Finite Group Databasebeta

← C2×C11×#2873 #14637247

Subgroups — C2×C11×#2873 #14637247

Order 2816.

3342 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C212yesmaximal
2C22×C11×#117C211yesmaximal, characteristic
3C11×#2873C2116yesmaximal, direct product factor
4C2×C11×#405C218yesmaximal, complemented
5C2×C4×C11×M16C214yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16C4132yescomplemented
8C22×C11×M16C2214yes—
9C22×C11×M16C2214yes—
10C22×C11×M16C22116yes—
11C23×C8×C11C2214yes—
12C2×C11×#117C414yes—
13C2×C11×#117C418yes—
14C2×C11×#117C2214yes—
15C2×C11×#117C2218yes—
16C22×C11×C4⋊C4C412yes—
17C22×C11×C22⋊C4C412yes—
18C22×C42×C11C2212yes—
19C11×#405C22164yescomplemented
20C4×C11×M16C22132yescomplemented
21C2×C11×#97C2218yescomplemented
22C2×C4×C8×C11C2218yescomplemented
23C25×C11C2×C411yescharacteristic
24C23×C4×C11C2×C414yes—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C412yes—
27C23×C4×C11C2×C414yes—
28C23×C4×C11C2×C4116yes—
29C23×C4×C11C2314yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2312yes—
32C2×C11×M16C2×C4132yes—
33C2×C11×M16C2×C4132yescomplemented
34C2×C11×M16C2×C41128yescomplemented
35C2×C11×M16C23116yes—
36C2×C11×M16C23116yes—
37C22×C8×C11C2×C4132yescomplemented
38C22×C8×C11C2318yes—
39C22×C8×C11C23116yes—
40C11×#117C2×C4116yes—
41C11×#117C2×C4132yes—
42C11×#117C23116yes—
43C2×C11×C4⋊C4C2×C418yes—
44C2×C11×C4⋊C4C2×C4116yes—
45C2×C11×C22⋊C4C2×C418yes—
46C2×C11×C22⋊C4C2×C4116yes—
47C2×C42×C11C2×C414yes—
48C2×C42×C11C2×C418yes—
49C2×C42×C11C2318yes—
50C2×C42×C11C2314yes—
51C11×#97C23132yescomplemented
52C4×C8×C11C23132yescomplemented
53C2×#2873C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—44no—
55C24×C11C4218yes—
56C24×C11C22×C412yes—
57C24×C11C22×C411yescharacteristic
58C24×C11C22×C414yes—
59C22×C4×C11—48no—
60C22×C4×C11C4218yes—
61C22×C4×C11C42116yes—
62C22×C4×C11C42132yes—
63C22×C4×C11C22×C418yes—
64C22×C4×C11C22×C4116yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C22×C412yes—
67C22×C4×C11C22×C414yes—
68C22×C4×C11C22×C412yes—
69C22×C4×C11C22×C418yes—
70C22×C4×C11C22×C414yes—
71C22×C4×C11C22×C418yes—
72C22×C4×C11C22×C418yes—
73C22×C4×C11C22×C418yes—
74C22×C4×C11C22×C4132yes—
75C22×C4×C11C2412yes—
76C22×C4×C11C2414yes—
77C22×C4×C11C2411yescharacteristic
78C11×M16C22×C4164yes—
79C11×M16C22×C4164yescomplemented
80C2×C8×C11C22×C4132yes—
81C2×C8×C11C22×C4164yescomplemented
82C2×C8×C11C24116yes—
83C11×C4⋊C4C22×C4132yes—
84C11×C22⋊C4C22×C4132yes—
85C42×C11C22×C4116yes—
86C42×C11C22×C418yes—
87C42×C11C2418yes—
88C23×M16C2×C1112yes—
89C22×#117C2×C1111yescharacteristic
90#2873C2×C11116yesdirect product factor
91C2×#405C2×C1118yescomplemented
92C2×C4×M16C2×C1114yescomplemented
93C23×C11—24no—
94C23×C11—28no—
95C23×C11—416no—
96C23×C11—48no—
97C23×C11C2×C4218yes—
98C23×C11C2×C4214yes—
99C23×C11C2×C42116yes—
100C23×C11C23×C414yes—
101C23×C11C23×C412yes—
102C23×C11C23×C411yescharacteristic
103C2×C4×C11—216no—
104C2×C4×C11—416no—
105C2×C4×C11C2×C4218yes—
106C2×C4×C11C2×C42116yes—
107C2×C4×C11C2×C42116yes—
108C2×C4×C11C2×C42132yes—
109C2×C4×C11C2×C4214yes—
110C2×C4×C11C2×C4218yes—
111C2×C4×C11C23×C4116yes—
112C2×C4×C11C23×C414yes—
113C2×C4×C11C23×C418yes—
114C2×C4×C11C23×C418yes—
115C2×C4×C11C23×C418yes—
116C2×C4×C11C23×C412yes—
117C2×C4×C11C23×C411yescharacteristic
118C2×C4×C11C23×C414yes—
119C2×C4×C11C2511yescharacteristic
120C8×C11C23×C4132yes—
121C24×C4C22×C1111yescharacteristic
122C22×M16C4×C11132yescomplemented
123C22×M16C22×C1114yes—
124C22×M16C22×C1114yes—
125C22×M16C22×C11116yes—
126C23×C8C22×C1114yes—
127C2×#117C4×C1114yes—
128C2×#117C4×C1118yes—
129C2×#117C22×C1114yes—
130C2×#117C22×C1118yes—
131C22×C4⋊C4C4×C1112yes—
132C22×C22⋊C4C4×C1112yes—
133C22×C42C22×C1112yes—
134#405C22×C11164yescomplemented
135C4×M16C22×C11132yescomplemented
136C2×#97C22×C1118yescomplemented
137C2×C4×C8C22×C1118yescomplemented
138C22×C11—28no—
139C22×C11—216no—
140C22×C11—24no—
141C22×C11—28no—
142C22×C11—416no—
143C22×C11C22×C4218yes—
144C22×C11C22×C4214yes—
145C22×C11C22×C4212yes—
146C22×C11#56814yes—
147C22×C11C24×C411yescharacteristic
148C4×C11—216no—
149C4×C11C22×C4212yes—
150C4×C11C22×C4218yes—
151C4×C11C22×C4214yes—
152C4×C11C24×C412yes—
153C25C2×C4×C1111yescharacteristic
154C23×C4C2×C4×C1114yes—
155C23×C4C2×C4×C1111yescharacteristic
156C23×C4C2×C4×C1112yes—
157C23×C4C2×C4×C1114yes—
158C23×C4C2×C4×C11116yes—
159C23×C4C23×C1112yes—
160C23×C4C23×C1114yes—
161C23×C4C23×C1111yescharacteristic
162C2×M16C2×C4×C11132yes—
163C2×M16C2×C4×C11132yescomplemented
164C2×M16C2×C4×C111128yescomplemented
165C2×M16C23×C11116yes—
166C2×M16C23×C11116yes—
167C22×C8C2×C4×C11132yescomplemented
168C22×C8C23×C1118yes—
169C22×C8C23×C11116yes—
170#117C2×C4×C11116yes—
171#117C2×C4×C11132yes—
172#117C23×C11116yes—
173C2×C4⋊C4C2×C4×C1118yes—
174C2×C4⋊C4C2×C4×C11116yes—
175C2×C22⋊C4C2×C4×C1118yes—
176C2×C22⋊C4C2×C4×C11116yes—
177C2×C42C2×C4×C1114yes—
178C2×C42C2×C4×C1118yes—
179C2×C42C23×C1114yes—
180C2×C42C23×C1118yes—
181#97C23×C11132yescomplemented
182C4×C8C23×C11132yescomplemented
183C2×C11—24no—
184C2×C11—28no—
185C2×C11#287314yesdirect product factor
186C2×C11C23×C4211yescharacteristic
187C2×C11C2×#56812yes—
188C24—44no—
189C24C42×C1118yes—
190C24C22×C4×C1112yes—
191C24C22×C4×C1111yescharacteristic
192C24C22×C4×C1114yes—
193C22×C4—48no—
194C22×C4C42×C1118yes—
195C22×C4C42×C11116yes—
196C22×C4C42×C11132yes—
197C22×C4C22×C4×C1118yes—
198C22×C4C22×C4×C11116yes—
199C22×C4C22×C4×C1112yes—
200C22×C4C22×C4×C1111yescharacteristic
201C22×C4C22×C4×C1114yes—
202C22×C4C22×C4×C1112yes—
203C22×C4C22×C4×C1114yes—
204C22×C4C22×C4×C1118yes—
205C22×C4C22×C4×C1118yes—
206C22×C4C22×C4×C1118yes—
207C22×C4C22×C4×C1118yes—
208C22×C4C22×C4×C11132yes—
209C22×C4C24×C1111yescharacteristic
210C22×C4C24×C1112yes—
211C22×C4C24×C1114yes—
212M16C22×C4×C11164yes—
213M16C22×C4×C11164yescomplemented
214C2×C8C22×C4×C11132yes—
215C2×C8C22×C4×C11164yescomplemented
216C2×C8C24×C11116yes—
217C4⋊C4C22×C4×C11132yes—
218C22⋊C4C22×C4×C11132yes—
219C42C22×C4×C1118yes—
220C42C22×C4×C11116yes—
221C42C24×C1118yes—
222C11C2×#287311yescharacteristic, direct product factor, Sylow
223C23—24no—
224C23—28no—
225C23—416no—
226C23—48no—
227C23C2×C42×C1118yes—
228C23C2×C42×C1114yes—
229C23C2×C42×C11116yes—
230C23C23×C4×C1114yes—
231C23C23×C4×C1112yes—
232C23C23×C4×C1111yescharacteristic
233C2×C4—216no—
234C2×C4—416no—
235C2×C4C2×C42×C1118yes—
236C2×C4C2×C42×C11116yes—
237C2×C4C2×C42×C11116yes—
238C2×C4C2×C42×C11132yes—
239C2×C4C2×C42×C1114yes—
240C2×C4C2×C42×C1118yes—
241C2×C4C23×C4×C11116yes—
242C2×C4C23×C4×C1112yes—
243C2×C4C23×C4×C1111yescharacteristic
244C2×C4C23×C4×C1114yes—
245C2×C4C23×C4×C1114yes—
246C2×C4C23×C4×C1118yes—
247C2×C4C23×C4×C1118yes—
248C2×C4C23×C4×C1118yes—
249C2×C4C25×C1111yescharacteristic
250C8C23×C4×C11132yes—
251C22—24no—
252C22—28no—
253C22—28no—
254C22—216no—
255C22—416no—
256C22C22×C42×C1118yes—
257C22C22×C42×C1114yes—
258C22C22×C42×C1112yes—
259C22C11×#56814yes—
260C22C24×C4×C1111yescharacteristic
261C4—216no—
262C4C22×C42×C1112yes—
263C4C22×C42×C1114yes—
264C4C22×C42×C1118yes—
265C4C24×C4×C1112yes—
266C2—24no—
267C2—28no—
268C2C11×#287314yesdirect product factor
269C2C23×C42×C1111yescharacteristic
270C2C2×C11×#56812yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC2C23×C42×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2873C2direct (N × H)
4. C2×C11×#405C2semidirect
5. C2×C4×C11×M16C2semidirect
7. C22×C11×M16C4semidirect
19. C11×#405C22semidirect
20. C4×C11×M16C22semidirect
21. C2×C11×#97C22semidirect
22. C2×C4×C8×C11C22semidirect
33. C2×C11×M16C2×C4semidirect
34. C2×C11×M16C2×C4semidirect
37. C22×C8×C11C2×C4semidirect
51. C11×#97C23semidirect
52. C4×C8×C11C23semidirect
53. C2×#2873C11direct (N × H)
79. C11×M16C22×C4semidirect
81. C2×C8×C11C22×C4semidirect
90. #2873C2×C11direct (N × H)
91. C2×#405C2×C11semidirect
92. C2×C4×M16C2×C11semidirect
122. C22×M16C4×C11semidirect
134. #405C22×C11semidirect
135. C4×M16C22×C11semidirect
136. C2×#97C22×C11semidirect
137. C2×C4×C8C22×C11semidirect
163. C2×M16C2×C4×C11semidirect
164. C2×M16C2×C4×C11semidirect
167. C22×C8C2×C4×C11semidirect
181. #97C23×C11semidirect
182. C4×C8C23×C11semidirect
185. C2×C11#2873direct (N × H)
213. M16C22×C4×C11semidirect
215. C2×C8C22×C4×C11semidirect
222. C11C2×#2873direct (N × H)
268. C2C11×#2873direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×M162
C22×C11×#1172
C11×#28732
C2×C11×#4052
C2×C4×C11×M162
C2×#287311