Finite Group Databasebeta

← C22×C11×#541 #14639874

Subgroups — C22×C11×#541 #14639874

Order 2816.

7110 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C2148yesmaximal, direct product factor
2C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C22×C11×#126C214yesmaximal
4C22×C11×#125C211yesmaximal, characteristic, complemented
5C22×C11×#125C214yesmaximal, complemented
6C22×C11×C22⋊Q8C212yesmaximal
7C22×C4×Q8×C11C212yesmaximal, complemented
8C22×C11×#117C211yesmaximal, characteristic
9C23×Q8×C11C2212yes—
10C24×C4×C11C2211yescharacteristic
11C11×#541C221256yesdirect product factor
12C2×C11×C4⋊Q8C22124yescomplemented
13C2×C11×#126C22196yes—
14C2×C11×#125C22124yescomplemented
15C2×C11×#125C22196yescomplemented
16C2×C11×C22⋊Q8C22148yes—
17C2×C4×Q8×C11C22148yescomplemented
18C2×C11×#117C22124yes—
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2214yes—
22C22×C11×C4⋊C4C2214yes—
23C22×C11×C4⋊C4C2214yes—
24C22×C11×C4⋊C4C2214yes—
25C22×C11×C22⋊C4C2212yes—
26C22×C11×C22⋊C4C2214yes—
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2214yes—
30C25×C11C2311yescharacteristic
31C22×Q8×C11—216no—
32C22×Q8×C11C23124yes—
33C23×C4×C11—28no—
34C23×C4×C11C23112yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2314yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C11×C4⋊Q8C23164yescomplemented
42C11×#126C231256yes—
43C11×#125C23164yescomplemented
44C11×#125C231256yescomplemented
45C11×C22⋊Q8C231128yes—
46C4×Q8×C11C231128yescomplemented
47C11×#117C23164yes—
48C2×C11×C4⋊C4C23124yes—
49C2×C11×C4⋊C4C23124yes—
50C2×C11×C4⋊C4C23148yes—
51C2×C11×C4⋊C4C23148yes—
52C2×C11×C4⋊C4C23148yes—
53C2×C11×C4⋊C4C23148yes—
54C2×C11×C22⋊C4C23124yes—
55C2×C11×C22⋊C4C23148yes—
56C2×C42×C11C23112yes—
57C2×C42×C11C23112yes—
58C2×C42×C11C23148yes—
59C22×#541C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—24no—
61C24×C11—28no—
62C24×C11C2416yes—
63C24×C11C2411yescharacteristic
64C2×Q8×C11—296no—
65C2×Q8×C11C24132yes—
66C22×C4×C11—24no—
67C22×C4×C11—216no—
68C22×C4×C11—28no—
69C22×C4×C11—28no—
70C22×C4×C11—216no—
71C22×C4×C11—248no—
72C22×C4×C11#4118yes—
73C22×C4×C11C24112yes—
74C22×C4×C11C24112yes—
75C22×C4×C11C24124yes—
76C22×C4×C11C24124yes—
77C22×C4×C11C2416yes—
78C22×C4×C11C24116yes—
79C22×C4×C11C2416yes—
80C11×C4⋊C4C24132yes—
81C11×C4⋊C4C24132yes—
82C11×C4⋊C4C24164yes—
83C11×C4⋊C4C24164yes—
84C11×C4⋊C4C24164yes—
85C11×C4⋊C4C24164yes—
86C11×C22⋊C4C24132yes—
87C11×C22⋊C4C24164yes—
88C42×C11C24116yes—
89C42×C11C24116yes—
90C42×C11C24164yes—
91C2×#541C2×C11148yesdirect product factor
92C22×C4⋊Q8C2×C1111yescharacteristic, complemented
93C22×#126C2×C1114yes—
94C22×#125C2×C1114yescomplemented
95C22×#125C2×C1111yescharacteristic, complemented
96C22×C22⋊Q8C2×C1112yes—
97C22×C4×Q8C2×C1112yescomplemented
98C22×#117C2×C1111yescharacteristic
99C23×C11—212no—
100C23×C11—224no—
101C23×C11—416no—
102C23×C11C2×#4114yes—
103C23×C112−1+418yes—
104C23×C11C2514yes—
105C23×C11C2513yes—
106Q8×C11—264no—
107C2×C4×C11—212no—
108C2×C4×C11—248no—
109C2×C4×C11—224no—
110C2×C4×C11—224no—
111C2×C4×C11—248no—
112C2×C4×C11—232no—
113C2×C4×C11C2×#41124yes—
114C2×C4×C11C2518yes—
115C2×C4×C11C2518yes—
116C2×C4×C11C25116yes—
117C2×C4×C11C25116yes—
118C2×C4×C11C2514yes—
119C2×C4×C11C2514yes—
120C23×Q8C22×C1112yes—
121C24×C4C22×C1111yescharacteristic
122#541C22×C111256yesdirect product factor
123C2×C4⋊Q8C22×C11124yescomplemented
124C2×#126C22×C11196yes—
125C2×#125C22×C11124yescomplemented
126C2×#125C22×C11196yescomplemented
127C2×C22⋊Q8C22×C11148yes—
128C2×C4×Q8C22×C11148yescomplemented
129C2×#117C22×C11124yes—
130C22×C4⋊C4C22×C1112yes—
131C22×C4⋊C4C22×C1112yes—
132C22×C4⋊C4C22×C1114yes—
133C22×C4⋊C4C22×C1114yes—
134C22×C4⋊C4C22×C1114yes—
135C22×C4⋊C4C22×C1114yes—
136C22×C22⋊C4C22×C1112yes—
137C22×C22⋊C4C22×C1114yes—
138C22×C42C22×C1111yescharacteristic
139C22×C42C22×C1111yescharacteristic
140C22×C42C22×C1114yes—
141C22×C11—24no—
142C22×C11—28no—
143C22×C11—424no—
144C22×C11#541116yesdirect product factor
145C22×C11C22×#4116yes—
146C22×C11C2×2−1+4112yes—
147C22×C11C2611yescharacteristic
148C4×C11—24no—
149C4×C11—216no—
150C4×C11—28no—
151C4×C11—28no—
152C4×C11—216no—
153C4×C11C22×#4118yes—
154C25C23×C1111yescharacteristic
155C22×Q8—216no—
156C22×Q8C23×C11124yes—
157C23×C4—28no—
158C23×C4C23×C1112yes—
159C23×C4C23×C1114yes—
160C23×C4C23×C1114yes—
161C23×C4C23×C1112yes—
162C23×C4C23×C1111yescharacteristic
163C23×C4C23×C11112yes—
164C23×C4C23×C1111yescharacteristic
165C4⋊Q8C23×C11164yescomplemented
166#126C23×C111256yes—
167#125C23×C11164yescomplemented
168#125C23×C111256yescomplemented
169C22⋊Q8C23×C111128yes—
170C4×Q8C23×C111128yescomplemented
171#117C23×C11164yes—
172C2×C4⋊C4C23×C11124yes—
173C2×C4⋊C4C23×C11124yes—
174C2×C4⋊C4C23×C11148yes—
175C2×C4⋊C4C23×C11148yes—
176C2×C4⋊C4C23×C11148yes—
177C2×C4⋊C4C23×C11148yes—
178C2×C22⋊C4C23×C11124yes—
179C2×C22⋊C4C23×C11148yes—
180C2×C42C23×C11112yes—
181C2×C42C23×C11112yes—
182C2×C42C23×C11148yes—
183C2×C11—44no—
184C2×C11C2×#541112yesdirect product factor
185C2×C11C23×#4111yescharacteristic
186C2×C11C22×2−1+412yes—
187C24—24no—
188C24—28no—
189C24C24×C1116yes—
190C24C24×C1111yescharacteristic
191C2×Q8—296no—
192C2×Q8C24×C11132yes—
193C22×C4—24no—
194C22×C4—216no—
195C22×C4—28no—
196C22×C4—216no—
197C22×C4—28no—
198C22×C4—248no—
199C22×C4C11×#4118yes—
200C22×C4C24×C11112yes—
201C22×C4C24×C11112yes—
202C22×C4C24×C11124yes—
203C22×C4C24×C11124yes—
204C22×C4C24×C1116yes—
205C22×C4C24×C11116yes—
206C22×C4C24×C1116yes—
207C4⋊C4C24×C11132yes—
208C4⋊C4C24×C11132yes—
209C4⋊C4C24×C11164yes—
210C4⋊C4C24×C11164yes—
211C4⋊C4C24×C11164yes—
212C4⋊C4C24×C11164yes—
213C22⋊C4C24×C11132yes—
214C22⋊C4C24×C11164yes—
215C42C24×C11116yes—
216C42C24×C11116yes—
217C42C24×C11164yes—
218C11C22×#54111yescharacteristic, direct product factor, Sylow
219C23—212no—
220C23—224no—
221C23—416no—
222C23C2×C11×#4114yes—
223C23C11×2−1+418yes—
224C23C25×C1114yes—
225C23C25×C1113yes—
226Q8—264no—
227C2×C4—212no—
228C2×C4—248no—
229C2×C4—224no—
230C2×C4—224no—
231C2×C4—248no—
232C2×C4—232no—
233C2×C4C2×C11×#41124yes—
234C2×C4C25×C1118yes—
235C2×C4C25×C1118yes—
236C2×C4C25×C11116yes—
237C2×C4C25×C11116yes—
238C2×C4C25×C1114yes—
239C2×C4C25×C1114yes—
240C22—24no—
241C22—28no—
242C22—424no—
243C22C11×#541116yesdirect product factor
244C22C22×C11×#4116yes—
245C22C2×C11×2−1+4112yes—
246C22C26×C1111yescharacteristic
247C4—24no—
248C4—216no—
249C4—28no—
250C4—28no—
251C4—216no—
252C4C22×C11×#4118yes—
253C2—44no—
254C2C2×C11×#541112yesdirect product factor
255C2C23×C11×#4111yescharacteristic
256C2C22×C11×2−1+412yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC22C26×C11
prime radicalC25×C11C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#541C2direct (N × H)
2. C22×C11×C4⋊Q8C2semidirect
4. C22×C11×#125C2semidirect
5. C22×C11×#125C2semidirect
7. C22×C4×Q8×C11C2semidirect
11. C11×#541C22direct (N × H)
12. C2×C11×C4⋊Q8C22semidirect
14. C2×C11×#125C22semidirect
15. C2×C11×#125C22semidirect
17. C2×C4×Q8×C11C22semidirect
41. C11×C4⋊Q8C23semidirect
43. C11×#125C23semidirect
44. C11×#125C23semidirect
46. C4×Q8×C11C23semidirect
59. C22×#541C11direct (N × H)
91. C2×#541C2×C11direct (N × H)
92. C22×C4⋊Q8C2×C11semidirect
94. C22×#125C2×C11semidirect
95. C22×#125C2×C11semidirect
97. C22×C4×Q8C2×C11semidirect
122. #541C22×C11direct (N × H)
123. C2×C4⋊Q8C22×C11semidirect
125. C2×#125C22×C11semidirect
126. C2×#125C22×C11semidirect
128. C2×C4×Q8C22×C11semidirect
144. C22×C11#541direct (N × H)
165. C4⋊Q8C23×C11semidirect
167. #125C23×C11semidirect
168. #125C23×C11semidirect
170. C4×Q8C23×C11semidirect
184. C2×C11C2×#541direct (N × H)
218. C11C22×#541direct (N × H)
243. C22C11×#541direct (N × H)
254. C2C2×C11×#541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C22×C11×C4⋊Q82
C22×C11×#1262
C22×C11×#1252
C22×C11×C22⋊Q82
C22×C4×Q8×C112
C22×C11×#1172
C22×#54111