Finite Group Databasebeta

← #17993567

Subgroups — #17993567

Order 4736.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558114C211yesmaximal, characteristic
2#14557674C212yesmaximal, complemented
3#14557453C211yesmaximal, characteristic, complemented
4#14557268C212yesmaximal, complemented
5C37×#324C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7C22×Dic74C2211yescharacteristic
8C2×#10596930—22no—
9#11924516—22no—
10#11924511—22no—
11#11924510—21no—
12#11924510C2212yes—
13C2×#10596936—21no—
14#11924461—22no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C22×C4×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24C22×Dic37—21no—
25#10596962—42no—
26#10596962—42no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D412yes—
30C2×C4×D37—22no—
31C2×Dic74—22no—
32C2×Dic74—21no—
33C2×Dic74—42no—
34C2×C8×C37—22no—
35C4⋊C4×C37—22no—
36#10596938—22no—
37#10596938—22no—
38C4⋊Dic37—21no—
39C4⋊Dic37D412yes—
40#10596936—42no—
41#10596930—44no—
42C23×C37C2×D411yescharacteristic
43C22×D37—22no—
44C2×C4×C37—21no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37—41no—
48C2×C4×C37—41no—
49C2×C4×C37SD1612yescomplemented
50C2×C4×C37C2×D412yes—
51C22⋊D37—42no—
52C22⋊D37—42no—
53C2×Dic37—22no—
54C2×Dic37—22no—
55C2×Dic37—22no—
56C2×Dic37—41no—
57C2×Dic37—41no—
58C2×Dic37—41no—
59C2×Dic37—41no—
60D148—42no—
61D148—42no—
62D148—81no—
63C4×D37—44no—
64Dic74—24no—
65Dic74—42no—
66Dic74—42no—
67C8×C37—42no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37#12011yescharacteristic
71C22×C37C2×SD1611yescharacteristic
72C22×C37AGL(1,ℤ/8)11yescharacteristic
73C2×D37—42no—
74C2×D37—42no—
75C2×D37—42no—
76C4×C37—22no—
77C4×C37—22no—
78C4×C37—41no—
79Dic37—42no—
80Dic37—42no—
81Dic37—42no—
82#1604—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37#45011yescharacteristic
86C2×C37#45611yescharacteristic
87C2×C37B(4,𝔽2)11yescharacteristic
88D37—82no—
89#537—371no—
90#448—372no—
91#395—371no—
92#327—372no—
93#324D3711yescharacteristic, complemented
94C37#160411yescharacteristic, complemented, Sylow
95C2×#41—741no—
96C22×Q8—371no—
97C2×SD16—742no—
98C22⋊Q8—742no—
99#121—372no—
100#121—742no—
101#121—741no—
102C2×C4⋊C4—741no—
103C2×C4⋊C4C2×D3711yescharacteristic
104#103—742no—
105C22⋊C8C2×D3712yes—
106#95—371no—
107#95—741no—
108#41—1482no—
109#41—1482no—
110C2×Q8—741no—
111C2×Q8—742no—
112C2×Q8—1482no—
113C2×D4—372no—
114C2×D4—741no—
115C2×D4—741no—
116C2×D4—742no—
117C22×C4—742no—
118C22×C4—741no—
119C22×C4—741no—
120C22×C4D14811yescharacteristic
121C22×C4D14811yescharacteristic
122C22×C4C22×D3711yescharacteristic
123SD16—1484no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—372no—
127C4⋊C4—741no—
128C4⋊C4—1482no—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C23—742no—
132C23C2×D14811yescharacteristic
133Q8—744no—
134Q8—1482no—
135Q8—1482no—
136D4—2961no—
137D4—1482no—
138D4—1482no—
139D4—1482no—
140D4—1482no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—742no—
147C2×C4—742no—
148C2×C4—742no—
149C2×C4—1484no—
150C2×C4—1481no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4—1481no—
154C2×C4#1059693012yescomplemented
155C2×C4D4×D3712yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—1482no—
160C22—1482no—
161C22—1482no—
162C22#1192450611yescharacteristic
163C22C2×#1059693011yescharacteristic
164C22#1192456411yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—1482no—
169C4—1482no—
170C4—1482no—
171C2—21no—
172C2—21no—
173C2—2962no—
174C2#1455768611yescharacteristic
175C2#1455771811yescharacteristic
176C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37#120
prime radical#14558114C2
hypercenter#324D37
hypocenterC37#1604
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14557674C2semidirect
3. #14557453C2semidirect
4. #14557268C2semidirect
5. C37×#324C2semidirect
49. C2×C4×C37SD16semidirect
93. #324D37semidirect
94. C37#1604semidirect
154. C2×C4#10596930semidirect

Maximal subgroups

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

subgroupindex
#145581142
#145576742
#145574532
#145572682
C37×#3242
#160437