Finite Group Databasebeta

← #17995011

Subgroups — #17995011

Order 4736.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#14558299C211yesmaximal, characteristic, complemented
2#14558044C211yesmaximal, characteristic
3#14557515C211yesmaximal, characteristic, complemented
4#14557497C211yesmaximal, characteristic, complemented
5#14557305C211yesmaximal, characteristic, complemented
6#14557304C211yesmaximal, characteristic, complemented
7C37×#407C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924544—22no—
10#11924542—22no—
11C2×#10596934C2211yescharacteristic
12C2×#10596934C2211yescharacteristic
13M16×D37—22no—
14#11924519C412yes—
15#11924515—21no—
16#11924510—21no—
17#11924505C412yes—
18C4×C22⋊D37—22no—
19#11924495C2211yescharacteristic
20#11924454—21no—
21#11924452—21no—
22C22⋊#64436—22no—
23C23×C4×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×M16×C37C2211yescharacteristic
26C22⋊C8×C37—22no—
27C24×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37—21no—
32C22×C4×C37—21no—
33C22×C4×C37—21no—
34C22×C4×C37C2×C411yescharacteristic
35C22×C4×C37C2311yescharacteristic
36C2×C22⋊D37—22no—
37C2×C22⋊D37C2×C412yes—
38#10596962—21no—
39#10596962—21no—
40#10596962—21no—
41#10596962—21no—
42C2×D148D411yescharacteristic
43C2×C4×D37D412yes—
44C2×Dic74D411yescharacteristic
45M16×C37—21no—
46M16×C37—21no—
47M16×C37—21no—
48M16×C37—21no—
49C2×C8×C37—21no—
50C2×C8×C37D412yescomplemented
51C22⋊Dic37—22no—
52C22⋊Dic37C2×C412yes—
53#10596938—22no—
54C4⋊Dic37—21no—
55#10596936—22no—
56C4×Dic37—21no—
57#10596934—21no—
58#10596934—21no—
59#10596934—21no—
60#10596934—21no—
61C2×#64436—21no—
62C2×#64436D412yescomplemented
63#10596929—24no—
64C8×D37—24no—
65C23×C37—21no—
66C23×C37—21no—
67C23×C37—21no—
68C23×C37—42no—
69C23×C37C22×C411yescharacteristic
70C22×D37C22⋊C412yes—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C22⋊D37—22no—
85C22⋊D37—22no—
86C22⋊D37—44no—
87C2×Dic37—22no—
88C2×Dic37C22⋊C412yes—
89D148—21no—
90D148—21no—
91C4×D37—22no—
92C4×D37—22no—
93Dic74—21no—
94Dic74—21no—
95C8×C37—22no—
96C8×C37—41no—
97#64436—22no—
98#64436—41no—
99C22×C37—22no—
100C22×C37—22no—
101C22×C37—22no—
102C22×C37—41no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37C2×C22⋊C411yescharacteristic
108C22×C37C4×D411yescharacteristic
109C22×C37C4×D411yescharacteristic
110C2×D37—22no—
111C2×D37—42no—
112C4×C37—41no—
113C4×C37#12011yescharacteristic
114C4×C37#12111yescharacteristic
115C4×C37#12111yescharacteristic
116C4×C37#12311yescharacteristic
117Dic37—22no—
118Dic37—42no—
119#1891—371nomaximal, Sylow
120C2×C37—21no—
121C2×C37—21no—
122C2×C37—21no—
123C2×C37—42no—
124C2×C37#38611yescharacteristic
125D37—42no—
126#568—371no—
127#525—371no—
128#413—371no—
129#407—371no—
130#407D3711yescharacteristic, complemented
131#344—371no—
132#344—371no—
133C37#189111yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C23×C4C2×D3711yescharacteristic
136#131—742no—
137#131—742no—
138C2×M16—371no—
139C2×M16—371no—
140C2×M16—742no—
141C2×M16C2×D3711yescharacteristic
142C2×M16C2×D3711yescharacteristic
143#123—372no—
144C22⋊Q8—741no—
145#121—741no—
146#120—372no—
147C4×D4—742no—
148#117—371no—
149#101—741no—
150#100—741no—
151C22⋊C8—22no—
152C22⋊C8—742no—
153C24C4×D3711yescharacteristic
154#41—741no—
155#41—741no—
156#41—741no—
157#41—741no—
158C2×Q8—371no—
159C2×D4—372no—
160C2×D4—371no—
161C2×D4—742no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—372no—
169C22×C4C4×D3711yescharacteristic
170C22×C4C22×D3711yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—744no—
176M16—741no—
177M16—741no—
178M16—741no—
179M16—741no—
180C2×C8—21no—
181C2×C8—372no—
182C2×C8—744no—
183C2×C8—741no—
184C2×C8C22⋊D3712yescomplemented
185C4⋊C4—742no—
186C4⋊C4—741no—
187C22⋊C4—372no—
188C22⋊C4—742no—
189C22⋊C4—742no—
190C42—741no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—372no—
196C23C2×C4×D3711yescharacteristic
197Q8—741no—
198Q8—741no—
199D4—742no—
200D4—742no—
201D4—741no—
202D4—741no—
203D4—1484no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—372no—
212C2×C4—742no—
213C2×C4—742no—
214C2×C4—742no—
215C2×C4#1059696211yescharacteristic
216C2×C4D4×D3711yescharacteristic
217C2×C4D4×D3711yescharacteristic
218C2×C4D4×D3711yescharacteristic
219C2×C4#1059696411yescharacteristic
220C2×C4C2×C22⋊D3711yescharacteristic
221C8—22no—
222C8—41no—
223C8—742no—
224C8—1481no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—742no—
234C22—1482no—
235C22C22⋊C4×D3711yescharacteristic
236C22#1192449611yescharacteristic
237C22C4×C22⋊D3711yescharacteristic
238C4—41no—
239C4—742no—
240C4—1482no—
241C4#1192450411yescharacteristic
242C4#1192450711yescharacteristic
243C4#1192450911yescharacteristic
244C4#1192451811yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—1482no—
250C2#1455740911yescharacteristic
subgroupG/H
centerC4#11924504
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#407C2
socleC2×C37#386
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenter#407D37
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14558299C2semidirect
3. #14557515C2semidirect
4. #14557497C2semidirect
5. #14557305C2semidirect
6. #14557304C2semidirect
7. C37×#407C2semidirect
50. C2×C8×C37D4semidirect
62. C2×#64436D4semidirect
130. #407D37semidirect
133. C37#1891semidirect
184. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145580442
#145575152
#145574972
#145573052
#145573042
C37×#4072
#189137