Finite Group Databasebeta

← #14919894

Subgroups — #14919894

Order 2816.

1800 conjugacy classes of subgroups; only the 1089 normal subgroups are shown.

normal subgroups only

This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 1089 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#13071802C213yesmaximal
2#13071716C2112yesmaximal
3#13071422C2112yesmaximal
4#125×Dic11C213yesmaximal
5C2×C11×#564C211yesmaximal, characteristic
6C11×#564C4116yescomplemented
7C2×C11×#125C22112yes—
8C2×C11×#125C2213yes—
9#10622598C22112yes—
10#10622598C22112yes—
11#10622598C2216yes—
12#10622594C22112yes—
13#10622594C22112yes—
14#10622594C22112yes—
15#10622594C22112yes—
16#10622594C22112yes—
17C4⋊C4×Dic11C2216yes—
18C4⋊C4×Dic11C22112yes—
19C4⋊C4×Dic11C22112yes—
20#10622550C2214yes—
21#10622549C2213yes—
22C4×C4⋊Dic11C22112yes—
23C42×Dic11C2211yescharacteristic
24C11×#125C2×C4196yes—
25C11×#125C2×C4124yes—
26C2×C11×C4⋊C4C2316yes—
27C2×C11×C4⋊C4C23112yes—
28C2×C11×C4⋊C4C23112yes—
29C2×C42×C11C2311yescharacteristic
30C2×C42×C11C2314yes—
31C2×C4⋊Dic11C23112yes—
32C2×C4⋊Dic11C23112yes—
33C2×C4⋊Dic11C2316yes—
34C2×C4×Dic11C2313yes—
35C2×C4×Dic11C2313yes—
36C2×C4×Dic11C23112yes—
37C2×C4×Dic11C23112yes—
38C11⋊#95C23112yes—
39C11⋊#95C23112yes—
40C11⋊#95C23112yes—
41C11⋊#95C23112yes—
42C11⋊#95C23112yes—
43#34526—111nomaximal, Sylow
44C22×C4×C11C2413yes—
45C22×C4×C11C24112yes—
46C22×Dic11C2411yescharacteristic
47C22×Dic11C24112yes—
48C22×Dic11C2413yes—
49C11×C4⋊C4C22×C4124yes—
50C11×C4⋊C4C22×C4148yes—
51C11×C4⋊C4C22×C4148yes—
52C42×C11C22×C414yes—
53C42×C11C22×C4116yes—
54C4⋊Dic11—224no—
55C4⋊Dic11—412no—
56C4⋊Dic11—46no—
57C4×Dic11—26no—
58C4×Dic11—412no—
59C4×Dic11—412no—
60C4×Dic11—43no—
61C2×#564D1111yescharacteristic
62#2382—113no—
63#2370—1112no—
64#2336—1112no—
65C4×#125—113no—
66C23×C11C2511yescharacteristic
67C2×C4×C11—23no—
68C2×C4×C11—212no—
69C2×C4×C11—212no—
70C2×C4×C11—23no—
71C2×C4×C11C23×C416yes—
72C2×C4×C11C23×C4124yes—
73C2×Dic11—26no—
74C2×Dic11—23no—
75C2×Dic11—212no—
76C2×Dic11—212no—
77C2×Dic11—212no—
78C2×Dic112−1+416yes—
79#564Dic11116yescomplemented
80C2×#125C2×D1113yes—
81C2×#125C2×D11112yes—
82#389—116no—
83#389—1112no—
84#389—1112no—
85#387—1112no—
86#387—1112no—
87#387—1112no—
88#387—1112no—
89#387—1112no—
90#383—114no—
91#382—113no—
92C4×C4⋊C4—116no—
93C4×C4⋊C4—1112no—
94C4×C4⋊C4—1112no—
95C4×C4⋊C4—1112no—
96C43—111no—
97C22×C11C24×C411yescharacteristic
98C22×C11C2×2−1+413yes—
99C22×C11#58513yes—
100C4×C11—26no—
101C4×C11—224no—
102Dic11—26no—
103Dic11—412no—
104Dic11—41no—
105#125C2×Dic11124yes—
106#125C2×Dic11196yes—
107C2×C4⋊C4—1112no—
108C2×C4⋊C4—116no—
109C2×C4⋊C4—1112no—
110C2×C4⋊C4C22×D1116yes—
111C2×C4⋊C4C22×D11112yes—
112C2×C4⋊C4C22×D11112yes—
113C2×C42—113no—
114C2×C42—113no—
115C2×C42—1112no—
116C2×C42—1112no—
117C2×C42C22×D1111yescharacteristic
118C2×C42C22×D1114yes—
119#95—1112no—
120#95—1112no—
121#95—1112no—
122#95—1112no—
123#95—1112no—
124C2×C11C4×2−1+413yes—
125C2×C11#355313yes—
126C2×C11#355611yescharacteristic
127C22×C4—113no—
128C22×C4—111no—
129C22×C4—1112no—
130C22×C4C23×D1113yes—
131C22×C4C23×D11112yes—
132C4⋊C4—2224no—
133C4⋊C4—4412no—
134C4⋊C4—446no—
135C4⋊C4C22×Dic11124yes—
136C4⋊C4C22×Dic11148yes—
137C4⋊C4C22×Dic11148yes—
138C42—226no—
139C42—4412no—
140C42—4412no—
141C42—443no—
142C42C22×Dic1114yes—
143C42C22×Dic11116yes—
144C11#3452611yescharacteristic, complemented, Sylow
145C23C24×D1111yescharacteristic
146C2×C4—23no—
147C2×C4—212no—
148C2×C4—212no—
149C2×C4—23no—
150C2×C4—116no—
151C2×C4—226no—
152C2×C4—223no—
153C2×C4—2212no—
154C2×C4—2212no—
155C2×C4—2212no—
156C2×C4C23×Dic1116yes—
157C2×C4C23×Dic11124yes—
158C22D11×2−1+413yes—
159C22#1062345713yes—
160C22C24×Dic1111yescharacteristic
161C4—26no—
162C4—224no—
163C4—226no—
164C4—4412no—
165C4—441no—
166C22−1+4×Dic1113yes—
167C2#1308307313yes—
168C2#1308311011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#564C2
socle, prime radical, cosocleC23×C11C25
hypercenterC2×#564D11
hypocenterC11#34526
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
6. C11×#564C4semidirect
79. #564Dic11semidirect
144. C11#34526semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130717162
#130714222
#125×Dic112
C2×C11×#5642
#3452611