Finite Group Databasebeta

← #18005062

Subgroups — #18005062

Order 4736.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11924569C212yesmaximal, complemented
2C2×#11924564C212yesmaximal, complemented
3#14558083C211yesmaximal, characteristic, complemented
4C2×#11924524C211yesmaximal, characteristic, complemented
5#14557927C212yesmaximal, complemented
6#14557922C212yesmaximal, complemented
7#14557917C214yesmaximal, complemented
8C4×M16×C37C211yesmaximal, characteristic, complemented
9C2×#10596962C2212yes—
10C22×Dic74C2211yescharacteristic
11C22×D148C2211yescharacteristic
12#11924569—28no—
13#11924564—28no—
14C2×Dic148C2214yescomplemented
15C2×#10596930C2214yes—
16C2×#10596930C2214yescomplemented
17C2×D296C2214yes—
18#11924536C2211yescharacteristic, complemented
19#11924533C2211yescharacteristic, complemented
20#11924524—22no—
21#11924524C2212yes—
22#11924524C2212yes—
23#11924524C2212yescomplemented
24#11924510—22no—
25C4×D148—22no—
26C2×#10596938—22no—
27C2×M16×C37C2212yes—
28C2×C42×C37C2211yescharacteristic
29#97×C37C2212yescomplemented
30C4×C8×C37C2212yescomplemented
31C23×D37—21no—
32C22×C4×C37D412yes—
33C22×C4×C37C2311yescharacteristic
34C2×C22⋊D37—22no—
35C22×Dic37—21no—
36#10596962—24no—
37#10596962—24no—
38C2×D148—24no—
39C2×D148—22no—
40C2×D148—21no—
41C2×D148C2312yes—
42C2×D148C2312yes—
43C2×C4×D37—22no—
44C2×Dic74—24no—
45C2×Dic74—21no—
46C2×Dic74C2312yes—
47C2×Dic74C2312yes—
48M16×C37D418yescomplemented
49C2×C8×C37C2314yes—
50C42×C37D412yes—
51C42×C37C2311yescharacteristic
52C42×C37C2311yescharacteristic
53#10596938—24no—
54#10596938—24no—
55#10596938—24no—
56C4⋊Dic37—22no—
57Dic148—28no—
58D296—28no—
59#10596930—28no—
60#10596930—28no—
61C23×C37C2×D411yescharacteristic
62C22×D37—22no—
63C22×D37—22no—
64C22×D37—44no—
65C22×D37—42no—
66C2×C4×C37—42no—
67C2×C4×C37C2×D412yes—
68C2×C4×C37C2×D412yes—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D414yes—
71C2×C4×C37C2411yescharacteristic
72C22⋊D37—44no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—42no—
76D148—22no—
77D148—24no—
78D148—22no—
79D148—44no—
80D148—42no—
81C4×D37—44no—
82Dic74—22no—
83Dic74—24no—
84Dic74—22no—
85Dic74—42no—
86C8×C37C2×D418yes—
87C22×C37—22no—
88C22×C37#12712yes—
89C22×C37C22×D411yescharacteristic
90C2×D37—42no—
91C2×D37—42no—
92C2×D37—44no—
93C2×D37—44no—
94C2×D37—84no—
95C4×C37—22no—
96C4×C37—22no—
97C4×C37#12712yes—
98C4×C37C22×D412yes—
99Dic37—42no—
100Dic37—42no—
101#3153—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37C2×#12711yescharacteristic
104C2×C37#57512yes—
105D37—82no—
106D37—82no—
107C2×#137—372no—
108C2×AGL(1,ℤ/8)—372no—
109#532—371no—
110C2×#124—371no—
111#497—372no—
112#496—372no—
113#495—374no—
114C4×M16D3711yescharacteristic, complemented
115C37#315311yescharacteristic, complemented, Sylow
116C2×#41—372no—
117C22×Q8—371no—
118C22×D4—371no—
119#137—748no—
120AGL(1,ℤ/8)—748no—
121C2×Q16—374no—
122C2×SD16—374no—
123C2×SD16—374no—
124C2×D8—374no—
125C2×M16C2×D3712yes—
126C4⋊Q8—371no—
127#127—371no—
128#124—372no—
129#124—372no—
130#124—372no—
131#124—742no—
132#121—742no—
133C4×D4—742no—
134C2×C22⋊C4—742no—
135C2×C42C2×D3711yescharacteristic
136#97C2×D3712yescomplemented
137C4×C8C2×D3712yescomplemented
138C24—741no—
139#41—744no—
140#41—744no—
141C2×Q8—372no—
142C2×Q8—372no—
143C2×Q8—741no—
144C2×Q8—744no—
145C2×D4—372no—
146C2×D4—372no—
147C2×D4—742no—
148C2×D4—744no—
149C2×D4—742no—
150C2×D4—741no—
151C22×C4—741no—
152C22×C4—742no—
153C22×C4D14812yes—
154C22×C4C22×D3711yescharacteristic
155Q16—748no—
156SD16—748no—
157SD16—748no—
158D8—748no—
159M16D14818yescomplemented
160C2×C8C22×D3714yes—
161C4⋊C4—742no—
162C22⋊C4—744no—
163C22⋊C4—744no—
164C22⋊C4—744no—
165C42D14812yes—
166C42C22×D3711yescharacteristic
167C42C22×D3711yescharacteristic
168C23—742no—
169C23—742no—
170C23—1484no—
171C23—1482no—
172C23C2×D14811yescharacteristic
173Q8—742no—
174Q8—744no—
175Q8—742no—
176Q8—1482no—
177D4—742no—
178D4—744no—
179D4—742no—
180D4—1484no—
181D4—1484no—
182D4—1482no—
183C2×C4—42no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—1482no—
187C2×C4—1484no—
188C2×C4C2×D14812yes—
189C2×C4C2×D14812yes—
190C2×C4C2×D14811yescharacteristic
191C2×C4C2×D14814yes—
192C2×C4C23×D3711yescharacteristic
193C8C2×D14818yes—
194C22—22no—
195C22—2964no—
196C22—1482no—
197C22—1482no—
198C22—1484no—
199C22—1484no—
200C22#1192453312yes—
201C22C22×D14811yescharacteristic
202C4—22no—
203C4—22no—
204C4—1482no—
205C4—1482no—
206C4#1192453312yes—
207C4C22×D14812yes—
208C2—22no—
209C2—2962no—
210C2—2962no—
211C2C2×#1192453311yescharacteristic
212C2#1455833312yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×M16×C37C2
socleC22×C37C22×D4
hypercenterC4×M16D37
hypocenterC37#3153
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
2. C2×#11924564C2semidirect
3. #14558083C2semidirect
4. C2×#11924524C2semidirect
5. #14557927C2semidirect
6. #14557922C2semidirect
7. #14557917C2semidirect
8. C4×M16×C37C2semidirect
14. C2×Dic148C22semidirect
16. C2×#10596930C22semidirect
18. #11924536C22semidirect
19. #11924533C22semidirect
23. #11924524C22semidirect
29. #97×C37C22semidirect
30. C4×C8×C37C22semidirect
48. M16×C37D4semidirect
114. C4×M16D37semidirect
115. C37#3153semidirect
136. #97C2×D37semidirect
137. C4×C8C2×D37semidirect
159. M16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245642
#145580832
C2×#119245242
#145579272
#145579222
#145579172
C4×M16×C372
#315337