Finite Group Databasebeta

← #17993173

Subgroups — #17993173

Order 4736.

218 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 77 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#14557586C211yesmaximal, characteristic, complemented
2#14557401C211yesmaximal, characteristic, complemented
3#14557270C212yesmaximal, complemented
4#14557267C212yesmaximal
5C37×#529C211yesmaximal, characteristic
6C4⋊#64436—21no—
7C22⋊#64436C2212yes—
8C4×#64436—21no—
9#11924443—21no—
10#11924443—21no—
11#11924443C2212yes—
12#126×C37—21no—
13#125×C37C411yescharacteristic, complemented
14#124×C37C411yescharacteristic, complemented
15#123×C37—21no—
16C22⋊Q8×C37C2211yescharacteristic
17#121×C37C2211yescharacteristic
18C4×Q8×C37C411yescharacteristic, complemented
19C4×D4×C37—21no—
20C4×D4×C37C411yescharacteristic, complemented
21#117×C37—21no—
22C2×C42×C37C2211yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37—21no—
25C2×D4×C37C2×C411yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—22no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37C2×C411yescharacteristic
36C4⋊C4×C37C2×C411yescharacteristic
37C22⋊C4×C37—21no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C42×C37—21no—
43C42×C37C2×C411yescharacteristic
44C42×C37C2×C411yescharacteristic
45C42×C37D411yescharacteristic
46C42×C37D411yescharacteristic
47C2×#64436—22no—
48C23×C37—21no—
49C23×C37C2×D411yescharacteristic
50Q8×C37—41no—
51D4×C37—41no—
52D4×C37—42no—
53C2×C4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—42no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22×C411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×Dic37—42no—
67C2×Dic37—42no—
68C2×Dic37—42no—
69#64436—42no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C22×C37#13512yes—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—21no—
83C4×C37—41no—
84C4×C37—41no—
85C4×C37—41no—
86Dic37—82no—
87#1521—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37—81no—
90C2×C37#41011yescharacteristic
91C2×C37#41611yescharacteristic
92C2×C37#42111yescharacteristic
93#529D3711yescharacteristic
94#431—371no—
95#383—371no—
96#328—372no—
97#327—372no—
98C37#152111yescharacteristic, complemented, Sylow
99#126—21no—
100#125Dic3711yescharacteristic, complemented
101#124Dic3711yescharacteristic, complemented
102#123—21no—
103C22⋊Q8C2×D3711yescharacteristic
104#121C2×D3711yescharacteristic
105C4×Q8Dic3711yescharacteristic, complemented
106C4×D4—21no—
107C4×D4Dic3711yescharacteristic, complemented
108#117—21no—
109C2×C42C2×D3711yescharacteristic
110C4⋊C8—741no—
111C22⋊C8—372no—
112C4×C8—741no—
113#95—372no—
114#95—741no—
115#95—741no—
116C2×Q8C2×Dic3711yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic3711yescharacteristic
119C22×C4—21no—
120C22×C4—742no—
121C22×C4C22⋊D3711yescharacteristic
122C22×C4C22⋊D3711yescharacteristic
123C22×C4C22×D3711yescharacteristic
124C2×C8—742no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×Dic3711yescharacteristic
130C4⋊C4C2×Dic3711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42C2×Dic3711yescharacteristic
138C42C2×Dic3711yescharacteristic
139C42C22⋊D3711yescharacteristic
140C42C22⋊D3711yescharacteristic
141C23—21no—
142C23C2×C22⋊D3711yescharacteristic
143Q8—41no—
144D4—41no—
145D4—42no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—1482no—
154C2×C4—1482no—
155C2×C4—1482no—
156C2×C4C22⋊Dic3711yescharacteristic
157C2×C4C22⋊Dic3711yescharacteristic
158C2×C4C22⋊Dic3711yescharacteristic
159C2×C4C22⋊Dic3711yescharacteristic
160C2×C4C22×Dic3711yescharacteristic
161C2×C4C2×C22⋊D3711yescharacteristic
162C8—1482no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22C2×C22⋊Dic3711yescharacteristic
169C22#1192455612yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—2962no—
180C2—22no—
181C2—81no—
182C2#1455750711yescharacteristic
183C2#1455752911yescharacteristic
184C2#1455755011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#529C2
socleC22×C37C2×C22⋊C4
prime radical#121×C37C22
cosocleC22×C4×C37C23
hypercenter#529D37
hypocenterC37#1521
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14557586C2semidirect
2. #14557401C2semidirect
3. #14557270C2semidirect
13. #125×C37C4semidirect
14. #124×C37C4semidirect
18. C4×Q8×C37C4semidirect
20. C4×D4×C37C4semidirect
98. C37#1521semidirect
100. #125Dic37semidirect
101. #124Dic37semidirect
105. C4×Q8Dic37semidirect
107. C4×D4Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575862
#145574012
#145572702
#145572672
C37×#5292
#152137