Finite Group Databasebeta

← #17992925

Subgroups — #17992925

Order 4736.

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

normal subgroups only

This group has 312 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
1C22×#10596936C211yesmaximal, characteristic
2#14557497C211yesmaximal, characteristic
3#14557258C214yesmaximal, complemented
4C37×#407C211yesmaximal, characteristic
5C23×Dic37C411yescharacteristic
6C23×Dic37C411yescharacteristic
7C2×#10596934—21no—
8C2×#10596936—21no—
9C2×#10596936—21no—
10C2×#10596936—21no—
11C2×#10596936—21no—
12C2×#10596936C412yes—
13C2×#10596936C2212yes—
14C22⋊#64436—21no—
15C22⋊#64436C2212yes—
16C23×C4×C37C2211yescharacteristic
17C2×M16×C37—21no—
18C22⋊C8×C37—21no—
19C22⋊C8×C37C2212yes—
20C24×C37C2×C411yescharacteristic
21C22×C4×C37—42no—
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37D411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D411yescharacteristic
27C22×C4×C37C2311yescharacteristic
28C22×Dic37—21no—
29C22×Dic37—21no—
30C22×Dic37—24no—
31C22×Dic37—21no—
32C22×Dic37—21no—
33C22×Dic37—42no—
34C22×Dic37C2×C412yes—
35C22×Dic37C2×C412yes—
36M16×C37—42no—
37C2×C8×C37—22no—
38#10596936—22no—
39#10596936—22no—
40#10596936—22no—
41#10596936—22no—
42#10596934—42no—
43C2×#64436—22no—
44C23×C37—22no—
45C23×C37—22no—
46C23×C37—22no—
47C23×C37C22⋊C411yescharacteristic
48C23×C37C22⋊C411yescharacteristic
49C23×C37C22×C411yescharacteristic
50C2×C4×C37—22no—
51C2×C4×C37—22no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×Dic37—24no—
61C2×Dic37—24no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—22no—
65C2×Dic37—42no—
66C2×Dic37—42no—
67C2×Dic37—42no—
68C2×Dic37M1614yescomplemented
69C8×C37—42no—
70#64436—42no—
71C22×C37—28no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37#9912yes—
79C22×C37#10112yes—
80C22×C37C2×C22⋊C411yescharacteristic
81C22×C37C2×M1612yes—
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—21no—
86Dic37—24no—
87Dic37—42no—
88#1463—371nomaximal, Sylow
89C2×C37—22no—
90C2×C37—22no—
91C2×C37—22no—
92C2×C37#40711yescharacteristic
93C2×C37C2×#9911yescharacteristic
94C2×C37C2×#10111yescharacteristic
95C22×C4⋊C4—371no—
96#407—371no—
97#407D3711yescharacteristic
98#324—374no—
99C37#146311yescharacteristic, complemented, Sylow
100C23×C4—371no—
101C23×C4—371no—
102C23×C4C2×D3711yescharacteristic
103C2×M16—21no—
104C2×M16—741no—
105C2×C4⋊C4—372no—
106C2×C4⋊C4—372no—
107C2×C4⋊C4—741no—
108C2×C4⋊C4—741no—
109C2×C4⋊C4—741no—
110C2×C4⋊C4—741no—
111C22⋊C8—21no—
112C22⋊C8—372no—
113C22⋊C8—741no—
114C22⋊C8C2×D3712yes—
115C24C4×D3711yescharacteristic
116C22×C4—42no—
117C22×C4—372no—
118C22×C4—372no—
119C22×C4—744no—
120C22×C4—741no—
121C22×C4—741no—
122C22×C4—741no—
123C22×C4—741no—
124C22×C4—1482no—
125C22×C4C4×D3711yescharacteristic
126C22×C4D14811yescharacteristic
127C22×C4D14811yescharacteristic
128C22×C4C22⋊D3711yescharacteristic
129C22×C4C22⋊D3711yescharacteristic
130C22×C4C22×D3711yescharacteristic
131M16—42no—
132M16—1482no—
133C2×C8—22no—
134C2×C8—742no—
135C4⋊C4—742no—
136C4⋊C4—742no—
137C4⋊C4—742no—
138C4⋊C4—742no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23#1059693811yescharacteristic
143C23#1059693811yescharacteristic
144C23C2×C4×D3711yescharacteristic
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—374no—
152C2×C4—744no—
153C2×C4—744no—
154C2×C4—742no—
155C2×C4—742no—
156C2×C4—742no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4#1059693811yescharacteristic
161C2×C4#1059693811yescharacteristic
162C2×C4C2×D14811yescharacteristic
163C2×C4C2×C22⋊D3711yescharacteristic
164C8—42no—
165C8—1482no—
166C22—28no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22#1192445012yes—
174C22#1192445412yes—
175C22C2×#1059693811yescharacteristic
176C22M16×D3712yes—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—744no—
182C4—1482no—
183C2—22no—
184C2—22no—
185C2—22no—
186C2#1455749611yescharacteristic
187C2C2×#1192445011yescharacteristic
188C2C2×#1192445411yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#407C2
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×C4×C37C23
hypercenter#407D37
hypocenterC37#1463
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #14557258C2semidirect
68. C2×Dic37M16semidirect
99. C37#1463semidirect

Maximal subgroups

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

subgroupindex
C22×#105969362
#145574972
#145572582
C37×#4072
#146337