Finite Group Databasebeta

← #18004127

Subgroups — #18004127

Order 4736.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×Dic148C211yesmaximal, characteristic, complemented
3#14558109C211yesmaximal, characteristic
4#14558010C211yesmaximal, characteristic, complemented
5#14557756C214yesmaximal, complemented
6#14557744C214yesmaximal, complemented
7#14557543C211yesmaximal, characteristic, complemented
8#14557530C211yesmaximal, characteristic
9C37×#424C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12C22×Dic74C2211yescharacteristic
13#11924569—24no—
14C2×Dic148—24no—
15C2×Dic148C2212yes—
16C2×Dic148C2214yes—
17C2×#10596930C2212yes—
18#11924536C2212yes—
19#11924524C2212yes—
20#11924520—22no—
21#11924516—22no—
22C4×Dic74C2214yes—
23#11924501—22no—
24#11924495C2211yescharacteristic
25#11924492—22no—
26#11924461C2212yes—
27#11924461C2214yes—
28#11924458C2212yes—
29C2×M16×C37C2211yescharacteristic
30C22×C8×C37C2211yescharacteristic
31#117×C37C2211yescharacteristic
32C4⋊C8×C37C2214yes—
33C22×C4×C37C2311yescharacteristic
34C2×C22⋊D37—21no—
35C22×Dic37—21no—
36C22×Dic37—21no—
37#10596962—22no—
38#10596962—22no—
39C2×D148C2311yescharacteristic
40C2×C4×D37—21no—
41C2×Dic74—21no—
42C2×Dic74—22no—
43C2×Dic74—22no—
44C2×Dic74—22no—
45C2×Dic74—21no—
46C2×Dic74D414yes—
47C2×Dic74C2312yes—
48C2×Dic74C2311yescharacteristic
49C2×Dic74C2312yes—
50M16×C37—22no—
51C2×C8×C37—22no—
52C2×C8×C37C2312yes—
53C2×C8×C37C2312yes—
54C4⋊C4×C37D412yes—
55C22⋊C4×C37D412yes—
56C42×C37C2312yes—
57C22⋊Dic37—21no—
58#10596938—24no—
59C4⋊Dic37—24no—
60C4⋊Dic37C2312yes—
61#10596936—24no—
62C4×Dic37—24no—
63C4×Dic37—21no—
64Dic148—28no—
65Dic148—24no—
66#10596930—24no—
67C23×C37C2×D411yescharacteristic
68C22×D37—21no—
69C2×C4×C37C2×D414yes—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D412yes—
72C2×C4×C37#4112yes—
73C2×C4×C37C2411yescharacteristic
74C22⋊D37—42no—
75C2×Dic37—24no—
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37—21no—
79C2×Dic37—22no—
80C2×Dic37—42no—
81D148—21no—
82D148—21no—
83C4×D37—42no—
84Dic74—24no—
85Dic74—22no—
86Dic74—22no—
87Dic74—21no—
88Dic74—22no—
89Dic74—21no—
90Dic74—42no—
91Dic74C2×D414yes—
92C8×C37—22no—
93C8×C37—22no—
94C22×C37—22no—
95C22×C37#12112yes—
96C22×C37C22×D411yescharacteristic
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—24no—
100C4×C37#12112yes—
101C4×C37C22×D411yescharacteristic
102C4×C37C2×#4111yescharacteristic
103Dic37—24no—
104Dic37—42no—
105Dic37—41no—
106Dic37—42no—
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#424D3711yescharacteristic, complemented
119#419—371no—
120#416—371no—
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41—371no—
123C22×Q8—371no—
124C22×Q8—371no—
125#137—744no—
126C2×Q16—374no—
127C2×Q16—372no—
128C2×Q16—744no—
129C2×SD16—372no—
130C2×M16C2×D3711yescharacteristic
131C22×C8C2×D3711yescharacteristic
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⋊C8C2×D3714yes—
142#103—372no—
143#103—374no—
144#102—372no—
145#41—742no—
146#41—742no—
147C2×Q8—374no—
148C2×Q8—372no—
149C2×Q8—372no—
150C2×Q8—371no—
151C2×Q8—741no—
152C2×Q8—741no—
153C2×Q8—742no—
154C2×Q8—742no—
155C2×Q8—742no—
156C2×D4—371no—
157C2×D4—741no—
158C22×C4—741no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—748no—
163Q16—744no—
164SD16—744no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D3712yes—
168C2×C8C22×D3712yes—
169C4⋊C4—372no—
170C4⋊C4—744no—
171C4⋊C4—744no—
172C4⋊C4D14812yes—
173C22⋊C4—741no—
174C22⋊C4—744no—
175C22⋊C4D14812yes—
176C42—741no—
177C42—744no—
178C42C22×D3712yes—
179C23—741no—
180C23C2×D14811yescharacteristic
181Q8—374no—
182Q8—744no—
183Q8—742no—
184Q8—742no—
185Q8—741no—
186Q8—742no—
187Q8—741no—
188Q8—1482no—
189D4—741no—
190D4—741no—
191D4—1482no—
192C2×C4—744no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4—741no—
197C2×C4—1482no—
198C2×C4—1482no—
199C2×C4C2×D14814yes—
200C2×C4C2×D14811yescharacteristic
201C2×C4D4×D3712yes—
202C2×C4#1059696612yes—
203C2×C4C23×D3711yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—1481no—
208C22—1482no—
209C22#1192451112yes—
210C22C22×D14811yescharacteristic
211C4—24no—
212C4—744no—
213C4—1481no—
214C4—1482no—
215C4—1482no—
216C4#1192451112yes—
217C4C2×D4×D3711yescharacteristic
218C4C2×#1059696611yescharacteristic
219C2—22no—
220C2—2961no—
221C2C2×#1192451111yescharacteristic
222C2#1455835012yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#424C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenter#424D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic148C2semidirect
4. #14558010C2semidirect
5. #14557756C2semidirect
6. #14557744C2semidirect
7. #14557543C2semidirect
9. C37×#424C2semidirect
118. #424D37semidirect
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×Dic1482
#145581092
#145580102
#145577562
#145577442
#145575432
#145575302
C37×#4242
#304437