Finite Group Databasebeta

← #18004125

Subgroups — #18004125

Order 4736.

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

normal subgroups only

This group has 458 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
2C22×#10596942C211yesmaximal, characteristic, complemented
3#14558107C211yesmaximal, characteristic
4#14558010C211yesmaximal, characteristic, complemented
5#14557758C214yesmaximal, complemented
6#14557742C214yesmaximal, complemented
7#14557561C211yesmaximal, characteristic, complemented
8#14557527C211yesmaximal, characteristic
9C37×#419C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924569—24no—
13C2×Dic148C2212yes—
14C2×#10596942—24no—
15C2×#10596942C2214yes—
16C2×#10596930C2212yes—
17C22×#64436C2211yescharacteristic
18#11924534C2212yes—
19#11924525C2212yes—
20#11924519—22no—
21#11924512—22no—
22C4×Dic74—22no—
23#11924501C2214yes—
24#11924495C2211yescharacteristic
25#11924492—22no—
26#11924465C2214yes—
27#11924459C2212yes—
28#11924456C2212yes—
29C22×Q8×C37C2211yescharacteristic
30C2×M16×C37C2211yescharacteristic
31#117×C37C2211yescharacteristic
32#103×C37C2214yes—
33C2×Q8×C37—21no—
34C2×Q8×C37—22no—
35C2×Q8×C37—22no—
36C2×Q8×C37C2312yes—
37C22×C4×C37—21no—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—21no—
40C22×Dic37—21no—
41#10596962—22no—
42#10596962—22no—
43C2×D148C2311yescharacteristic
44C2×C4×D37—21no—
45C2×Dic74—21no—
46C2×Dic74—22no—
47C2×Dic74D414yes—
48C2×Dic74C2311yescharacteristic
49C2×Dic74C2312yes—
50M16×C37—22no—
51C2×C8×C37C2312yes—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—21no—
54C42×C37—21no—
55C22⋊Dic37D412yes—
56#10596942—28no—
57#10596938—24no—
58C4⋊Dic37D412yes—
59#10596936—24no—
60#10596936—24no—
61C4×Dic37—24no—
62C4×Dic37C2312yes—
63C2×#64436—22no—
64C2×#64436C2312yes—
65Dic148—24no—
66#10596930—24no—
67C23×C37C2×D411yescharacteristic
68C22×D37—21no—
69Q8×C37—22no—
70Q8×C37—22no—
71Q8×C37—42no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—42no—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D412yes—
77C2×C4×C37#4112yes—
78C2×C4×C37C2411yescharacteristic
79C22⋊D37—42no—
80C2×Dic37—24no—
81C2×Dic37—22no—
82C2×Dic37—21no—
83C2×Dic37C2×D414yes—
84D148—21no—
85D148—21no—
86C4×D37—42no—
87Dic74—24no—
88Dic74—22no—
89Dic74—21no—
90Dic74—21no—
91Dic74C2×D414yes—
92C8×C37—22no—
93#64436—22no—
94C22×C37—22no—
95C22×C37#12112yes—
96C22×C37C22×D411yescharacteristic
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—42no—
100C4×C37—42no—
101C4×C37#12112yes—
102C4×C37C22×D411yescharacteristic
103C4×C37C2×#4111yescharacteristic
104Dic37—24no—
105Dic37—24no—
106Dic37—41no—
107#3044—371nomaximal, Sylow
108C2×C37—22no—
109C2×C37C2×#12111yescharacteristic
110C2×C37#57812yes—
111D37—81no—
112C2×#137—371no—
113C22×Q16—371no—
114#536—371no—
115#519—371no—
116#464—374no—
117#462—374no—
118#424—371no—
119#419D3711yescharacteristic, complemented
120#416—371no—
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41—371no—
123C22×Q8—371no—
124C22×Q8C2×D3711yescharacteristic
125#137—744no—
126C2×Q16—374no—
127C2×Q16—372no—
128C2×Q16—744no—
129C2×SD16—372no—
130C2×M16C2×D3711yescharacteristic
131C22×C8—371no—
132C4⋊Q8—372no—
133#124—372no—
134#123—742no—
135C22⋊Q8—742no—
136C4×Q8—374no—
137C4×Q8—742no—
138#117—371no—
139#117—742no—
140#117C2×D3711yescharacteristic
141C4⋊C8—374no—
142#103—372no—
143#103C2×D3714yes—
144#102—372no—
145#41—742no—
146#41—742no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—374no—
151C2×Q8—372no—
152C2×Q8—371no—
153C2×Q8—742no—
154C2×Q8—741no—
155C2×Q8C22×D3712yes—
156C2×D4—371no—
157C2×D4—741no—
158C22×C4—21no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—744no—
163Q16—748no—
164SD16—744no—
165M16—22no—
166C2×C8—372no—
167C2×C8—742no—
168C2×C8C22×D3712yes—
169C4⋊C4—372no—
170C4⋊C4—744no—
171C4⋊C4—744no—
172C4⋊C4C22×D3712yes—
173C22⋊C4—21no—
174C22⋊C4—372no—
175C22⋊C4—744no—
176C42—21no—
177C42—372no—
178C42—744no—
179C23—741no—
180C23D4×D3711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—42no—
184Q8—374no—
185Q8—744no—
186Q8—742no—
187Q8—741no—
188Q8—741no—
189D4—741no—
190D4—741no—
191D4—1482no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—374no—
196C2×C4—744no—
197C2×C4—742no—
198C2×C4—741no—
199C2×C4—1482no—
200C2×C4#1059696212yes—
201C2×C4D4×D3711yescharacteristic
202C2×C4D4×D3712yes—
203C2×C4C23×D3711yescharacteristic
204C8—22no—
205C8—742no—
206C22—22no—
207C22—1481no—
208C22—1482no—
209C22#1192450912yes—
210C22C2×D4×D3711yescharacteristic
211C4—42no—
212C4—42no—
213C4—744no—
214C4—744no—
215C4—1481no—
216C4#1192450912yes—
217C4C2×D4×D3711yescharacteristic
218C4C2×#1059696211yescharacteristic
219C2—22no—
220C2—2961no—
221C2C2×#1192450911yescharacteristic
222C2#1455834912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#419C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenter#419D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C22×#10596942C2semidirect
4. #14558010C2semidirect
5. #14557758C2semidirect
6. #14557742C2semidirect
7. #14557561C2semidirect
9. C37×#419C2semidirect
119. #419D37semidirect
121. C37#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C22×#105969422
#145581072
#145580102
#145577582
#145577422
#145575612
#145575272
C37×#4192
#304437