Finite Group Databasebeta

← #18004205

Subgroups — #18004205

Order 4736.

500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924558C211yesmaximal, characteristic, complemented
2#14558044C212yesmaximal, complemented
3#14557791C212yesmaximal, complemented
4#14557786C212yesmaximal, complemented
5#14557779C214yesmaximal, complemented
6#14557571C211yesmaximal, characteristic, complemented
7#14557530C212yesmaximal, complemented
8C22×M16×C37C211yesmaximal, characteristic, complemented
9C2×#10596962C2212yes—
10#11924558—24no—
11C2×Dic148C2211yescharacteristic, complemented
12C2×#10596930C2212yescomplemented
13C2×D296C2211yescharacteristic, complemented
14#11924519—22no—
15#11924515C2214yes—
16#11924510C2214yes—
17#11924505—22no—
18C4×C22⋊D37—24no—
19#11924495C2212yes—
20#11924470C2212yescomplemented
21#11924468C2212yescomplemented
22#11924461C2214yescomplemented
23#11924458C2214yescomplemented
24C23×C4×C37C2211yescharacteristic
25C2×M16×C37—24no—
26C2×M16×C37C2212yes—
27C2×M16×C37C2212yes—
28C22×C8×C37C2211yescharacteristic
29C22×C8×C37C2211yescharacteristic
30C24×C37D411yescharacteristic
31C22×C4×C37—22no—
32C22×C4×C37—22no—
33C22×C4×C37D412yes—
34C22×C4×C37D411yescharacteristic
35C22×C4×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—24no—
38C2×C22⋊D37—22no—
39#10596962—24no—
40#10596962—24no—
41C2×D148C2312yes—
42C2×C4×D37—22no—
43C2×Dic74C2312yes—
44M16×C37—24no—
45M16×C37—24no—
46C2×C8×C37—22no—
47C2×C8×C37D414yescomplemented
48C2×C8×C37C2312yes—
49C2×C8×C37C2311yescharacteristic
50C2×C8×C37C2311yescharacteristic
51C22⋊Dic37—22no—
52C22⋊Dic37—24no—
53#10596938—24no—
54C4⋊Dic37C2314yes—
55#10596936—24no—
56C4×Dic37—22no—
57Dic148—22no—
58D296—22no—
59#10596930—24no—
60C23×C37—22no—
61C23×C37—42no—
62C23×C37C2×D412yes—
63C23×C37C2×D411yescharacteristic
64C22×D37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—24no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37C2×D412yes—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D412yes—
72C2×C4×C37#4112yes—
73C2×C4×C37C2411yescharacteristic
74C22⋊D37—48no—
75C22⋊D37—44no—
76C2×Dic37—24no—
77C2×Dic37—22no—
78D148—22no—
79D148—22no—
80C4×D37—44no—
81Dic74—22no—
82Dic74—22no—
83C8×C37—22no—
84C8×C37C2×D412yes—
85C8×C37C2×D412yes—
86C22×C37—22no—
87C22×C37—22no—
88C22×C37—24no—
89C22×C37—44no—
90C22×C37#12112yes—
91C22×C37C22×D411yescharacteristic
92C2×D37—42no—
93C2×D37—44no—
94C4×C37—22no—
95C4×C37#12112yes—
96C4×C37C22×D411yescharacteristic
97C4×C37C2×#4111yescharacteristic
98Dic37—42no—
99Dic37—44no—
100#3054—371nomaximal, Sylow
101C2×C37—22no—
102C2×C37—42no—
103C2×C37C2×#12111yescharacteristic
104C2×C37#57512yes—
105D37—82no—
106C2×#135—371no—
107C22×M16D3711yescharacteristic, complemented
108#525—372no—
109#470—372no—
110#469—372no—
111#468—374no—
112#427—371no—
113#416—372no—
114C37#305411yescharacteristic, complemented, Sylow
115C2×#41—372no—
116C23×C4C2×D3711yescharacteristic
117#135—744no—
118C2×Q16—371no—
119C2×SD16—372no—
120C2×D8—371no—
121C2×M16—24no—
122C2×M16C2×D3712yes—
123C2×M16C2×D3712yes—
124C22×C8C2×D3711yescharacteristic
125C22×C8C2×D3711yescharacteristic
126#123—742no—
127C22⋊Q8—374no—
128#121—374no—
129#120—742no—
130C4×D4—744no—
131#117—372no—
132#107—372no—
133#106—372no—
134#103—374no—
135#102—374no—
136C24D14811yescharacteristic
137#41—744no—
138#41—744no—
139C2×Q8—372no—
140C2×D4—372no—
141C2×D4—744no—
142C2×D4—742no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—742no—
146C22×C4D14811yescharacteristic
147C22×C4D14812yes—
148C22×C4C22×D3712yes—
149C22×C4C22×D3711yescharacteristic
150Q16—742no—
151SD16—744no—
152D8—742no—
153M16—24no—
154M16—24no—
155C2×C8—22no—
156C2×C8C22⋊D3714yescomplemented
157C2×C8C22×D3712yes—
158C2×C8C22×D3711yescharacteristic
159C2×C8C22×D3711yescharacteristic
160C4⋊C4—374no—
161C4⋊C4—744no—
162C22⋊C4—742no—
163C22⋊C4—744no—
164C22⋊C4—744no—
165C42—742no—
166C23—22no—
167C23—42no—
168C23—742no—
169C23C2×D14812yes—
170C23C2×D14811yescharacteristic
171Q8—742no—
172Q8—742no—
173D4—742no—
174D4—742no—
175D4—1488no—
176D4—1484no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—744no—
182C2×C4—742no—
183C2×C4—1484no—
184C2×C4C2×D14812yes—
185C2×C4C2×D14811yescharacteristic
186C2×C4#1059696212yes—
187C2×C4C2×C22⋊D3712yes—
188C2×C4C23×D3711yescharacteristic
189C8—22no—
190C8C2×C22⋊D3712yes—
191C8C2×C22⋊D3712yes—
192C22—22no—
193C22—22no—
194C22—24no—
195C22—44no—
196C22—1482no—
197C22—1484no—
198C22#1192451012yes—
199C22C22×D14811yescharacteristic
200C4—22no—
201C4—1482no—
202C4—1484no—
203C4#1192451012yes—
204C4C22×C22⋊D3711yescharacteristic
205C4C2×#1059696211yescharacteristic
206C2—22no—
207C2—42no—
208C2—2962no—
209C2C2×#1192451011yescharacteristic
210C2#1455833312yes—
subgroupG/H
centerC2×C4C2×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×M16×C37C2
socleC22×C37C22×D4
hypercenterC22×M16D37
hypocenterC37#3054
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11924558C2semidirect
2. #14558044C2semidirect
3. #14557791C2semidirect
4. #14557786C2semidirect
5. #14557779C2semidirect
6. #14557571C2semidirect
7. #14557530C2semidirect
8. C22×M16×C37C2semidirect
11. C2×Dic148C22semidirect
12. C2×#10596930C22semidirect
13. C2×D296C22semidirect
20. #11924470C22semidirect
21. #11924468C22semidirect
22. #11924461C22semidirect
23. #11924458C22semidirect
47. C2×C8×C37D4semidirect
107. C22×M16D37semidirect
114. C37#3054semidirect
156. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245582
#145580442
#145577912
#145577862
#145577792
#145575712
#145575302
C22×M16×C372
#305437