Finite Group Databasebeta

← #17994964

Subgroups — #17994964

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×#11924569C211yesmaximal, characteristic
2#14558014C211yesmaximal, characteristic
3C2×#11924462C211yesmaximal, characteristic
4#14557543C211yesmaximal, characteristic, complemented
5#14557438C211yesmaximal, characteristic, complemented
6#14557294C211yesmaximal, characteristic, complemented
7C37×#343C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569C414yescomplemented
12C2×Dic148—21no—
13C2×#10596930—21no—
14#11924501—21no—
15#11924498—21no—
16C4×C22⋊D37—22no—
17#11924495C2211yescharacteristic
18#11924494—21no—
19C4⋊C4×D37—21no—
20C2×C4×Dic37C2211yescharacteristic
21#11924462—22no—
22#11924461—21no—
23#11924461—21no—
24#11924443—22no—
25C2×M16×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28C22×C4×C37D412yes—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C22×Dic37—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962C2×C412yes—
36#10596962D412yes—
37C2×D148D411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—22no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74C2×C412yescomplemented
46C2×Dic74D411yescharacteristic
47M16×C37—21no—
48M16×C37—21no—
49M16×C37—21no—
50M16×C37C2×C412yescomplemented
51C2×C8×C37—21no—
52C2×C8×C37—21no—
53C4⋊C4×C37—21no—
54C4⋊C4×C37—21no—
55C22⋊Dic37—21no—
56#10596938—22no—
57C4⋊Dic37D411yescharacteristic
58C4⋊Dic37D411yescharacteristic
59#10596936—22no—
60C4×Dic37—22no—
61C4×Dic37—21no—
62C4×Dic37—21no—
63C4×Dic37—21no—
64Dic148—24no—
65#10596930—24no—
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C2×C4×C37—22no—
69C2×C4×C37—42no—
70C2×C4×C37C22×C411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C22⋊D37—22no—
77C22⋊D37—22no—
78C2×Dic37—21no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—21no—
82C2×Dic37—21no—
83C2×Dic37—41no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87D148—21no—
88D148C22⋊C412yes—
89C4×D37—22no—
90C4×D37—22no—
91C4×D37—82no—
92Dic74—21no—
93Dic74—22no—
94Dic74—22no—
95Dic74—41no—
96Dic74—41no—
97Dic74C22⋊C412yes—
98C8×C37—22no—
99C8×C37—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×C37C2×C22⋊C411yescharacteristic
110C4×C37C4×D411yescharacteristic
111C4×C37#12111yescharacteristic
112C4×C37#12311yescharacteristic
113Dic37—22no—
114Dic37—42no—
115Dic37—42no—
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#391—371no—
130#343D3711yescharacteristic, complemented
131#339—371no—
132C37#188211yescharacteristic, complemented, Sylow
133C2×#41—371no—
134C22×Q8—371no—
135#137—374no—
136#137—742no—
137C2×Q16—741no—
138C2×SD16—741no—
139C2×M16C2×D3711yescharacteristic
140C2×M16C2×D3711yescharacteristic
141C4×Q8—741no—
142C4×D4—741no—
143C4×D4—742no—
144#117—371no—
145#117—741no—
146C2×C4⋊C4—741no—
147C2×C4⋊C4C2×D3711yescharacteristic
148C2×C42—371no—
149#104—742no—
150#103—741no—
151#103—741no—
152#95—742no—
153#41—372no—
154#41—372no—
155#41—741no—
156#41—741no—
157C2×Q8—372no—
158C2×Q8—371no—
159C2×Q8—741no—
160C2×Q8—741no—
161C2×Q8—741no—
162C2×Q8—741no—
163C2×Q8—741no—
164C2×D4—371no—
165C2×D4—741no—
166C22×C4—742no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4—741no—
170C22×C4D14812yes—
171C22×C4C22×D3711yescharacteristic
172Q16—744no—
173SD16—744no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16C4×D3712yescomplemented
178C2×C8—21no—
179C2×C8—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—371no—
183C4⋊C4—371no—
184C4⋊C4—742no—
185C22⋊C4—742no—
186C22⋊C4—741no—
187C42—742no—
188C42—741no—
189C42—741no—
190C42—741no—
191C23—741no—
192C23C2×D14811yescharacteristic
193Q8—372no—
194Q8—741no—
195Q8—742no—
196Q8—742no—
197Q8—1481no—
198Q8—1481no—
199D4—372no—
200D4—742no—
201D4—742no—
202D4—741no—
203C2×C4—22no—
204C2×C4—42no—
205C2×C4—2962no—
206C2×C4—741no—
207C2×C4—742no—
208C2×C4—742no—
209C2×C4—742no—
210C2×C4—742no—
211C2×C4—741no—
212C2×C4—741no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1481no—
217C2×C4C2×C4×D3711yescharacteristic
218C2×C4#1059696211yescharacteristic
219C2×C4D4×D3711yescharacteristic
220C2×C4D4×D3711yescharacteristic
221C2×C4D4×D3711yescharacteristic
222C2×C4#1059696611yescharacteristic
223C8—22no—
224C8—41no—
225C22—21no—
226C22—21no—
227C22—742no—
228C22—1481no—
229C22—1481no—
230C22C4×D14811yescharacteristic
231C22#1192450611yescharacteristic
232C22#1192451111yescharacteristic
233C4—42no—
234C4—742no—
235C4—1482no—
236C4—1481no—
237C4—1481no—
238C4—1482no—
239C4C22⋊C4×D3711yescharacteristic
240C4#1192449811yescharacteristic
241C4#1192450911yescharacteristic
242C4#1192452111yescharacteristic
243C2—21no—
244C2—21no—
245C2—1482no—
246C2#1455741111yescharacteristic
247C2#1455771311yescharacteristic
248C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1882
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. #14557543C2semidirect
5. #14557438C2semidirect
6. #14557294C2semidirect
7. C37×#343C2semidirect
11. #11924569C4semidirect
45. C2×Dic74C2×C4semidirect
50. M16×C37C2×C4semidirect
130. #343D37semidirect
132. C37#1882semidirect
177. M16C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145580142
C2×#119244622
#145575432
#145574382
#145572942
C37×#3432
#188237