Finite Group Databasebeta

← #14658269

Subgroups — #14658269

Order 2816.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#13068785C213yesmaximal
2#13066497C213yesmaximal
3C11×#2844C211yesmaximal, characteristic
4C11×#400—23no—
5C11×#395—23no—
6C11×#382C2213yes—
7C2×#66872—23no—
8C2×#66871—23no—
9#10622548C2211yescharacteristic
10C2×#66867C2213yes—
11C22×Q8×C11—21no—
12C2×C11×C4⋊C4—23no—
13C2×C11×C4⋊C4D413yes—
14C2×C11×C4⋊C4D413yes—
15C2×C42×C11C2311yescharacteristic
16C2×C4⋊Dic11—23no—
17C22×C11⋊C8—23no—
18C11×#95—23no—
19C11×#95—21no—
20C11×#95—26no—
21#66872—46no—
22#66871—46no—
23#66867—23no—
24#66867Q816yescomplemented
25#10583—111nomaximal, Sylow
26C2×Q8×C11—83no—
27C22×C4×C11—23no—
28C22×C4×C11—23no—
29C22×C4×C11C2×D413yes—
30C22×Dic11—41no—
31C11×C4⋊C4—43no—
32C11×C4⋊C4—43no—
33C11×C4⋊C4—83no—
34C42×C11C2×Q813yes—
35C42×C11#4111yescharacteristic
36C4⋊Dic11—43no—
37C4⋊Dic11—43no—
38C2×C11⋊C8—26no—
39C2×C11⋊C8—26no—
40C2×C11⋊C8—26no—
41#2844D1111yescharacteristic
42#1847—113no—
43#1295—113no—
44C23×C11#12011yescharacteristic
45Q8×C11—84no—
46C2×C4×C11—23no—
47C2×C4×C11—23no—
48C2×C4×C11—43no—
49C2×C4×C11—43no—
50C2×C4×C11—46no—
51C2×C4×C11—46no—
52C2×C4×C11C22⋊Q813yes—
53C2×C4×C11C4⋊Q813yes—
54C2×Dic11—83no—
55C11⋊C8—212no—
56C2×#107—223no—
57C2×#106—223no—
58C2×#97—113no—
59#400—23no—
60#395—23no—
61#384—111no—
62#382C2×D1113yes—
63C22×C11#39511yescharacteristic
64C22×C11#45313yes—
65C22×C11#45613yes—
66C4×C11—23no—
67C4×C11—23no—
68C4×C11—83no—
69C4×C11—83no—
70Dic11—161no—
71C22×Q8—21no—
72C22×C8—223no—
73C2×C4⋊C4—23no—
74C2×C4⋊C4—223no—
75C2×C4⋊C4C22⋊D1113yes—
76C2×C4⋊C4C22⋊D1113yes—
77C2×C42C22×D1111yescharacteristic
78#107—446no—
79#106—446no—
80#97—116no—
81#97—223no—
82#95—23no—
83#95—21no—
84#95—26no—
85C2×C11#165511yescharacteristic
86C2×C11#166013yes—
87C2×C11#206013yes—
88C2×Q8—83no—
89C22×C4—23no—
90C22×C4—23no—
91C22×C4—441no—
92C22×C4C2×C22⋊D1113yes—
93C2×C8—226no—
94C2×C8—226no—
95C2×C8—226no—
96C4⋊C4—43no—
97C4⋊C4—43no—
98C4⋊C4—83no—
99C4⋊C4—443no—
100C4⋊C4—443no—
101C42Q8×D1113yes—
102C42#434311yescharacteristic
103C11#1058311yescharacteristic, complemented, Sylow
104C23#6700611yescharacteristic
105Q8—84no—
106C2×C4—23no—
107C2×C4—23no—
108C2×C4—43no—
109C2×C4—43no—
110C2×C4—46no—
111C2×C4—46no—
112C2×C4—883no—
113C2×C4#6699713yes—
114C2×C4#6699913yes—
115C8—2212no—
116C22#1062284211yescharacteristic
117C22#1062285413yes—
118C22#1062285913yes—
119C4—23no—
120C4—23no—
121C4—83no—
122C4—83no—
123C4—1761no—
124C2#1306790511yescharacteristic
125C2#1306792713yes—
126C2#1306995813yes—
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2844C2
socle, prime radicalC23×C11#120
hypercenter#2844D11
hypocenterC11#10583
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
24. #66867Q8semidirect
103. C11#10583semidirect

Maximal subgroups

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

subgroupindex
#130687852
#130664972
C11×#28442
#1058311