Finite Group Databasebeta

← #18010038

Subgroups — #18010038

Order 4736.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558551C211yesmaximal, characteristic, complemented
2#14558478C211yesmaximal, characteristic, complemented
3#14558386C212yesmaximal, complemented
4#14558384C212yesmaximal
5#14558065C211yesmaximal, characteristic
6#11924603—21no—
7#11924593C2212yes—
8C4×#64438—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12#11924529—21no—
13#11924527C411yescharacteristic, complemented
14#11924523C411yescharacteristic, complemented
15#11924518—21no—
16#11924516C2211yescharacteristic
17#11924507C2211yescharacteristic
18C4×Dic74C411yescharacteristic, complemented
19C4×C22⋊D37—21no—
20#11924495—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37—21no—
26C2×C22⋊D37—21no—
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37C2311yescharacteristic
30C2×Dic74C2×C411yescharacteristic
31C2×#64438—22no—
32C4⋊C4×C37C2×C411yescharacteristic
33C22⋊C4×C37—21no—
34C42×C37C2×C411yescharacteristic
35C22⋊Dic37—21no—
36C22⋊Dic37—21no—
37C22⋊Dic37—21no—
38#10596938—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C23×C37—21no—
49C22×D37C2×D411yescharacteristic
50C2×#3866—42no—
51C2×#3866—42no—
52C2×#3866—42no—
53D4×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—42no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C22⋊D37—42no—
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C4×D37—22no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—41no—
69#64438—42no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37—41no—
73C22×C37C2×C22⋊C411yescharacteristic
74C2×D37—21no—
75C2×D37—21no—
76C2×D37#13512yes—
77#3866—82no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—41no—
82Dic37—21no—
83Dic37—21no—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87#1521—371nomaximal, Sylow
88C2×C37—81no—
89C2×C37#41011yescharacteristic
90C2×C37#41611yescharacteristic
91C2×C37#42111yescharacteristic
92D37—22no—
93#529—371no—
94#431—371no—
95#383—371no—
96#328—372no—
97#327—372no—
98C37#152111yescharacteristic, complemented, Sylow
99#126—741no—
100#125—371no—
101#124—371no—
102#123—741no—
103C22⋊Q8—371no—
104#121—371no—
105C4×Q8—371no—
106C4×D4—741no—
107C4×D4#386611yescharacteristic, complemented
108#117—741no—
109C2×C42—371no—
110C4⋊C8—741no—
111C22⋊C8—372no—
112C4×C8—741no—
113#95—372no—
114#95—741no—
115#95—741no—
116C2×Q8—371no—
117C2×D4—741no—
118C2×D4C2×#386611yescharacteristic
119C22×C4—21no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—742no—
124C2×C8—742no—
125C4⋊C4—371no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4C2×#386611yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C22⋊C4—741no—
136C42—371no—
137C42—371no—
138C42—371no—
139C42—741no—
140C42C2×#386611yescharacteristic
141C23—21no—
142C23—371no—
143Q8—1481no—
144D4—41no—
145D4—1482no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—371no—
151C2×C4—742no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—1481no—
155C2×C4—1481no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4C22⋊#386611yescharacteristic
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22×#386611yescharacteristic
162C8—1482no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—372no—
167C22—741no—
168C22—741no—
169C22C2×C22⋊#386611yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—2962no—
175C4—741no—
176C4—741no—
177C4—741no—
178C4—1481no—
179C4—1481no—
180C2—81no—
181C2—742no—
182C2#1455851211yescharacteristic
183C2#1455852311yescharacteristic
184C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924507C22
cosocleC2×C4×D37C23
hypercenterC4×D4#3866
hypocenterC37#1521
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. #14558478C2semidirect
3. #14558386C2semidirect
13. #11924527C4semidirect
14. #11924523C4semidirect
18. C4×Dic74C4semidirect
22. C4×D4×C37C4semidirect
98. C37#1521semidirect
107. C4×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145584782
#145583862
#145583842
#145580652
#152137