Finite Group Databasebeta

← #18004529

Subgroups — #18004529

Order 4736.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#14558044C211yesmaximal, characteristic
2C2×#11924495C211yesmaximal, characteristic, complemented
3#14557875C214yesmaximal, complemented
4#14557858C214yesmaximal, complemented
5#14557575C212yesmaximal, complemented
6#14557535C212yesmaximal, complemented
7C37×#407C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924519—21no—
10#11924515C2212yes—
11#11924510C2212yes—
12#11924505—21no—
13C4×C22⋊D37—22no—
14#11924495—22no—
15#11924495C2214yes—
16#11924495C2211yescharacteristic
17C2×C4⋊Dic37C2212yes—
18C2×C22⋊Dic37—21no—
19C2×C4×Dic37—21no—
20#11924470C2214yescomplemented
21#11924468C2214yescomplemented
22#11924461C2214yescomplemented
23#11924458C2214yescomplemented
24C23×C4×C37C2211yescharacteristic
25C2×M16×C37C2212yes—
26C22⋊C8×C37C2214yes—
27C24×C37D411yescharacteristic
28C22×C4×C37—24no—
29C22×C4×C37D411yescharacteristic
30C22×C4×C37D412yes—
31C22×C4×C37C2312yes—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—22no—
34C2×C22⋊D37—21no—
35C22×Dic37—22no—
36#10596962—24no—
37C2×D148C2311yescharacteristic
38C2×C4×D37—21no—
39C2×Dic74C2311yescharacteristic
40M16×C37—24no—
41C2×C8×C37C2314yes—
42C22⋊Dic37—24no—
43C22⋊Dic37—21no—
44C22⋊Dic37—22no—
45#10596938—22no—
46C4⋊Dic37—22no—
47C4⋊Dic37C2314yes—
48C4⋊Dic37C2312yes—
49#10596936—22no—
50C4×Dic37—24no—
51C4×Dic37—21no—
52C23×C37—22no—
53C23×C37—42no—
54C23×C37C2×D412yes—
55C23×C37C2×D411yescharacteristic
56C22×D37—21no—
57C2×C4×C37—22no—
58C2×C4×C37—24no—
59C2×C4×C37—24no—
60C2×C4×C37C2×D412yes—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37#4114yes—
63C2×C4×C37C2411yescharacteristic
64C22⋊D37—44no—
65C22⋊D37—42no—
66C2×Dic37—24no—
67C2×Dic37—22no—
68C2×Dic37—21no—
69C2×Dic37—44no—
70D148—22no—
71C4×D37—42no—
72Dic74—22no—
73C8×C37—24no—
74C22×C37—22no—
75C22×C37—22no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—44no—
79C22×C37#12312yes—
80C22×C37C22×D411yescharacteristic
81C2×D37—41no—
82C2×D37—42no—
83C4×C37—22no—
84C4×C37#12312yes—
85C4×C37C2×#4112yes—
86Dic37—41no—
87Dic37—44no—
88Dic37—42no—
89#3093—371nomaximal, Sylow
90C2×C37—22no—
91C2×C37—42no—
92C2×C37C2×#12311yescharacteristic
93C2×C37#57512yes—
94D37—81no—
95#525—371no—
96C2×#117—371no—
97#485—374no—
98#482—374no—
99#428—372no—
100#417—372no—
101#407D3711yescharacteristic, complemented
102C37#309311yescharacteristic, complemented, Sylow
103C2×#41—371no—
104C23×C4C2×D3711yescharacteristic
105C2×M16C2×D3712yes—
106#123—741no—
107C22⋊Q8—372no—
108#121—372no—
109#120—741no—
110C4×D4—742no—
111#117—374no—
112#117—371no—
113#117—742no—
114C2×C4⋊C4—372no—
115C2×C22⋊C4—741no—
116C2×C42—741no—
117#107—374no—
118#106—374no—
119#103—374no—
120#102—374no—
121C22⋊C8C2×D3714yes—
122C24D14811yescharacteristic
123#41—744no—
124C2×Q8—371no—
125C2×D4—371no—
126C2×D4—742no—
127C2×D4—741no—
128C22×C4—24no—
129C22×C4—742no—
130C22×C4—741no—
131C22×C4D14811yescharacteristic
132C22×C4D14812yes—
133C22×C4C22×D3712yes—
134C22×C4C22×D3711yescharacteristic
135M16—24no—
136C2×C8C22×D3714yes—
137C4⋊C4—374no—
138C4⋊C4—372no—
139C4⋊C4—742no—
140C4⋊C4—742no—
141C22⋊C4—744no—
142C22⋊C4—741no—
143C22⋊C4—742no—
144C22⋊C4—742no—
145C42—744no—
146C42—741no—
147C23—22no—
148C23—42no—
149C23—741no—
150C23C2×D14812yes—
151C23C2×D14811yescharacteristic
152Q8—742no—
153D4—742no—
154D4—1484no—
155D4—1482no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—744no—
160C2×C4—742no—
161C2×C4—741no—
162C2×C4—1484no—
163C2×C4—1482no—
164C2×C4C2×D14812yes—
165C2×C4C2×D14811yescharacteristic
166C2×C4#1059696414yes—
167C2×C4C23×D3711yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1481no—
175C22—1482no—
176C22#1192452012yes—
177C22C22×D14811yescharacteristic
178C4—22no—
179C4—1481no—
180C4—1484no—
181C4—1482no—
182C4#1192452012yes—
183C4C2×#1059696412yes—
184C2—22no—
185C2—42no—
186C2—2961no—
187C2C2×#1192452011yescharacteristic
188C2#1455833312yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#407C2
socleC22×C37C22×D4
prime radical#14558044C2
hypercenter#407D37
hypocenterC37#3093
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#11924495C2semidirect
3. #14557875C2semidirect
4. #14557858C2semidirect
5. #14557575C2semidirect
6. #14557535C2semidirect
7. C37×#407C2semidirect
20. #11924470C22semidirect
21. #11924468C22semidirect
22. #11924461C22semidirect
23. #11924458C22semidirect
101. #407D37semidirect
102. C37#3093semidirect

Maximal subgroups

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

subgroupindex
#145580442
C2×#119244952
#145578752
#145578582
#145575752
#145575352
C37×#4072
#309337