Finite Group Databasebeta

← #17993113

Subgroups — #17993113

Order 4736.

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

normal subgroups only

This group has 346 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
1C2×#11924510C211yesmaximal, characteristic
2C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
3#14557268C214yesmaximal, complemented
4C37×#407C211yesmaximal, characteristic, complemented
5C22×D148C411yescharacteristic, complemented
6C22×C22⋊D37—21no—
7#11924510—21no—
8#11924510—21no—
9#11924510C412yescomplemented
10#11924510C2212yes—
11C2×C4⋊Dic37C411yescharacteristic, complemented
12C2×C22⋊Dic37—21no—
13C2×#10596938—21no—
14C2×C4×Dic37—21no—
15#11924443C2212yescomplemented
16C23×C4×C37C2211yescharacteristic
17C2×M16×C37—21no—
18C22⋊C8×C37—21no—
19C22⋊C8×C37C2212yescomplemented
20C24×C37D411yescharacteristic
21C23×D37—21no—
22C22×C4×C37—42no—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—44no—
32C22×Dic37—21no—
33C22×Dic37—22no—
34C2×D148—21no—
35C2×D148—42no—
36C2×D148C2×C412yes—
37M16×C37—42no—
38C2×C8×C37—22no—
39C22⋊Dic37—24no—
40#10596938—22no—
41#10596938—22no—
42C4⋊Dic37—21no—
43C4⋊Dic37C2×C412yes—
44C4×Dic37—42no—
45C23×C37—22no—
46C23×C37—22no—
47C23×C37—41no—
48C23×C37C22⋊C411yescharacteristic
49C23×C37C22⋊C411yescharacteristic
50C23×C37C2×D411yescharacteristic
51C22×D37—22no—
52C22×D37—42no—
53C22×D37—42no—
54C22×D37—42no—
55C2×C4×C37—22no—
56C2×C4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C22⋊D37—44no—
66C22⋊D37—44no—
67C2×Dic37—24no—
68C2×Dic37—22no—
69C2×Dic37—42no—
70C2×Dic37—42no—
71C2×Dic37—42no—
72D148—42no—
73D148—42no—
74C8×C37—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—21no—
82C22×C37—44no—
83C22×C37#10412yes—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37AGL(1,ℤ/8)12yes—
86C2×D37—42no—
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—84no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—21no—
93C4×C37#9912yes—
94Dic37—44no—
95Dic37—42no—
96#1507—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37—22no—
99C2×C37—41no—
100C2×C37C2×#9911yescharacteristic
101C2×C37#41811yescharacteristic
102C2×C37C2×#10411yescharacteristic
103D37—82no—
104C2×#121—371no—
105#407D3711yescharacteristic, complemented
106C4×C22⋊C4—371no—
107#327—374no—
108C37#150711yescharacteristic, complemented, Sylow
109C22×D4—371no—
110C22×D4—741no—
111C23×C4C2×D3711yescharacteristic
112C2×M16—21no—
113#121—372no—
114#121—372no—
115#121—741no—
116#121—741no—
117C2×C4⋊C4—371no—
118C2×C22⋊C4—741no—
119C2×C22⋊C4—741no—
120C2×C42—741no—
121C22⋊C8—21no—
122C22⋊C8C2×D3712yescomplemented
123#95—372no—
124C24—741no—
125C24D14811yescharacteristic
126C2×D4—372no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—741no—
130C2×D4—1482no—
131C2×D4—1484no—
132C22×C4—42no—
133C22×C4—741no—
134C22×C4—742no—
135C22×C4C4×D3711yescharacteristic
136C22×C4C4×D3711yescharacteristic
137C22×C4D14811yescharacteristic
138C22×C4C22⋊D3711yescharacteristic
139C22×C4C22⋊D3711yescharacteristic
140C22×C4C22×D3711yescharacteristic
141M16—42no—
142C2×C8—22no—
143C4⋊C4—372no—
144C4⋊C4—741no—
145C22⋊C4—744no—
146C22⋊C4—742no—
147C22⋊C4—742no—
148C42—1482no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—742no—
153C23—1482no—
154C23—1482no—
155C23—1482no—
156C23#1059693811yescharacteristic
157C23#1059693811yescharacteristic
158C23C2×D14811yescharacteristic
159D4—1482no—
160D4—1484no—
161D4—1484no—
162D4—1482no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—744no—
170C2×C4—742no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4#1059693811yescharacteristic
175C2×C4#1059693811yescharacteristic
176C2×C4C2×C4×D3711yescharacteristic
177C2×C4C2×C22⋊D3711yescharacteristic
178C8—42no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—2964no—
188C22—1482no—
189C22—1482no—
190C22—1482no—
191C22#1192446212yes—
192C22C2×#1059693811yescharacteristic
193C22#1192456412yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—1484no—
198C4—1482no—
199C4#1192445012yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—2962no—
204C2C2×#1192445011yescharacteristic
205C2#1455753911yescharacteristic
206C2C2×#1192446211yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#407C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924510C2
cosocleC22×C4×C37C23
hypercenter#407D37
hypocenterC37#1507
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic37C2semidirect
3. #14557268C2semidirect
4. C37×#407C2semidirect
5. C22×D148C4semidirect
9. #11924510C4semidirect
11. C2×C4⋊Dic37C4semidirect
15. #11924443C22semidirect
19. C22⋊C8×C37C22semidirect
105. #407D37semidirect
108. C37#1507semidirect
122. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245102
C4×C22⋊Dic372
#145572682
C37×#4072
#150737