Finite Group Databasebeta

← #14657025

Subgroups — #14657025

Order 2816.

542 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068688C213yesmaximal
2C11⋊#1304C213yesmaximal
3C11×#2840C211yesmaximal, characteristic
4C22×C22⋊Dic11C2211yescharacteristic
5C11×#393—26no—
6C11×#379C2213yes—
7#10622860C2213yes—
8#10622165—26no—
9C25×C11C2311yescharacteristic
10C22×Q8×C11—22no—
11C23×Dic11Q812yescomplemented
12C2×C11×C22⋊C4—26no—
13C2×C11×C22⋊C4D416yes—
14C2×C22⋊Dic11—23no—
15C2×C22⋊Dic11—23no—
16C2×C22⋊Dic11—23no—
17C2×C22⋊Dic11—26no—
18C11×#95—26no—
19#10391—111nomaximal, Sylow
20C24×C11—42no—
21C24×C11—82no—
22C24×C11C2×D413yes—
23C24×C11C2×Q811yescharacteristic
24C24×C11#4113yes—
25C2×Q8×C11—84no—
26C2×Q8×C11—82no—
27C22×C4×C11—26no—
28C22×Dic11—26no—
29C22×Dic11—43no—
30C22×Dic11—82no—
31C11×C22⋊C4—46no—
32C11×C22⋊C4—86no—
33C22⋊Dic11—46no—
34C22⋊Dic11—41no—
35C22⋊Dic11—43no—
36C22⋊Dic11—86no—
37#2840D1111yescharacteristic
38#1819—113no—
39#1304—113no—
40C23×C11—26no—
41C23×C11—42no—
42C23×C11—41no—
43C23×C11—46no—
44C23×C11—46no—
45C23×C11—43no—
46C23×C11—88no—
47C23×C11#12011yescharacteristic
48C23×C11C22⋊Q813yes—
49C23×C11#12413yes—
50Q8×C11—88no—
51C2×C4×C11—412no—
52C2×C4×C11—46no—
53C2×Dic11—42no—
54C2×Dic11—86no—
55C2×Dic11—83no—
56C2×Dic11—86no—
57C22×C22⋊C4—111no—
58#393—26no—
59#379—113no—
60#379C2×D1113yes—
61#342—226no—
62C22×C11—22no—
63C22×C11—23no—
64C22×C11—23no—
65C22×C11—26no—
66C22×C11—26no—
67C22×C11—44no—
68C22×C11—86no—
69C22×C11—86no—
70C22×C11#39311yescharacteristic
71C22×C11#45812yes—
72C4×C11—86no—
73Dic11—82no—
74Dic11—163no—
75C25C22×D1111yescharacteristic
76C22×Q8—22no—
77C23×C4—112no—
78C2×C22⋊C4—26no—
79C2×C22⋊C4—223no—
80C2×C22⋊C4—223no—
81C2×C22⋊C4—223no—
82C2×C22⋊C4—226no—
83C2×C22⋊C4C22⋊D1116yes—
84#95—26no—
85C2×C11—22no—
86C2×C11—43no—
87C2×C11—43no—
88C2×C11#203011yescharacteristic
89C2×C11#203212yes—
90C24—42no—
91C24—82no—
92C24Q8×D1111yescharacteristic
93C24#434313yes—
94C24C2×C22⋊D1113yes—
95C2×Q8—84no—
96C2×Q8—82no—
97C22×C4—26no—
98C22×C4—226no—
99C22×C4—443no—
100C22×C4—882no—
101C22⋊C4—46no—
102C22⋊C4—86no—
103C22⋊C4—443no—
104C22⋊C4—441no—
105C22⋊C4—446no—
106C22⋊C4—886no—
107C11#1039111yescharacteristic, complemented, Sylow
108C23—26no—
109C23—42no—
110C23—41no—
111C23—46no—
112C23—46no—
113C23—43no—
114C23—88no—
115C23#6699913yes—
116C23#6700013yes—
117C23#6700611yescharacteristic
118Q8—88no—
119C2×C4—412no—
120C2×C4—46no—
121C2×C4—442no—
122C2×C4—886no—
123C2×C4—883no—
124C2×C4—886no—
125C22—22no—
126C22—23no—
127C22—23no—
128C22—26no—
129C22—26no—
130C22—44no—
131C22—86no—
132C22—86no—
133C22#1062284411yescharacteristic
134C22#1062285612yes—
135C4—86no—
136C4—882no—
137C4—1763no—
138C2—22no—
139C2—43no—
140C2—43no—
141C2#1306978211yescharacteristic
142C2#1306979212yes—
subgroupG/H
centerC22#10622844
commutator, prime radical, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#2840C2
socleC22×C11#393
hypercenter#2840D11
hypocenterC11#10391
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2840

Complements

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

NH ≅ G/Ntype
11. C23×Dic11Q8semidirect
107. C11#10391semidirect

Maximal subgroups

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

subgroupindex
#130686882
C11⋊#13042
C11×#28402
#1039111