Finite Group Databasebeta

← #14656739

Subgroups — #14656739

Order 2816.

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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#13072897C213yesmaximal
2#13068688C213yesmaximal
3C11×#1304C211yesmaximal, characteristic
4C22×C22⋊Dic11C2213yes—
5C11×#379C2213yes—
6#10622860C2211yescharacteristic
7#10622566—26no—
8#10622563—26no—
9#10622556—26no—
10#10622165—26no—
11C25×C11C2311yescharacteristic
12C23×Dic11D416yes—
13C2×C11×C22⋊C4—26no—
14C2×C11×C22⋊C4D416yes—
15C2×C22⋊Dic11—26no—
16C2×C22⋊Dic11—26no—
17C2×C22⋊Dic11—23no—
18C2×C22⋊Dic11—23no—
19C2×C22⋊Dic11—23no—
20C2×C4⋊Dic11—26no—
21C11⋊#95—26no—
22C11⋊#95—212no—
23#10339—111nomaximal, Sylow
24C24×C11—46no—
25C24×C11C2×D413yes—
26C24×C11C2×D413yes—
27C24×C11#4111yescharacteristic
28C22×C4×C11—26no—
29C22×Dic11—26no—
30C22×Dic11—26no—
31C22×Dic11—26no—
32C22×Dic11—412no—
33C22×Dic11—41no—
34C11×C22⋊C4—412no—
35C11×C22⋊C4—46no—
36C22⋊Dic11—46no—
37C22⋊Dic11—43no—
38C22⋊Dic11—46no—
39C22⋊Dic11—43no—
40C4⋊Dic11—86no—
41#2483—113no—
42#1819—113no—
43#1304D1111yescharacteristic
44C23×C11—212no—
45C23×C11—26no—
46C23×C11—43no—
47C23×C11—46no—
48C23×C11—43no—
49C23×C11—88no—
50C23×C11#12013yes—
51C23×C11#12113yes—
52C23×C11#12711yescharacteristic
53C2×C4×C11—412no—
54C2×C4×C11—46no—
55C2×Dic11—412no—
56C2×Dic11—46no—
57C2×Dic11—412no—
58C2×Dic11—86no—
59C2×Dic11—83no—
60C22×C22⋊C4—113no—
61#397—226no—
62#385—226no—
63#381—226no—
64#379—111no—
65#379C2×D1113yes—
66#342—226no—
67C22×C11—26no—
68C22×C11—23no—
69C22×C11—26no—
70C22×C11—23no—
71C22×C11—412no—
72C22×C11—86no—
73C22×C11—82no—
74C22×C11#39211yescharacteristic
75C22×C11#45816yes—
76C4×C11—86no—
77Dic11—86no—
78Dic11—161no—
79C25C22×D1111yescharacteristic
80C23×C4—116no—
81C2×C4⋊C4—226no—
82C2×C22⋊C4—26no—
83C2×C22⋊C4—223no—
84C2×C22⋊C4—226no—
85C2×C22⋊C4—226no—
86C2×C22⋊C4—223no—
87C2×C22⋊C4—223no—
88C2×C22⋊C4D4416yes—
89#95—226no—
90#95—2212no—
91C2×C11—26no—
92C2×C11—41no—
93C2×C11—43no—
94C2×C11#202213yes—
95C24—46no—
96C24C2×D4413yes—
97C24D4×D1113yes—
98C24#434311yescharacteristic
99C22×C4—26no—
100C22×C4—226no—
101C22×C4—226no—
102C22×C4—226no—
103C22×C4—4412no—
104C22×C4—441no—
105C4⋊C4—886no—
106C22⋊C4—412no—
107C22⋊C4—46no—
108C22⋊C4—443no—
109C22⋊C4—443no—
110C22⋊C4—446no—
111C22⋊C4—446no—
112C11#1033911yescharacteristic, complemented, Sylow
113C23—212no—
114C23—26no—
115C23—43no—
116C23—46no—
117C23—43no—
118C23—88no—
119C23#6692711yescharacteristic
120C23#6693513yes—
121C23#6694813yes—
122C2×C4—412no—
123C2×C4—46no—
124C2×C4—4412no—
125C2×C4—446no—
126C2×C4—4412no—
127C2×C4—886no—
128C2×C4—883no—
129C22—26no—
130C22—23no—
131C22—26no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22#1062228411yescharacteristic
137C22#1062235516yes—
138C4—86no—
139C4—886no—
140C4—1761no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2#1306974813yes—
subgroupG/H
centerC22#10622284
commutator, prime radical, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#1304C2
socleC22×C11#392
hypercenter#1304D11
hypocenterC11#10339
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
112. C11#10339semidirect

Maximal subgroups

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

subgroupindex
#130728972
#130686882
C11×#13042
#1033911