Finite Group Databasebeta

← #17994669

Subgroups — #17994669

Order 4736.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C22⋊C4×D37C211yesmaximal, characteristic
2#14557388C212yesmaximal
3#14557300C211yesmaximal, characteristic, complemented
4#14557299C212yesmaximal, complemented
5C37×#342C211yesmaximal, characteristic, complemented
6C24×D37C2211yescharacteristic
7C22×C4×D37C412yescomplemented
8C2×C22⋊Dic37C2212yes—
9C2×C22⋊Dic37C2211yescharacteristic
10C2×#10596938—24no—
11C2×#10596938C412yescomplemented
12C22⋊C4×D37—24no—
13C2×C22⋊C4×C37C2212yes—
14C2×C22⋊C4×C37C2211yescharacteristic
15C24×C37C2311yescharacteristic
16C23×D37—22no—
17C23×D37—21no—
18C23×D37—21no—
19C23×D37—44no—
20C23×D37C2×C411yescharacteristic
21C23×D37C2×C411yescharacteristic
22C23×D37D414yes—
23C22×C4×C37—22no—
24C22×C4×C37C2×C412yes—
25C22×Dic37—22no—
26C22×Dic37C2×C412yes—
27C2×C4×D37—22no—
28C2×C4×D37—22no—
29C2×C4×D37—44no—
30C22⋊C4×C37—22no—
31C22⋊C4×C37—22no—
32C22⋊C4×C37—22no—
33C22⋊Dic37—22no—
34C22⋊Dic37—22no—
35C22⋊Dic37—22no—
36#10596938—24no—
37#10596938—48no—
38C23×C37—42no—
39C23×C37C22×C411yescharacteristic
40C23×C37C2×D412yes—
41C23×C37#4112yes—
42C23×C37#4111yescharacteristic
43C23×C37#4111yescharacteristic
44C22×D37—21no—
45C22×D37—21no—
46C22×D37—24no—
47C22×D37—21no—
48C22×D37—21no—
49C22×D37—24no—
50C22×D37—24no—
51C22×D37—28no—
52C22×D37—42no—
53C22×D37—44no—
54C22×D37—48no—
55C22×D37—44no—
56C22×D37—44no—
57C22×D37C22⋊C412yes—
58C22×D37C22⋊C412yes—
59C2×C4×C37—22no—
60C2×C4×C37—42no—
61C2×C4×C37—44no—
62C2×C4×C37—42no—
63C2×Dic37—22no—
64C2×Dic37—42no—
65C2×Dic37—44no—
66C2×Dic37—42no—
67C4×D37—44no—
68C4×D37—44no—
69C22×C37—22no—
70C22×C37—24no—
71C22×C37—42no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37C2×C22⋊C411yescharacteristic
75C22×C37#11711yescharacteristic
76C22×C37#11711yescharacteristic
77C22×C37#12312yes—
78C22×C37#12312yes—
79C2×D37—24no—
80C2×D37—24no—
81C2×D37—22no—
82C2×D37—22no—
83C2×D37—22no—
84C2×D37—24no—
85C2×D37—48no—
86C2×D37—48no—
87C2×D37—42no—
88C2×D37—42no—
89C2×D37#9914yes—
90C4×C37—42no—
91C4×C37—82no—
92Dic37—42no—
93Dic37—82no—
94#1819—371nomaximal, Sylow
95C2×C37—22no—
96C2×C37—22no—
97C2×C37—21no—
98C2×C37—21no—
99C2×C37#38111yescharacteristic
100C2×C37C2×#9912yes—
101D37—24no—
102D37—42no—
103C22×C22⋊C4—371no—
104#379—372no—
105#342—372no—
106#342—371no—
107#342D3711yescharacteristic, complemented
108C37#181911yescharacteristic, complemented, Sylow
109C25—371no—
110C23×C4—372no—
111C2×C22⋊C4—371no—
112C2×C22⋊C4—372no—
113C2×C22⋊C4—372no—
114C2×C22⋊C4—744no—
115C2×C22⋊C4—744no—
116C2×C22⋊C4C2×D3712yes—
117C2×C22⋊C4C2×D3711yescharacteristic
118C24—371no—
119C24—374no—
120C24—371no—
121C24—742no—
122C24—741no—
123C24—741no—
124C24—1484no—
125C24C22×D3711yescharacteristic
126C22×C4—22no—
127C22×C4—372no—
128C22×C4—742no—
129C22×C4—742no—
130C22×C4—742no—
131C22×C4—1484no—
132C22×C4C4×D3712yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—744no—
137C22⋊C4—742no—
138C22⋊C4—742no—
139C22⋊C4—742no—
140C22⋊C4—1488no—
141C23—42no—
142C23—372no—
143C23—372no—
144C23—744no—
145C23—748no—
146C23—741no—
147C23—741no—
148C23—741no—
149C23—741no—
150C23—744no—
151C23—744no—
152C23—1482no—
153C23—1484no—
154C23—1488no—
155C23—1484no—
156C23—1484no—
157C23C2×C4×D3711yescharacteristic
158C23#1059696212yes—
159C23D4×D3712yes—
160C23#1059696411yescharacteristic
161C23#1059696611yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—742no—
167C2×C4—1484no—
168C2×C4—1484no—
169C2×C4—1484no—
170C2×C4—1482no—
171C2×C4—1482no—
172C22—22no—
173C22—24no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—374no—
178C22—744no—
179C22—744no—
180C22—742no—
181C22—742no—
182C22—744no—
183C22—742no—
184C22—1488no—
185C22—1488no—
186C22—1482no—
187C22—1482no—
188C22C22⋊C4×D3711yescharacteristic
189C22#1192449311yescharacteristic
190C22#1192449411yescharacteristic
191C22#1192451812yes—
192C22#1192452112yes—
193C4—42no—
194C4—82no—
195C4—2962no—
196C4—1482no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—744no—
202C2—1482no—
203C2#1455739511yescharacteristic
204C2#99×D3712yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37C2×C22⋊C4
prime radicalC24×D37C22
cosocleC24×C37C23
hypercenter#342D37
hypocenterC37#1819
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #14557300C2semidirect
4. #14557299C2semidirect
5. C37×#342C2semidirect
7. C22×C4×D37C4semidirect
11. C2×#10596938C4semidirect
107. #342D37semidirect
108. C37#1819semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D372
#145573882
#145573002
#145572992
C37×#3422
#181937