Finite Group Databasebeta

← #18009871

Subgroups — #18009871

Order 4736.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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
1#14558504C211yesmaximal, characteristic, complemented
2D37⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#14558376C214yesmaximal, complemented
4C2×#11924507C211yesmaximal, characteristic
5C2×#10596953—21no—
6C2×D37⋊C8—21no—
7#11924593—21no—
8#11924593—21no—
9C22⋊#64438C2212yes—
10C22⋊#64438C2212yes—
11C22×C22⋊D37C412yes—
12C22×C4×D37C2211yescharacteristic
13#11924507—21no—
14#11924507—21no—
15#11924507—21no—
16#11924507—21no—
17C2×C4⋊Dic37C411yescharacteristic
18C2×C22⋊Dic37C2212yes—
19C22×D4×C37C411yescharacteristic
20C24×C37C2×C412yes—
21C23×D37C2×C411yescharacteristic
22C2×D4×C37—21no—
23C2×D4×C37—21no—
24C2×D4×C37—42no—
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—22no—
27C2×C22⋊D37—22no—
28C2×C22⋊D37—44no—
29C22×Dic37C2×C412yes—
30C22×Dic37C2311yescharacteristic
31C2×C4×D37—42no—
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×#64438—22no—
37C2×#64438—22no—
38#10596953—42no—
39D37⋊C8—42no—
40C22⋊Dic37—22no—
41C22⋊Dic37—22no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44C23×C37—22no—
45C23×C37—24no—
46C23×C37—42no—
47C23×C37—42no—
48C23×C37C22×C411yescharacteristic
49C22×D37—22no—
50C22×D37—22no—
51C22×D37—41no—
52C22×D37C22⋊C411yescharacteristic
53C22×D37C22⋊C411yescharacteristic
54D4×C37—42no—
55D4×C37—42no—
56C2×C4×C37—22no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C22⋊D37—44no—
60C22⋊D37—44no—
61C2×Dic37—22no—
62C2×Dic37—41no—
63C2×Dic37—42no—
64C2×Dic37C2×D411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66C4×D37—22no—
67C4×D37—22no—
68C4×D37—41no—
69C4×D37—41no—
70#64438—42no—
71#64438—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—42no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—84no—
78C22×C37C2×C22⋊C411yescharacteristic
79C22×C37#13112yes—
80C2×D37—21no—
81C2×D37—21no—
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—44no—
86C2×D37#10012yes—
87C4×C37—21no—
88C4×C37#9912yes—
89Dic37—21no—
90Dic37—21no—
91Dic37—42no—
92#1471—371nomaximal, Sylow
93C2×C37—22no—
94C2×C37—82no—
95C2×C37#40811yescharacteristic
96C2×C37C2×#9911yescharacteristic
97C2×C37C2×#10011yescharacteristic
98D37—22no—
99D37—41no—
100C2×#121—371no—
101#407—371no—
102C2×C22⋊C8—371no—
103#323—374no—
104C37#147111yescharacteristic, complemented, Sylow
105C22×D4—372no—
106C22×D4#386611yescharacteristic
107C23×C4—371no—
108C2×M16—741no—
109C22×C8—741no—
110#121—741no—
111#121—741no—
112#121—741no—
113#121—741no—
114C2×C4⋊C4—371no—
115C2×C22⋊C4—372no—
116C22⋊C8—372no—
117C22⋊C8—372no—
118C22⋊C8—741no—
119C22⋊C8—741no—
120C24—371no—
121C24C2×#386612yes—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—42no—
125C2×D4—742no—
126C2×D4—742no—
127C2×D4—1484no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—372no—
134C22×C4—1482no—
135C22×C4C2×#386611yescharacteristic
136M16—1482no—
137C2×C8—742no—
138C2×C8—742no—
139C2×C8—1482no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C23—22no—
145C23—24no—
146C23—42no—
147C23—42no—
148C23—371no—
149C23—371no—
150C23—742no—
151C23—742no—
152C23—1481no—
153C23C22×#386611yescharacteristic
154D4—42no—
155D4—42no—
156D4—1484no—
157D4—1484no—
158C2×C4—22no—
159C2×C4—371no—
160C2×C4—371no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—742no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4—1481no—
167C2×C4—1482no—
168C2×C4C22⋊#386611yescharacteristic
169C2×C4C22⋊#386611yescharacteristic
170C8—1482no—
171C8—1482no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—84no—
178C22—372no—
179C22—741no—
180C22—741no—
181C22—741no—
182C22—741no—
183C22—741no—
184C22—1484no—
185C22C2×C22⋊#386611yescharacteristic
186C22#1192462312yes—
187C4—21no—
188C4—741no—
189C4—741no—
190C4—1482no—
191C4#1192459412yes—
192C2—22no—
193C2—82no—
194C2—742no—
195C2—1481no—
196C2#1455850711yescharacteristic
197C2C2×#1192459411yescharacteristic
198C2D37⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC22×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924507C2
cosocleC22×Dic37C23
hypercenterC22×D4#3866
hypocenterC37#1471
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558504C2semidirect
2. D37⋊(C22⋊C8)C2semidirect
3. #14558376C2semidirect
104. C37#1471semidirect

Maximal subgroups

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

subgroupindex
#145585042
D37⋊(C22⋊C8)2
#145583762
C2×#119245072
#147137