Finite Group Databasebeta

← #11856158

Subgroups — #11856158

Order 1152.

10266 conjugacy classes of subgroups; only the 825 normal subgroups are shown.

normal subgroups only

This group has 10266 conjugacy classes of subgroups — too many to draw. Only its 825 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
1C26×C32C211yesmaximal, characteristic, complemented
2C2×#64162C217yesmaximal, complemented
3#10592946C217yesmaximal, complemented
4#84128—34nomaximal
5C25×C32—228no—
6C25×C32C2217yes—
7C22×#638C2217yescomplemented
8#64162—228no—
9C2×#3757C22121yescomplemented
10C26×C3D314yescomplemented
11C2×#953—328no—
12#5247—328no—
13C24×C32—2224no—
14C24×C32—284no—
15C24×C32D4128yescomplemented
16C24×C32C2317yes—
17C23×C3⋊D3C2311yescharacteristic, complemented
18C2×#638—242no—
19C22×C3⋊Dic3C2317yescomplemented
20#3757—242no—
21#2846—91noSylow
22C25×C3—2112no—
23C25×C3C2×D3128yes—
24C22×#67—328no—
25#953—6112no—
26C2×#217—384no—
27C23×C32—2256no—
28C23×C32—2224no—
29C23×C32—2168no—
30C23×C32—228no—
31C23×C32C2×D4142yes—
32C23×C32C2411yescharacteristic
33C22×C3⋊D3—27no—
34#638—428no—
35C2×C3⋊Dic3—221no—
36C26C3⋊D311yescharacteristic, complemented
37C2×#120—97no—
38#379—97no—
39C24×C3—2896no—
40C24×C3—2336no—
41C24×C3#671112yescomplemented
42C24×C3C22×D3128yes—
43C23×D3—34no—
44C2×#67—6168no—
45C22×Dic3—328no—
46#217—6168no—
47C22×C32—2224no—
48C22×C32—284no—
49C22×C32#120128yescomplemented
50C22×C32C22×D417yes—
51C2×C3⋊D3—47no—
52C3⋊Dic3—47no—
53C25—228no—
54C25C2×C3⋊D317yes—
55C22×D4—97no—
56#120—1828no—
57C2×C22⋊C4—921no—
58C23×C3—21024no—
59C23×C3—2896no—
60C23×C3—2672no—
61C23×C3—2112no—
62C23×C3C2×#671168yes—
63C23×C3C23×D314yes—
64C22×D3—628no—
65#67—12112no—
66C2×Dic3—684no—
67C2×C32—228no—
68C2×C32C2×#12017yes—
69C3⋊D3—81no—
70C24—2224no—
71C24—284no—
72C24—91no—
73C24#638128yescomplemented
74C24C22×C3⋊D317yes—
75C2×D4—1842no—
76C22×C4—97no—
77C22⋊C4—1842no—
78C22×C3—2896no—
79C22×C3—2336no—
80C22×C3#9531112yescomplemented
81C22×C3C22×#67128yes—
82C2×D3—1228no—
83Dic3—1228no—
84C32#284611yescharacteristic, complemented, Sylow
85C23—2256no—
86C23—2224no—
87C23—228no—
88C23—2168no—
89C23—187no—
90C23C2×#638142yes—
91C23C23×C3⋊D311yescharacteristic
92D4—3628no—
93C2×C4—1821no—
94C2×C3—2112no—
95C2×C3C2×#953128yes—
96D3—244no—
97C22—2224no—
98C22—284no—
99C22—367no—
100C22#64162128yescomplemented
101C22C22×#63817yes—
102C4—367no—
103C3#8412814yescomplemented
104C2—228no—
105C2—721no—
106C2C2×#6416217yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC26×C32C2
hypercenterC26C3⋊D3
hypocenterC32#2846
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C26×C32C2semidirect
2. C2×#64162C2semidirect
3. #10592946C2semidirect
7. C22×#638C22semidirect
9. C2×#3757C22semidirect
10. C26×C3D3semidirect
15. C24×C32D4semidirect
17. C23×C3⋊D3C23semidirect
19. C22×C3⋊Dic3C23semidirect
36. C26C3⋊D3semidirect
41. C24×C3#67semidirect
49. C22×C32#120semidirect
73. C24#638semidirect
80. C22×C3#953semidirect
84. C32#2846semidirect
100. C22#64162semidirect
103. C3#84128semidirect

Maximal subgroups

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

subgroupindex
C26×C322
C2×#641622
#105929462
#841283