Finite Group Databasebeta

← #14643087

Subgroups — #14643087

Order 2816.

322 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#13070179C213yesmaximal
2#13066439C213yesmaximal
3C11×#2810C211yesmaximal, characteristic
4C11×#400—23no—
5C11×#389C2213yes—
6C11×#387—23no—
7#10622548C2211yescharacteristic
8#10622167—23no—
9#10622167—23no—
10#10622162C2213yes—
11C2×C11×C4⋊C4—23no—
12C2×C11×C4⋊C4D413yes—
13C2×C11×C4⋊C4D413yes—
14C2×C42×C11—21no—
15C2×C42×C11C2311yescharacteristic
16C2×C4⋊Dic11—23no—
17C22×C11⋊C8—23no—
18C11×#95—23no—
19C11×#95—23no—
20C11×#95—21no—
21C11×#95—23no—
22#7832—111nomaximal, Sylow
23C22×C4×C11—23no—
24C22×C4×C11—23no—
25C22×C4×C11C2×D413yes—
26C22×Dic11—41no—
27C11×C4⋊C4—23no—
28C11×C4⋊C4—23no—
29C11×C4⋊C4—43no—
30C11×C4⋊C4—43no—
31C11×C4⋊C4—43no—
32C42×C11—41no—
33C42×C11—81no—
34C4⋊Dic11—46no—
35C2×C11⋊C8—43no—
36C2×C11⋊C8—43no—
37C2×C11⋊C8—43no—
38#2810D1111yescharacteristic
39#2100—113no—
40#1271—113no—
41C23×C11#12011yescharacteristic
42C2×C4×C11—23no—
43C2×C4×C11—23no—
44C2×C4×C11—43no—
45C2×C4×C11—43no—
46C2×C4×C11—43no—
47C2×C4×C11—43no—
48C2×C4×C11—43no—
49C2×C4×C11—43no—
50C2×C4×C11#13513yes—
51C2×C4×C11#13713yes—
52C2×Dic11—83no—
53C11⋊C8—83no—
54#400—23no—
55#389C2×D1113yes—
56#387—23no—
57#384—111no—
58#340—223no—
59#340—223no—
60#336—113no—
61C22×C11#45213yes—
62C22×C11#45413yes—
63C22×C11#45811yescharacteristic
64C4×C11—23no—
65C4×C11—23no—
66C4×C11—83no—
67C4×C11—83no—
68Dic11—161no—
69C22×C8—223no—
70C2×C4⋊C4—23no—
71C2×C4⋊C4—223no—
72C2×C4⋊C4C22⋊D1113yes—
73C2×C4⋊C4C22⋊D1113yes—
74C2×C42—21no—
75C2×C42C22×D1111yescharacteristic
76#95—23no—
77#95—23no—
78#95—21no—
79#95—23no—
80C2×C11#161513yes—
81C2×C11#163813yes—
82C2×C11#165811yescharacteristic
83C22×C4—23no—
84C22×C4—23no—
85C22×C4—441no—
86C22×C4C2×C22⋊D1113yes—
87C2×C8—443no—
88C2×C8—443no—
89C2×C8—443no—
90C4⋊C4—23no—
91C4⋊C4—23no—
92C4⋊C4—43no—
93C4⋊C4—43no—
94C4⋊C4—43no—
95C4⋊C4—446no—
96C42—41no—
97C42—81no—
98C11#783211yescharacteristic, complemented, Sylow
99C23#6700611yescharacteristic
100C2×C4—23no—
101C2×C4—23no—
102C2×C4—43no—
103C2×C4—43no—
104C2×C4—43no—
105C2×C4—43no—
106C2×C4—43no—
107C2×C4—43no—
108C2×C4—883no—
109C2×C4#6700313yes—
110C2×C4#6700413yes—
111C8—883no—
112C22#1062285213yes—
113C22#1062285611yescharacteristic
114C22#1062285813yes—
115C4—23no—
116C4—23no—
117C4—83no—
118C4—83no—
119C4—1761no—
120C2#1306764713yes—
121C2#1306778813yes—
122C2#1306791811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2810C2
socle, prime radicalC23×C11#120
hypercenter#2810D11
hypocenterC11#7832
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
98. C11#7832semidirect

Maximal subgroups

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

subgroupindex
#130701792
#130664392
C11×#28102
#783211