Finite Group Databasebeta

← #18009855

Subgroups — #18009855

Order 4736.

300 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558554C212yesmaximal, complemented
2#14558377C212yesmaximal, complemented
3#14558376C212yesmaximal, complemented
4C2×C4×C22⋊D37C211yesmaximal, characteristic
5C4⋊#64438—22no—
6C22⋊#64438C2214yes—
7#11924591—22no—
8C22×C22⋊D37C411yescharacteristic
9C22×C4×D37C411yescharacteristic
10C4×C22⋊D37—22no—
11C4×C22⋊D37—22no—
12C2×#10596936C411yescharacteristic
13C2×C22⋊Dic37C2211yescharacteristic
14C2×#10596938C2211yescharacteristic
15C2×C4×Dic37C2211yescharacteristic
16C23×C4×C37C411yescharacteristic
17C24×C37C2×C411yescharacteristic
18C23×D37C2×C411yescharacteristic
19C22×C4×C37—21no—
20C22×C4×C37—21no—
21C22×C4×C37—42no—
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C2×C22⋊D37—22no—
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2311yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37—42no—
33C2×#64438—24no—
34C22⋊Dic37—22no—
35#10596938—22no—
36#10596936—22no—
37C4×Dic37D412yes—
38C4×Dic37D412yes—
39C23×C37—21no—
40C23×C37—21no—
41C23×C37—41no—
42C23×C37—41no—
43C23×C37M1612yes—
44C23×C37C22×C411yescharacteristic
45C22×D37—21no—
46C22×D37—21no—
47C22×D37—41no—
48C22×D37—41no—
49C22×D37M1612yes—
50C2×C4×C37—22no—
51C2×C4×C37—21no—
52C2×C4×C37—42no—
53C2×C4×C37—42no—
54C2×C4×C37—41no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C22⋊D37—28no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37C22⋊C412yes—
64C2×Dic37C2×D412yes—
65C4×D37—42no—
66C4×D37—42no—
67#64438—44no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—22no—
71C22×C37—42no—
72C22×C37—42no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C22×C37C2×M1611yescharacteristic
77C22×C37C2×M1611yescharacteristic
78C2×D37—22no—
79C2×D37—42no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—42no—
83C4×C37—21no—
84C4×C37—41no—
85C4×C37#10012yes—
86Dic37—22no—
87Dic37—22no—
88Dic37—41no—
89#1466—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37—21no—
92C2×C37—42no—
93C2×C37#40711yescharacteristic
94C2×C37#41011yescharacteristic
95C2×C37C2×#10011yescharacteristic
96D37—42no—
97C2×C4×D4—371no—
98#432—372no—
99#323—372no—
100#323—372no—
101C37#146611yescharacteristic, complemented, Sylow
102C22×D4—371no—
103C23×C4—371no—
104C23×C4#386611yescharacteristic
105C4×D4—742no—
106C4×D4—742no—
107C2×C4⋊C4—371no—
108C2×C22⋊C4—371no—
109C2×C22⋊C4—371no—
110C2×C42—371no—
111C4⋊C8—742no—
112C22⋊C8—374no—
113#97—742no—
114C24—371no—
115C24C2×#386611yescharacteristic
116C2×D4—742no—
117C2×D4—742no—
118C2×D4—742no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—42no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—741no—
126C22×C4—741no—
127C22×C4—1482no—
128C22×C4C2×#386611yescharacteristic
129C22×C4C2×#386611yescharacteristic
130C2×C8—744no—
131C4⋊C4—742no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C42—372no—
135C42—372no—
136C23—21no—
137C23—21no—
138C23—41no—
139C23—41no—
140C23—372no—
141C23—741no—
142C23—741no—
143C23—1481no—
144C23—1481no—
145C23#1059695312yes—
146C23C22×#386611yescharacteristic
147D4—748no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—372no—
154C2×C4—372no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—1482no—
159C2×C4—1481no—
160C2×C4—1482no—
161C2×C4—1481no—
162C2×C4C22⋊#386611yescharacteristic
163C2×C4C22⋊#386611yescharacteristic
164C8—1484no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—742no—
173C22—1482no—
174C22—1482no—
175C22—1481no—
176C22—1481no—
177C22C2×C22⋊#386611yescharacteristic
178C22D37⋊M1611yescharacteristic
179C22C2×#1059695311yescharacteristic
180C4—21no—
181C4—41no—
182C4—742no—
183C4—742no—
184C4—1481no—
185C4#1192459612yes—
186C2—21no—
187C2—21no—
188C2—42no—
189C2—1482no—
190C2#1455850411yescharacteristic
191C2#1455851211yescharacteristic
192C2C2×#1192459611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C4
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37#1466
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #14558554C2semidirect
2. #14558377C2semidirect
3. #14558376C2semidirect
101. C37#1466semidirect

Maximal subgroups

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

subgroupindex
#145585542
#145583772
#145583762
C2×C4×C22⋊D372
#146637