Finite Group Databasebeta

← #18009500

Subgroups — #18009500

Order 4736.

192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 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#14558504C211yesmaximal, characteristic
2#14558476C211yesmaximal, characteristic
3#14557495C211yesmaximal, characteristic
4C2×#10596953—21no—
5C2×C22⋊#3866C412yes—
6#11924593—21no—
7C22⋊#64438C412yescomplemented
8(C2×#3866)⋊C4—21no—
9(C2×#3866)⋊C4—21no—
10C22×C4×D37C2211yescharacteristic
11C2×#10596929—21no—
12C22⋊#64436C411yescharacteristic, complemented
13#11924448—21no—
14C22⋊C8×C37C411yescharacteristic, complemented
15C23×D37C2×C411yescharacteristic
16C22×#3866—22no—
17C22×C4×C37C2×C411yescharacteristic
18C22×Dic37C2×C411yescharacteristic
19C2×C4×D37—42no—
20C2×C4×D37D411yescharacteristic
21C2×C4×D37D411yescharacteristic
22C2×C4×D37D411yescharacteristic
23C2×C4×D37Q811yescharacteristic
24C22⋊#3866—42no—
25C2×#64438—22no—
26#10596953—42no—
27C2×C8×C37—21no—
28C2×#64436—21no—
29#10596929—42no—
30C23×C37C4211yescharacteristic
31C22×D37—22no—
32C22×D37—41no—
33C22×D37—41no—
34C22×D37C22⋊C411yescharacteristic
35C22×D37C4⋊C411yescharacteristic
36C2×#3866—42no—
37C2×#3866—42no—
38C2×#3866—42no—
39C2×C4×C37—41no—
40C2×C4×C37C22⋊C411yescharacteristic
41C2×C4×C37C4⋊C411yescharacteristic
42C2×Dic37—41no—
43C2×Dic37C22⋊C411yescharacteristic
44C2×Dic37C4⋊C411yescharacteristic
45C4×D37—22no—
46C4×D37—22no—
47C4×D37—41no—
48C4×D37—41no—
49#64438—42no—
50C8×C37—41no—
51#64436—41no—
52C22×C37—21no—
53C22×C37—21no—
54C22×C37—21no—
55C22×C37#9511yescharacteristic
56C2×D37—21no—
57C2×D37—21no—
58C2×D37—21no—
59C2×D37—21no—
60C2×D37—21no—
61C2×D37—44no—
62C2×D37#9912yes—
63#3866—82no—
64C4×C37—21no—
65C4×C37—21no—
66Dic37—21no—
67Dic37—21no—
68#1306—371nomaximal, Sylow
69C2×C37—41no—
70C2×C37#34211yescharacteristic
71C2×C37#34411yescharacteristic
72C2×C37#34411yescharacteristic
73D37—22no—
74D37—41no—
75#407—371no—
76#407—371no—
77#381—371no—
78C37#130611yescharacteristic, complemented, Sylow
79C23×C4—371no—
80C2×M16—741no—
81C2×M16—741no—
82C2×C22⋊C4—372no—
83C22⋊C8—372no—
84C22⋊C8—371no—
85C22⋊C8—741no—
86C22⋊C8—741no—
87C22⋊C8#386611yescharacteristic, complemented
88#95—741no—
89#95—741no—
90C24—371no—
91C22×C4—371no—
92C22×C4—371no—
93C22×C4—371no—
94C22×C4—371no—
95C22×C4—371no—
96C22×C4—742no—
97C22×C4—1482no—
98C22×C4C2×#386611yescharacteristic
99M16—1482no—
100M16—1482no—
101C2×C8—21no—
102C2×C8—742no—
103C2×C8—741no—
104C22⋊C4—1482no—
105C23—371no—
106C23—371no—
107C23—742no—
108C23—1481no—
109C23—1481no—
110C23C4×#386611yescharacteristic
111C2×C4—41no—
112C2×C4—371no—
113C2×C4—371no—
114C2×C4—742no—
115C2×C4—742no—
116C2×C4—1481no—
117C2×C4—1481no—
118C2×C4—1482no—
119C2×C4—1482no—
120C2×C4—1482no—
121C2×C4—1481no—
122C2×C4C4⋊#386611yescharacteristic
123C2×C4C22⋊#386611yescharacteristic
124C8—41no—
125C8—1481no—
126C8—1482no—
127C22—21no—
128C22—21no—
129C22—21no—
130C22—372no—
131C22—741no—
132C22—741no—
133C22—741no—
134C22—741no—
135C22—741no—
136C22—1484no—
137C22(C2×#3866)⋊C411yescharacteristic
138C4—21no—
139C4—21no—
140C4—2962no—
141C4—741no—
142C4—741no—
143C2—41no—
144C2—742no—
145C2—1481no—
146C2#1455841011yescharacteristic
147C2#1455841511yescharacteristic
148C2#1455841611yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC23×C37C42
FrattiniC22×C4C2×#3866
FittingC22⋊C8×C37C4
socleC22×C37#95
prime radicalC23×D37C2×C4
cosocleC22×C4×D37C22
hypercenterC22⋊C8#3866
hypocenterC37#1306
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
7. C22⋊#64438C4semidirect
12. C22⋊#64436C4semidirect
14. C22⋊C8×C37C4semidirect
78. C37#1306semidirect
87. C22⋊C8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145584762
#145574952
#130637