Finite Group Databasebeta

← #18009846

Subgroups — #18009846

Order 4736.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558503C212yesmaximal
2#14558379C214yesmaximal, complemented
3C22×#10596936C211yesmaximal, characteristic
4C2×#10596957—22no—
5C22⋊#64438—22no—
6C22⋊#64438C2214yes—
7C23×Dic37C411yescharacteristic
8C23×Dic37C2211yescharacteristic
9C2×#10596936—22no—
10C2×#10596936—22no—
11C2×#10596936C412yes—
12C2×#10596936C2212yes—
13C23×C4×C37C411yescharacteristic
14C24×C37C2×C411yescharacteristic
15C22×C4×C37—21no—
16C22×C4×C37—21no—
17C22×C4×C37—42no—
18C22×C4×C37C2×C412yes—
19C22×Dic37—21no—
20C22×Dic37—21no—
21C22×Dic37—24no—
22C22×Dic37—42no—
23C22×Dic37C2×C412yes—
24C22×Dic37C2×C411yescharacteristic
25C22×Dic37D412yes—
26C22×Dic37D412yes—
27C22×Dic37C2311yescharacteristic
28#10596957—44no—
29C2×#64438—24no—
30#10596936—24no—
31#10596936—24no—
32C23×C37—22no—
33C23×C37—22no—
34C23×C37—22no—
35C23×C37C22⋊C411yescharacteristic
36C23×C37C22⋊C411yescharacteristic
37C23×C37C22×C411yescharacteristic
38C2×C4×C37—22no—
39C2×C4×C37—42no—
40C2×C4×C37—42no—
41C2×C4×C37—42no—
42C2×Dic37—24no—
43C2×Dic37—24no—
44C2×Dic37—24no—
45C2×Dic37—22no—
46C2×Dic37—22no—
47C2×Dic37—41no—
48C2×Dic37—42no—
49C2×Dic37—41no—
50C2×Dic37C22⋊C412yes—
51C2×Dic37M1614yescomplemented
52C2×Dic37C2×D412yes—
53#64438—44no—
54C22×C37—28no—
55C22×C37—21no—
56C22×C37—21no—
57C22×C37—21no—
58C22×C37—21no—
59C22×C37—21no—
60C22×C37—21no—
61C22×C37#9912yes—
62C22×C37#10112yes—
63C22×C37C2×C22⋊C411yescharacteristic
64C22×C37C2×M1612yes—
65C4×C37—42no—
66Dic37—24no—
67Dic37—22no—
68Dic37—22no—
69#1463—371nomaximal, Sylow
70C2×C37—22no—
71C2×C37—22no—
72C2×C37—22no—
73C2×C37#40711yescharacteristic
74C2×C37C2×#9911yescharacteristic
75C2×C37C2×#10111yescharacteristic
76C22×C4⋊C4—371no—
77#407—372no—
78#324—374no—
79C37#146311yescharacteristic, complemented, Sylow
80C23×C4—371no—
81C23×C4—371no—
82C23×C4#386611yescharacteristic
83C2×M16—742no—
84C2×C4⋊C4—372no—
85C2×C4⋊C4—372no—
86C2×C4⋊C4—742no—
87C2×C4⋊C4—742no—
88C22⋊C8—374no—
89C22⋊C8—742no—
90C24C2×#386611yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—42no—
94C22×C4—372no—
95C22×C4—372no—
96C22×C4—372no—
97C22×C4—371no—
98C22×C4—371no—
99C22×C4—744no—
100C22×C4—741no—
101C22×C4—741no—
102C22×C4—1482no—
103C22×C4C2×#386612yes—
104M16—1484no—
105C2×C8—744no—
106C4⋊C4—744no—
107C4⋊C4—744no—
108C23—22no—
109C23—22no—
110C23—22no—
111C23C22⋊#386611yescharacteristic
112C23C22⋊#386611yescharacteristic
113C23C22×#386611yescharacteristic
114C2×C4—22no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—372no—
119C2×C4—372no—
120C2×C4—374no—
121C2×C4—744no—
122C2×C4—744no—
123C2×C4—744no—
124C2×C4—742no—
125C2×C4—742no—
126C2×C4—1481no—
127C2×C4—1482no—
128C2×C4—1481no—
129C8—1484no—
130C22—28no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22#1192459412yes—
138C22#1192459712yes—
139C22C2×C22⋊#386611yescharacteristic
140C22D37⋊M1612yes—
141C4—42no—
142C4—744no—
143C4—742no—
144C4—742no—
145C2—22no—
146C2—22no—
147C2—22no—
148C2#1455850511yescharacteristic
149C2C2×#1192459411yescharacteristic
150C2C2×#1192459711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37#1463
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #14558379C2semidirect
51. C2×Dic37M16semidirect
79. C37#1463semidirect

Maximal subgroups

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

subgroupindex
#145585032
#145583792
C22×#105969362
#146337