Finite Group Databasebeta

← #18005191

Subgroups — #18005191

Order 4736.

408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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#14558083C211yesmaximal, characteristic, complemented
2#14558067C211yesmaximal, characteristic, complemented
3#14557942C211yesmaximal, characteristic, complemented
4#14557922C211yesmaximal, characteristic, complemented
5#14557898C211yesmaximal, characteristic, complemented
6#14557893C211yesmaximal, characteristic, complemented
7#14557786C212yesmaximal, complemented
8#14557779C212yesmaximal, complemented
9C4×#10596930C212yesmaximal, complemented
10C4×D296C212yesmaximal, complemented
11C4×M16×C37C211yesmaximal, characteristic, complemented
12C2×#10596962—21no—
13C2×#10596930C2212yes—
14C2×D296C2212yes—
15#11924536C2211yescharacteristic
16#11924533C2211yescharacteristic
17#11924530—21no—
18#11924528C2211yescharacteristic
19#11924524—21no—
20#11924524C2211yescharacteristic
21#11924519—21no—
22#11924515C2211yescharacteristic
23#11924510—21no—
24#11924510C2212yes—
25#11924510C2211yescharacteristic
26C4×Dic74C2211yescharacteristic
27C4×D148—21no—
28C4×D148C2211yescharacteristic
29C4×D148C2212yes—
30C4×C22⋊D37—21no—
31#11924493—21no—
32#11924470C2212yes—
33#11924468C2212yes—
34#11924461C2212yes—
35#11924458C2212yes—
36#11924458C2212yes—
37#11924458C2212yes—
38C2×M16×C37C2212yes—
39C2×C42×C37C2211yescharacteristic
40#97×C37C2211yescharacteristic
41#97×C37C2211yescharacteristic
42C4×C8×C37C2212yes—
43C22×C4×C37D411yescharacteristic
44C22×C4×C37D411yescharacteristic
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C2×C22⋊D37—22no—
48#10596962—44no—
49C2×D148—21no—
50C2×D148—21no—
51C2×D148C2311yescharacteristic
52C2×D148C2312yes—
53C2×C4×D37—21no—
54C2×C4×D37—22no—
55C2×Dic74—21no—
56C2×Dic74C2311yescharacteristic
57M16×C37—24no—
58C2×C8×C37C2312yes—
59C2×C8×C37C2312yes—
60C42×C37D411yescharacteristic
61C42×C37D411yescharacteristic
62C42×C37C2311yescharacteristic
63C42×C37C2311yescharacteristic
64C22⋊Dic37—21no—
65#10596938—21no—
66#10596938—21no—
67#10596938—21no—
68#10596938—22no—
69#10596938—22no—
70#10596938—21no—
71C4⋊Dic37—21no—
72C4⋊Dic37C2312yes—
73C4⋊Dic37C2311yescharacteristic
74C4⋊Dic37C2311yescharacteristic
75#10596936—21no—
76#10596936—21no—
77#10596936—21no—
78#10596936—21no—
79C4×Dic37—21no—
80D296—24no—
81#10596930—24no—
82C23×C37C2×D411yescharacteristic
83C22×D37—21no—
84C22×D37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—41no—
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—44no—
95C22⋊D37—42no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37—21no—
99C2×Dic37—22no—
100D148—22no—
101D148—22no—
102D148—22no—
103D148—42no—
104D148—42no—
105C4×D37—42no—
106C4×D37—44no—
107Dic74—22no—
108Dic74—42no—
109C8×C37—22no—
110C8×C37#4114yescomplemented
111C22×C37—21no—
112C22×C37—21no—
113C22×C37—21no—
114C22×C37C22×D411yescharacteristic
115C2×D37—42no—
116C2×D37—41no—
117C2×D37—42no—
118C2×D37—41no—
119C2×D37—42no—
120C2×D37—41no—
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—21no—
124C4×C37—21no—
125C4×C37AGL(1,ℤ/8)12yes—
126C4×C37C2×#4112yes—
127Dic37—41no—
128Dic37—42no—
129Dic37—41no—
130Dic37—41no—
131#3171—371nomaximal, Sylow
132C2×C37—41no—
133C2×C37#53211yescharacteristic
134C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C37#57511yescharacteristic
136D37—82no—
137D37—81no—
138#532—371no—
139#529—371no—
140#501—371no—
141#496—371no—
142#490—371no—
143#489—371no—
144#469—372no—
145#468—372no—
146C4×SD16—372no—
147C4×D8—372no—
148C4×M16D3711yescharacteristic, complemented
149C37#317111yescharacteristic, complemented, Sylow
150C2×#41—741no—
151C2×SD16—372no—
152C2×D8—372no—
153C2×M16C2×D3712yes—
154C4⋊Q8—371no—
155#127—371no—
156#126—741no—
157#125—371no—
158#124—371no—
159#124—741no—
160#123—741no—
161C22⋊Q8—371no—
162#121—371no—
163#121—372no—
164#121—741no—
165C4×Q8—371no—
166C4×D4—371no—
167C4×D4—372no—
168C4×D4—741no—
169C4×D4—741no—
170#117—741no—
171C2×C42C2×D3711yescharacteristic
172#107—372no—
173#106—372no—
174#103—372no—
175#102—372no—
176#102—372no—
177#102—372no—
178#97C2×D3711yescharacteristic
179#97C2×D3711yescharacteristic
180C4×C8C2×D3712yes—
181#41—1484no—
182C2×Q8—371no—
183C2×Q8—741no—
184C2×D4—371no—
185C2×D4—372no—
186C2×D4—741no—
187C2×D4—742no—
188C2×D4—741no—
189C2×D4—741no—
190C22×C4—741no—
191C22×C4—742no—
192C22×C4D14811yescharacteristic
193C22×C4D14811yescharacteristic
194C22×C4C22×D3711yescharacteristic
195SD16—744no—
196D8—744no—
197M16—24no—
198C2×C8C22×D3712yes—
199C2×C8C22×D3712yes—
200C4⋊C4—371no—
201C4⋊C4—371no—
202C4⋊C4—372no—
203C4⋊C4—741no—
204C4⋊C4—741no—
205C4⋊C4—741no—
206C4⋊C4—741no—
207C4⋊C4—741no—
208C22⋊C4—741no—
209C22⋊C4—741no—
210C22⋊C4—741no—
211C22⋊C4—742no—
212C22⋊C4—741no—
213C22⋊C4—742no—
214C22⋊C4—741no—
215C42—741no—
216C42D14811yescharacteristic
217C42D14811yescharacteristic
218C42C22×D3711yescharacteristic
219C42C22×D3711yescharacteristic
220C23—741no—
221C23—742no—
222C23C2×D14811yescharacteristic
223Q8—742no—
224Q8—1482no—
225D4—742no—
226D4—742no—
227D4—742no—
228D4—1482no—
229D4—1482no—
230D4—1484no—
231D4—1482no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—741no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—742no—
239C2×C4—1484no—
240C2×C4—1482no—
241C2×C4C2×D14811yescharacteristic
242C2×C4C2×D14811yescharacteristic
243C2×C4C2×D14811yescharacteristic
244C2×C4C2×D14811yescharacteristic
245C2×C4C2×D14811yescharacteristic
246C2×C4C23×D3711yescharacteristic
247C8—22no—
248C8#1059696214yescomplemented
249C22—21no—
250C22—21no—
251C22—21no—
252C22—1482no—
253C22—1481no—
254C22—1482no—
255C22—1481no—
256C22—1481no—
257C22—1482no—
258C22C22×D14811yescharacteristic
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—1482no—
264C4—1481no—
265C4—1481no—
266C4—1481no—
267C4#1192456412yes—
268C4C2×#1059696212yes—
269C2—41no—
270C2—2962no—
271C2—2961no—
272C2#1455808311yescharacteristic
273C2C2×#1192456411yescharacteristic
274C2#1455833311yescharacteristic
subgroupG/H
centerC2×C4C2×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×M16×C37C2
socleC22×C37C22×D4
hypercenterC4×M16D37
hypocenterC37#3171
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. #14558083C2semidirect
2. #14558067C2semidirect
3. #14557942C2semidirect
4. #14557922C2semidirect
5. #14557898C2semidirect
6. #14557893C2semidirect
7. #14557786C2semidirect
8. #14557779C2semidirect
9. C4×#10596930C2semidirect
10. C4×D296C2semidirect
11. C4×M16×C37C2semidirect
110. C8×C37#41semidirect
148. C4×M16D37semidirect
149. C37#3171semidirect
248. C8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145580832
#145580672
#145579422
#145579222
#145578982
#145578932
#145577862
#145577792
C4×#105969302
C4×D2962
C4×M16×C372
#317137