Finite Group Databasebeta

← #17993923

Subgroups — #17993923

Order 4736.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C37⋊#564C211yesmaximal, characteristic
2#14557939C211yesmaximal, characteristic
3#14557901C211yesmaximal, characteristic
4#14557275C211yesmaximal, characteristic
5#14557274C211yesmaximal, characteristic
6#14557274C211yesmaximal, characteristic
7C37×#501C211yesmaximal, characteristic
8#11924528C2211yescharacteristic
9#11924528C2211yescharacteristic
10#11924527—21no—
11#11924527—21no—
12#11924526—21no—
13#11924526—21no—
14#11924526—21no—
15#11924526—21no—
16#11924469—21no—
17#11924467—21no—
18#11924460—21no—
19#11924460—21no—
20#11924447C2211yescharacteristic
21#11924447C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23#125×C37C2211yescharacteristic
24#107×C37—21no—
25#106×C37—21no—
26#97×C37C2211yescharacteristic
27C2×Q8×C37—21no—
28C2×C8×C37—21no—
29C4⋊C4×C37—21no—
30C4⋊C4×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D411yescharacteristic
34C4⋊C4×C37D411yescharacteristic
35C42×C37C2311yescharacteristic
36C4⋊Dic37—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37D411yescharacteristic
39C4⋊Dic37D411yescharacteristic
40C4⋊Dic37D411yescharacteristic
41C4⋊Dic37D411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C2×#64436—21no—
53C2×#64436—21no—
54Q8×C37—42no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C8×C37—22no—
66#64436—22no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C4×C37—21no—
70C4×C37—21no—
71C4×C37—21no—
72C4×C37—41no—
73C4×C37—41no—
74C4×C37—81no—
75Dic37—41no—
76Dic37—41no—
77Dic37—41no—
78Dic37—41no—
79#1663—371nomaximal, Sylow
80C2×C37#45411yescharacteristic
81C2×C37#45611yescharacteristic
82C2×C37#45611yescharacteristic
83#564—371no—
84#501—371no—
85#501D3711yescharacteristic
86#491—371no—
87#330—371no—
88#330—371no—
89#330—371no—
90C37#166311yescharacteristic, complemented, Sylow
91C4⋊Q8C2×D3711yescharacteristic
92#125—371no—
93#125—371no—
94#125—741no—
95#125—741no—
96#125—741no—
97#125—741no—
98#125—741no—
99#125—741no—
100#125C2×D3711yescharacteristic
101#107—21no—
102#107—741no—
103#106—21no—
104#106—741no—
105#103—741no—
106#103—741no—
107#97—371no—
108#97—371no—
109#97C2×D3711yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—741no—
113C2×C8—741no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—371no—
119C4⋊C4—371no—
120C4⋊C4—371no—
121C4⋊C4—371no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4C22⋊D3711yescharacteristic
133C4⋊C4C22⋊D3711yescharacteristic
134C42—741no—
135C42—741no—
136C42C22×D3711yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—741no—
142C2×C4—741no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4D4×D3711yescharacteristic
146C2×C4D4×D3711yescharacteristic
147C2×C4C2×C22⋊D3711yescharacteristic
148C8—22no—
149C8—742no—
150C8—1481no—
151C22#1192450411yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—1481no—
159C4—1481no—
160C4—1481no—
161C4—1481no—
162C2#1455770411yescharacteristic
163C2#1455771411yescharacteristic
164C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#501C2
socle, prime radicalC22×C37#120
hypercenter#501D37
hypocenterC37#1663
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
90. C37#1663semidirect

Maximal subgroups

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

subgroupindex
C37⋊#5642
#145579392
#145579012
#145572752
#145572742
C37×#5012
#166337