Finite Group Databasebeta

← C11×#14673 #14591866

Subgroups — C11×#14673 #14591866

Order 2816.

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 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
1C2×C11×#379C212yesmaximal
2C2×C11×#379C211yesmaximal, characteristic
3C11×#1439C2112yesmaximal, complemented
4C26×C11C2211yescharacteristic
5C22×C11×C4⋊C4C2214yescomplemented
6C22×C11×C22⋊C4C22112yes—
7C22×C11×C22⋊C4C2216yes—
8C11×#379—28no—
9C11×#379C418yescomplemented
10C2×C11×#95C22112yescomplemented
11C25×C11—46no—
12C25×C11—46no—
13C25×C11C2×C414yes—
14C25×C11D414yes—
15C25×C11Q814yes—
16C25×C11C2313yes—
17C23×C4×C11C2318yes—
18C23×C4×C11C2314yes—
19C2×C11×C4⋊C4—412no—
20C2×C11×C22⋊C4—224no—
21C2×C11×C22⋊C4—46no—
22C2×C11×C22⋊C4—46no—
23C2×C11×C22⋊C4—412no—
24C2×C11×C22⋊C4—412no—
25C2×C11×C22⋊C4C2×C4124yes—
26C11×#95—412no—
27#14673C1111yesmaximal, characteristic, direct product factor, Sylow
28C24×C11—26no—
29C24×C11—26no—
30C24×C11—212no—
31C24×C11—212no—
32C24×C11—424no—
33C24×C11—424no—
34C24×C11—412no—
35C24×C11—412no—
36C24×C11—448no—
37C24×C11—416no—
38C24×C11C4⋊C4116yescomplemented
39C24×C11C22×C416yes—
40C24×C11C2×D416yes—
41C24×C11C2×Q816yes—
42C24×C11C2411yescharacteristic
43C22×C4×C11—212no—
44C22×C4×C11—212no—
45C22×C4×C11—28no—
46C22×C4×C11—224no—
47C22×C4×C11—224no—
48C22×C4×C11C22×C418yes—
49C11×C4⋊C4—416no—
50C11×C22⋊C4—424no—
51C11×C22⋊C4—448no—
52C2×#379C2×C1112yes—
53C2×#379C2×C1111yescharacteristic
54#1439C2×C11112yescomplemented
55C23×C11—212no—
56C23×C11—224no—
57C23×C11—224no—
58C23×C11—212no—
59C23×C11—26no—
60C23×C11—212no—
61C23×C11—26no—
62C23×C11—212no—
63C23×C11—448no—
64C23×C11—416no—
65C23×C11—448no—
66C23×C11—464no—
67C23×C11—464no—
68C23×C11—424no—
69C23×C11—412no—
70C23×C11—412no—
71C23×C11C2×C4⋊C4112yes—
72C23×C11C23×C411yescharacteristic
73C23×C11C22×D411yescharacteristic
74C23×C11C22×Q811yescharacteristic
75C23×C11H(5,𝔽2)16yes—
76C23×C11H(5,𝔽2)16yes—
77C2×C4×C11—224no—
78C2×C4×C11—412no—
79C2×C4×C11—44no—
80C2×C4×C11—424no—
81C2×C4×C11—424no—
82C2×C4×C11—48no—
83C26C22×C1111yescharacteristic
84C22×C4⋊C4C22×C1114yescomplemented
85C22×C22⋊C4C22×C11112yes—
86C22×C22⋊C4C22×C1116yes—
87#379—28no—
88#379C4×C1118yescomplemented
89C2×#95C22×C11112yescomplemented
90C22×C11—212no—
91C22×C11—224no—
92C22×C11—464no—
93C22×C11—46no—
94C22×C11—46no—
95C22×C11—412no—
96C22×C11—424no—
97C22×C11—424no—
98C22×C11C22×C4⋊C411yescharacteristic
99C22×C11#51816yes—
100C22×C11#53416yes—
101C22×C11#54313yes—
102C22×C11#54313yes—
103C22×C11#560112yes—
104C22×C11H(3,𝔽4)14yes—
105C4×C11—48no—
106C4×C11—88no—
107C25—46no—
108C25—46no—
109C25C2×C4×C1114yes—
110C25D4×C1114yes—
111C25Q8×C1114yes—
112C25C23×C1113yes—
113C23×C4C23×C1118yes—
114C23×C4C23×C1114yes—
115C2×C4⋊C4—412no—
116C2×C22⋊C4—224no—
117C2×C22⋊C4—46no—
118C2×C22⋊C4—46no—
119C2×C22⋊C4—412no—
120C2×C22⋊C4—412no—
121C2×C22⋊C4C2×C4×C11124yes—
122#95—412no—
123C2×C11—412no—
124C2×C11#231513yes—
125C2×C11#237514yes—
126C2×C11#281214yes—
127C2×C11#284011yescharacteristic
128C2×C11#284213yes—
129C24—26no—
130C24—26no—
131C24—212no—
132C24—212no—
133C24—424no—
134C24—424no—
135C24—412no—
136C24—412no—
137C24—448no—
138C24—416no—
139C24C11×C4⋊C4116yescomplemented
140C24C22×C4×C1116yes—
141C24C2×D4×C1116yes—
142C24C2×Q8×C1116yes—
143C24C24×C1111yescharacteristic
144C22×C4—212no—
145C22×C4—212no—
146C22×C4—28no—
147C22×C4—224no—
148C22×C4—224no—
149C22×C4C22×C4×C1118yes—
150C4⋊C4—416no—
151C22⋊C4—424no—
152C22⋊C4—448no—
153C11#1467311yescharacteristic, direct product factor, Sylow
154C23—212no—
155C23—224no—
156C23—224no—
157C23—212no—
158C23—26no—
159C23—212no—
160C23—26no—
161C23—212no—
162C23—448no—
163C23—464no—
164C23—416no—
165C23—448no—
166C23—464no—
167C23—424no—
168C23—412no—
169C23—412no—
170C23C2×C11×C4⋊C4112yes—
171C23C23×C4×C1111yescharacteristic
172C23C22×D4×C1111yescharacteristic
173C23C22×Q8×C1111yescharacteristic
174C23C11×H(5,𝔽2)16yes—
175C23C11×H(5,𝔽2)16yes—
176C2×C4—224no—
177C2×C4—412no—
178C2×C4—44no—
179C2×C4—424no—
180C2×C4—424no—
181C2×C4—48no—
182C22—212no—
183C22—224no—
184C22—464no—
185C22—424no—
186C22—46no—
187C22—46no—
188C22—412no—
189C22—424no—
190C22C22×C11×C4⋊C411yescharacteristic
191C22C11×#51816yes—
192C22C11×#53416yes—
193C22C11×#54313yes—
194C22C11×#54313yes—
195C22C11×#560112yes—
196C22C11×H(3,𝔽4)14yes—
197C4—48no—
198C4—88no—
199C2—412no—
200C2C11×#231513yes—
201C2C11×#237514yes—
202C2C11×#281214yes—
203C2C11×#284011yescharacteristic
204C2C11×#284213yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC26×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1439C2semidirect
5. C22×C11×C4⋊C4C22semidirect
9. C11×#379C4semidirect
10. C2×C11×#95C22semidirect
27. #14673C11direct (N × H)
38. C24×C11C4⋊C4semidirect
54. #1439C2×C11semidirect
84. C22×C4⋊C4C22×C11semidirect
88. #379C4×C11semidirect
89. C2×#95C22×C11semidirect
139. C24C11×C4⋊C4semidirect
153. C11#14673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3792
C11×#14392
#1467311