Finite Group Databasebeta

← #17992913

Subgroups — #17992913

Order 4736.

332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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×#11924498C211yesmaximal, characteristic
2C22⋊C8×D37C212yesmaximal, complemented
3#14557259C211yesmaximal, characteristic, complemented
4#14557256C212yesmaximal, complemented
5C37×#324C211yesmaximal, characteristic, complemented
6C22×D148C411yescharacteristic
7C22×C4×D37C411yescharacteristic
8C22×C4×D37C2211yescharacteristic
9C2×C8×D37—22no—
10#11924498—22no—
11#11924498—22no—
12C2×#10596938C411yescharacteristic
13C2×#10596938C2211yescharacteristic
14C2×C4×Dic37C411yescharacteristic
15C22⋊#64436C2212yes—
16#11924448—22no—
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C23×D37C2×C411yescharacteristic
20C23×D37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37C2311yescharacteristic
24C22×Dic37C2×C411yescharacteristic
25C22×Dic37C2×C411yescharacteristic
26C2×D148—22no—
27C2×D148—22no—
28C2×D148C814yescomplemented
29C2×C4×D37—21no—
30C2×C4×D37—21no—
31C2×C4×D37—42no—
32C2×C4×D37—42no—
33C2×C4×D37D412yes—
34C2×C4×D37D412yes—
35C2×C8×C37—22no—
36C4⋊C4×C37—22no—
37#10596938—22no—
38#10596938—22no—
39C4×Dic37—21no—
40C4×Dic37—21no—
41C2×#64436—22no—
42C8×D37—44no—
43C23×C37C22×C411yescharacteristic
44C22×D37—21no—
45C22×D37—21no—
46C22×D37—41no—
47C22×D37—41no—
48C22×D37—41no—
49C22×D37—41no—
50C22×D37C22⋊C412yes—
51C22×D37C2×C812yes—
52C22×D37C2×C812yescomplemented
53C22×D37M1612yes—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×C812yescomplemented
60C2×C4×C37C2×D412yes—
61C2×Dic37—22no—
62C2×Dic37—21no—
63C2×Dic37—41no—
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C22⋊C411yescharacteristic
66D148—28no—
67C4×D37—24no—
68C4×D37—42no—
69C4×D37—42no—
70C4×D37—42no—
71C8×C37—42no—
72#64436—42no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37C2×C22⋊C411yescharacteristic
76C22×C37C22×C811yescharacteristic
77C22×C37C2×M1611yescharacteristic
78C2×D37—22no—
79C2×D37—22no—
80C2×D37—22no—
81C2×D37—42no—
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—42no—
87C2×D37C22⋊C814yes—
88C4×C37—22no—
89C4×C37—22no—
90C4×C37—41no—
91Dic37—21no—
92Dic37—41no—
93Dic37#9912yes—
94#1459—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37C2×C22⋊C811yescharacteristic
98C2×C37C2×#9911yescharacteristic
99C2×C37#41311yescharacteristic
100D37—24no—
101D37—42no—
102C2×C4×D4—371no—
103C2×C22⋊C8—372no—
104#324—371no—
105#324D3711yescharacteristic, complemented
106#323—372no—
107C37#145911yescharacteristic, complemented, Sylow
108C22×D4—371no—
109C23×C4—371no—
110C23×C4—371no—
111C22×C8—742no—
112C4×D4—742no—
113C4×D4—742no—
114C2×C4⋊C4C2×D3711yescharacteristic
115C2×C22⋊C4—371no—
116C2×C22⋊C4—371no—
117C2×C42—371no—
118C22⋊C8—372no—
119C22⋊C8—742no—
120C22⋊C8C2×D3712yes—
121C24—371no—
122C24—371no—
123C2×D4—374no—
124C2×D4—742no—
125C2×D4—742no—
126C22×C4—371no—
127C22×C4—372no—
128C22×C4—372no—
129C22×C4—371no—
130C22×C4—741no—
131C22×C4—741no—
132C22×C4—1482no—
133C22×C4—1482no—
134C22×C4C4×D3711yescharacteristic
135C22×C4C4×D3711yescharacteristic
136C22×C4C22×D3711yescharacteristic
137C2×C8—22no—
138C2×C8—742no—
139C2×C8—1484no—
140C4⋊C4—22no—
141C22⋊C4—742no—
142C22⋊C4—742no—
143C42—741no—
144C42—741no—
145C23—372no—
146C23—372no—
147C23—372no—
148C23—372no—
149C23—741no—
150C23—741no—
151C23—1481no—
152C23—1481no—
153C23—1481no—
154C23—1481no—
155C23C2×C4×D3711yescharacteristic
156D4—748no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—744no—
165C2×C4—742no—
166C2×C4—741no—
167C2×C4—1482no—
168C2×C4—1482no—
169C2×C4—1482no—
170C2×C4—1481no—
171C2×C4C8×D3712yescomplemented
172C2×C4D4×D3712yes—
173C8—42no—
174C8—1482no—
175C22—21no—
176C22—21no—
177C22—374no—
178C22—742no—
179C22—742no—
180C22—742no—
181C22—1482no—
182C22—1482no—
183C22—1482no—
184C22—1482no—
185C22—1481no—
186C22—1481no—
187C22C22⋊C4×D3711yescharacteristic
188C22C2×C8×D3711yescharacteristic
189C22M16×D3711yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—372no—
194C4—741no—
195C4—1481no—
196C2—21no—
197C2—21no—
198C2—744no—
199C2—1482no—
200C2C22⋊C8×D3711yescharacteristic
201C2#99×D3711yescharacteristic
202C2#1455751611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC22×C37C22×C8
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC22×C4×C37C23
hypercenter#324D37
hypocenterC37#1459
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D37C2semidirect
3. #14557259C2semidirect
4. #14557256C2semidirect
5. C37×#324C2semidirect
28. C2×D148C8semidirect
52. C22×D37C2×C8semidirect
59. C2×C4×C37C2×C8semidirect
105. #324D37semidirect
107. C37#1459semidirect
171. C2×C4C8×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119244982
C22⋊C8×D372
#145572592
#145572562
C37×#3242
#145937