Finite Group Databasebeta

← #17994696

Subgroups — #17994696

Order 4736.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11924495C211yesmaximal, characteristic
2#14557497C211yesmaximal, characteristic
3#14557293C214yesmaximal, complemented
4C4×C22⋊C4×C37C211yesmaximal, characteristic
5C2×#10596934C2212yes—
6#11924495—21no—
7#11924495—21no—
8#11924495C412yescomplemented
9#11924495C2212yes—
10C2×C4⋊Dic37C411yescharacteristic, complemented
11C2×C4⋊Dic37C411yescharacteristic, complemented
12C2×C22⋊Dic37—21no—
13C2×C4×Dic37—21no—
14C22⋊#64436—21no—
15C22⋊#64436—21no—
16C23×C4×C37C2211yescharacteristic
17C2×C22⋊C4×C37—21no—
18C2×C42×C37C2212yes—
19#95×C37—21no—
20C24×C37D411yescharacteristic
21C22×C4×C37—24no—
22C22×C4×C37—22no—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37—21no—
31C22⋊C4×C37—24no—
32C42×C37—24no—
33C22⋊Dic37—22no—
34C22⋊Dic37—22no—
35C4⋊Dic37—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37C2×C412yes—
38C4⋊Dic37C2×C412yes—
39C4×Dic37—22no—
40C4×Dic37—22no—
41#10596934—24no—
42C2×#64436—22no—
43C23×C37—22no—
44C23×C37—22no—
45C23×C37—41no—
46C23×C37C22⋊C411yescharacteristic
47C23×C37C22⋊C411yescharacteristic
48C23×C37C2×D411yescharacteristic
49C2×C4×C37—22no—
50C2×C4×C37—22no—
51C2×C4×C37—22no—
52C2×C4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37—24no—
55C2×C4×C37—42no—
56C2×C4×C37—42no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37#4114yes—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—42no—
65C2×Dic37—42no—
66#64436—42no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—44no—
75C22×C37#10412yes—
76C22×C37C2×C22⋊C411yescharacteristic
77C22×C37#12312yes—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—44no—
81C4×C37#11712yes—
82C4×C37#12312yes—
83Dic37—42no—
84Dic37—42no—
85#1826—371nomaximal, Sylow
86C2×C37—22no—
87C2×C37—22no—
88C2×C37—41no—
89C2×C37#38111yescharacteristic
90C2×C37C2×#10411yescharacteristic
91C2×C37#42111yescharacteristic
92C2×#117—371no—
93#407—371no—
94C4×C22⋊C4D3711yescharacteristic
95#339—374no—
96C37#182611yescharacteristic, complemented, Sylow
97C23×C4C2×D3711yescharacteristic
98C2×M16—372no—
99#117—372no—
100#117—372no—
101#117—741no—
102#117—741no—
103C2×C4⋊C4—371no—
104C2×C4⋊C4—371no—
105C2×C22⋊C4—21no—
106C2×C22⋊C4—741no—
107C2×C42—741no—
108C2×C42C2×D3712yes—
109C22⋊C8—741no—
110C22⋊C8—741no—
111#95—21no—
112C24C22⋊D3711yescharacteristic
113C22×C4—24no—
114C22×C4—22no—
115C22×C4—741no—
116C22×C4—741no—
117C22×C4C4×D3711yescharacteristic
118C22×C4C4×D3711yescharacteristic
119C22×C4D14811yescharacteristic
120C22×C4D14811yescharacteristic
121C22×C4C22⋊D3711yescharacteristic
122C22×C4C22×D3711yescharacteristic
123M16—744no—
124C2×C8—742no—
125C4⋊C4—372no—
126C4⋊C4—372no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C22⋊C4—24no—
130C22⋊C4—742no—
131C22⋊C4—742no—
132C42—24no—
133C42—742no—
134C42—742no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23#1059693811yescharacteristic
139C23#1059693811yescharacteristic
140C23C2×C22⋊D3711yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—742no—
150C2×C4—742no—
151C2×C4—1482no—
152C2×C4—1482no—
153C2×C4#1059693811yescharacteristic
154C2×C4#1059693811yescharacteristic
155C2×C4C2×C4×D3711yescharacteristic
156C2×C4C2×D14811yescharacteristic
157C2×C4#1059696414yes—
158C8—1482no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#1192446412yes—
168C22C2×#1059693811yescharacteristic
169C22#1192451712yes—
170C4—21no—
171C4—21no—
172C4—44no—
173C4—1482no—
174C4—1482no—
175C4#1192449212yes—
176C4#1192452012yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#1455739411yescharacteristic
181C2C2×#1192446411yescharacteristic
182C2#1455755111yescharacteristic
subgroupG/H
centerC2×C4C2×D148
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC4×C22⋊C4×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC24×C37D4
cosocleC22×C4×C37C23
hypercenterC4×C22⋊C4D37
hypocenterC37#1826
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14557293C2semidirect
8. #11924495C4semidirect
10. C2×C4⋊Dic37C4semidirect
11. C2×C4⋊Dic37C4semidirect
96. C37#1826semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
#145574972
#145572932
C4×C22⋊C4×C372
#182637