Finite Group Databasebeta

← #17994968

Subgroups — #17994968

Order 4736.

334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11924567C211yesmaximal, characteristic
2#14558014C211yesmaximal, characteristic
3C2×#11924464C211yesmaximal, characteristic
4#14557542C211yesmaximal, characteristic, complemented
5#14557302C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C37×#391C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—22no—
10#11924567C414yescomplemented
11C2×#10596942—21no—
12C2×#10596941—21no—
13C2×#10596934C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924501—21no—
16#11924498—21no—
17C4×C22⋊D37—22no—
18#11924495C2211yescharacteristic
19#11924494—21no—
20C4⋊C4×D37—21no—
21#11924464—22no—
22#11924460—21no—
23#11924460—21no—
24C22×Q8×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27#95×C37—22no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37C2×C412yescomplemented
34C22×C4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37D412yes—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—21no—
39#10596962—21no—
40#10596962—21no—
41#10596962C2×C412yes—
42#10596962D412yes—
43C2×D148D411yescharacteristic
44C2×C4×D37—21no—
45C2×C4×D37—22no—
46C2×Dic74D411yescharacteristic
47C4⋊C4×C37—21no—
48C4⋊C4×C37—21no—
49C42×C37—21no—
50C42×C37—21no—
51C22⋊Dic37—21no—
52#10596942—24no—
53#10596941—24no—
54#10596938—22no—
55C4⋊Dic37D411yescharacteristic
56C4⋊Dic37D411yescharacteristic
57#10596936—22no—
58C4×Dic37—22no—
59C4×Dic37—21no—
60#10596934—21no—
61#10596934—21no—
62#10596934—21no—
63#10596934C2×C412yescomplemented
64C2×#64436—21no—
65C2×#64436—21no—
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68Q8×C37—22no—
69Q8×C37—22no—
70Q8×C37—41no—
71Q8×C37—41no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37—42no—
80C2×C4×C37C22×C411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C2×C4×C37#4111yescharacteristic
86C22⋊D37—22no—
87C22⋊D37—22no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37—21no—
91D148—21no—
92D148C22⋊C412yes—
93C4×D37—22no—
94C4×D37—22no—
95C4×D37—82no—
96Dic74—21no—
97Dic74C22⋊C412yes—
98#64436—22no—
99#64436—41no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37C4×D411yescharacteristic
103C22×C37#12011yescharacteristic
104C22×C37#12111yescharacteristic
105C2×D37—22no—
106C2×D37—41no—
107C2×D37—41no—
108C4×C37—42no—
109C4×C37—42no—
110C4×C37—42no—
111C4×C37C2×C22⋊C411yescharacteristic
112C4×C37C4×D411yescharacteristic
113C4×C37#12111yescharacteristic
114C4×C37#12311yescharacteristic
115Dic37—22no—
116Dic37—41no—
117Dic37—41no—
118#1882—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—21no—
121C2×C37#38611yescharacteristic
122C2×C37#45511yescharacteristic
123C2×C37#45611yescharacteristic
124D37—42no—
125C2×#137—371no—
126#520—371no—
127C2×#104—371no—
128#419—371no—
129#391D3711yescharacteristic, complemented
130#343—371no—
131#339—371no—
132C37#188211yescharacteristic, complemented, Sylow
133C2×#41—371no—
134C22×Q8C2×D3711yescharacteristic
135#137—374no—
136#137—742no—
137C2×Q16—741no—
138C2×SD16—741no—
139C2×M16—371no—
140C2×M16—371no—
141C4×Q8—741no—
142C4×D4—741no—
143C4×D4—742no—
144#117—371no—
145#117—741no—
146C2×C4⋊C4—741no—
147C2×C4⋊C4C2×D3711yescharacteristic
148C2×C42C2×D3711yescharacteristic
149#104—742no—
150#103—741no—
151#103—741no—
152#95—22no—
153#41—372no—
154#41—372no—
155#41—741no—
156#41—741no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—371no—
163C2×Q8C4×D3712yescomplemented
164C2×D4—371no—
165C2×D4—741no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—742no—
169C22×C4—741no—
170C22×C4C22⋊D3712yes—
171C22×C4C22×D3711yescharacteristic
172Q16—744no—
173SD16—744no—
174M16—372no—
175M16—741no—
176M16—741no—
177M16—741no—
178C2×C8—741no—
179C2×C8—741no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—371no—
183C4⋊C4—371no—
184C4⋊C4—742no—
185C22⋊C4—742no—
186C22⋊C4—741no—
187C42—21no—
188C42—21no—
189C42—742no—
190C42—741no—
191C23—741no—
192C23C2×C22⋊D3711yescharacteristic
193Q8—22no—
194Q8—22no—
195Q8—41no—
196Q8—41no—
197Q8—372no—
198Q8—741no—
199D4—372no—
200D4—742no—
201D4—742no—
202D4—741no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—2962no—
212C2×C4—741no—
213C2×C4—742no—
214C2×C4—742no—
215C2×C4—741no—
216C2×C4—741no—
217C2×C4C2×C4×D3711yescharacteristic
218C2×C4#1059696211yescharacteristic
219C2×C4D4×D3711yescharacteristic
220C2×C4D4×D3711yescharacteristic
221C2×C4D4×D3711yescharacteristic
222C2×C4#1059696411yescharacteristic
223C8—742no—
224C8—1481no—
225C22—21no—
226C22—21no—
227C22—742no—
228C22—1481no—
229C22—1481no—
230C22C4×C22⋊D3711yescharacteristic
231C22#1192450411yescharacteristic
232C22#1192450711yescharacteristic
233C4—42no—
234C4—42no—
235C4—42no—
236C4—742no—
237C4—1481no—
238C4—1481no—
239C4C22⋊C4×D3711yescharacteristic
240C4#1192449611yescharacteristic
241C4#1192450911yescharacteristic
242C4#1192451811yescharacteristic
243C2—21no—
244C2—21no—
245C2—1482no—
246C2#1455740911yescharacteristic
247C2#1455771011yescharacteristic
248C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#391C2
socleC22×C37#120
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#391D37
hypocenterC37#1882
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #14557542C2semidirect
5. #14557302C2semidirect
6. #14557293C2semidirect
7. C37×#391C2semidirect
10. #11924567C4semidirect
33. C2×Q8×C37C2×C4semidirect
63. #10596934C2×C4semidirect
129. #391D37semidirect
132. C37#1882semidirect
163. C2×Q8C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
#145580142
C2×#119244642
#145575422
#145573022
#145572932
C37×#3912
#188237