Finite Group Databasebeta

← #18004120

Subgroups — #18004120

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×#11924566C211yesmaximal, characteristic, complemented
2C22×#10596930C211yesmaximal, characteristic, complemented
3#14558097C211yesmaximal, characteristic
4#14558010C211yesmaximal, characteristic, complemented
5#14557758C214yesmaximal, complemented
6#14557732C214yesmaximal, complemented
7#14557559C211yesmaximal, characteristic, complemented
8#14557537C211yesmaximal, characteristic, complemented
9C37×#416C211yesmaximal, characteristic, complemented
10C22×Dic74C2211yescharacteristic
11C22×D148C2211yescharacteristic
12#11924566—24no—
13C2×#10596942C2212yescomplemented
14C2×#10596930—24no—
15C2×#10596930C2214yes—
16C2×#10596940C2212yescomplemented
17C2×#10596934C2211yescharacteristic
18#11924532C2212yes—
19#11924525C2212yes—
20#11924510—22no—
21#11924504—22no—
22C4×Dic74—22no—
23#11924501C2214yescomplemented
24#11924495C2211yescharacteristic
25#11924492—22no—
26#11924465C2214yescomplemented
27#11924456C2214yes—
28C2×#41×C37C2211yescharacteristic
29C22×C8×C37C2211yescharacteristic
30#117×C37C2211yescharacteristic
31#103×C37C2212yescomplemented
32#102×C37C2212yescomplemented
33C23×D37—21no—
34#41×C37—22no—
35#41×C37—22no—
36C2×Q8×C37C2311yescharacteristic
37C2×D4×C37—21no—
38C2×D4×C37C2311yescharacteristic
39C22×C4×C37—21no—
40C22×C4×C37C2311yescharacteristic
41C2×C22⋊D37—24no—
42C22×Dic37—21no—
43C2×D148—22no—
44C2×D148—22no—
45C2×D148—21no—
46C2×D148C2312yes—
47C2×Dic74—21no—
48C2×Dic74—22no—
49C2×Dic74D414yescomplemented
50C2×Dic74C2312yes—
51C2×C8×C37—22no—
52C2×C8×C37C2312yes—
53C4⋊C4×C37C2312yes—
54C22⋊C4×C37—21no—
55C42×C37—21no—
56C22⋊Dic37D412yes—
57#10596942—24no—
58#10596940—24no—
59#10596938—24no—
60C4⋊Dic37D412yes—
61#10596936—24no—
62C4×Dic37—24no—
63C4×Dic37C2312yes—
64#10596934—22no—
65C2×#64436C2312yes—
66#10596930—28no—
67C23×C37—21no—
68C23×C37C2×D411yescharacteristic
69C22×D37—22no—
70C22×D37—42no—
71C22×D37—82no—
72Q8×C37—21no—
73Q8×C37—21no—
74D4×C37—21no—
75D4×C37—21no—
76D4×C37—42no—
77C2×C4×C37—22no—
78C2×C4×C37—21no—
79C2×C4×C37—42no—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D412yes—
82C2×C4×C37#4112yes—
83C2×C4×C37C2411yescharacteristic
84C22⋊D37—84no—
85C2×Dic37—24no—
86C2×Dic37—22no—
87C2×Dic37C2×D414yes—
88D148—22no—
89D148—22no—
90D148—42no—
91Dic74—24no—
92Dic74—22no—
93Dic74C2×D414yes—
94C8×C37—22no—
95#64436—22no—
96C22×C37—22no—
97C22×C37—41no—
98C22×C37—42no—
99C22×C37#12112yes—
100C22×C37C22×D411yescharacteristic
101C2×D37—42no—
102C2×D37—44no—
103C2×D37—84no—
104C4×C37—41no—
105C4×C37—42no—
106C4×C37#12112yes—
107C4×C37C22×D411yescharacteristic
108C4×C37C2×#4111yescharacteristic
109Dic37—24no—
110Dic37—24no—
111#3043—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—81no—
114C2×C37C2×#12111yescharacteristic
115C2×C37#57712yes—
116D37—82no—
117C2×#137—371no—
118C22×SD16—371no—
119#535—371no—
120#519—371no—
121#464—374no—
122#460—374no—
123#424—371no—
124#418—371no—
125#416D3711yescharacteristic, complemented
126C37#304311yescharacteristic, complemented, Sylow
127C2×#41C2×D3711yescharacteristic
128C22×Q8—371no—
129C22×D4—371no—
130#137—744no—
131C2×Q16—372no—
132C2×SD16—372no—
133C2×SD16—374no—
134C2×SD16—744no—
135C2×M16—371no—
136C22×C8C2×D3711yescharacteristic
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#103C2×D3712yescomplemented
148#102—374no—
149#102C2×D3712yescomplemented
150C24—741no—
151#41—22no—
152#41—22no—
153C2×Q8—374no—
154C2×Q8—372no—
155C2×Q8—742no—
156C2×Q8—741no—
157C2×Q8C22×D3711yescharacteristic
158C2×D4—21no—
159C2×D4—372no—
160C2×D4—744no—
161C2×D4—742no—
162C2×D4—742no—
163C2×D4—741no—
164C2×D4C22×D3711yescharacteristic
165C22×C4—21no—
166C22×C4—741no—
167C22×C4C22×D3711yescharacteristic
168Q16—744no—
169SD16—748no—
170SD16—744no—
171M16—742no—
172C2×C8—22no—
173C2×C8—372no—
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—21no—
185C23—2962no—
186C23—742no—
187C23—1482no—
188C23D4×D3711yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—374no—
192Q8—744no—
193Q8—742no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—2964no—
198D4—742no—
199D4—742no—
200D4—1482no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—374no—
205C2×C4—744no—
206C2×C4—742no—
207C2×C4#1059696212yes—
208C2×C4D4×D3711yescharacteristic
209C2×C4D4×D3712yes—
210C2×C4C23×D3711yescharacteristic
211C8—22no—
212C8—742no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—2964no—
217C22—1482no—
218C22—1484no—
219C22#1192450912yes—
220C22C2×D4×D3711yescharacteristic
221C4—41no—
222C4—42no—
223C4—744no—
224C4—744no—
225C4#1192450912yes—
226C4C2×D4×D3711yescharacteristic
227C4C2×#1059696211yescharacteristic
228C2—22no—
229C2—81no—
230C2—2962no—
231C2C2×#1192450911yescharacteristic
232C2#1455834012yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radical#14558097C2
hypercenter#416D37
hypocenterC37#3043
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
2. C22×#10596930C2semidirect
4. #14558010C2semidirect
5. #14557758C2semidirect
6. #14557732C2semidirect
7. #14557559C2semidirect
8. #14557537C2semidirect
9. C37×#416C2semidirect
13. C2×#10596942C22semidirect
16. C2×#10596940C22semidirect
23. #11924501C22semidirect
26. #11924465C22semidirect
31. #103×C37C22semidirect
32. #102×C37C22semidirect
49. C2×Dic74D4semidirect
125. #416D37semidirect
126. C37#3043semidirect
147. #103C2×D37semidirect
149. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C22×#105969302
#145580972
#145580102
#145577582
#145577322
#145575592
#145575372
C37×#4162
#304337