Finite Group Databasebeta

← #14558512

Subgroups — #14558512

Order 2368.

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

normal subgroups only

This group has 158 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#11924615C212yesmaximal, complemented
2#11924595C212yesmaximal, complemented
3#11924594C212yesmaximal, complemented
4C2×#10596962C211yesmaximal, characteristic
5C22×C4×C37C411yescharacteristic, complemented
6C2×C22⋊D37C411yescharacteristic, complemented
7C2×C22⋊D37C2211yescharacteristic
8#10596962—22no—
9#10596962—22no—
10C2×D148C2211yescharacteristic
11C2×C4×D37C411yescharacteristic, complemented
12C2×C4×D37C2211yescharacteristic
13C2×Dic74C411yescharacteristic, complemented
14C22⋊#3866C2214yes—
15C4⋊#3866—22no—
16C4×#3866—22no—
17C23×C37C2×C411yescharacteristic
18C22×D37C2×C411yescharacteristic
19C22×D37C2311yescharacteristic
20C2×#3866—24no—
21C2×C4×C37—21no—
22C2×C4×C37—21no—
23C2×C4×C37C2×C411yescharacteristic
24C2×C4×C37C2×C411yescharacteristic
25C22⋊D37—22no—
26C22⋊D37—22no—
27C2×Dic37C2×C411yescharacteristic
28C2×Dic37C2×C411yescharacteristic
29D148—22no—
30C4×D37—21no—
31C4×D37—21no—
32C4×D37D412yes—
33C4×D37D412yes—
34Dic74—22no—
35C22×C37—21no—
36C22×C37—41no—
37C22×C37C22×C411yescharacteristic
38C2×D37—21no—
39C2×D37—41no—
40C2×D37—41no—
41C2×D37C2×D412yes—
42#3866—44no—
43C4×C37—21no—
44C4×C37C22⋊C411yescharacteristic
45C4×C37C22⋊C411yescharacteristic
46Dic37—21no—
47Dic37C22⋊C412yes—
48C2×C37—21no—
49C2×C37—41no—
50C2×C37C2×C22⋊C411yescharacteristic
51D37—22no—
52D37—41no—
53#410—371nomaximal, Sylow
54C37#41011yescharacteristic, complemented, Sylow
55C2×#41—371no—
56#117—372no—
57#99—372no—
58#99—372no—
59#41—742no—
60#41—742no—
61C2×Q8—371no—
62C2×D4—371no—
63C2×D4—371no—
64C2×D4—371no—
65C22×C4—371no—
66C22×C4—371no—
67C22×C4#386611yescharacteristic, complemented
68C4⋊C4—742no—
69C22⋊C4—374no—
70C42—742no—
71C23—371no—
72C23—371no—
73C23C2×#386611yescharacteristic
74Q8—742no—
75D4—742no—
76D4—742no—
77D4—742no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—371no—
81C2×C4—372no—
82C2×C4—372no—
83C2×C4—371no—
84C2×C4—741no—
85C2×C4—741no—
86C2×C4—744no—
87C2×C4C2×#386611yescharacteristic
88C2×C4C2×#386611yescharacteristic
89C22—21no—
90C22—41no—
91C22—372no—
92C22—741no—
93C22—1481no—
94C22—1481no—
95C22C22×#386611yescharacteristic
96C4—21no—
97C4—372no—
98C4—741no—
99C4—1484no—
100C4C22⋊#386611yescharacteristic
101C4C22⋊#386611yescharacteristic
102C2—21no—
103C2—41no—
104C2—742no—
105C2—1481no—
106C2C2×C22⋊#386611yescharacteristic
subgroupG/H
centerC4C22⋊#3866
commutatorC22×C37C22×C4
FrattiniC22C22×#3866
FittingC22×C4×C37C4
socleC2×C37C2×C22⋊C4
prime radicalC2×#10596962C2
cosocleC22×D37C23
hypercenterC22×C4#3866
hypocenterC37#410
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11924615C2semidirect
2. #11924595C2semidirect
3. #11924594C2semidirect
5. C22×C4×C37C4semidirect
6. C2×C22⋊D37C4semidirect
11. C2×C4×D37C4semidirect
13. C2×Dic74C4semidirect
54. C37#410semidirect
67. C22×C4#3866semidirect

Maximal subgroups

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

subgroupindex
#119246152
#119245952
#119245942
C2×#105969622
#41037