Finite Group Databasebeta

← C23×#107×C47 #26099800

Subgroups — C23×#107×C47 #26099800

Order 12032.

3614 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C8×C47C211yesmaximal, characteristic
2C23×C4⋊C4×C47C212yesmaximal
3C22×#107×C47C2128yesmaximal, direct product factor
4C24×C4×C47—22no—
5C24×C4×C47C2211yescharacteristic
6C23×C8×C47C4116yescomplemented
7C23×C8×C47C22114yes—
8C22×C4⋊C4×C47—214no—
9C22×C4⋊C4×C47C22128yes—
10C2×#107×C47C221112yesdirect product factor
11C25×C47D411yescharacteristic
12C23×C4×C47—228no—
13C23×C4×C47—416no—
14C23×C4×C47C2×C418yes—
15C23×C4×C47D417yes—
16C23×C4×C47Q818yes—
17C23×C4×C47C2317yes—
18C22×C8×C47C2×C41112yescomplemented
19C22×C8×C47C23128yes—
20C2×C4⋊C4×C47—284no—
21C2×C4⋊C4×C47C23156yes—
22#107×C47C23164yesdirect product factor
23C24×C47C4⋊C418yes—
24C24×C47D818yes—
25C24×C47Q1618yes—
26C24×C47C2×D417yes—
27C22×C4×C47—256no—
28C22×C4×C47—4112no—
29C22×C4×C47C4⋊C4156yes—
30C22×C4×C47C22×C4128yes—
31C22×C4×C47C2×D4121yes—
32C22×C4×C47C2×Q8128yes—
33C22×C4×C47C2417yes—
34C2×C8×C47C22×C41112yescomplemented
35C2×C8×C47C2418yes—
36C4⋊C4×C47—256no—
37C4⋊C4×C47C24116yes—
38C23×C47#107164yesdirect product factor
39C23×C47C2×C4⋊C4128yes—
40C23×C47C2×D8128yes—
41C23×C47C2×Q16128yes—
42C23×C47C22×D417yes—
43C2×C4×C47—216no—
44C2×C4×C47—4112no—
45C2×C4×C47C2×C4⋊C4184yes—
46C2×C4×C47C23×C4114yes—
47C2×C4×C47C22×D417yes—
48C2×C4×C47C22×Q8114yes—
49C2×C4×C47C2511yescharacteristic
50C8×C47C23×C4116yescomplemented
51C23×#107C4711yesmaximal, characteristic, direct product factor, Sylow
52C22×C47C2×#1071112yesdirect product factor
53C22×C47C22×C4⋊C4114yes—
54C22×C47C22×D8114yes—
55C22×C47C22×Q16114yes—
56C22×C47C23×D411yescharacteristic
57C4×C47—416no—
58C4×C47C22×C4⋊C4114yes—
59C4×C47C24×C411yescharacteristic
60C4×C47C23×Q811yescharacteristic
61C24×C8C2×C4711yescharacteristic
62C23×C4⋊C4C2×C4712yes—
63C22×#107C2×C47128yesdirect product factor
64C2×C47C22×#107128yesdirect product factor
65C2×C47C23×C4⋊C411yescharacteristic
66C2×C47C23×D811yescharacteristic
67C2×C47C23×Q1611yescharacteristic
68C24×C4—22no—
69C24×C4C22×C4711yescharacteristic
70C23×C8C4×C47116yescomplemented
71C23×C8C22×C47114yes—
72C22×C4⋊C4—214no—
73C22×C4⋊C4C22×C47128yes—
74C2×#107C22×C471112yesdirect product factor
75C47C23×#10711yescharacteristic, direct product factor, Sylow
76C25D4×C4711yescharacteristic
77C23×C4—228no—
78C23×C4—416no—
79C23×C4C2×C4×C4718yes—
80C23×C4D4×C4717yes—
81C23×C4Q8×C4718yes—
82C23×C4C23×C4717yes—
83C22×C8C2×C4×C471112yescomplemented
84C22×C8C23×C47128yes—
85C2×C4⋊C4—284no—
86C2×C4⋊C4C23×C47156yes—
87#107C23×C47164yesdirect product factor
88C24C4⋊C4×C4718yes—
89C24D8×C4718yes—
90C24Q16×C4718yes—
91C24C2×D4×C4717yes—
92C22×C4—256no—
93C22×C4—4112no—
94C22×C4C4⋊C4×C47156yes—
95C22×C4C22×C4×C47128yes—
96C22×C4C2×D4×C47121yes—
97C22×C4C2×Q8×C47128yes—
98C22×C4C24×C4717yes—
99C2×C8C22×C4×C471112yescomplemented
100C2×C8C24×C4718yes—
101C4⋊C4—256no—
102C4⋊C4C24×C47116yes—
103C23#107×C47164yesdirect product factor
104C23C2×C4⋊C4×C47128yes—
105C23C2×D8×C47128yes—
106C23C2×Q16×C47128yes—
107C23C22×D4×C4717yes—
108C2×C4—216no—
109C2×C4—4112no—
110C2×C4C2×C4⋊C4×C47184yes—
111C2×C4C23×C4×C47114yes—
112C2×C4C22×D4×C4717yes—
113C2×C4C22×Q8×C47114yes—
114C2×C4C25×C4711yescharacteristic
115C8C23×C4×C47116yescomplemented
116C22C2×#107×C471112yesdirect product factor
117C22C22×C4⋊C4×C47114yes—
118C22C22×D8×C47114yes—
119C22C22×Q16×C47114yes—
120C22C23×D4×C4711yescharacteristic
121C4—416no—
122C4C22×C4⋊C4×C47114yes—
123C4C24×C4×C4711yescharacteristic
124C4C23×Q8×C4711yescharacteristic
125C2C22×#107×C47128yesdirect product factor
126C2C23×C4⋊C4×C4711yescharacteristic
127C2C23×D8×C4711yescharacteristic
128C2C23×Q16×C4711yescharacteristic
subgroupG/H
center, socle, prime radicalC25×C47D4
commutatorC4C24×C4×C47
Frattini, cosocleC2×C4C25×C47
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×#107×C47C2direct (N × H)
6. C23×C8×C47C4semidirect
10. C2×#107×C47C22direct (N × H)
18. C22×C8×C47C2×C4semidirect
22. #107×C47C23direct (N × H)
34. C2×C8×C47C22×C4semidirect
38. C23×C47#107direct (N × H)
50. C8×C47C23×C4semidirect
51. C23×#107C47direct (N × H)
52. C22×C47C2×#107direct (N × H)
63. C22×#107C2×C47direct (N × H)
64. C2×C47C22×#107direct (N × H)
70. C23×C8C4×C47semidirect
74. C2×#107C22×C47direct (N × H)
75. C47C23×#107direct (N × H)
83. C22×C8C2×C4×C47semidirect
87. #107C23×C47direct (N × H)
99. C2×C8C22×C4×C47semidirect
103. C23#107×C47direct (N × H)
115. C8C23×C4×C47semidirect
116. C22C2×#107×C47direct (N × H)
125. C2C22×#107×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C8×C472
C23×C4⋊C4×C472
C22×#107×C472
C23×#10747