Finite Group Databasebeta

← #18009833

Subgroups — #18009833

Order 4736.

332 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 80 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
1D37⋊(C22⋊C8)C212yesmaximal, complemented
2#14558378C212yesmaximal, complemented
3#14558377C212yesmaximal, complemented
4C2×C4×D148C211yesmaximal, characteristic
5C2×D37⋊C8—22no—
6#11924593—22no—
7C22⋊#64438C2214yes—
8C22×D148C411yescharacteristic
9C22×C4×D37C411yescharacteristic
10C22×C4×D37C2211yescharacteristic
11C4×D148—22no—
12C4×D148—22no—
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596938C411yescharacteristic
15C2×#10596938C2211yescharacteristic
16C2×C42×C37C411yescharacteristic
17C23×D37C2×C411yescharacteristic
18C23×D37C2×C411yescharacteristic
19C22×C4×C37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C22×Dic37C2×C411yescharacteristic
23C22×Dic37C2311yescharacteristic
24C2×D148—22no—
25C2×D148—22no—
26C2×D148C814yescomplemented
27C2×C4×D37—21no—
28C2×C4×D37—21no—
29C2×C4×D37—42no—
30C2×C4×D37—42no—
31C2×C4×D37D412yes—
32C2×C4×D37D412yes—
33C2×#64438—24no—
34D37⋊C8—44no—
35C42×C37—21no—
36C42×C37—21no—
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—22no—
40C23×C37C22×C411yescharacteristic
41C22×D37—21no—
42C22×D37—21no—
43C22×D37—41no—
44C22×D37—41no—
45C22×D37—41no—
46C22×D37—41no—
47C22×D37C22⋊C412yes—
48C22×D37C2×C812yes—
49C22×D37C2×C812yescomplemented
50C22×D37M1612yes—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C2×C812yescomplemented
59C2×Dic37—21no—
60C2×Dic37—41no—
61C2×Dic37—41no—
62C2×Dic37C2×D412yes—
63D148—28no—
64C4×D37—24no—
65C4×D37—42no—
66C4×D37—42no—
67C4×D37—42no—
68#64438—44no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37C2×C22⋊C411yescharacteristic
72C22×C37C22×C811yescharacteristic
73C22×C37C2×M1611yescharacteristic
74C2×D37—22no—
75C2×D37—22no—
76C2×D37—22no—
77C2×D37—42no—
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—42no—
83C2×D37C22⋊C814yes—
84C4×C37—22no—
85C4×C37—21no—
86C4×C37—41no—
87C4×C37#9912yes—
88Dic37—22no—
89Dic37—41no—
90#1459—371nomaximal, Sylow
91C2×C37—21no—
92C2×C37—21no—
93C2×C37C2×C22⋊C811yescharacteristic
94C2×C37C2×#9911yescharacteristic
95C2×C37#41311yescharacteristic
96D37—24no—
97D37—42no—
98C2×C4×D4—371no—
99C2×C22⋊C8—372no—
100#324—372no—
101#323—372no—
102C37#145911yescharacteristic, complemented, Sylow
103C22×D4—371no—
104C23×C4—371no—
105C23×C4—371no—
106C22×C8—742no—
107C4×D4—742no—
108C4×D4—742no—
109C2×C4⋊C4—371no—
110C2×C22⋊C4—371no—
111C2×C22⋊C4—371no—
112C2×C42#386611yescharacteristic
113C22⋊C8—374no—
114C22⋊C8—742no—
115C24—371no—
116C24—371no—
117C2×D4—374no—
118C2×D4—742no—
119C2×D4—742no—
120C22×C4—371no—
121C22×C4—372no—
122C22×C4—372no—
123C22×C4—371no—
124C22×C4—741no—
125C22×C4—741no—
126C22×C4—1482no—
127C22×C4—1482no—
128C22×C4C2×#386611yescharacteristic
129C22×C4C2×#386611yescharacteristic
130C22×C4C2×#386611yescharacteristic
131C2×C8—744no—
132C2×C8—1484no—
133C4⋊C4—742no—
134C22⋊C4—742no—
135C22⋊C4—742no—
136C42—21no—
137C42—21no—
138C23—372no—
139C23—372no—
140C23—372no—
141C23—372no—
142C23—741no—
143C23—741no—
144C23—1481no—
145C23—1481no—
146C23—1481no—
147C23—1481no—
148C23C22×#386611yescharacteristic
149D4—748no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—372no—
156C2×C4—744no—
157C2×C4—741no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4—1482no—
162C2×C4—1481no—
163C2×C4D37⋊C812yescomplemented
164C2×C4C22⋊#386611yescharacteristic
165C2×C4C22⋊#386611yescharacteristic
166C8—1484no—
167C22—21no—
168C22—21no—
169C22—374no—
170C22—742no—
171C22—742no—
172C22—742no—
173C22—1482no—
174C22—1482no—
175C22—1482no—
176C22—1482no—
177C22—1481no—
178C22—1481no—
179C22C2×C22⋊#386611yescharacteristic
180C22C2×D37⋊C811yescharacteristic
181C22D37⋊M1611yescharacteristic
182C4—22no—
183C4—21no—
184C4—41no—
185C4—742no—
186C4—1481no—
187C4#1192459512yes—
188C2—21no—
189C2—21no—
190C2—744no—
191C2—1482no—
192C2D37⋊(C22⋊C8)11yescharacteristic
193C2C2×#1192459511yescharacteristic
194C2#1455851911yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC22×C37C22×C8
FrattiniC23C22×#3866
FittingC2×C42×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC22×Dic37C23
hypercenterC2×C42#3866
hypocenterC37#1459
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. D37⋊(C22⋊C8)C2semidirect
2. #14558378C2semidirect
3. #14558377C2semidirect
26. C2×D148C8semidirect
49. C22×D37C2×C8semidirect
58. C2×C4×C37C2×C8semidirect
102. C37#1459semidirect
163. C2×C4D37⋊C8semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C22⋊C8)2
#145583782
#145583772
C2×C4×D1482
#145937