Finite Group Databasebeta

← #18011072

Subgroups — #18011072

Order 4736.

672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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#14558483C218yesmaximal, complemented
2#14558475C212yesmaximal, complemented
3#14558474C212yesmaximal
4C4×C22⋊#3866C212yesmaximal, complemented
5C2×C22⋊C4×D37C211yesmaximal, characteristic
6C2×C4⋊#3866C2214yescomplemented
7C2×C22⋊#3866C2214yes—
8C2×C22⋊#3866C2214yes—
9C2×C22⋊#3866C2214yes—
10C2×C4×#3866C2214yescomplemented
11(C2×#3866)⋊C4C2214yescomplemented
12(C2×#3866)⋊C4C2214yescomplemented
13C24×D37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16C2×C22⋊Dic37C411yescharacteristic, complemented
17C2×#10596938C411yescharacteristic, complemented
18C2×#10596938C411yescharacteristic, complemented
19C22⋊C4×D37C414yescomplemented
20C22⋊C4×D37C2214yes—
21C2×C22⋊C4×C37C411yescharacteristic, complemented
22C24×C37C2×C411yescharacteristic
23C23×D37—24no—
24C23×D37—42no—
25C23×D37—42no—
26C23×D37C2×C412yes—
27C23×D37C2×C411yescharacteristic
28C23×D37C2312yes—
29C23×D37C2311yescharacteristic
30C22×#3866C2318yes—
31C22×C4×C37C2×C411yescharacteristic
32C22×C4×C37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37C2×C411yescharacteristic
35C2×C4×D37—42no—
36C2×C4×D37—42no—
37C2×C4×D37C2×C412yes—
38C2×C4×D37C2×C412yes—
39C2×C4×D37C2312yes—
40C2×C4×D37C2312yes—
41C22⋊#3866—28no—
42C22⋊#3866—44no—
43C22⋊#3866—44no—
44C4⋊#3866—44no—
45C4×#3866—44no—
46C22⋊C4×C37C2×C414yes—
47C22⋊Dic37C2×C414yes—
48#10596938C2×C414yes—
49#10596938C2×C414yes—
50C23×C37—22no—
51C23×C37—41no—
52C23×C37—41no—
53C23×C37C22×C412yes—
54C23×C37C22×C411yescharacteristic
55C22×D37—22no—
56C22×D37—22no—
57C22×D37—22no—
58C22×D37—24no—
59C22×D37—24no—
60C22×D37—24no—
61C22×D37—24no—
62C22×D37—42no—
63C22×D37—42no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37—416no—
67C22×D37C22×C412yes—
68C22×D37C22×C411yescharacteristic
69C22×D37#4114yes—
70C22×D37C2411yescharacteristic
71C2×#3866—28no—
72C2×#3866—28no—
73C2×#3866—28no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37C22×C412yes—
77C2×C4×C37C22×C412yes—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37C22×C412yes—
81C2×Dic37C22×C412yes—
82C4×D37—24no—
83C4×D37—24no—
84C4×D37—42no—
85C4×D37—42no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—22no—
89C22×C37—22no—
90C22×C37—22no—
91C22×C37—44no—
92C22×C37#11712yes—
93C22×C37C23×C411yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—28no—
97C2×D37—22no—
98C2×D37—22no—
99C2×D37—22no—
100C2×D37—48no—
101C2×D37—44no—
102C2×D37—48no—
103C2×D37#11712yes—
104C2×D37C2×#4112yes—
105C2×D37H(5,𝔽2)12yes—
106C2×D37H(5,𝔽2)12yes—
107#3866—48no—
108C4×C37—22no—
109C4×C37—22no—
110Dic37—22no—
111Dic37—22no—
112#2312—371nomaximal, Sylow
113C2×C37—22no—
114C2×C37—42no—
115C2×C37C2×#11711yescharacteristic
116C2×C37#51811yescharacteristic
117C2×C37#51811yescharacteristic
118D37—22no—
119D37—42no—
120D37#53814yes—
121C22×C22⋊C4—371no—
122#388—378no—
123#380—372no—
124#379—372no—
125C4×C22⋊C4—372no—
126C37#231211yescharacteristic, complemented, Sylow
127C25—371no—
128C23×C4—371no—
129C23×C4—371no—
130C2×C4⋊C4—374no—
131C2×C22⋊C4—371no—
132C2×C22⋊C4—371no—
133C2×C22⋊C4—371no—
134C2×C22⋊C4—374no—
135C2×C22⋊C4—374no—
136C2×C22⋊C4—374no—
137C2×C22⋊C4—374no—
138C2×C22⋊C4—374no—
139C2×C22⋊C4#386611yescharacteristic, complemented
140C2×C42—374no—
141#95—374no—
142#95—374no—
143C24—371no—
144C24—372no—
145C24—372no—
146C24—371no—
147C24—744no—
148C24—1482no—
149C24—1482no—
150C24C2×#386611yescharacteristic
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—372no—
154C22×C4—372no—
155C22×C4—372no—
156C22×C4—372no—
157C22×C4—378no—
158C22×C4—1482no—
159C22×C4—1482no—
160C22×C4C2×#386611yescharacteristic
161C22×C4C2×#386611yescharacteristic
162C4⋊C4—1484no—
163C22⋊C4—374no—
164C22⋊C4—374no—
165C22⋊C4—374no—
166C22⋊C4—748no—
167C22⋊C4—1484no—
168C22⋊C4—1484no—
169C22⋊C4C2×#386614yes—
170C42—1484no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—371no—
175C23—374no—
176C23—371no—
177C23—372no—
178C23—742no—
179C23—742no—
180C23—744no—
181C23—744no—
182C23—744no—
183C23—744no—
184C23—742no—
185C23—1481no—
186C23—1481no—
187C23—1482no—
188C23—1482no—
189C23—14816no—
190C23C22×#386612yes—
191C23C22×#386611yescharacteristic
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—372no—
195C2×C4—372no—
196C2×C4—744no—
197C2×C4—744no—
198C2×C4—748no—
199C2×C4—748no—
200C2×C4—748no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4C22×#386612yes—
206C2×C4C22×#386612yes—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—22no—
211C22—22no—
212C22—44no—
213C22—372no—
214C22—372no—
215C22—372no—
216C22—372no—
217C22—748no—
218C22—741no—
219C22—741no—
220C22—742no—
221C22—742no—
222C22—742no—
223C22—1484no—
224C22—1488no—
225C22—1488no—
226C22#1192461512yes—
227C22C23×#386611yescharacteristic
228C4—22no—
229C4—22no—
230C4—742no—
231C4—742no—
232C4—1488no—
233C2—22no—
234C2—42no—
235C2—374no—
236C2—742no—
237C2—1482no—
238C2C2×#1192461511yescharacteristic
239C2#1455860011yescharacteristic
240C2#1455860011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#3866
commutator, socleC22×C37C23×C4
FittingC2×C22⋊C4×C37C4
prime radicalC24×D37C22
cosocleC22×D37C24
hypercenterC2×C22⋊C4#3866
hypocenterC37#2312
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558483C2semidirect
2. #14558475C2semidirect
4. C4×C22⋊#3866C2semidirect
6. C2×C4⋊#3866C22semidirect
10. C2×C4×#3866C22semidirect
11. (C2×#3866)⋊C4C22semidirect
12. (C2×#3866)⋊C4C22semidirect
16. C2×C22⋊Dic37C4semidirect
17. C2×#10596938C4semidirect
18. C2×#10596938C4semidirect
19. C22⋊C4×D37C4semidirect
21. C2×C22⋊C4×C37C4semidirect
126. C37#2312semidirect
139. C2×C22⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584832
#145584752
#145584742
C4×C22⋊#38662
C2×C22⋊C4×D372
#231237