Finite Group Databasebeta

← #18009910

Subgroups — #18009910

Order 4736.

212 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558552C211yesmaximal, characteristic, complemented
2#14558552C211yesmaximal, characteristic, complemented
3#14558383C212yesmaximal, complemented
4#14558381C212yesmaximal, complemented
5#14558068C211yesmaximal, characteristic
6C4⋊#64438—21no—
7C4⋊#64438C2212yes—
8#11924593—21no—
9#11924593—21no—
10C4×#64438—21no—
11C4×#64438C2212yes—
12#11924531—21no—
13#11924524C411yescharacteristic
14#11924521—21no—
15#11924516C411yescharacteristic
16#11924511C411yescharacteristic
17#11924501C2211yescharacteristic
18#11924498—21no—
19#11924498C2211yescharacteristic
20#11924494—21no—
21C42×D37C2211yescharacteristic
22#125×C37C411yescharacteristic
23C2×D148—21no—
24C2×D148C2×C411yescharacteristic
25C2×C4×D37—21no—
26C2×C4×D37C2×C411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×Dic74C2×C411yescharacteristic
30C2×#64438—22no—
31C2×#64438—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37C2×C411yescharacteristic
35C4⋊C4×C37C2×C411yescharacteristic
36C42×C37C2×C411yescharacteristic
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41#10596938—21no—
42C4⋊Dic37—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37D411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37C2311yescharacteristic
48C22×D37—21no—
49C22×D37C22⋊C411yescharacteristic
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C2×D411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59D148—22no—
60D148—42no—
61C4×D37—22no—
62C4×D37—22no—
63C4×D37—41no—
64C4×D37—42no—
65Dic74—22no—
66#64438—42no—
67#64438—42no—
68C22×C37C2×C22⋊C411yescharacteristic
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—21no—
72C2×D37—41no—
73C2×D37—41no—
74C2×D37—41no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79C4×C37#13112yes—
80Dic37—21no—
81Dic37—21no—
82Dic37—41no—
83Dic37#13512yes—
84#1482—371nomaximal, Sylow
85C2×C37#40811yescharacteristic
86C2×C37#41611yescharacteristic
87C2×C37#42111yescharacteristic
88D37—41no—
89D37—81no—
90#529—371no—
91#431—371no—
92#431—371no—
93Q8⋊C8—372no—
94D4⋊C8—372no—
95C37#148211yescharacteristic, complemented, Sylow
96#126—741no—
97#125#386611yescharacteristic
98#124—371no—
99#123—741no—
100C22⋊Q8—371no—
101#121—371no—
102C4×Q8—371no—
103C4×D4—371no—
104C4×D4—741no—
105#117—741no—
106C2×C42—371no—
107C4⋊C8—372no—
108C4⋊C8—741no—
109C22⋊C8—741no—
110C22⋊C8—741no—
111C4×C8—372no—
112C4×C8—741no—
113C2×Q8—371no—
114C2×D4—371no—
115C2×D4—741no—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—741no—
120C2×C8—742no—
121C2×C8—742no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4C2×#386611yescharacteristic
127C4⋊C4C2×#386611yescharacteristic
128C22⋊C4—741no—
129C22⋊C4—741no—
130C22⋊C4—741no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C42—371no—
134C42—371no—
135C42—371no—
136C42—741no—
137C42C2×#386611yescharacteristic
138C23—371no—
139C23—741no—
140Q8—742no—
141D4—742no—
142D4—1482no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—371no—
148C2×C4—742no—
149C2×C4—742no—
150C2×C4—741no—
151C2×C4—1481no—
152C2×C4—1482no—
153C2×C4C22⋊#386611yescharacteristic
154C2×C4C22⋊#386611yescharacteristic
155C2×C4C22×#386611yescharacteristic
156C8—1482no—
157C8—1482no—
158C22—741no—
159C22—741no—
160C22—741no—
161C22—1481no—
162C22—1481no—
163C22—1481no—
164C22C2×C22⋊#386611yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—372no—
170C4—741no—
171C4—741no—
172C4—1481no—
173C4#1192462412yes—
174C2—2961no—
175C2—1481no—
176C2#1455850811yescharacteristic
177C2#1455852311yescharacteristic
178C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#125×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC4×Dic37C23
hypercenter#125#3866
hypocenterC37#1482
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #14558552C2semidirect
2. #14558552C2semidirect
3. #14558383C2semidirect
4. #14558381C2semidirect
95. C37#1482semidirect

Maximal subgroups

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

subgroupindex
#145585522
#145583832
#145583812
#145580682
#148237