Finite Group Databasebeta

← #14646376

Subgroups — #14646376

Order 2816.

2618 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 2618 conjugacy classes of subgroups — too many to draw. Only its 163 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#13068531C216yesmaximal, complemented
2C22×C11×#120C211yesmaximal, characteristic
3C26×C11C411yescharacteristic, complemented
4C23×D4×C11C2213yes—
5C2×C11×#120—212no—
6C22×C11×C22⋊C4C413yescomplemented
7#10622860C2214yescomplemented
8C2×#66898—212no—
9C25×C11—26no—
10C25×C11—412no—
11C25×C11C2×C413yes—
12C25×C11C2311yescharacteristic
13C22×D4×C11—212no—
14C22×D4×C11—412no—
15C22×D4×C11D4112yes—
16C23×C4×C11C2×C413yes—
17C11×#120—232no—
18C2×C11×C22⋊C4—26no—
19C2×C11×C22⋊C4—212no—
20C2×C22⋊Dic11—212no—
21#66898—424no—
22#8541—111nomaximal, Sylow
23C24×C11—212no—
24C24×C11—26no—
25C24×C11—28no—
26C24×C11—46no—
27C24×C11—448no—
28C24×C11—412no—
29C24×C11—412no—
30C24×C11—464no—
31C24×C11—412no—
32C24×C11C22⋊C416yes—
33C24×C11C22×C411yescharacteristic
34C24×C11C2×D416yes—
35C2×D4×C11—224no—
36C2×D4×C11—224no—
37C2×D4×C11—412no—
38C2×D4×C11—448no—
39C22×C4×C11—26no—
40C22×C4×C11—46no—
41C22×C4×C11C22⋊C416yes—
42C22×Dic11—44no—
43C11×C22⋊C4—224no—
44C22⋊Dic11—424no—
45C22×#120D1111yescharacteristic
46#1781—116no—
47C23×C11—26no—
48C23×C11—224no—
49C23×C11—26no—
50C23×C11—26no—
51C23×C11—212no—
52C23×C11—412no—
53C23×C11—412no—
54C23×C11—448no—
55C23×C11—412no—
56C23×C11—448no—
57C23×C11—496no—
58C23×C11—496no—
59C23×C11—412no—
60C23×C11—88no—
61C23×C11#99112yescomplemented
62C23×C11C2×C22⋊C413yes—
63C23×C11#12014yes—
64D4×C11—448no—
65C2×C4×C11—26no—
66C2×C4×C11—212no—
67C2×C4×C11—412no—
68C2×Dic11—812no—
69C26Dic1111yescharacteristic, complemented
70C23×D4C2×D1113yes—
71C2×#120—212no—
72C22×C22⋊C4Dic1113yescomplemented
73C2×#99—2212no—
74#379—114no—
75C22×C11—28no—
76C22×C11—26no—
77C22×C11—212no—
78C22×C11—212no—
79C22×C11—412no—
80C22×C11—448no—
81C22×C11—412no—
82C22×C11—464no—
83C22×C11—412no—
84C22×C11—812no—
85C22×C11#37911yescharacteristic
86C22×C11C2×#9916yes—
87C4×C11—46no—
88Dic11—164no—
89C25—26no—
90C25—412no—
91C25C2×Dic1113yes—
92C25C22×D1111yescharacteristic
93C22×D4—212no—
94C22×D4—412no—
95C22×D4C22⋊D11112yes—
96C23×C4C2×Dic1113yes—
97#120—232no—
98C2×C22⋊C4—26no—
99C2×C22⋊C4—212no—
100C2×C22⋊C4—2212no—
101#99—4424no—
102C2×C11—26no—
103C2×C11—44no—
104C2×C11—412no—
105C2×C11#178113yes—
106C24—212no—
107C24—26no—
108C24—28no—
109C24—46no—
110C24—412no—
111C24—448no—
112C24—412no—
113C24—464no—
114C24—412no—
115C24C22⋊Dic1116yes—
116C24C22×Dic1111yescharacteristic
117C24C2×C22⋊D1116yes—
118C2×D4—224no—
119C2×D4—224no—
120C2×D4—412no—
121C2×D4—448no—
122C22×C4—26no—
123C22×C4—46no—
124C22×C4—444no—
125C22×C4C22⋊Dic1116yes—
126C22⋊C4—224no—
127C22⋊C4—4424no—
128C11#854111yescharacteristic, complemented, Sylow
129C23—26no—
130C23—224no—
131C23—26no—
132C23—26no—
133C23—212no—
134C23—412no—
135C23—412no—
136C23—448no—
137C23—412no—
138C23—448no—
139C23—496no—
140C23—496no—
141C23—412no—
142C23—88no—
143C23#66898112yescomplemented
144C23C2×C22⋊Dic1113yes—
145C23#6700614yes—
146D4—448no—
147C2×C4—212no—
148C2×C4—26no—
149C2×C4—412no—
150C2×C4—8812no—
151C22—28no—
152C22—26no—
153C22—212no—
154C22—212no—
155C22—412no—
156C22—448no—
157C22—412no—
158C22—464no—
159C22—412no—
160C22—812no—
161C22C2×#6689816yes—
162C22#1062286011yescharacteristic
163C4—46no—
164C4—1764no—
165C2—26no—
166C2—44no—
167C2—412no—
168C2#1306853113yes—
subgroupG/H
centerC22#10622860
commutatorC24×C11C22×C4
FrattiniC25C22×D11
Fitting, prime radicalC22×C11×#120C2
socleC22×C11#379
cosocleC25×C11C23
hypercenterC22×#120D11
hypocenterC11#8541
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. #13068531C2semidirect
3. C26×C11C4semidirect
6. C22×C11×C22⋊C4C4semidirect
7. #10622860C22semidirect
61. C23×C11#99semidirect
69. C26Dic11semidirect
72. C22×C22⋊C4Dic11semidirect
128. C11#8541semidirect
143. C23#66898semidirect

Maximal subgroups

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

subgroupindex
#130685312
C22×C11×#1202
#854111