Finite Group Databasebeta

← #18004920

Subgroups — #18004920

Order 4736.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14557889C214yesmaximal, complemented
4#14557883C211yesmaximal, characteristic, complemented
5#14557881C211yesmaximal, characteristic, complemented
6#14557880C211yesmaximal, characteristic, complemented
7#14557528C214yesmaximal, complemented
8C4×C8×D37C211yesmaximal, characteristic, complemented
9C37×#487C211yesmaximal, characteristic, complemented
10C2×#10596966C2212yes—
11C2×C8×D37C2212yes—
12#11924536C2211yescharacteristic
13#11924533C2211yescharacteristic
14#11924527C2212yes—
15#11924525C2212yes—
16#11924516—21no—
17#11924512—21no—
18#11924511—21no—
19#11924511—21no—
20Q8×Dic37—21no—
21#11924501—21no—
22#11924498—21no—
23#11924498—21no—
24#11924494C2212yes—
25C42×D37C2211yescharacteristic
26#11924460C2214yes—
27#11924458C2214yes—
28#11924456C2214yes—
29C4×#64436C2211yescharacteristic
30C8×Dic37C2212yes—
31C4⋊Q8×C37C2211yescharacteristic
32C4⋊Q8×C37C2211yescharacteristic
33#103×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×Q8×C37C2312yes—
37#10596966—28no—
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×Dic74—21no—
47C2×C8×C37C2312yes—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37C2312yes—
52C42×C37C2311yescharacteristic
53#10596938—22no—
54#10596938—22no—
55#10596938—22no—
56C4⋊Dic37—21no—
57C4⋊Dic37—22no—
58C4⋊Dic37C2312yes—
59#10596936—22no—
60C4×Dic37—22no—
61C4×Dic37D411yescharacteristic
62C4×Dic37D411yescharacteristic
63C4×Dic37C2311yescharacteristic
64C2×#64436C2312yes—
65C8×D37—24no—
66C22×D37—22no—
67C22×D37C2×D411yescharacteristic
68Q8×C37—24no—
69Q8×C37—42no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2411yescharacteristic
75C2×Dic37—22no—
76C2×Dic37C2×D411yescharacteristic
77C2×Dic37C2×D411yescharacteristic
78C2×Dic37C2×D411yescharacteristic
79D148—24no—
80D148—44no—
81D148—42no—
82D148—42no—
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—44no—
86C4×D37#4114yes—
87Dic74—42no—
88C8×C37—22no—
89#64436—22no—
90C22×C37C22×D411yescharacteristic
91C2×D37—21no—
92C2×D37—21no—
93C2×D37—42no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37#12412yes—
97C4×C37—42no—
98C4×C37—42no—
99C4×C37#13512yes—
100C4×C37#13512yes—
101C4×C37C2×#4112yes—
102Dic37—21no—
103Dic37—21no—
104Dic37—42no—
105Dic37#12412yes—
106#3131—371nomaximal, Sylow
107C2×C37C2×#12411yescharacteristic
108C2×C37C2×#13511yescharacteristic
109C2×C37C2×#13511yescharacteristic
110D37—22no—
111D37—82no—
112#533—371no—
113#532—371no—
114#488—374no—
115#487—371no—
116#487D3711yescharacteristic, complemented
117#486—371no—
118#486—371no—
119#416—374no—
120C2×C4×C8—371no—
121C37#313111yescharacteristic, complemented, Sylow
122C2×#41—372no—
123C22×C8—372no—
124C4⋊Q8—371no—
125C4⋊Q8C2×D3711yescharacteristic
126C4⋊Q8C2×D3711yescharacteristic
127#127—371no—
128#125—372no—
129#124—372no—
130C22⋊Q8—741no—
131C22⋊Q8—741no—
132#121—741no—
133#121—741no—
134C4×Q8—741no—
135C4×Q8—741no—
136C4×D4—741no—
137C4×D4—741no—
138#117—372no—
139C2×C42—371no—
140#103—374no—
141#103C2×D3714yes—
142#102—374no—
143#102—374no—
144C4×C8—372no—
145C4×C8—371no—
146C4×C8C2×D3711yescharacteristic
147#41—748no—
148C2×Q8—21no—
149C2×Q8—741no—
150C2×Q8C22×D3712yes—
151C2×D4—372no—
152C2×D4—742no—
153C2×D4—741no—
154C2×D4—741no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—742no—
159C2×C8—372no—
160C2×C8—744no—
161C2×C8C22×D3712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—372no—
166C4⋊C4—742no—
167C4⋊C4—742no—
168C4⋊C4—741no—
169C4⋊C4C22×D3712yes—
170C22⋊C4—742no—
171C22⋊C4—742no—
172C22⋊C4—742no—
173C42—371no—
174C42—371no—
175C42—371no—
176C42—742no—
177C42C22×D3711yescharacteristic
178C23—371no—
179C23—742no—
180Q8—24no—
181Q8—42no—
182Q8—1482no—
183D4—744no—
184D4—1484no—
185D4—1482no—
186D4—1482no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—371no—
190C2×C4—374no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4—1484no—
197C2×C4D4×D3711yescharacteristic
198C2×C4D4×D3711yescharacteristic
199C2×C4C23×D3711yescharacteristic
200C8—22no—
201C8—742no—
202C22—372no—
203C22—741no—
204C22—741no—
205C22—1482no—
206C22—1482no—
207C22—1482no—
208C22C2×D4×D3711yescharacteristic
209C4—42no—
210C4—42no—
211C4—372no—
212C4—741no—
213C4—741no—
214C4—1482no—
215C4#1192455712yes—
216C4#1192455912yes—
217C4#41×D3712yes—
218C2—2962no—
219C2—742no—
220C2#124×D3711yescharacteristic
221C2C2×#1192455711yescharacteristic
222C2C2×#1192455911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#487C2
socleC22×C37C22×D4
prime radical#14558084C2
hypercenter#487D37
hypocenterC37#3131
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557889C2semidirect
4. #14557883C2semidirect
5. #14557881C2semidirect
6. #14557880C2semidirect
7. #14557528C2semidirect
8. C4×C8×D37C2semidirect
9. C37×#487C2semidirect
116. #487D37semidirect
121. C37#3131semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145580842
#145578892
#145578832
#145578812
#145578802
#145575282
C4×C8×D372
C37×#4872
#313137