Finite Group Databasebeta

← #18009468

Subgroups — #18009468

Order 4736.

184 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 48 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#14558504C212yesmaximal
2C2×#11924448C211yesmaximal, characteristic
3C2×#10596953—22no—
4#11924593C414yes—
5C22⋊#64438—22no—
6C22×C4×D37C2211yescharacteristic
7C22×#64436C411yescharacteristic
8#11924448—22no—
9C22×C8×C37C411yescharacteristic
10C23×D37Q811yescharacteristic
11C22×C4×C37C2×C411yescharacteristic
12C22×Dic37D411yescharacteristic
13C2×C4×D37—41no—
14C2×C4×D37—41no—
15C2×C4×D37C2×C412yes—
16C2×C4×D37D412yes—
17C2×#64438—24no—
18#10596953—42no—
19#10596953—42no—
20C2×C8×C37—21no—
21C2×C8×C37—41no—
22C2×#64436—21no—
23C2×#64436—41no—
24C23×C37C4⋊C411yescharacteristic
25C22×D37—21no—
26C22×D37—21no—
27C22×D37—41no—
28C22×D37—41no—
29C22×D37C4⋊C412yes—
30C2×C4×C37—21no—
31C2×C4×C37—21no—
32C2×C4×C37C4211yescharacteristic
33C2×C4×C37C22⋊C411yescharacteristic
34C2×Dic37—41no—
35C2×Dic37C22⋊C412yes—
36C4×D37—22no—
37C4×D37—22no—
38C4×D37—42no—
39#64438—44no—
40C8×C37—41no—
41#64436—41no—
42C22×C37—21no—
43C22×C37—21no—
44C22×C37#9511yescharacteristic
45C22×C37#10811yescharacteristic
46C22×C37#10811yescharacteristic
47C2×D37—22no—
48C2×D37—22no—
49C2×D37—22no—
50C2×D37—42no—
51C2×D37—42no—
52C4×C37—21no—
53C4×C37#9911yescharacteristic
54C4×C37#9911yescharacteristic
55Dic37—22no—
56#1293—371nomaximal, Sylow
57C2×C37—21no—
58C2×C37—21no—
59C2×C37#33811yescharacteristic
60C2×C37#34111yescharacteristic
61C2×C37#34211yescharacteristic
62D37—42no—
63#407—372no—
64C2×C22⋊C8—371no—
65C37#129311yescharacteristic, complemented, Sylow
66C23×C4—371no—
67C2×M16—742no—
68C22×C8—371no—
69C22×C8#386611yescharacteristic
70C22⋊C8—374no—
71C22⋊C8—742no—
72C22⋊C8—742no—
73C24—371no—
74C22×C4—371no—
75C22×C4—372no—
76C22×C4—372no—
77C22×C4—1481no—
78C22×C4—1481no—
79C22×C4C2×#386611yescharacteristic
80M16—1482no—
81M16—1482no—
82C2×C8—21no—
83C2×C8—41no—
84C2×C8—744no—
85C2×C8—741no—
86C2×C8—1481no—
87C23—372no—
88C23—741no—
89C23—741no—
90C23—1481no—
91C23—1481no—
92C23C4⋊#386611yescharacteristic
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—372no—
96C2×C4—742no—
97C2×C4—742no—
98C2×C4—1482no—
99C2×C4—1481no—
100C2×C4C4×#386611yescharacteristic
101C2×C4C22⋊#386611yescharacteristic
102C8—41no—
103C8—1484no—
104C8—1481no—
105C22—21no—
106C22—21no—
107C22—742no—
108C22—742no—
109C22—742no—
110C22—1482no—
111C22—1482no—
112C22(C2×#3866)⋊C411yescharacteristic
113C22#1192460611yescharacteristic
114C22#1192460711yescharacteristic
115C4—21no—
116C4—742no—
117C4#1192459411yescharacteristic
118C4#1192459511yescharacteristic
119C2—21no—
120C2—21no—
121C2—1482no—
122C2#1455840211yescharacteristic
123C2#1455840911yescharacteristic
124C2#1455841111yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC2×C4×C37C42
FrattiniC22×C4C2×#3866
FittingC22×C8×C37C4
socleC22×C37#95
prime radicalC23×D37Q8
cosocleC22×C4×D37C22
hypercenterC22×C8#3866
hypocenterC37#1293
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
65. C37#1293semidirect

Maximal subgroups

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

subgroupindex
#145585042
C2×#119244482
#129337