Finite Group Databasebeta

← #17996976

Subgroups — #17996976

Order 4736.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D37C211yesmaximal, characteristic
2C2×#11924492C212yesmaximal, complemented
3#14557396C211yesmaximal, characteristic, complemented
4#14557392C214yesmaximal, complemented
5#14557388C212yesmaximal
6#14557380C214yesmaximal, complemented
7C37×#381C211yesmaximal, characteristic, complemented
8C24×D37C2211yescharacteristic
9C23×Dic37C2211yescharacteristic
10C22×C4×D37—28no—
11C22×C4×D37C418yescomplemented
12C22×C4×D37C2212yes—
13C22×C4×D37C2212yes—
14#11924492—28no—
15C2×#10596936C2214yescomplemented
16C2×C22⋊Dic37C2212yes—
17C2×#10596938C2218yes—
18C2×C4×Dic37C2214yescomplemented
19#11924443C2214yescomplemented
20C23×C4×C37C2211yescharacteristic
21C2×C22⋊C4×C37C2212yes—
22#95×C37C2214yescomplemented
23C24×C37C2311yescharacteristic
24C23×D37—24no—
25C23×D37—28no—
26C23×D37C2×C414yes—
27C23×D37C2312yes—
28C22×C4×C37—24no—
29C22×C4×C37C2×C414yes—
30C22×C4×C37C2314yes—
31C22×C4×C37C2312yes—
32C22×Dic37C2×C414yes—
33C22×Dic37D418yes—
34C22×Dic37C2314yes—
35C22×Dic37C2311yescharacteristic
36C22×Dic37C2311yescharacteristic
37C2×C4×D37—232no—
38C2×C4×D37—28no—
39C2×C4×D37—28no—
40C2×C4×D37C2×C418yes—
41C2×C4×D37C2×C418yes—
42C22⋊C4×C37—24no—
43C22⋊Dic37—24no—
44#10596938—216no—
45#10596936—28no—
46C4×Dic37—28no—
47C23×C37—24no—
48C23×C37C22×C412yes—
49C23×C37C2×D414yes—
50C23×C37C2411yescharacteristic
51C22×D37—232no—
52C22×D37—28no—
53C22×D37—24no—
54C22×D37—24no—
55C22×D37—216no—
56C22×D37C22×C414yes—
57C22×D37#4118yes—
58C2×C4×C37—28no—
59C2×C4×C37—24no—
60C2×C4×C37—24no—
61C2×C4×C37—28no—
62C2×C4×C37C22×C414yes—
63C2×Dic37—24no—
64C2×Dic37—28no—
65C2×Dic37C22⋊C4116yescomplemented
66C2×Dic37C22×C412yes—
67C2×Dic37C22×C412yes—
68C2×Dic37C2×D414yes—
69C2×Dic37C2×D414yes—
70C4×D37—216no—
71C4×D37—216no—
72C22×C37—24no—
73C22×C37—28no—
74C22×C37C2×C22⋊C414yes—
75C22×C37C23×C411yescharacteristic
76C22×C37C22×D412yes—
77C22×C37C2×#4114yes—
78C2×D37—232no—
79C2×D37—24no—
80C2×D37—24no—
81C2×D37—216no—
82C2×D37#11718yescomplemented
83C4×C37—24no—
84C4×C37—44no—
85Dic37—44no—
86Dic37C2×C22⋊C414yes—
87Dic37C2×C22⋊C414yes—
88#2280—371nomaximal, Sylow
89C2×C37—24no—
90C2×C37C22×C22⋊C411yescharacteristic
91C2×C37C2×#11712yes—
92C2×C37#52514yes—
93D37—28no—
94C24×C4—371no—
95C2×#117—372no—
96#381—371no—
97#381D3711yescharacteristic, complemented
98#380—374no—
99#379—372no—
100C4×C22⋊C4—374no—
101C37#228011yescharacteristic, complemented, Sylow
102C25—371no—
103C23×C4—371no—
104C23×C4—378no—
105C23×C4—372no—
106C23×C4—372no—
107C23×C4—748no—
108C23×C4C2×D3711yescharacteristic
109#117—748no—
110C2×C4⋊C4—374no—
111C2×C22⋊C4—372no—
112C2×C22⋊C4—378no—
113C2×C22⋊C4C2×D3712yes—
114C2×C42—374no—
115#95—374no—
116#95C2×D3714yescomplemented
117C24—372no—
118C24—374no—
119C24—748no—
120C24—744no—
121C24C22×D3711yescharacteristic
122C22×C4—24no—
123C22×C4—374no—
124C22×C4—378no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—378no—
128C22×C4—378no—
129C22×C4—374no—
130C22×C4—7432no—
131C22×C4—748no—
132C22×C4—748no—
133C22×C4C4×D3714yes—
134C22×C4C22×D3714yes—
135C22×C4C22×D3712yes—
136C4⋊C4—748no—
137C22⋊C4—24no—
138C22⋊C4—7416no—
139C22⋊C4—744no—
140C42—748no—
141C23—24no—
142C23—374no—
143C23—378no—
144C23—7416no—
145C23—7432no—
146C23—748no—
147C23—744no—
148C23—744no—
149C23C2×C4×D3712yes—
150C23D4×D3714yes—
151C23C23×D3711yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—3716no—
157C2×C4—372no—
158C2×C4—372no—
159C2×C4—374no—
160C2×C4—374no—
161C2×C4—7416no—
162C2×C4—7416no—
163C2×C4—744no—
164C2×C4—748no—
165C2×C4C2×C4×D3714yes—
166C22—24no—
167C22—28no—
168C22—378no—
169C22—7432no—
170C22—744no—
171C22—744no—
172C22—7416no—
173C22C22⋊C4×D3714yes—
174C22C22×C4×D3711yescharacteristic
175C22C2×D4×D3712yes—
176C22#41×D3714yes—
177C4—24no—
178C4—44no—
179C4—374no—
180C4—374no—
181C4—1484no—
182C2—24no—
183C2—748no—
184C2C2×C22⋊C4×D3711yescharacteristic
185C2#117×D3712yes—
186C2#1455804114yes—
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#381C2
socle, cosocleC23×C37C24
prime radicalC24×D37C22
hypercenter#381D37
hypocenterC37#2280
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11924492C2semidirect
3. #14557396C2semidirect
4. #14557392C2semidirect
6. #14557380C2semidirect
7. C37×#381C2semidirect
11. C22×C4×D37C4semidirect
15. C2×#10596936C22semidirect
18. C2×C4×Dic37C22semidirect
19. #11924443C22semidirect
22. #95×C37C22semidirect
65. C2×Dic37C22⋊C4semidirect
82. C2×D37#117semidirect
97. #381D37semidirect
101. C37#2280semidirect
116. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D372
C2×#119244922
#145573962
#145573922
#145573882
#145573802
C37×#3812
#228037