Finite Group Databasebeta

← #17993559

Subgroups — #17993559

Order 4736.

244 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 53 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#14557688C211yesmaximal, characteristic, complemented
2#14557671C211yesmaximal, characteristic
3#14557453C211yesmaximal, characteristic, complemented
4#14557270C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic
6#14557259C211yesmaximal, characteristic, complemented
7C37×#539C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C2×#10596942—21no—
10C2×#10596940—21no—
11C2×#10596936—21no—
12#11924459—21no—
13#11924459—21no—
14C22⋊#64436C2211yescharacteristic
15C22⋊#64436C2211yescharacteristic
16#11924443—21no—
17#11924443C2211yescharacteristic
18#126×C37—21no—
19#125×C37—21no—
20#123×C37—21no—
21#123×C37—21no—
22C22⋊Q8×C37—21no—
23C22⋊Q8×C37C2211yescharacteristic
24#121×C37C2211yescharacteristic
25C4×D4×C37—21no—
26C2×C4⋊C4×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C2×D4×C37—21no—
29C2×D4×C37D411yescharacteristic
30C22×C4×C37—21no—
31C22×C4×C37D411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C22×C4×C37C2311yescharacteristic
34C22×Dic37—21no—
35C22×Dic37—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—42no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37D411yescharacteristic
46C4⋊C4×C37D411yescharacteristic
47C22⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37—21no—
50C22⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C42×C37—21no—
53#10596942—42no—
54#10596940—42no—
55#10596936—42no—
56C2×#64436—21no—
57C2×#64436—21no—
58C23×C37—21no—
59C23×C37C2×D411yescharacteristic
60Q8×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63D4×C37—41no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—81no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82Dic74—22no—
83Dic74—22no—
84Dic74—41no—
85Dic74—41no—
86#64436—41no—
87#64436—41no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37#12011yescharacteristic
94C22×C37#13511yescharacteristic
95C22×C37#13711yescharacteristic
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—41no—
99C4×C37—41no—
100C4×C37—41no—
101C4×C37—41no—
102C4×C37—41no—
103Dic37—42no—
104Dic37—42no—
105#1603—371nomaximal, Sylow
106C2×C37—21no—
107C2×C37—21no—
108C2×C37—81no—
109C2×C37#45211yescharacteristic
110C2×C37#45611yescharacteristic
111C2×C37B(4,𝔽2)11yescharacteristic
112#539D3711yescharacteristic
113#451—371no—
114#448—371no—
115#395—371no—
116#328—371no—
117#327—371no—
118#324—371no—
119C37#160311yescharacteristic, complemented, Sylow
120C22×Q8—371no—
121C2×Q16—741no—
122C2×SD16—741no—
123#126—21no—
124#125—21no—
125#123—21no—
126#123—21no—
127C22⋊Q8—21no—
128C22⋊Q8C2×D3711yescharacteristic
129#121C2×D3711yescharacteristic
130C4×D4—21no—
131C2×C4⋊C4—741no—
132C2×C4⋊C4C2×D3711yescharacteristic
133#103—741no—
134#103—741no—
135C22⋊C8—371no—
136C22⋊C8—371no—
137#95—371no—
138#95—741no—
139C2×Q8—741no—
140C2×Q8—741no—
141C2×Q8—1482no—
142C2×Q8C22⋊D3711yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D3711yescharacteristic
145C22×C4—21no—
146C22×C4—741no—
147C22×C4—741no—
148C22×C4C22⋊D3711yescharacteristic
149C22×C4C22⋊D3711yescharacteristic
150C22×C4C22×D3711yescharacteristic
151Q16—1482no—
152SD16—1482no—
153C2×C8—741no—
154C2×C8—741no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1482no—
162C4⋊C4C22⋊D3711yescharacteristic
163C4⋊C4C22⋊D3711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C42—21no—
170C23—21no—
171C23C2×C22⋊D3711yescharacteristic
172Q8—41no—
173Q8—742no—
174Q8—742no—
175Q8—1481no—
176Q8—1481no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—1481no—
193C2×C4—1481no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4C2×C22⋊D3711yescharacteristic
197C2×C4C2×C22⋊D3711yescharacteristic
198C8—1481no—
199C8—1481no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1192450511yescharacteristic
206C22#1192455611yescharacteristic
207C22#1192456611yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—1482no—
216C4—1482no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1455769511yescharacteristic
221C2#1455771611yescharacteristic
222C2#1455772011yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#539C2
socleC22×C37#120
prime radical#121×C37C22
hypercenter#539D37
hypocenterC37#1603
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #14557688C2semidirect
3. #14557453C2semidirect
4. #14557270C2semidirect
6. #14557259C2semidirect
119. C37#1603semidirect

Maximal subgroups

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

subgroupindex
#145576882
#145576712
#145574532
#145572702
#145572672
#145572592
C37×#5392
#160337