Finite Group Databasebeta

← #17993174

Subgroups — #17993174

Order 4736.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558067C211yesmaximal, characteristic
2#14557401C211yesmaximal, characteristic, complemented
3#14557271C212yesmaximal, complemented
4#14557268C212yesmaximal
5C37×#431C211yesmaximal, characteristic, complemented
6#11924530—21no—
7#11924528C411yescharacteristic, complemented
8#11924524C411yescharacteristic, complemented
9#11924519—21no—
10#11924515C2211yescharacteristic
11#11924510C2211yescharacteristic
12C4×Dic74C411yescharacteristic, complemented
13C4×D148C411yescharacteristic, complemented
14C4×C22⋊D37—21no—
15#11924493—21no—
16#11924443—21no—
17#11924443—21no—
18#11924443C2212yes—
19C2×C42×C37C2211yescharacteristic
20C4⋊C8×C37—21no—
21C22⋊C8×C37C2212yes—
22C4×C8×C37—21no—
23C22×C4×C37D411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C2×C22⋊D37—21no—
27C22×Dic37—22no—
28C2×D148C2×C411yescharacteristic
29C2×C4×D37—21no—
30C2×Dic74C2×C411yescharacteristic
31C2×C8×C37—22no—
32C42×C37C2×C411yescharacteristic
33C42×C37C2×C411yescharacteristic
34C42×C37D411yescharacteristic
35C42×C37D411yescharacteristic
36C22⋊Dic37—21no—
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37—21no—
48C23×C37C2×D411yescharacteristic
49C22×D37—21no—
50C2×C4×C37—22no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—42no—
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—42no—
64C2×Dic37—42no—
65C2×Dic37—42no—
66D148—41no—
67C4×D37—42no—
68Dic74—41no—
69C8×C37—42no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37C2×C22⋊C411yescharacteristic
73C22×C37#13512yes—
74C2×D37—41no—
75C2×D37—41no—
76C2×D37—41no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—21no—
83Dic37—41no—
84Dic37—41no—
85Dic37—41no—
86Dic37—82no—
87#1521—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37#41011yescharacteristic
90C2×C37#41611yescharacteristic
91C2×C37#42111yescharacteristic
92D37—81no—
93#529—371no—
94#431D3711yescharacteristic, complemented
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—371no—
107C4×D4—741no—
108#117—741no—
109C2×C42C2×D3711yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D3712yes—
112C4×C8—21no—
113#95—372no—
114#95—741no—
115#95—741no—
116C2×Q8—371no—
117C2×D4—371no—
118C2×D4—741no—
119C22×C4—741no—
120C22×C4—742no—
121C22×C4D14811yescharacteristic
122C22×C4D14811yescharacteristic
123C22×C4C22×D3711yescharacteristic
124C2×C8—22no—
125C4⋊C4—371no—
126C4⋊C4—371no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C22⋊C4—741no—
136C42—741no—
137C42C4×D3711yescharacteristic
138C42C4×D3711yescharacteristic
139C42C22⋊D3711yescharacteristic
140C42C22⋊D3711yescharacteristic
141C23—741no—
142C23C2×D14811yescharacteristic
143Q8—1481no—
144D4—1481no—
145D4—1482no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—1482no—
153C2×C4—1482no—
154C2×C4—1482no—
155C2×C4—1482no—
156C2×C4#1059693811yescharacteristic
157C2×C4#1059693811yescharacteristic
158C2×C4#1059693811yescharacteristic
159C2×C4#1059693811yescharacteristic
160C2×C4C2×C4×D3711yescharacteristic
161C2×C4C2×C22⋊D3711yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—1481no—
166C22—1481no—
167C22—1481no—
168C22C2×#1059693811yescharacteristic
169C22#1192455812yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—2962no—
177C4—1481no—
178C4—1481no—
179C4—1481no—
180C2—22no—
181C2—2961no—
182C2#1455750611yescharacteristic
183C2#1455753011yescharacteristic
184C2#1455754911yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#431C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C22
cosocleC22×C4×C37C23
hypercenter#431D37
hypocenterC37#1521
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #14557401C2semidirect
3. #14557271C2semidirect
5. C37×#431C2semidirect
7. #11924528C4semidirect
8. #11924524C4semidirect
12. C4×Dic74C4semidirect
13. C4×D148C4semidirect
94. #431D37semidirect
98. C37#1521semidirect

Maximal subgroups

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

subgroupindex
#145580672
#145574012
#145572712
#145572682
C37×#4312
#152137