Finite Group Databasebeta

← #18005174

Subgroups — #18005174

Order 4736.

456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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#14558084C211yesmaximal, characteristic, complemented
2#14558081C211yesmaximal, characteristic, complemented
3#14557936C211yesmaximal, characteristic, complemented
4#14557909C211yesmaximal, characteristic, complemented
5#14557880C211yesmaximal, characteristic, complemented
6#14557768C214yesmaximal, complemented
7#14557613C214yesmaximal, complemented
8C4×C8×D37C211yesmaximal, characteristic, complemented
9C37×#486C211yesmaximal, characteristic, complemented
10C2×#10596966—21no—
11C2×#10596964—21no—
12C2×#10596939C2214yes—
13C2×C8×D37C2212yes—
14#11924536C2211yescharacteristic
15#11924533C2211yescharacteristic
16#11924525—21no—
17#11924523—21no—
18#11924511—21no—
19#11924511C2212yes—
20#11924507—21no—
21#11924507C2212yes—
22D4×Dic37—21no—
23D4×Dic37C2212yes—
24#11924498—21no—
25#11924498C2212yes—
26C42×D37C2211yescharacteristic
27#11924469C2214yes—
28#11924458C2214yes—
29C4×#64436C2211yescharacteristic
30C8×Dic37C2212yes—
31C4⋊Q8×C37C2211yescharacteristic
32#127×C37C2211yescharacteristic
33#102×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37C2312yes—
39C2×C22⋊D37—22no—
40C22×Dic37—22no—
41#10596966—44no—
42#10596964—44no—
43C2×D148—22no—
44C2×D148—21no—
45C2×D148—21no—
46C2×D148C2312yes—
47C2×C4×D37—22no—
48C2×C4×D37D411yescharacteristic
49C2×C4×D37D411yescharacteristic
50C2×C4×D37C2311yescharacteristic
51C2×Dic74—21no—
52C2×C8×C37C2312yes—
53C4⋊C4×C37—21no—
54C4⋊C4×C37C2312yes—
55C42×C37C2311yescharacteristic
56C22⋊Dic37—22no—
57C22⋊Dic37—22no—
58#10596939—28no—
59#10596938—22no—
60#10596938—22no—
61C4⋊Dic37—21no—
62C4⋊Dic37C2312yes—
63C4×Dic37D411yescharacteristic
64C4×Dic37D411yescharacteristic
65C4×Dic37C2311yescharacteristic
66C2×#64436C2312yes—
67C8×D37—24no—
68C23×C37—22no—
69C22×D37—22no—
70C22×D37C2×D411yescharacteristic
71Q8×C37—42no—
72D4×C37—24no—
73D4×C37—42no—
74D4×C37—42no—
75C2×C4×C37—22no—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2411yescharacteristic
79C22⋊D37—44no—
80C2×Dic37—22no—
81C2×Dic37—44no—
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84C2×Dic37C2×D411yescharacteristic
85D148—24no—
86D148—44no—
87D148—42no—
88D148—42no—
89C4×D37—22no—
90C4×D37—22no—
91C4×D37—44no—
92C4×D37D814yescomplemented
93Dic74—42no—
94C8×C37—22no—
95#64436#4114yescomplemented
96C22×C37—42no—
97C22×C37—42no—
98C22×C37—42no—
99C22×C37C22×D411yescharacteristic
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—42no—
103C2×D37—42no—
104C2×D37—42no—
105C2×D37C2×D812yes—
106C4×C37—42no—
107C4×C37C2×D812yes—
108C4×C37#13512yes—
109C4×C37C2×#4112yes—
110Dic37—21no—
111Dic37—21no—
112Dic37—42no—
113Dic37C2×D812yes—
114#3169—371nomaximal, Sylow
115C2×C37—82no—
116C2×C37#53211yescharacteristic
117C2×C37C22×D811yescharacteristic
118C2×C37C2×#13511yescharacteristic
119D37—22no—
120D37—82no—
121#532—371no—
122#532—371no—
123#500—371no—
124#493—371no—
125#486—371no—
126#486D3711yescharacteristic, complemented
127#466—374no—
128C4×D8—374no—
129C2×C4×C8—371no—
130C37#316911yescharacteristic, complemented, Sylow
131C2×#41—741no—
132C2×#41—741no—
133C2×D8—374no—
134C22×C8—372no—
135C4⋊Q8—371no—
136C4⋊Q8C2×D3711yescharacteristic
137#127—371no—
138#127C2×D3711yescharacteristic
139#124—741no—
140#124—741no—
141#121—372no—
142#121—372no—
143#121—741no—
144#121—741no—
145C4×D4—372no—
146C4×D4—372no—
147C4×D4—741no—
148C4×D4—741no—
149C2×C42—371no—
150#107—374no—
151#102—374no—
152#102C2×D3714yes—
153C4×C8—372no—
154C4×C8—371no—
155C4×C8C2×D3711yescharacteristic
156#41—1484no—
157#41—1484no—
158C2×Q8—21no—
159C2×Q8—741no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—372no—
163C2×D4—742no—
164C2×D4—742no—
165C2×D4—741no—
166C2×D4—741no—
167C2×D4C22×D3712yes—
168C22×C4—371no—
169C22×C4—371no—
170C22×C4—371no—
171C22×C4—742no—
172C22×C4—742no—
173D8—748no—
174C2×C8—372no—
175C2×C8—744no—
176C2×C8C22×D3712yes—
177C4⋊C4—21no—
178C4⋊C4—372no—
179C4⋊C4—741no—
180C4⋊C4C22×D3712yes—
181C22⋊C4—742no—
182C22⋊C4—742no—
183C22⋊C4—742no—
184C22⋊C4—742no—
185C42—371no—
186C42—371no—
187C42—371no—
188C42C22×D3711yescharacteristic
189C23—22no—
190C23—371no—
191C23—742no—
192Q8—42no—
193Q8—1482no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—744no—
198D4—1484no—
199D4—1484no—
200D4—1482no—
201D4—1482no—
202C2×C4—22no—
203C2×C4—371no—
204C2×C4—374no—
205C2×C4—371no—
206C2×C4—371no—
207C2×C4—742no—
208C2×C4—742no—
209C2×C4—742no—
210C2×C4—1484no—
211C2×C4—1484no—
212C2×C4D4×D3711yescharacteristic
213C2×C4D4×D3711yescharacteristic
214C2×C4C23×D3711yescharacteristic
215C8—22no—
216C8—374no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—372no—
221C22—741no—
222C22—741no—
223C22—1482no—
224C22—1482no—
225C22—1482no—
226C22C2×D4×D3711yescharacteristic
227C4—42no—
228C4—372no—
229C4—741no—
230C4—741no—
231C4—1482no—
232C4D8×D3712yes—
233C4#1192455712yes—
234C4#41×D3712yes—
235C2—82no—
236C2—2962no—
237C2—742no—
238C2#1455808211yescharacteristic
239C2C2×D8×D3711yescharacteristic
240C2C2×#1192455711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
hypercenter#486D37
hypocenterC37#3169
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14558084C2semidirect
2. #14558081C2semidirect
3. #14557936C2semidirect
4. #14557909C2semidirect
5. #14557880C2semidirect
6. #14557768C2semidirect
7. #14557613C2semidirect
8. C4×C8×D37C2semidirect
9. C37×#486C2semidirect
92. C4×D37D8semidirect
95. #64436#41semidirect
126. #486D37semidirect
130. C37#3169semidirect

Maximal subgroups

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

subgroupindex
#145580842
#145580812
#145579362
#145579092
#145578802
#145577682
#145576132
C4×C8×D372
C37×#4862
#316937