Finite Group Databasebeta

← #17993565

Subgroups — #17993565

Order 4736.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557671C212yesmaximal, complemented
2#14557453C211yesmaximal, characteristic, complemented
3#14557267C212yesmaximal, complemented
4#14557259C211yesmaximal, characteristic, complemented
5C37×#537C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7C2×#10596940—22no—
8C2×#10596936—21no—
9#11924459—22no—
10C22⋊#64436C2212yes—
11#11924443—21no—
12#11924443C2211yescharacteristic
13C2×#41×C37—21no—
14C22⋊Q8×C37—22no—
15#121×C37—22no—
16#121×C37—21no—
17#121×C37C2212yes—
18C2×C4⋊C4×C37C2211yescharacteristic
19#41×C37—42no—
20#41×C37—42no—
21C2×Q8×C37—21no—
22C2×D4×C37—21no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37D412yes—
26C22×C4×C37—22no—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37—21no—
32C2×Dic74—22no—
33C2×Dic74—42no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—22no—
36C4⋊C4×C37D412yes—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39#10596940—44no—
40#10596936—42no—
41C2×#64436—22no—
42C23×C37—22no—
43C23×C37C2×D411yescharacteristic
44Q8×C37—42no—
45D4×C37—42no—
46D4×C37—42no—
47D4×C37—42no—
48D4×C37—42no—
49D4×C37—81no—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37—22no—
54C2×C4×C37—41no—
55C2×C4×C37—44no—
56C2×C4×C37—41no—
57C2×C4×C37SD1612yescomplemented
58C2×C4×C37C2×D412yes—
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37—41no—
64C2×Dic37—41no—
65Dic74—24no—
66Dic74—42no—
67#64436—42no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—42no—
71C22×C37—42no—
72C22×C37—42no—
73C22×C37#12011yescharacteristic
74C22×C37C2×SD1611yescharacteristic
75C22×C37AGL(1,ℤ/8)11yescharacteristic
76C4×C37—22no—
77C4×C37—22no—
78C4×C37—42no—
79C4×C37—41no—
80Dic37—42no—
81Dic37—42no—
82#1604—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37—82no—
86C2×C37#45011yescharacteristic
87C2×C37#45611yescharacteristic
88C2×C37B(4,𝔽2)11yescharacteristic
89#537D3711yescharacteristic
90#448—372no—
91#395—371no—
92#327—372no—
93#324—371no—
94C37#160411yescharacteristic, complemented, Sylow
95C2×#41—21no—
96C22×Q8—371no—
97C2×SD16—742no—
98C22⋊Q8—22no—
99#121—22no—
100#121—21no—
101#121C2×D3712yes—
102C2×C4⋊C4—741no—
103C2×C4⋊C4C2×D3711yescharacteristic
104#103—742no—
105C22⋊C8—372no—
106#95—371no—
107#95—741no—
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—742no—
112C2×Q8—1482no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D3712yes—
117C22×C4—22no—
118C22×C4—741no—
119C22×C4—741no—
120C22×C4C22⋊D3711yescharacteristic
121C22×C4C22⋊D3711yescharacteristic
122C22×C4C22×D3711yescharacteristic
123SD16—1484no—
124C2×C8—742no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—1482no—
128C4⋊C4C22⋊D3712yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D3711yescharacteristic
133Q8—42no—
134Q8—744no—
135Q8—1482no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—742no—
149C2×C4—742no—
150C2×C4—1481no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4—1481no—
154C2×C4#1059694012yescomplemented
155C2×C4C2×C22⋊D3712yes—
156C8—1482no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1192450511yescharacteristic
163C22C2×#1059694011yescharacteristic
164C22#1192456211yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—42no—
169C4—1482no—
170C4—1482no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1455768411yescharacteristic
175C2#1455771611yescharacteristic
176C2#1455772011yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#537C2
socleC22×C37#120
hypercenter#537D37
hypocenterC37#1604
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14557671C2semidirect
2. #14557453C2semidirect
3. #14557267C2semidirect
4. #14557259C2semidirect
57. C2×C4×C37SD16semidirect
94. C37#1604semidirect
154. C2×C4#10596940semidirect

Maximal subgroups

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

subgroupindex
#145576712
#145574532
#145572672
#145572592
C37×#5372
#160437