Finite Group Databasebeta

← #18004177

Subgroups — #18004177

Order 4736.

520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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#14557774C212yesmaximal, complemented
4#14557769C212yesmaximal, complemented
5#14557762C214yesmaximal, complemented
6#14557571C211yesmaximal, characteristic, complemented
7#14557530C212yesmaximal, complemented
8C23×C8×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
25C22×C8×C37—24no—
26C22×C8×C37C2212yes—
27C22×C8×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—
44C2×C8×C37—22no—
45C2×C8×C37—24no—
46C2×C8×C37—24no—
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—24no—
62C23×C37C2×D411yescharacteristic
63C23×C37C2×D412yes—
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—44no—
75C22⋊D37—48no—
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—28no—
87C22×C37—22no—
88C22×C37—22no—
89C22×C37—22no—
90C22×C37#12112yes—
91C22×C37#13514yescomplemented
92C22×C37C22×D411yescharacteristic
93C2×D37—42no—
94C2×D37—44no—
95C4×C37—22no—
96C4×C37#12112yes—
97C4×C37C22×D411yescharacteristic
98C4×C37C2×#4111yescharacteristic
99Dic37—42no—
100Dic37—44no—
101#3050—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37—24no—
104C2×C37C2×#12111yescharacteristic
105C2×C37C2×#13512yes—
106D37—82no—
107C2×#135—371no—
108C23×C8D3711yescharacteristic, complemented
109#525—372no—
110#467—372no—
111#466—372no—
112#465—374no—
113#427—371no—
114#416—372no—
115C37#305011yescharacteristic, complemented, Sylow
116C2×#41—372no—
117C23×C4C2×D3711yescharacteristic
118#135—744no—
119C2×Q16—371no—
120C2×SD16—372no—
121C2×D8—371no—
122C22×C8—24no—
123C22×C8C2×D3711yescharacteristic
124C22×C8C2×D3712yes—
125C22×C8C2×D3712yes—
126C22×C8C2×D3711yescharacteristic
127#123—742no—
128C22⋊Q8—374no—
129#121—374no—
130#120—742no—
131C4×D4—744no—
132#117—372no—
133#107—372no—
134#106—372no—
135#103—374no—
136#102—374no—
137C24D14811yescharacteristic
138#41—744no—
139#41—744no—
140C2×Q8—372no—
141C2×D4—372no—
142C2×D4—744no—
143C2×D4—742no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—742no—
147C22×C4D14811yescharacteristic
148C22×C4D14812yes—
149C22×C4C22×D3712yes—
150C22×C4C22×D3711yescharacteristic
151Q16—742no—
152SD16—744no—
153D8—742no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8C22⋊D3714yescomplemented
158C2×C8C22×D3712yes—
159C2×C8C22×D3711yescharacteristic
160C2×C8C22×D3711yescharacteristic
161C4⋊C4—374no—
162C4⋊C4—744no—
163C22⋊C4—742no—
164C22⋊C4—744no—
165C22⋊C4—744no—
166C42—742no—
167C23—22no—
168C23—24no—
169C23—742no—
170C23C2×D14811yescharacteristic
171C23C2×D14812yes—
172Q8—742no—
173Q8—742no—
174D4—742no—
175D4—742no—
176D4—1484no—
177D4—1488no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—744no—
183C2×C4—742no—
184C2×C4—1484no—
185C2×C4C2×D14812yes—
186C2×C4C2×D14811yescharacteristic
187C2×C4#1059696212yes—
188C2×C4C2×C22⋊D3712yes—
189C2×C4C23×D3711yescharacteristic
190C8—22no—
191C8C2×C22⋊D3712yes—
192C8C2×C22⋊D3712yes—
193C22—28no—
194C22—22no—
195C22—22no—
196C22—22no—
197C22—1482no—
198C22—1484no—
199C22#1192451012yes—
200C22#1192455814yescomplemented
201C22C22×D14811yescharacteristic
202C4—22no—
203C4—1482no—
204C4—1484no—
205C4#1192451012yes—
206C4C22×C22⋊D3711yescharacteristic
207C4C2×#1059696211yescharacteristic
208C2—22no—
209C2—24no—
210C2—2962no—
211C2C2×#1192451011yescharacteristic
212C2C2×#1192455812yes—
subgroupG/H
centerC2×C4C2×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC23×C8×C37C2
socleC22×C37C22×D4
hypercenterC23×C8D37
hypocenterC37#3050
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C2×#11924558C2semidirect
2. #14558044C2semidirect
3. #14557774C2semidirect
4. #14557769C2semidirect
5. #14557762C2semidirect
6. #14557571C2semidirect
7. #14557530C2semidirect
8. C23×C8×C37C2semidirect
11. C2×Dic148C22semidirect
12. C2×#10596930C22semidirect
13. C2×D296C22semidirect
20. #11924470C22semidirect
21. #11924468C22semidirect
22. #11924461C22semidirect
23. #11924458C22semidirect
47. C2×C8×C37D4semidirect
91. C22×C37#135semidirect
108. C23×C8D37semidirect
115. C37#3050semidirect
157. C2×C8C22⋊D37semidirect
200. C22#11924558semidirect

Maximal subgroups

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

subgroupindex
C2×#119245582
#145580442
#145577742
#145577692
#145577622
#145575712
#145575302
C23×C8×C372
#305037