Finite Group Databasebeta

← #18004525

Subgroups — #18004525

Order 4736.

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

normal subgroups only

This group has 414 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×#11924495C211yesmaximal, characteristic, complemented
2#14557871C214yesmaximal, complemented
3#14557854C214yesmaximal, complemented
4#14557576C212yesmaximal, complemented
5#14557534C212yesmaximal, complemented
6#14557497C211yesmaximal, characteristic, complemented
7C37×#525C211yesmaximal, characteristic
8C2×#10596934C2212yes—
9#11924495—22no—
10#11924495C2214yes—
11C2×C4⋊Dic37C2212yes—
12C2×C22⋊Dic37—21no—
13C2×C4×Dic37—21no—
14#11924469C2214yescomplemented
15#11924467C2214yescomplemented
16#11924460C2214yescomplemented
17#11924457C2214yescomplemented
18C22⋊#64436C2214yes—
19C2×#41×C37C2211yescharacteristic
20C23×C4×C37C2211yescharacteristic
21#123×C37—21no—
22C22⋊Q8×C37C2212yes—
23#121×C37C2212yes—
24#120×C37—21no—
25C4×D4×C37—22no—
26#117×C37C2211yescharacteristic
27C24×C37D411yescharacteristic
28#41×C37—24no—
29C2×Q8×C37C2311yescharacteristic
30C2×D4×C37—22no—
31C2×D4×C37—21no—
32C2×D4×C37C2311yescharacteristic
33C22×C4×C37—24no—
34C22×C4×C37—21no—
35C22×C4×C37D411yescharacteristic
36C22×C4×C37D412yes—
37C22×C4×C37C2312yes—
38C22×C4×C37C2311yescharacteristic
39C22×Dic37—22no—
40C4⋊C4×C37—22no—
41C4⋊C4×C37C2312yes—
42C22⋊C4×C37—21no—
43C22⋊C4×C37—22no—
44C22⋊C4×C37—22no—
45C42×C37—21no—
46C22⋊Dic37—24no—
47C4⋊Dic37—22no—
48C4⋊Dic37C2314yes—
49C4×Dic37—24no—
50#10596934—24no—
51C2×#64436C2314yes—
52C23×C37—22no—
53C23×C37—21no—
54C23×C37—42no—
55C23×C37C2×D412yes—
56C23×C37C2×D411yescharacteristic
57Q8×C37—22no—
58D4×C37—22no—
59D4×C37—44no—
60D4×C37—42no—
61C2×C4×C37—22no—
62C2×C4×C37—24no—
63C2×C4×C37—24no—
64C2×C4×C37—22no—
65C2×C4×C37—21no—
66C2×C4×C37—42no—
67C2×C4×C37C2×D412yes—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37#4114yes—
70C2×C4×C37C2411yescharacteristic
71C2×Dic37—24no—
72C2×Dic37—44no—
73#64436—24no—
74C22×C37—22no—
75C22×C37—22no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—44no—
79C22×C37—41no—
80C22×C37—42no—
81C22×C37#12312yes—
82C22×C37C22×D411yescharacteristic
83C4×C37—22no—
84C4×C37—41no—
85C4×C37—42no—
86C4×C37#12312yes—
87C4×C37C2×#4112yes—
88Dic37—44no—
89#3093—371nomaximal, Sylow
90C2×C37—22no—
91C2×C37—42no—
92C2×C37—81no—
93C2×C37C2×#12311yescharacteristic
94C2×C37#57512yes—
95#525D3711yescharacteristic
96C2×#117—371no—
97#485—374no—
98#482—374no—
99#428—372no—
100#417—372no—
101#407—371no—
102C37#309311yescharacteristic, complemented, Sylow
103C2×#41C2×D3711yescharacteristic
104C23×C4C2×D3711yescharacteristic
105C2×M16—372no—
106#123—21no—
107C22⋊Q8C2×D3712yes—
108#121C2×D3712yes—
109#120—21no—
110C4×D4—22no—
111#117—374no—
112#117—742no—
113#117C2×D3711yescharacteristic
114C2×C4⋊C4—372no—
115C2×C22⋊C4—741no—
116C2×C42—741no—
117#107—374no—
118#106—374no—
119#103—374no—
120#102—374no—
121C22⋊C8—374no—
122C24C22⋊D3711yescharacteristic
123#41—24no—
124C2×Q8C22×D3711yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D3711yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—742no—
131C22×C4C22⋊D3711yescharacteristic
132C22×C4C22⋊D3712yes—
133C22×C4C22×D3712yes—
134C22×C4C22×D3711yescharacteristic
135M16—744no—
136C2×C8—374no—
137C4⋊C4—22no—
138C4⋊C4—374no—
139C4⋊C4—742no—
140C4⋊C4C22×D3712yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—744no—
145C42—21no—
146C42—744no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D3712yes—
151C23C2×C22⋊D3711yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—744no—
163C2×C4—1484no—
164C2×C4#1059696414yes—
165C2×C4C2×C22⋊D3712yes—
166C2×C4C2×C22⋊D3711yescharacteristic
167C2×C4C23×D3711yescharacteristic
168C8—744no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#1192451712yes—
177C22C22×C22⋊D3711yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—1484no—
182C4#1192451712yes—
183C4C2×#1059696412yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#1192451711yescharacteristic
188C2#1455833112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#525C2
socleC22×C37C22×D4
hypercenter#525D37
hypocenterC37#3093
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11924495C2semidirect
2. #14557871C2semidirect
3. #14557854C2semidirect
4. #14557576C2semidirect
5. #14557534C2semidirect
6. #14557497C2semidirect
14. #11924469C22semidirect
15. #11924467C22semidirect
16. #11924460C22semidirect
17. #11924457C22semidirect
102. C37#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
#145578712
#145578542
#145575762
#145575342
#145574972
C37×#5252
#309337