Finite Group Databasebeta

← C23×Q8×C3⋊D3 #11919173

Subgroups — C23×Q8×C3⋊D3 #11919173

Order 1152.

18792 conjugacy classes of subgroups; only the 5257 normal subgroups are shown.

normal subgroups only

This group has 18792 conjugacy classes of subgroups — too many to draw. Only its 5257 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
1C23×C32×Q8C211yesmaximal, characteristic, complemented
2C22×Q8×C3⋊D3C2156yesmaximal, direct product factor
3C23×C4×C3⋊D3C213yesmaximal
4C23×#634C213yesmaximal, complemented
5C23×D3×Q8—34nomaximal
6C24×C3⋊D3C2211yescharacteristic
7C22×C32×Q8C22128yescomplemented
8C23×C32×C4C2213yes—
9C23×C3⋊Dic3C2213yes—
10C2×Q8×C3⋊D3C221448yesdirect product factor
11C22×C4×C3⋊D3C22184yes—
12C22×#634C22184yescomplemented
13C23×C3×Q8D314yescomplemented
14C22×D3×Q8—3224no—
15C23×C4×D3—312no—
16C23×Dic6—312no—
17C24×C32C2311yescharacteristic
18C23×C3⋊D3Q8116yesdirect product factor
19C23×C3⋊D3C23114yes—
20C2×C32×Q8C231112yescomplemented
21C22×C32×C4C23142yes—
22C22×C3⋊Dic3C23142yes—
23Q8×C3⋊D3C231512yesdirect product factor
24C2×C4×C3⋊D3C231336yes—
25C2×#634C231336yescomplemented
26C24×Q8—91noSylow
27C24×D3—34no—
28C22×C3×Q8C2×D31112yescomplemented
29C23×C3×C4C2×D3112yes—
30C23×Dic3—312no—
31C2×D3×Q8—31792no—
32C22×C4×D3—3336no—
33C22×Dic6—3336no—
34C23×C32C2×Q818yescomplemented
35C23×C32C2417yes—
36C22×C3⋊D3C2×Q81112yesdirect product factor
37C22×C3⋊D3C24128yes—
38C32×Q8C24164yescomplemented
39C2×C32×C4C24184yes—
40C2×C3⋊Dic3C24184yes—
41C4×C3⋊D3C241192yes—
42#634C241192yescomplemented
43C23×Q8—956no—
44C23×Q8—93no—
45C23×Q8C3⋊D311yescharacteristic, direct product factor
46C24×C4—93no—
47C24×C3C22×D314yes—
48C23×D3—364no—
49C23×D3—356no—
50C2×C3×Q8C22×D31448yescomplemented
51C22×C3×C4C22×D31168yes—
52C22×Dic3—3168no—
53D3×Q8—32048no—
54C2×C4×D3—31344no—
55C2×Dic6—31344no—
56C22×C32C22×Q8128yescomplemented
57C22×C32C2517yes—
58C2×C3⋊D3C22×Q81112yesdirect product factor
59C2×C3⋊D3C2518yes—
60C32×C4C25124yes—
61C3⋊Dic3C25124yes—
62C25—91no—
63C22×Q8—9448no—
64C22×Q8—984no—
65C22×Q8C2×C3⋊D3128yesdirect product factor
66C23×C4—93no—
67C23×C4—984no—
68C23×C4C2×C3⋊D313yes—
69C23×C3D3×Q8132yescomplemented
70C23×C3C23×D3128yes—
71C22×D3—3448no—
72C22×D3—3112no—
73C3×Q8C23×D31256yescomplemented
74C2×C3×C4C23×D31336yes—
75C2×Dic3—3336no—
76C4×D3—3768no—
77Dic6—3768no—
78C2×C32C23×Q8114yescomplemented
79C2×C32C2611yescharacteristic
80C3⋊D3C23×Q8116yesdirect product factor
81C24—914no—
82C24—916no—
83C24C22×C3⋊D311yescharacteristic
84C2×Q8—9512no—
85C2×Q8—9336no—
86C2×Q8C22×C3⋊D31112yesdirect product factor
87C22×C4—942no—
88C22×C4—9336no—
89C22×C4C22×C3⋊D3142yes—
90C22×C3C2×D3×Q81112yescomplemented
91C22×C3C24×D3128yes—
92C2×D3—3448no—
93C2×D3—332no—
94C3×C4C24×D3196yes—
95Dic3—396no—
96C32C24×Q811yescharacteristic, complemented, Sylow
97C23—9112no—
98C23—928no—
99C23Q8×C3⋊D318yesdirect product factor
100C23C23×C3⋊D317yes—
101Q8—9192no—
102Q8C23×C3⋊D3164yesdirect product factor
103C2×C4—984no—
104C2×C4—9192no—
105C2×C4C23×C3⋊D3184yes—
106C2×C3C22×D3×Q8156yescomplemented
107C2×C3C25×D314yes—
108D3—364no—
109C22—9112no—
110C22—98no—
111C22C2×Q8×C3⋊D3128yesdirect product factor
112C22C24×C3⋊D317yes—
113C4—924no—
114C4C24×C3⋊D3124yes—
115C3C23×D3×Q814yescomplemented
116C2—916no—
117C2C22×Q8×C3⋊D3114yesdirect product factor
118C2C25×C3⋊D311yescharacteristic
subgroupG/H
centerC24C22×C3⋊D3
commutator, cosocleC2×C32C26
FrattiniC2C25×C3⋊D3
FittingC23×C32×Q8C2
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×Q8C3⋊D3
hypocenterC32C24×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C23×C32×Q8C2semidirect
2. C22×Q8×C3⋊D3C2direct (N × H)
4. C23×#634C2semidirect
7. C22×C32×Q8C22semidirect
10. C2×Q8×C3⋊D3C22direct (N × H)
12. C22×#634C22semidirect
13. C23×C3×Q8D3semidirect
18. C23×C3⋊D3Q8direct (N × H)
20. C2×C32×Q8C23semidirect
23. Q8×C3⋊D3C23direct (N × H)
25. C2×#634C23semidirect
28. C22×C3×Q8C2×D3semidirect
34. C23×C32C2×Q8semidirect
36. C22×C3⋊D3C2×Q8direct (N × H)
38. C32×Q8C24semidirect
42. #634C24semidirect
45. C23×Q8C3⋊D3direct (N × H)
50. C2×C3×Q8C22×D3semidirect
56. C22×C32C22×Q8semidirect
58. C2×C3⋊D3C22×Q8direct (N × H)
65. C22×Q8C2×C3⋊D3direct (N × H)
69. C23×C3D3×Q8semidirect
73. C3×Q8C23×D3semidirect
78. C2×C32C23×Q8semidirect
80. C3⋊D3C23×Q8direct (N × H)
86. C2×Q8C22×C3⋊D3direct (N × H)
90. C22×C3C2×D3×Q8semidirect
96. C32C24×Q8semidirect
99. C23Q8×C3⋊D3direct (N × H)
102. Q8C23×C3⋊D3direct (N × H)
106. C2×C3C22×D3×Q8semidirect
111. C22C2×Q8×C3⋊D3direct (N × H)
115. C3C23×D3×Q8semidirect
117. C2C22×Q8×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×Q82
C22×Q8×C3⋊D32
C23×C4×C3⋊D32
C23×#6342
C23×D3×Q83