C4×C37#4111yescharacteristic
48C2×Dic37—21no—
49C2×Dic37—41no—
50D148—21no—
51D148—21no—
52C4×D37—41no—
53C4×D37—41no—
54Dic74—81no—
55C8×C37—41no—
56C8×C37—41no—
57#64436—21no—
58#64436—41no—
59#64436SD1612yescomplemented
60C22×C37#12111yescharacteristic
61C2×D37—41no—
62C2×D37—41no—
63C2×D37—41no—
64C4×C37—21no—
65C4×C37—81no—
66C4×C37C2×SD1611yescharacteristic
67C4×C37AGL(1,ℤ/8)11yescharacteristic
68C4×C37#13711yescharacteristic
69C4×C37#13711yescharacteristic
70Dic37—41no—
71Dic37—81no—
72#1691—371nomaximal, Sylow
73C2×C37#46111yescharacteristic
74C2×C37#46811yescharacteristic
75C2×C37#47111yescharacteristic
76D37—81no—
77#498—371no—
78#476—371no—
79#461—371no—
80#436—371no—
81#335—371no—
82#333—371no—
83#332D3711yescharacteristic, complemented
84C37#169111yescharacteristic, complemented, Sylow
85C2×SD16—741no—
86C2×M16—741no—
87C4⋊Q8—371no—
88C4⋊Q8C2×D3711yescharacteristic
89C4×D4—371no—
90#106—741no—
91#106—741no—
92#106—741no—
93C4⋊C8—371no—
94C4⋊C8C2×D3711yescharacteristic
95C4⋊C8C2×D3711yescharacteristic
96#103—741no—
97#102—741no—
98C22⋊C8—741no—
99C4×C8—371no—
100C2×Q8—21no—
101C2×Q8—741no—
102C2×D4—371no—
103C22×C4—741no—
104SD16—1482no—
105M16—1482no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—371no—
109C2×C8—371no—
110C2×C8—741no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—371no—
114C4⋊C4—741no—
115C4⋊C4—741no—
116C22⋊C4—741no—
117C42C22×D3711yescharacteristic
118C23—741no—
119Q8—41no—
120Q8—41no—
121Q8—2961no—
122D4—741no—
123D4—741no—
124C2×C4—41no—
125C2×C4—741no—
126C2×C4—1481no—
127C2×C4—1481no—
128C2×C4—1481no—
129C2×C4#1059696211yescharacteristic
130C2×C4D4×D3711yescharacteristic
131C2×C4D4×D3711yescharacteristic
132C8—41no—
133C8—41no—
134C8—372no—
135C8—741no—
136C8—1481no—
137C22—1481no—
138C22—1481no—
139C22—1481no—
140C22#1192450911yescharacteristic
141C4—21no—
142C4—81no—
143C4—2961no—
144C4—1481no—
145C4SD16×D3711yescharacteristic
146C4#1192456011yescharacteristic
147C4#1192456511yescharacteristic
148C4#1192456811yescharacteristic
149C2—2961no—
150C2#1455773711yescharacteristic
151C2#1455777811yescharacteristic
152C2#1455779911yescharacteristic
subgroupG/H
centerC22#11924509
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#121
prime radicalC2×D148D4
hypercenter#332D37
hypocenterC37#1691
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14557929C2semidirect
5. #14557285C2semidirect
6. #14557281C2semidirect
7. C37×#332C2semidirect
59. #64436SD16semidirect
83. #332D37semidirect
84. C37#1691semidirect

Maximal subgroups

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

subgroupindex
#145579292
#145578242
#145577352
#145576102
#145572852
#145572812
C37×#3322
#169137