Finite Group Databasebeta

← #17992928

Subgroups — #17992928

Order 4736.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924493C211yesmaximal, characteristic
2#14557590C211yesmaximal, characteristic, complemented
3#14557258C212yesmaximal, complemented
4#14557256C212yesmaximal
5C37×#432C211yesmaximal, characteristic, complemented
6C22×C4×D37C411yescharacteristic
7#11924493—21no—
8#11924493—21no—
9#11924493—21no—
10#11924493—21no—
11C2×#10596936C411yescharacteristic
12C2×#10596936C2211yescharacteristic
13C2×#10596938C411yescharacteristic
14C2×#10596938C2211yescharacteristic
15C2×C4×Dic37C411yescharacteristic
16C4⋊#64436—21no—
17C22⋊#64436C2212yes—
18#11924447—21no—
19C2×C42×C37C2211yescharacteristic
20C4⋊C8×C37—21no—
21C22⋊C8×C37C2212yes—
22#97×C37—21no—
23C23×D37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37C2311yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C2×C4×D37—22no—
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37—22no—
34C2×C8×C37—22no—
35C42×C37D411yescharacteristic
36C42×C37D411yescharacteristic
37C42×C37D411yescharacteristic
38C42×C37D411yescharacteristic
39#10596938—21no—
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37—21no—
48C4×Dic37—21no—
49C2×#64436—22no—
50C23×C37C22×C411yescharacteristic
51C22×D37—21no—
52C22×D37—21no—
53C22×D37—41no—
54C22×D37—41no—
55C22×D37M1612yes—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37M1612yes—
73C4×D37—24no—
74C4×D37—24no—
75C8×C37—42no—
76#64436—42no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37C2×C22⋊C411yescharacteristic
80C22×C37C2×M1611yescharacteristic
81C22×C37C2×M1611yescharacteristic
82C2×D37—22no—
83C2×D37—42no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—42no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—21no—
93Dic37—22no—
94Dic37—41no—
95Dic37—41no—
96#1464—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—21no—
99C2×C37#40711yescharacteristic
100C2×C37#41011yescharacteristic
101C2×C37#41311yescharacteristic
102D37—42no—
103C2×#117—371no—
104#432—371no—
105#432D3711yescharacteristic, complemented
106#324—372no—
107#323—372no—
108C37#146411yescharacteristic, complemented, Sylow
109C23×C4—371no—
110#117—741no—
111#117—741no—
112#117—741no—
113#117—741no—
114C2×C4⋊C4—371no—
115C2×C4⋊C4—371no—
116C2×C22⋊C4—371no—
117C2×C22⋊C4—371no—
118C2×C42—371no—
119C2×C42C2×D3711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—741no—
122C22⋊C8—372no—
123C22⋊C8C2×D3712yes—
124#97—21no—
125#97—741no—
126C24—371no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—742no—
131C22×C4—742no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4C4×D3711yescharacteristic
135C22×C4C4×D3711yescharacteristic
136C22×C4C22×D3711yescharacteristic
137C2×C8—22no—
138C2×C8—742no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C22⋊C4—741no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C42—741no—
148C42—741no—
149C42D14811yescharacteristic
150C42D14811yescharacteristic
151C42C22⋊D3711yescharacteristic
152C42C22⋊D3711yescharacteristic
153C23—372no—
154C23—741no—
155C23—741no—
156C23—1481no—
157C23—1481no—
158C23C2×C4×D3711yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—372no—
164C2×C4—744no—
165C2×C4—744no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4#1059693811yescharacteristic
173C2×C4#1059693811yescharacteristic
174C2×C4#1059693811yescharacteristic
175C2×C4#1059693811yescharacteristic
176C2×C4C2×D14811yescharacteristic
177C2×C4C2×C22⋊D3711yescharacteristic
178C8—42no—
179C8—1482no—
180C22—21no—
181C22—21no—
182C22—742no—
183C22—1482no—
184C22—1482no—
185C22—1481no—
186C22—1481no—
187C22C2×#1059693811yescharacteristic
188C22M16×D3711yescharacteristic
189C22M16×D3711yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—742no—
197C4—1481no—
198C4—1481no—
199C2—21no—
200C2—21no—
201C2—1482no—
202C2#1455749611yescharacteristic
203C2#1455750611yescharacteristic
204C2#1455751511yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#432C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#432D37
hypocenterC37#1464
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #14557590C2semidirect
3. #14557258C2semidirect
5. C37×#432C2semidirect
105. #432D37semidirect
108. C37#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#119244932
#145575902
#145572582
#145572562
C37×#4322
#146437