Finite Group Databasebeta

← #17993906

Subgroups — #17993906

Order 4736.

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

normal subgroups only

This group has 196 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
1#14558287C211yesmaximal, characteristic
2#14557939C211yesmaximal, characteristic, complemented
3#14557925C211yesmaximal, characteristic
4#14557275C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic
7C37×#501C211yesmaximal, characteristic, complemented
8C2×#10596942—21no—
9C2×#10596941—21no—
10#11924535—21no—
11#11924531—21no—
12#11924531—21no—
13#11924528C2211yescharacteristic
14#11924524C2211yescharacteristic
15#11924521—21no—
16#11924516—21no—
17#11924514—21no—
18#11924469—21no—
19#11924467—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×D148D411yescharacteristic
29C2×C4×D37—21no—
30C2×Dic74—21no—
31C2×Dic74D411yescharacteristic
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C4⋊C4×C37D411yescharacteristic
39C42×C37C2311yescharacteristic
40#10596942—42no—
41#10596941—42no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37D411yescharacteristic
49C4⋊Dic37D411yescharacteristic
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56C22×D37—21no—
57Q8×C37—41no—
58Q8×C37—41no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—41no—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68D148—41no—
69C4×D37—81no—
70Dic74—41no—
71Dic74—81no—
72C8×C37—22no—
73#64436—22no—
74#64436—22no—
75C22×C37#12011yescharacteristic
76C2×D37—41no—
77C2×D37—41no—
78C2×D37—41no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—41no—
83C4×C37—41no—
84C4×C37—81no—
85Dic37—41no—
86Dic37—41no—
87Dic37—41no—
88#1660—371nomaximal, Sylow
89C2×C37#45311yescharacteristic
90C2×C37#45611yescharacteristic
91C2×C37#45611yescharacteristic
92D37—81no—
93#563—371no—
94#501—371no—
95#501D3711yescharacteristic, complemented
96#497—371no—
97#330—371no—
98#330—371no—
99#329—371no—
100C37#166011yescharacteristic, complemented, Sylow
101C2×Q16—741no—
102C2×SD16—741no—
103C4⋊Q8—741no—
104C4⋊Q8C2×D3711yescharacteristic
105#126—741no—
106#126—741no—
107#125—371no—
108#125C2×D3711yescharacteristic
109#124—371no—
110#123—741no—
111C22⋊Q8—741no—
112C22⋊Q8—741no—
113#107—21no—
114#107—741no—
115#106—21no—
116#106—741no—
117#97—371no—
118#97—371no—
119#97C2×D3711yescharacteristic
120C2×Q8—21no—
121C2×Q8—371no—
122C2×Q8—741no—
123C2×D4—371no—
124C22×C4—741no—
125Q16—1482no—
126SD16—1482no—
127C2×C8—21no—
128C2×C8—741no—
129C2×C8—741no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—371no—
135C4⋊C4—371no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C4⋊C4—741no—
139C4⋊C4—741no—
140C4⋊C4C22⋊D3711yescharacteristic
141C4⋊C4C22⋊D3711yescharacteristic
142C22⋊C4—741no—
143C22⋊C4—741no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C42—741no—
148C42C22×D3711yescharacteristic
149C23—741no—
150Q8—41no—
151Q8—41no—
152Q8—2961no—
153Q8—1481no—
154D4—1481no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—2961no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4D4×D3711yescharacteristic
163C2×C4D4×D3711yescharacteristic
164C2×C4C2×C22⋊D3711yescharacteristic
165C8—22no—
166C8—742no—
167C8—742no—
168C22—1481no—
169C22—1481no—
170C22—1481no—
171C22#1192450411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—1481no—
179C4—1481no—
180C4—1481no—
181C2—2961no—
182C2#1455769911yescharacteristic
183C2#1455771411yescharacteristic
184C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#501C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#501D37
hypocenterC37#1660
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #14557939C2semidirect
4. #14557275C2semidirect
5. #14557274C2semidirect
7. C37×#501C2semidirect
95. #501D37semidirect
100. C37#1660semidirect

Maximal subgroups

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

subgroupindex
#145582872
#145579392
#145579252
#145572752
#145572742
#145572722
C37×#5012
#166037