Finite Group Databasebeta

← C23×C11×SD32 #14639819

Subgroups — C23×C11×SD32 #14639819

Order 2816.

2334 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1054 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×C11×Q16C211yesmaximal, characteristic, complemented
2C23×C11×D8C211yesmaximal, characteristic
3C22×C11×SD32C2128yesmaximal, direct product factor
4C23×C11×C16C211yesmaximal, characteristic, complemented
5C23×Q8×C11—21no—
6C23×D4×C11—21no—
7C22×C11×Q16—27no—
8C22×C11×Q16C22114yescomplemented
9C22×C11×D8—27no—
10C22×C11×D8C22114yes—
11C23×C8×C11C2211yescharacteristic
12C2×C11×SD32C221112yesdirect product factor
13C22×C11×C16C22114yescomplemented
14C25×C11—41no—
15C22×Q8×C11—214no—
16C22×Q8×C11—47no—
17C22×D4×C11—214no—
18C22×D4×C11—47no—
19C23×C4×C11—41no—
20C23×C4×C11D411yescharacteristic
21C2×C11×Q16—242no—
22C2×C11×Q16C23128yescomplemented
23C2×C11×D8—242no—
24C2×C11×D8C23128yes—
25C22×C8×C11D417yes—
26C22×C8×C11C2317yes—
27C11×SD32C23164yesdirect product factor
28C2×C11×C16C23128yescomplemented
29C23×SD32C1111yesmaximal, characteristic, direct product factor, Sylow
30C24×C11—414no—
31C24×C11—88no—
32C24×C11D811yescharacteristic
33C2×Q8×C11—228no—
34C2×Q8×C11—442no—
35C2×D4×C11—228no—
36C2×D4×C11—442no—
37C22×C4×C11—414no—
38C22×C4×C11D817yes—
39C22×C4×C11C2×D417yes—
40C11×Q16—228no—
41C11×Q16C2418yescomplemented
42C11×D8—228no—
43C11×D8C2418yes—
44C2×C8×C11C2×D4121yes—
45C2×C8×C11C2417yes—
46C11×C16C2418yescomplemented
47C23×Q16C2×C1111yescharacteristic, complemented
48C23×D8C2×C1111yescharacteristic
49C22×SD32C2×C11128yesdirect product factor
50C23×C16C2×C1111yescharacteristic, complemented
51C23×C11—428no—
52C23×C11—856no—
53C23×C11SD3218yesdirect product factor
54C23×C11C2×D817yes—
55Q8×C11—28no—
56Q8×C11—428no—
57D4×C11—28no—
58D4×C11—428no—
59C2×C4×C11—428no—
60C2×C4×C11C2×D8121yes—
61C2×C4×C11C22×D417yes—
62C8×C11C22×D417yes—
63C8×C11C2511yescharacteristic
64C23×Q8—21no—
65C23×D4—21no—
66C22×Q16—27no—
67C22×Q16C22×C11114yescomplemented
68C22×D8—27no—
69C22×D8C22×C11114yes—
70C23×C8C22×C1111yescharacteristic
71C2×SD32C22×C111112yesdirect product factor
72C22×C16C22×C11114yescomplemented
73C22×C11—48no—
74C22×C11—856no—
75C22×C11C2×SD32128yesdirect product factor
76C22×C11C22×D817yes—
77C4×C11—48no—
78C4×C11C22×D817yes—
79C4×C11C23×D411yescharacteristic
80C25—41no—
81C22×Q8—214no—
82C22×Q8—47no—
83C22×D4—214no—
84C22×D4—47no—
85C23×C4—41no—
86C23×C4D4×C1111yescharacteristic
87C2×Q16—242no—
88C2×Q16C23×C11128yescomplemented
89C2×D8—242no—
90C2×D8C23×C11128yes—
91C22×C8D4×C1117yes—
92C22×C8C23×C1117yes—
93SD32C23×C11164yesdirect product factor
94C2×C16C23×C11128yescomplemented
95C2×C11—88no—
96C2×C11C22×SD32114yesdirect product factor
97C2×C11C23×D811yescharacteristic
98C24—414no—
99C24—88no—
100C24C11×D811yescharacteristic
101C2×Q8—228no—
102C2×Q8—442no—
103C2×D4—228no—
104C2×D4—442no—
105C22×C4—414no—
106C22×C4C11×D817yes—
107C22×C4C2×D4×C1117yes—
108Q16—228no—
109Q16C24×C1118yescomplemented
110D8—228no—
111D8C24×C1118yes—
112C2×C8C2×D4×C11121yes—
113C2×C8C24×C1117yes—
114C16C24×C1118yescomplemented
115C11C23×SD3211yescharacteristic, direct product factor, Sylow
116C23—428no—
117C23—856no—
118C23C11×SD3218yesdirect product factor
119C23C2×C11×D817yes—
120Q8—28no—
121Q8—428no—
122D4—28no—
123D4—428no—
124C2×C4—428no—
125C2×C4C2×C11×D8121yes—
126C2×C4C22×D4×C1117yes—
127C8C22×D4×C1117yes—
128C8C25×C1111yescharacteristic
129C22—48no—
130C22—856no—
131C22C2×C11×SD32128yesdirect product factor
132C22C22×C11×D817yes—
133C4—48no—
134C4C22×C11×D817yes—
135C4C23×D4×C1111yescharacteristic
136C2—88no—
137C2C22×C11×SD32114yesdirect product factor
138C2C23×C11×D811yescharacteristic
subgroupG/H
center, socleC24×C11D8
commutator, Frattini, cosocleC8C25×C11
prime radicalC23×C11×D8C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×Q16C2semidirect
3. C22×C11×SD32C2direct (N × H)
4. C23×C11×C16C2semidirect
8. C22×C11×Q16C22semidirect
12. C2×C11×SD32C22direct (N × H)
13. C22×C11×C16C22semidirect
22. C2×C11×Q16C23semidirect
27. C11×SD32C23direct (N × H)
28. C2×C11×C16C23semidirect
29. C23×SD32C11direct (N × H)
41. C11×Q16C24semidirect
46. C11×C16C24semidirect
47. C23×Q16C2×C11semidirect
49. C22×SD32C2×C11direct (N × H)
50. C23×C16C2×C11semidirect
53. C23×C11SD32direct (N × H)
67. C22×Q16C22×C11semidirect
71. C2×SD32C22×C11direct (N × H)
72. C22×C16C22×C11semidirect
75. C22×C11C2×SD32direct (N × H)
88. C2×Q16C23×C11semidirect
93. SD32C23×C11direct (N × H)
94. C2×C16C23×C11semidirect
96. C2×C11C22×SD32direct (N × H)
109. Q16C24×C11semidirect
114. C16C24×C11semidirect
115. C11C23×SD32direct (N × H)
118. C23C11×SD32direct (N × H)
131. C22C2×C11×SD32direct (N × H)
137. C2C22×C11×SD32direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×Q162
C23×C11×D82
C22×C11×SD322
C23×C11×C162
C23×SD3211