Finite Group Databasebeta

← C23×C11×#120 #14639848

Subgroups — C23×C11×#120 #14639848

Order 2816.

42862 conjugacy classes of subgroups; only the 7902 normal subgroups are shown.

normal subgroups only

This group has 42862 conjugacy classes of subgroups — too many to draw. Only its 7902 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
1C27×C11C211yesmaximal, characteristic, complemented
2C24×D4×C11C213yesmaximal, complemented
3C22×C11×#120C2156yesmaximal, direct product factor
4C23×C11×C22⋊C4C213yesmaximal, complemented
5C26×C11—248no—
6C26×C11C2213yes—
7C26×C11C22128yescomplemented
8C26×C11C2211yescharacteristic, complemented
9C23×D4×C11—248no—
10C23×D4×C11C22184yescomplemented
11C24×C4×C11C2213yescomplemented
12C2×C11×#120C221448yesdirect product factor
13C22×C11×C22⋊C4C22184yescomplemented
14C25×C11—2512no—
15C25×C11—248no—
16C25×C11—2672no—
17C25×C11—224no—
18C25×C11D4148yescomplemented
19C25×C11C23142yes—
20C25×C11C2311yescharacteristic
21C25×C11C231112yescomplemented
22C25×C11C23114yescomplemented
23C22×D4×C11—2672no—
24C22×D4×C11C231336yescomplemented
25C23×C4×C11—224no—
26C23×C4×C11C23142yescomplemented
27C11×#120C231512yesdirect product factor
28C2×C11×C22⋊C4C231336yescomplemented
29C23×#120C1111yesmaximal, characteristic, direct product factor, Sylow
30C24×C11—23584no—
31C24×C11—2384no—
32C24×C11—2336no—
33C24×C11—21344no—
34C24×C11—2168no—
35C24×C11—464no—
36C24×C11C2×D4124yes—
37C24×C11C2×D41336yescomplemented
38C24×C11C24184yes—
39C24×C11C2417yes—
40C24×C11C24164yescomplemented
41C24×C11C24128yescomplemented
42C2×D4×C11—21344no—
43C2×D4×C11C241192yescomplemented
44C22×C4×C11—2168no—
45C22×C4×C11C24184yescomplemented
46C11×C22⋊C4C241192yescomplemented
47C27C2×C1111yescharacteristic, complemented
48C24×D4C2×C1113yescomplemented
49C22×#120C2×C11156yesdirect product factor
50C23×C22⋊C4C2×C1113yescomplemented
51C23×C11—23584no—
52C23×C11—21344no—
53C23×C11—2336no—
54C23×C11—2384no—
55C23×C11—2168no—
56C23×C11—4224no—
57C23×C11#120164yesdirect product factor
58C23×C11C22×D4184yes—
59C23×C11C22×D41336yescomplemented
60C23×C11C25124yes—
61C23×C11C2517yes—
62C23×C11C2518yescomplemented
63D4×C11—2384no—
64C2×C4×C11—2168no—
65C2×C4×C11C25124yescomplemented
66C26—248no—
67C26C22×C1113yes—
68C26C22×C11128yescomplemented
69C26C22×C1111yescharacteristic, complemented
70C23×D4—248no—
71C23×D4C22×C11184yescomplemented
72C24×C4C22×C1113yescomplemented
73C2×#120C22×C111448yesdirect product factor
74C22×C22⋊C4C22×C11184yescomplemented
75C22×C11—2512no—
76C22×C11—248no—
77C22×C11—2672no—
78C22×C11—224no—
79C22×C11—4112no—
80C22×C11C2×#1201112yesdirect product factor
81C22×C11C23×D4142yes—
82C22×C11C23×D4148yescomplemented
83C22×C11C2611yescharacteristic
84C4×C11—224no—
85C25—2512no—
86C25—248no—
87C25—2672no—
88C25—224no—
89C25D4×C11148yescomplemented
90C25C23×C11142yes—
91C25C23×C1111yescharacteristic
92C25C23×C111112yescomplemented
93C25C23×C11114yescomplemented
94C22×D4—2672no—
95C22×D4C23×C111336yescomplemented
96C23×C4—224no—
97C23×C4C23×C11142yescomplemented
98#120C23×C111512yesdirect product factor
99C2×C22⋊C4C23×C111336yescomplemented
100C2×C11—248no—
101C2×C11—48no—
102C2×C11C22×#120128yesdirect product factor
103C2×C11C24×D413yes—
104C24—23584no—
105C24—2384no—
106C24—2336no—
107C24—21344no—
108C24—2168no—
109C24—464no—
110C24C2×D4×C11124yes—
111C24C2×D4×C111336yescomplemented
112C24C24×C11184yes—
113C24C24×C1117yes—
114C24C24×C11164yescomplemented
115C24C24×C11128yescomplemented
116C2×D4—21344no—
117C2×D4C24×C111192yescomplemented
118C22×C4—2168no—
119C22×C4C24×C11184yescomplemented
120C22⋊C4C24×C111192yescomplemented
121C11C23×#12011yescharacteristic, direct product factor, Sylow
122C23—23584no—
123C23—21344no—
124C23—2336no—
125C23—2384no—
126C23—2168no—
127C23—4224no—
128C23C11×#120164yesdirect product factor
129C23C22×D4×C11184yes—
130C23C22×D4×C111336yescomplemented
131C23C25×C11124yes—
132C23C25×C1117yes—
133C23C25×C1118yescomplemented
134D4—2384no—
135C2×C4—2168no—
136C2×C4C25×C11124yescomplemented
137C22—2512no—
138C22—2672no—
139C22—248no—
140C22—224no—
141C22—4112no—
142C22C2×C11×#1201112yesdirect product factor
143C22C23×D4×C11142yes—
144C22C23×D4×C11148yescomplemented
145C22C26×C1111yescharacteristic
146C4—224no—
147C2—248no—
148C2—48no—
149C2C22×C11×#120128yesdirect product factor
150C2C24×D4×C1113yes—
subgroupG/H
center, socleC25×C11C23
commutator, Frattini, cosocleC22C26×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C11C2semidirect
2. C24×D4×C11C2semidirect
3. C22×C11×#120C2direct (N × H)
4. C23×C11×C22⋊C4C2semidirect
7. C26×C11C22semidirect
8. C26×C11C22semidirect
10. C23×D4×C11C22semidirect
11. C24×C4×C11C22semidirect
12. C2×C11×#120C22direct (N × H)
13. C22×C11×C22⋊C4C22semidirect
18. C25×C11D4semidirect
21. C25×C11C23semidirect
22. C25×C11C23semidirect
24. C22×D4×C11C23semidirect
26. C23×C4×C11C23semidirect
27. C11×#120C23direct (N × H)
28. C2×C11×C22⋊C4C23semidirect
29. C23×#120C11direct (N × H)
37. C24×C11C2×D4semidirect
40. C24×C11C24semidirect
41. C24×C11C24semidirect
43. C2×D4×C11C24semidirect
45. C22×C4×C11C24semidirect
46. C11×C22⋊C4C24semidirect
47. C27C2×C11semidirect
48. C24×D4C2×C11semidirect
49. C22×#120C2×C11direct (N × H)
50. C23×C22⋊C4C2×C11semidirect
57. C23×C11#120direct (N × H)
59. C23×C11C22×D4semidirect
62. C23×C11C25semidirect
65. C2×C4×C11C25semidirect
68. C26C22×C11semidirect
69. C26C22×C11semidirect
71. C23×D4C22×C11semidirect
72. C24×C4C22×C11semidirect
73. C2×#120C22×C11direct (N × H)
74. C22×C22⋊C4C22×C11semidirect
80. C22×C11C2×#120direct (N × H)
82. C22×C11C23×D4semidirect
89. C25D4×C11semidirect
92. C25C23×C11semidirect
93. C25C23×C11semidirect
95. C22×D4C23×C11semidirect
97. C23×C4C23×C11semidirect
98. #120C23×C11direct (N × H)
99. C2×C22⋊C4C23×C11semidirect
102. C2×C11C22×#120direct (N × H)
111. C24C2×D4×C11semidirect
114. C24C24×C11semidirect
115. C24C24×C11semidirect
117. C2×D4C24×C11semidirect
119. C22×C4C24×C11semidirect
120. C22⋊C4C24×C11semidirect
121. C11C23×#120direct (N × H)
128. C23C11×#120direct (N × H)
130. C23C22×D4×C11semidirect
133. C23C25×C11semidirect
136. C2×C4C25×C11semidirect
142. C22C2×C11×#120direct (N × H)
144. C22C23×D4×C11semidirect
149. C2C22×C11×#120direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C112
C24×D4×C112
C22×C11×#1202
C23×C11×C22⋊C42
C23×#12011