Finite Group Databasebeta

← #18004116

Subgroups — #18004116

Order 4736.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2C22×#10596940C211yesmaximal, characteristic, complemented
3#14558100C211yesmaximal, characteristic
4#14558010C211yesmaximal, characteristic, complemented
5#14557754C214yesmaximal, complemented
6#14557732C214yesmaximal, complemented
7#14557561C211yesmaximal, characteristic, complemented
8#14557527C211yesmaximal, characteristic, complemented
9C37×#418C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924569—24no—
13C2×Dic148C2212yescomplemented
14C2×#10596930C2212yescomplemented
15C2×#10596940—24no—
16C2×#10596940C2214yes—
17C22×#64436C2211yescharacteristic
18#11924532C2212yes—
19#11924523C2212yes—
20#11924507—22no—
21#11924505—22no—
22C4×Dic74—22no—
23#11924501C2214yescomplemented
24#11924495C2211yescharacteristic
25#11924492—22no—
26#11924465C2214yescomplemented
27#11924459C2212yescomplemented
28#11924456C2212yescomplemented
29C22×D4×C37C2211yescharacteristic
30C2×M16×C37C2211yescharacteristic
31#117×C37C2211yescharacteristic
32#102×C37C2214yes—
33C24×C37—21no—
34C2×D4×C37—22no—
35C2×D4×C37—21no—
36C2×D4×C37—22no—
37C2×D4×C37C2312yes—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—21no—
40C2×C22⋊D37—24no—
41C22×Dic37—21no—
42#10596962—22no—
43#10596962—22no—
44C2×D148C2311yescharacteristic
45C2×C4×D37—21no—
46C2×Dic74—21no—
47C2×Dic74—22no—
48C2×Dic74D414yescomplemented
49C2×Dic74C2311yescharacteristic
50C2×Dic74C2312yes—
51M16×C37—22no—
52C2×C8×C37C2312yes—
53C4⋊C4×C37C2312yes—
54C22⋊C4×C37—21no—
55C42×C37—21no—
56C22⋊Dic37—24no—
57C22⋊Dic37D412yes—
58#10596940—28no—
59C4⋊Dic37D412yes—
60#10596936—24no—
61C4×Dic37—24no—
62C4×Dic37C2312yes—
63C2×#64436—22no—
64C2×#64436C2312yes—
65Dic148—24no—
66#10596930—24no—
67C23×C37—22no—
68C23×C37—42no—
69C23×C37—82no—
70C23×C37C2×D411yescharacteristic
71C22×D37—21no—
72D4×C37—22no—
73D4×C37—22no—
74D4×C37—42no—
75C2×C4×C37—22no—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D412yes—
78C2×C4×C37#4112yes—
79C2×C4×C37C2411yescharacteristic
80C22⋊D37—42no—
81C22⋊D37—84no—
82C2×Dic37—24no—
83C2×Dic37—22no—
84C2×Dic37—21no—
85C2×Dic37C2×D414yes—
86D148—21no—
87D148—21no—
88C4×D37—42no—
89Dic74—24no—
90Dic74—22no—
91Dic74—21no—
92Dic74—21no—
93Dic74C2×D414yes—
94C8×C37—22no—
95#64436—22no—
96C22×C37—22no—
97C22×C37—42no—
98C22×C37—44no—
99C22×C37—84no—
100C22×C37#12112yes—
101C22×C37C22×D411yescharacteristic
102C2×D37—41no—
103C2×D37—42no—
104C4×C37—42no—
105C4×C37#12112yes—
106C4×C37C22×D411yescharacteristic
107C4×C37C2×#4111yescharacteristic
108Dic37—24no—
109Dic37—24no—
110Dic37—41no—
111#3043—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—82no—
114C2×C37C2×#12111yescharacteristic
115C2×C37#57712yes—
116D37—81no—
117C2×#137—371no—
118C22×SD16—371no—
119#535—371no—
120#519—371no—
121#464—374no—
122#460—374no—
123#424—371no—
124#418D3711yescharacteristic, complemented
125#416—371no—
126C37#304311yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C22×Q8—371no—
129C22×D4C2×D3711yescharacteristic
130#137—744no—
131C2×Q16—372no—
132C2×SD16—374no—
133C2×SD16—372no—
134C2×SD16—744no—
135C2×M16C2×D3711yescharacteristic
136C22×C8—371no—
137#127—372no—
138#124—372no—
139#121—742no—
140#120—742no—
141C4×Q8—374no—
142C4×Q8—742no—
143#117—371no—
144#117—742no—
145#117C2×D3711yescharacteristic
146C4⋊C8—374no—
147#103—372no—
148#102—372no—
149#102C2×D3714yes—
150C24—21no—
151#41—742no—
152#41—742no—
153C2×Q8—374no—
154C2×Q8—372no—
155C2×Q8—371no—
156C2×Q8—742no—
157C2×Q8—741no—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—371no—
162C2×D4—744no—
163C2×D4—741no—
164C2×D4C22×D3712yes—
165C22×C4—741no—
166C22×C4—741no—
167C22×C4C22×D3711yescharacteristic
168Q16—744no—
169SD16—744no—
170SD16—748no—
171M16—22no—
172C2×C8—372no—
173C2×C8—742no—
174C2×C8C22×D3712yes—
175C4⋊C4—372no—
176C4⋊C4—744no—
177C4⋊C4C22×D3712yes—
178C22⋊C4—21no—
179C22⋊C4—372no—
180C22⋊C4—744no—
181C42—21no—
182C42—372no—
183C42—744no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—741no—
188C23D4×D3711yescharacteristic
189Q8—374no—
190Q8—744no—
191Q8—742no—
192Q8—741no—
193Q8—741no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—2964no—
198D4—741no—
199D4—741no—
200D4—1482no—
201C2×C4—22no—
202C2×C4—374no—
203C2×C4—744no—
204C2×C4—742no—
205C2×C4—741no—
206C2×C4—1482no—
207C2×C4#1059696212yes—
208C2×C4D4×D3711yescharacteristic
209C2×C4D4×D3712yes—
210C2×C4C23×D3711yescharacteristic
211C8—22no—
212C8—742no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—1481no—
218C22—1482no—
219C22#1192450912yes—
220C22C2×D4×D3711yescharacteristic
221C4—42no—
222C4—744no—
223C4—744no—
224C4—1481no—
225C4#1192450912yes—
226C4C2×D4×D3711yescharacteristic
227C4C2×#1059696211yescharacteristic
228C2—22no—
229C2—82no—
230C2—2961no—
231C2C2×#1192450911yescharacteristic
232C2#1455834312yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#418C2
socleC22×C37C22×D4
prime radical#14558100C2
hypercenter#418D37
hypocenterC37#3043
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
2. C22×#10596940C2semidirect
4. #14558010C2semidirect
5. #14557754C2semidirect
6. #14557732C2semidirect
7. #14557561C2semidirect
8. #14557527C2semidirect
9. C37×#418C2semidirect
13. C2×Dic148C22semidirect
14. C2×#10596930C22semidirect
23. #11924501C22semidirect
26. #11924465C22semidirect
27. #11924459C22semidirect
28. #11924456C22semidirect
48. C2×Dic74D4semidirect
124. #418D37semidirect
126. C37#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C22×#105969402
#145581002
#145580102
#145577542
#145577322
#145575612
#145575272
C37×#4182
#304337