Finite Group Databasebeta

← C23×C11×#107 #14637295

Subgroups — C23×C11×#107 #14637295

Order 2816.

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×C11C211yesmaximal, characteristic
2C23×C11×C4⋊C4C212yesmaximal
3C22×C11×#107C2128yesmaximal, direct product factor
4C24×C4×C11—22no—
5C24×C4×C11C2211yescharacteristic
6C23×C8×C11C4116yescomplemented
7C23×C8×C11C22114yes—
8C22×C11×C4⋊C4—214no—
9C22×C11×C4⋊C4C22128yes—
10C2×C11×#107C221112yesdirect product factor
11C25×C11D411yescharacteristic
12C23×C4×C11—228no—
13C23×C4×C11—416no—
14C23×C4×C11C2×C418yes—
15C23×C4×C11D417yes—
16C23×C4×C11Q818yes—
17C23×C4×C11C2317yes—
18C22×C8×C11C2×C41112yescomplemented
19C22×C8×C11C23128yes—
20C2×C11×C4⋊C4—284no—
21C2×C11×C4⋊C4C23156yes—
22C11×#107C23164yesdirect product factor
23C23×#107C1111yesmaximal, characteristic, direct product factor, Sylow
24C24×C11C4⋊C418yes—
25C24×C11D818yes—
26C24×C11Q1618yes—
27C24×C11C2×D417yes—
28C22×C4×C11—256no—
29C22×C4×C11—4112no—
30C22×C4×C11C4⋊C4156yes—
31C22×C4×C11C22×C4128yes—
32C22×C4×C11C2×D4121yes—
33C22×C4×C11C2×Q8128yes—
34C22×C4×C11C2417yes—
35C2×C8×C11C22×C41112yescomplemented
36C2×C8×C11C2418yes—
37C11×C4⋊C4—256no—
38C11×C4⋊C4C24116yes—
39C24×C8C2×C1111yescharacteristic
40C23×C4⋊C4C2×C1112yes—
41C22×#107C2×C11128yesdirect product factor
42C23×C11#107164yesdirect product factor
43C23×C11C2×C4⋊C4128yes—
44C23×C11C2×D8128yes—
45C23×C11C2×Q16128yes—
46C23×C11C22×D417yes—
47C2×C4×C11—216no—
48C2×C4×C11—4112no—
49C2×C4×C11C2×C4⋊C4184yes—
50C2×C4×C11C23×C4114yes—
51C2×C4×C11C22×D417yes—
52C2×C4×C11C22×Q8114yes—
53C2×C4×C11C2511yescharacteristic
54C8×C11C23×C4116yescomplemented
55C24×C4—22no—
56C24×C4C22×C1111yescharacteristic
57C23×C8C4×C11116yescomplemented
58C23×C8C22×C11114yes—
59C22×C4⋊C4—214no—
60C22×C4⋊C4C22×C11128yes—
61C2×#107C22×C111112yesdirect product factor
62C22×C11C2×#1071112yesdirect product factor
63C22×C11C22×C4⋊C4114yes—
64C22×C11C22×D8114yes—
65C22×C11C22×Q16114yes—
66C22×C11C23×D411yescharacteristic
67C4×C11—416no—
68C4×C11C22×C4⋊C4114yes—
69C4×C11C24×C411yescharacteristic
70C4×C11C23×Q811yescharacteristic
71C25D4×C1111yescharacteristic
72C23×C4—228no—
73C23×C4—416no—
74C23×C4C2×C4×C1118yes—
75C23×C4D4×C1117yes—
76C23×C4Q8×C1118yes—
77C23×C4C23×C1117yes—
78C22×C8C2×C4×C111112yescomplemented
79C22×C8C23×C11128yes—
80C2×C4⋊C4—284no—
81C2×C4⋊C4C23×C11156yes—
82#107C23×C11164yesdirect product factor
83C2×C11C22×#107128yesdirect product factor
84C2×C11C23×C4⋊C411yescharacteristic
85C2×C11C23×D811yescharacteristic
86C2×C11C23×Q1611yescharacteristic
87C24C11×C4⋊C418yes—
88C24C11×D818yes—
89C24C11×Q1618yes—
90C24C2×D4×C1117yes—
91C22×C4—256no—
92C22×C4—4112no—
93C22×C4C11×C4⋊C4156yes—
94C22×C4C22×C4×C11128yes—
95C22×C4C2×D4×C11121yes—
96C22×C4C2×Q8×C11128yes—
97C22×C4C24×C1117yes—
98C2×C8C22×C4×C111112yescomplemented
99C2×C8C24×C1118yes—
100C4⋊C4—256no—
101C4⋊C4C24×C11116yes—
102C11C23×#10711yescharacteristic, direct product factor, Sylow
103C23C11×#107164yesdirect product factor
104C23C2×C11×C4⋊C4128yes—
105C23C2×C11×D8128yes—
106C23C2×C11×Q16128yes—
107C23C22×D4×C1117yes—
108C2×C4—216no—
109C2×C4—4112no—
110C2×C4C2×C11×C4⋊C4184yes—
111C2×C4C23×C4×C11114yes—
112C2×C4C22×D4×C1117yes—
113C2×C4C22×Q8×C11114yes—
114C2×C4C25×C1111yescharacteristic
115C8C23×C4×C11116yescomplemented
116C22C2×C11×#1071112yesdirect product factor
117C22C22×C11×C4⋊C4114yes—
118C22C22×C11×D8114yes—
119C22C22×C11×Q16114yes—
120C22C23×D4×C1111yescharacteristic
121C4—416no—
122C4C22×C11×C4⋊C4114yes—
123C4C24×C4×C1111yescharacteristic
124C4C23×Q8×C1111yescharacteristic
125C2C22×C11×#107128yesdirect product factor
126C2C23×C11×C4⋊C411yescharacteristic
127C2C23×C11×D811yescharacteristic
128C2C23×C11×Q1611yescharacteristic
subgroupG/H
center, socle, prime radicalC25×C11D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C11×#107C2direct (N × H)
6. C23×C8×C11C4semidirect
10. C2×C11×#107C22direct (N × H)
18. C22×C8×C11C2×C4semidirect
22. C11×#107C23direct (N × H)
23. C23×#107C11direct (N × H)
35. C2×C8×C11C22×C4semidirect
41. C22×#107C2×C11direct (N × H)
42. C23×C11#107direct (N × H)
54. C8×C11C23×C4semidirect
57. C23×C8C4×C11semidirect
61. C2×#107C22×C11direct (N × H)
62. C22×C11C2×#107direct (N × H)
78. C22×C8C2×C4×C11semidirect
82. #107C23×C11direct (N × H)
83. C2×C11C22×#107direct (N × H)
98. C2×C8C22×C4×C11semidirect
102. C11C23×#107direct (N × H)
103. C23C11×#107direct (N × H)
115. C8C23×C4×C11semidirect
116. C22C2×C11×#107direct (N × H)
125. C2C22×C11×#107direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C8×C112
C23×C11×C4⋊C42
C22×C11×#1072
C23×#10711