Finite Group Databasebeta

← #17992720

Subgroups — #17992720

Order 4736.

232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11924451C211yesmaximal, characteristic
2#14557436C211yesmaximal, characteristic
3C2×#99×C37C211yesmaximal, characteristic
4C2×C4⋊Dic37C411yescharacteristic, complemented
5C2×C22⋊Dic37—21no—
6C2×C22⋊Dic37—21no—
7C2×C22⋊Dic37—21no—
8C2×C4×Dic37C411yescharacteristic, complemented
9#11924451—21no—
10#11924451C412yescomplemented
11C22×D4×C37C2211yescharacteristic
12C2×C22⋊C4×C37—21no—
13#99×C37—21no—
14#99×C37C412yescomplemented
15C24×C37D411yescharacteristic
16C24×C37D411yescharacteristic
17C2×D4×C37—41no—
18C2×D4×C37—41no—
19C2×D4×C37C2×C411yescharacteristic
20C2×D4×C37C2×C411yescharacteristic
21C2×D4×C37D411yescharacteristic
22C2×D4×C37Q811yescharacteristic
23C22×C4×C37—41no—
24C22×C4×C37C2×C411yescharacteristic
25C22×Dic37—21no—
26C22×Dic37—21no—
27C22×Dic37—41no—
28C22⋊C4×C37—22no—
29C22⋊C4×C37—41no—
30C22⋊Dic37—22no—
31C22⋊Dic37—42no—
32C22⋊Dic37—42no—
33C22⋊Dic37—41no—
34C4⋊Dic37—41no—
35C4×Dic37—41no—
36C23×C37—21no—
37C23×C37—21no—
38C23×C37—21no—
39C23×C37—21no—
40C23×C37—41no—
41C23×C37—41no—
42C23×C37—41no—
43C23×C37—41no—
44C23×C37C22⋊C411yescharacteristic
45C23×C37C22⋊C411yescharacteristic
46C23×C37C22⋊C411yescharacteristic
47C23×C37C4⋊C411yescharacteristic
48C23×C37C4⋊C411yescharacteristic
49D4×C37—41no—
50D4×C37—41no—
51D4×C37—41no—
52D4×C37—41no—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—42no—
56C2×C4×C37—81no—
57C2×C4×C37—81no—
58C2×C4×C37C4211yescharacteristic
59C2×C4×C37C4⋊C411yescharacteristic
60C2×Dic37—22no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37—42no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67C2×Dic37—81no—
68C2×Dic37—81no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—81no—
84C22×C37—81no—
85C22×C37#9511yescharacteristic
86C22×C37#9911yescharacteristic
87C22×C37#9911yescharacteristic
88C4×C37—21no—
89C4×C37—21no—
90C4×C37—82no—
91Dic37—42no—
92Dic37—82no—
93Dic37—81no—
94#1393—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37—41no—
98C2×C37—41no—
99C2×C37—41no—
100C2×C37—41no—
101C2×C37#34211yescharacteristic
102C2×C37#35311yescharacteristic
103C2×C37#35411yescharacteristic
104C2×#99—371no—
105C2×#99D3711yescharacteristic
106#390—371no—
107C37#139311yescharacteristic, complemented, Sylow
108C22×D4C2×D3711yescharacteristic
109C2×C4⋊C4—371no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—741no—
112C2×C22⋊C4—741no—
113C2×C22⋊C4—741no—
114C2×C42—371no—
115#99—21no—
116#99—372no—
117#99—741no—
118#99Dic3712yescomplemented
119C24D14811yescharacteristic
120C24C22⋊D3711yescharacteristic
121C2×D4—41no—
122C2×D4—41no—
123C2×D4Dic7411yescharacteristic
124C2×D4C4×D3711yescharacteristic
125C2×D4C2×Dic3711yescharacteristic
126C2×D4C22⋊D3711yescharacteristic
127C22×C4—41no—
128C22×C4—741no—
129C22×C4—741no—
130C22×C4—1481no—
131C22×C4C4×D3711yescharacteristic
132C4⋊C4—1481no—
133C22⋊C4—22no—
134C22⋊C4—41no—
135C22⋊C4—742no—
136C22⋊C4—1482no—
137C22⋊C4—1482no—
138C22⋊C4—1481no—
139C42—1481no—
140C23—21no—
141C23—21no—
142C23—21no—
143C23—21no—
144C23—41no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23#1059693611yescharacteristic
149C23C4⋊Dic3711yescharacteristic
150C23#1059693811yescharacteristic
151C23#1059693811yescharacteristic
152C23C22⋊Dic3711yescharacteristic
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—2961no—
163C2×C4—2961no—
164C2×C4—742no—
165C2×C4—1482no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4C4×Dic3711yescharacteristic
172C2×C4#1059693611yescharacteristic
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22—81no—
189C22#1192444311yescharacteristic
190C22#1192445011yescharacteristic
191C22#1192445011yescharacteristic
192C4—21no—
193C4—21no—
194C4—82no—
195C4—2962no—
196C4—2961no—
197C4—1482no—
198C2—21no—
199C2—21no—
200C2—41no—
201C2—41no—
202C2—41no—
203C2—41no—
204C2#1455729911yescharacteristic
205C2#1455732511yescharacteristic
206C2#1455732711yescharacteristic
subgroupG/H
centerC22#11924450
commutatorC2×C4×C37C42
FrattiniC22×D4C2×D37
FittingC2×#99×C37C2
socleC22×C37#99
prime radical, cosocleC22×D4×C37C22
hypercenterC2×#99D37
hypocenterC37#1393
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic37C4semidirect
8. C2×C4×Dic37C4semidirect
10. #11924451C4semidirect
14. #99×C37C4semidirect
107. C37#1393semidirect
118. #99Dic37semidirect

Maximal subgroups

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

subgroupindex
C2×#119244512
#145574362
C2×#99×C372
#139337