Finite Group Databasebeta

← #18005157

Subgroups — #18005157

Order 4736.

412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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#14558088C211yesmaximal, characteristic, complemented
2#14558084C211yesmaximal, characteristic
3#14557906C211yesmaximal, characteristic, complemented
4#14557885C211yesmaximal, characteristic, complemented
5#14557881C211yesmaximal, characteristic, complemented
6#14557763C214yesmaximal, complemented
7#14557620C214yesmaximal, complemented
8C4×C8×D37C211yesmaximal, characteristic, complemented
9C37×#498C211yesmaximal, characteristic, complemented
10C2×#10596966—21no—
11C2×#10596930C2214yes—
12C2×C8×D37C2212yes—
13#11924536C2211yescharacteristic
14#11924533C2211yescharacteristic
15#11924527—21no—
16#11924525—21no—
17#11924516C2212yes—
18#11924512—21no—
19#11924511—21no—
20#11924511C2212yes—
21Q8×Dic37—21no—
22#11924501C2212yes—
23#11924498—21no—
24#11924498C2212yes—
25#11924494—21no—
26C42×D37C2211yescharacteristic
27#11924459C2214yes—
28#11924456C2214yes—
29C4×#64436C2211yescharacteristic
30C8×Dic37C2212yes—
31C4⋊Q8×C37C2211yescharacteristic
32C4⋊Q8×C37C2211yescharacteristic
33#106×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×Q8×C37—21no—
37#10596966—44no—
38C2×D148—22no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148C2312yes—
42C2×C4×D37—22no—
43C2×C4×D37D411yescharacteristic
44C2×C4×D37D411yescharacteristic
45C2×C4×D37C2311yescharacteristic
46C2×Dic74C2312yes—
47C2×C8×C37C2312yes—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37C2312yes—
51C4⋊C4×C37C2312yes—
52C42×C37C2311yescharacteristic
53#10596938—22no—
54#10596938—22no—
55#10596938—22no—
56C4⋊Dic37—21no—
57C4⋊Dic37—21no—
58C4⋊Dic37—22no—
59#10596936—22no—
60C4×Dic37—22no—
61C4×Dic37D411yescharacteristic
62C4×Dic37D411yescharacteristic
63C4×Dic37C2311yescharacteristic
64C2×#64436C2312yes—
65#10596930—28no—
66C8×D37—24no—
67C22×D37—22no—
68C22×D37C2×D411yescharacteristic
69Q8×C37—42no—
70Q8×C37—42no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2411yescharacteristic
76C2×Dic37—22no—
77C2×Dic37C2×D411yescharacteristic
78C2×Dic37C2×D411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80D148—24no—
81D148—44no—
82D148—42no—
83D148—42no—
84C4×D37—22no—
85C4×D37—22no—
86C4×D37—44no—
87C4×D37SD1614yescomplemented
88Dic74—24no—
89C8×C37#4114yescomplemented
90#64436—22no—
91C22×C37C22×D411yescharacteristic
92C2×D37—21no—
93C2×D37—21no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—42no—
97C2×D37C2×SD1612yes—
98C4×C37—42no—
99C4×C37—42no—
100C4×C37C2×SD1612yes—
101C4×C37#13512yes—
102C4×C37C2×#4112yes—
103Dic37—21no—
104Dic37—21no—
105Dic37—42no—
106Dic37C2×SD1612yes—
107#3167—371nomaximal, Sylow
108C2×C37#53211yescharacteristic
109C2×C37C22×SD1611yescharacteristic
110C2×C37C2×#13511yescharacteristic
111D37—22no—
112D37—82no—
113#533—371no—
114#532—371no—
115#498D3711yescharacteristic, complemented
116#492—371no—
117#487—371no—
118#486—371no—
119#465—374no—
120C4×SD16—374no—
121C2×C4×C8—371no—
122C37#316711yescharacteristic, complemented, Sylow
123C2×#41—741no—
124C2×SD16—374no—
125C22×C8—372no—
126C4⋊Q8—371no—
127C4⋊Q8C2×D3711yescharacteristic
128C4⋊Q8C2×D3711yescharacteristic
129#127—371no—
130#125—741no—
131#124—741no—
132C22⋊Q8—372no—
133C22⋊Q8—741no—
134#121—372no—
135#121—741no—
136C4×Q8—372no—
137C4×Q8—741no—
138C4×D4—372no—
139C4×D4—741no—
140#117—741no—
141C2×C42—371no—
142#106C2×D3714yes—
143#103—374no—
144#102—374no—
145C4×C8—372no—
146C4×C8—371no—
147C4×C8C2×D3711yescharacteristic
148#41—1484no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—372no—
152C2×D4—372no—
153C2×D4—742no—
154C2×D4—741no—
155C2×D4—741no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—742no—
160SD16—748no—
161C2×C8—372no—
162C2×C8—744no—
163C2×C8C22×D3712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—742no—
167C4⋊C4—742no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C4⋊C4C22×D3712yes—
171C4⋊C4C22×D3712yes—
172C22⋊C4—742no—
173C22⋊C4—742no—
174C22⋊C4—742no—
175C42—371no—
176C42—371no—
177C42—371no—
178C42—742no—
179C42C22×D3711yescharacteristic
180C23—371no—
181C23—742no—
182Q8—42no—
183Q8—42no—
184Q8—744no—
185D4—744no—
186D4—1484no—
187D4—1482no—
188D4—1482no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—371no—
192C2×C4—374no—
193C2×C4—371no—
194C2×C4—371no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—1484no—
199C2×C4D4×D3711yescharacteristic
200C2×C4D4×D3711yescharacteristic
201C2×C4C23×D3711yescharacteristic
202C8—742no—
203C8#1059696614yescomplemented
204C22—372no—
205C22—741no—
206C22—741no—
207C22—1482no—
208C22—1482no—
209C22—1482no—
210C22C2×D4×D3711yescharacteristic
211C4—42no—
212C4—42no—
213C4—372no—
214C4—741no—
215C4—741no—
216C4—1482no—
217C4SD16×D3712yes—
218C4#1192455712yes—
219C4C2×#1059696612yes—
220C2—2962no—
221C2—742no—
222C2#1455808411yescharacteristic
223C2C2×SD16×D3711yescharacteristic
224C2C2×#1192455711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#498C2
socleC22×C37C22×D4
prime radical#14558084C2
hypercenter#498D37
hypocenterC37#3167
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557906C2semidirect
4. #14557885C2semidirect
5. #14557881C2semidirect
6. #14557763C2semidirect
7. #14557620C2semidirect
8. C4×C8×D37C2semidirect
9. C37×#498C2semidirect
87. C4×D37SD16semidirect
89. C8×C37#41semidirect
115. #498D37semidirect
122. C37#3167semidirect
203. C8#10596966semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145580842
#145579062
#145578852
#145578812
#145577632
#145576202
C4×C8×D372
C37×#4982
#316737