Finite Group Databasebeta

← #18010040

Subgroups — #18010040

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#14558387C212yesmaximal, complemented
4#14558385C212yesmaximal
5#14558070C211yesmaximal, characteristic
6#11924603—21no—
7#11924593C2212yes—
8C4×#64438—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12#11924531—21no—
13#11924527C411yescharacteristic, complemented
14#11924525C411yescharacteristic, complemented
15#11924521—21no—
16#11924512C2211yescharacteristic
17#11924511C2211yescharacteristic
18C4×D148—21no—
19C4×D148C411yescharacteristic, complemented
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D148—21no—
26C2×D148C2×C411yescharacteristic
27C2×C4×D37—21no—
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37C2311yescharacteristic
31C2×#64438—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C42×C37—21no—
35C42×C37C2×C411yescharacteristic
36#10596938—21no—
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C22×D37—21no—
49C22×D37C2×D411yescharacteristic
50C2×#3866—42no—
51C2×#3866—42no—
52C2×#3866—42no—
53Q8×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63D148—41no—
64D148—42no—
65C4×D37—22no—
66C4×D37—41no—
67C4×D37—41no—
68C4×D37—42no—
69#64438—42no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C2×D37#13512yes—
77#3866—82no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—41no—
82C4×C37—41no—
83Dic37—21no—
84Dic37—21no—
85Dic37—21no—
86Dic37—41no—
87#1521—371nomaximal, Sylow
88C2×C37#41011yescharacteristic
89C2×C37#41611yescharacteristic
90C2×C37#42111yescharacteristic
91D37—22no—
92D37—81no—
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#386611yescharacteristic, complemented
106C4×D4—371no—
107C4×D4—741no—
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×Q8C2×#386611yescharacteristic
117C2×D4—371no—
118C2×D4—741no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—741no—
123C22×C4—742no—
124C2×C8—742no—
125C4⋊C4—21no—
126C4⋊C4—371no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4C2×#386611yescharacteristic
131C22⋊C4—741no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C22⋊C4—741no—
136C42—21no—
137C42—371no—
138C42—371no—
139C42—371no—
140C42C2×#386611yescharacteristic
141C23—371no—
142C23—741no—
143Q8—41no—
144D4—1481no—
145D4—1482no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—371no—
151C2×C4—742no—
152C2×C4—741no—
153C2×C4—1481no—
154C2×C4—1481no—
155C2×C4—1482no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4C22⋊#386611yescharacteristic
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22×#386611yescharacteristic
162C8—1482no—
163C22—372no—
164C22—741no—
165C22—741no—
166C22—1481no—
167C22—1481no—
168C22—1481no—
169C22C2×C22⋊#386611yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2962no—
176C4—741no—
177C4—741no—
178C4—741no—
179C4—1481no—
180C2—2961no—
181C2—742no—
182C2#1455851211yescharacteristic
183C2#1455852311yescharacteristic
184C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924511C22
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1521
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. #14558478C2semidirect
3. #14558387C2semidirect
13. #11924527C4semidirect
14. #11924525C4semidirect
19. C4×D148C4semidirect
22. C4×Q8×C37C4semidirect
98. C37#1521semidirect
105. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145584782
#145583872
#145583852
#145580702
#152137