Finite Group Databasebeta

← #17994702

Subgroups — #17994702

Order 4736.

296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 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#14558008C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic
3#14557300C212yesmaximal, complemented
4#14557299C212yesmaximal, complemented
5C2×#99×C37C211yesmaximal, characteristic
6D4×Dic37—22no—
7D4×Dic37—22no—
8#11924495C412yescomplemented
9C2×C22⋊Dic37C412yescomplemented
10C2×C22⋊Dic37C2212yes—
11C2×C22⋊Dic37C2211yescharacteristic
12C2×C22⋊Dic37C2211yescharacteristic
13#11924451—22no—
14C22×D4×C37C2211yescharacteristic
15C2×C22⋊C4×C37C2212yes—
16#99×C37—22no—
17C24×C37C2×C411yescharacteristic
18C24×C37C2311yescharacteristic
19C2×D4×C37—22no—
20C2×D4×C37—22no—
21C2×D4×C37D412yes—
22C2×D4×C37D412yes—
23C22×C4×C37—22no—
24C22×C4×C37C2×C411yescharacteristic
25C22×Dic37—22no—
26C22×Dic37—21no—
27C22×Dic37—21no—
28C22×Dic37—22no—
29C22⋊C4×C37—22no—
30C22⋊C4×C37—22no—
31C22⋊Dic37—22no—
32C22⋊Dic37—21no—
33C22⋊Dic37—21no—
34C22⋊Dic37—22no—
35C22⋊Dic37—22no—
36C22⋊Dic37C2×C412yes—
37C22⋊Dic37C2×C412yes—
38C4⋊Dic37—22no—
39C4×Dic37—22no—
40C23×C37—21no—
41C23×C37—21no—
42C23×C37—81no—
43C23×C37—81no—
44C23×C37C22⋊C412yes—
45C23×C37C22×C411yescharacteristic
46C23×C37C2×D411yescharacteristic
47C23×C37C2×D411yescharacteristic
48C23×C37#4112yes—
49C23×C37#4112yes—
50D4×C37—24no—
51D4×C37—24no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—42no—
55C2×C4×C37—82no—
56C2×C4×C37C22⋊C412yes—
57C2×Dic37—22no—
58C2×Dic37—22no—
59C2×Dic37—42no—
60C2×Dic37—81no—
61C2×Dic37—81no—
62C2×Dic37—82no—
63C2×Dic37—82no—
64C22×C37—22no—
65C22×C37—41no—
66C22×C37—41no—
67C22×C37—42no—
68C22×C37—42no—
69C22×C37—41no—
70C22×C37—42no—
71C22×C37—81no—
72C22×C37—81no—
73C22×C37C2×C22⋊C411yescharacteristic
74C22×C37#11711yescharacteristic
75C22×C37#11711yescharacteristic
76C22×C37#12312yes—
77C22×C37#12312yes—
78C4×C37—22no—
79C4×C37—82no—
80Dic37—42no—
81Dic37—42no—
82Dic37—82no—
83#1828—371nomaximal, Sylow
84C2×C37—21no—
85C2×C37—22no—
86C2×C37—22no—
87C2×C37—21no—
88C2×C37—21no—
89C2×C37—42no—
90C2×C37#38111yescharacteristic
91#518—371no—
92C2×#99—371no—
93C2×#99D3711yescharacteristic
94#342—372no—
95#342—372no—
96C37#182811yescharacteristic, complemented, Sylow
97C22×D4C2×D3711yescharacteristic
98C4×D4—742no—
99C4×D4—742no—
100#117—372no—
101C2×C22⋊C4—372no—
102C2×C22⋊C4—371no—
103C2×C22⋊C4—371no—
104C2×C22⋊C4—372no—
105C2×C22⋊C4C2×D3712yes—
106#99—22no—
107#99—742no—
108C24C4×D3711yescharacteristic
109C24C22×D3711yescharacteristic
110C2×D4—22no—
111C2×D4—22no—
112C2×D4D14812yes—
113C2×D4C22⋊D3712yes—
114C22×C4—22no—
115C22×C4—742no—
116C22×C4—741no—
117C22×C4—741no—
118C22×C4—742no—
119C22×C4C4×D3711yescharacteristic
120C4⋊C4—742no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C22⋊C4—372no—
124C22⋊C4—372no—
125C22⋊C4—742no—
126C22⋊C4—741no—
127C22⋊C4—741no—
128C22⋊C4—742no—
129C22⋊C4—742no—
130C42—742no—
131C23—21no—
132C23—21no—
133C23—81no—
134C23—81no—
135C23#1059693812yes—
136C23C2×C4×D3711yescharacteristic
137C23C2×D14811yescharacteristic
138C23#1059696412yes—
139C23#1059696412yes—
140C23C2×C22⋊D3711yescharacteristic
141D4—24no—
142D4—24no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—82no—
147C2×C4—2962no—
148C2×C4—2961no—
149C2×C4—2961no—
150C2×C4—2962no—
151C2×C4—742no—
152C2×C4—742no—
153C2×C4—1482no—
154C2×C4#1059693812yes—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22C2×#1059693811yescharacteristic
165C22#1192449211yescharacteristic
166C22#1192449211yescharacteristic
167C22#1192451712yes—
168C22#1192452012yes—
169C4—22no—
170C4—82no—
171C4—2962no—
172C4—1482no—
173C4—1482no—
174C2—22no—
175C2—22no—
176C2—21no—
177C2—21no—
178C2—21no—
179C2—42no—
180C2#1455739411yescharacteristic
subgroupG/H
centerC2#14557394
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC2×#99×C37C2
socleC2×C37#381
prime radicalC22×D4×C37C22
cosocleC24×C37C23
hypercenterC2×#99D37
hypocenterC37#1828
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #14557300C2semidirect
4. #14557299C2semidirect
8. #11924495C4semidirect
9. C2×C22⋊Dic37C4semidirect
96. C37#1828semidirect

Maximal subgroups

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

subgroupindex
#145580082
C2×#119244512
#145573002
#145572992
C2×#99×C372
#182837