Finite Group Databasebeta

← #18010492

Subgroups — #18010492

Order 4736.

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

normal subgroups only

This group has 504 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#14558474C212yesmaximal
2#14558411C214yesmaximal, complemented
3C2×C22⋊C4×D37C211yesmaximal, characteristic
4C2×C22⋊#3866—24no—
5C2×C22⋊#3866C2214yes—
6C24×D37C2211yescharacteristic
7C22×C4×D37C412yescomplemented
8C2×C22⋊Dic37C411yescharacteristic, complemented
9C2×#10596938C2212yes—
10C22⋊C4×D37—24no—
11C2×C22⋊C4×C37C411yescharacteristic, complemented
12C24×C37C2×C411yescharacteristic
13C23×D37—24no—
14C23×D37—44no—
15C23×D37C2×C411yescharacteristic
16C23×D37D414yes—
17C23×D37C2311yescharacteristic
18C22×#3866—24no—
19C22×C4×C37C2×C412yes—
20C22×Dic37C2×C412yes—
21C2×C4×D37—22no—
22C2×C4×D37—22no—
23C2×C4×D37—44no—
24C22⋊#3866—28no—
25C22⋊#3866—48no—
26C22⋊C4×C37—22no—
27C22⋊Dic37—22no—
28#10596938—24no—
29C23×C37—22no—
30C23×C37—42no—
31C23×C37C22⋊C412yes—
32C23×C37C22×C411yescharacteristic
33C22×D37—22no—
34C22×D37—24no—
35C22×D37—28no—
36C22×D37—28no—
37C22×D37—44no—
38C22×D37—42no—
39C22×D37—416no—
40C22×D37C22⋊C412yes—
41C22×D37C2×D412yes—
42C22×D37#4114yes—
43C2×#3866—48no—
44C2×#3866—44no—
45C2×C4×C37—22no—
46C2×C4×C37—42no—
47C2×Dic37—22no—
48C2×Dic37—42no—
49C4×D37—44no—
50C4×D37—44no—
51C22×C37—22no—
52C22×C37—22no—
53C22×C37—24no—
54C22×C37—44no—
55C22×C37C2×C22⋊C411yescharacteristic
56C22×C37#11712yes—
57C2×D37—28no—
58C2×D37—22no—
59C2×D37—22no—
60C2×D37—24no—
61C2×D37—44no—
62C2×D37—416no—
63C2×D37#9914yes—
64C2×D37#12314yes—
65#3866—84no—
66C4×C37—42no—
67Dic37—42no—
68#1819—371nomaximal, Sylow
69C2×C37—22no—
70C2×C37—42no—
71C2×C37#38111yescharacteristic
72C2×C37C2×#9912yes—
73D37—24no—
74D37—24no—
75C22×C22⋊C4—371no—
76#379—372no—
77#342—374no—
78C37#181911yescharacteristic, complemented, Sylow
79C25—371no—
80C23×C4—372no—
81C2×C22⋊C4—371no—
82C2×C22⋊C4—372no—
83C2×C22⋊C4—374no—
84C2×C22⋊C4—744no—
85C2×C22⋊C4—744no—
86C2×C22⋊C4#386611yescharacteristic, complemented
87C24—371no—
88C24—371no—
89C24—374no—
90C24—744no—
91C24—1484no—
92C24C2×#386611yescharacteristic
93C22×C4—372no—
94C22×C4—742no—
95C22×C4—742no—
96C22×C4—744no—
97C22×C4—1484no—
98C22×C4C2×#386612yes—
99C22⋊C4—22no—
100C22⋊C4—744no—
101C22⋊C4—742no—
102C22⋊C4—748no—
103C22⋊C4—1488no—
104C23—22no—
105C23—42no—
106C23—372no—
107C23—372no—
108C23—374no—
109C23—744no—
110C23—748no—
111C23—748no—
112C23—742no—
113C23—1482no—
114C23—1484no—
115C23—14816no—
116C23C22⋊#386612yes—
117C23C22×#386611yescharacteristic
118C2×C4—22no—
119C2×C4—42no—
120C2×C4—742no—
121C2×C4—1484no—
122C2×C4—1484no—
123C2×C4—1484no—
124C2×C4—1488no—
125C2×C4—1482no—
126C22—22no—
127C22—22no—
128C22—24no—
129C22—44no—
130C22—374no—
131C22—374no—
132C22—748no—
133C22—742no—
134C22—744no—
135C22—742no—
136C22—1484no—
137C22—14816no—
138C22C2×C22⋊#386611yescharacteristic
139C22#1192461512yes—
140C4—42no—
141C4—2964no—
142C4—1482no—
143C2—22no—
144C2—42no—
145C2—744no—
146C2—744no—
147C2#1455847611yescharacteristic
148C2D37⋊#9912yes—
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×D37C22
cosocleC23×D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1819
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14558411C2semidirect
7. C22×C4×D37C4semidirect
8. C2×C22⋊Dic37C4semidirect
11. C2×C22⋊C4×C37C4semidirect
78. C37#1819semidirect
86. C2×C22⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584742
#145584112
C2×C22⋊C4×D372
#181937