Finite Group Databasebeta

← C2×C11×#2401 #14611742

Subgroups — C2×C11×#2401 #14611742

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2401C2116yesmaximal, direct product factor
2C2×C11×#401C211yesmaximal, characteristic, complemented
3C2×C11×#400C213yesmaximal, complemented
4C2×C11×#397C213yesmaximal
5C2×C11×#396C211yesmaximal, characteristic
6C2×C4×C11×C4⋊C4C213yesmaximal, complemented
7C2×C4×C11×C22⋊C4C213yesmaximal
8C2×C11×#376C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2213yes—
11C22×C11×C4⋊C4C2213yes—
12C22×C11×C22⋊C4C2213yes—
13C22×C11×C22⋊C4C2213yes—
14C22×C42×C11C2213yes—
15C22×C42×C11C2213yes—
16C11×#401C2218yescomplemented
17C11×#400C22124yescomplemented
18C11×#397C22124yes—
19C11×#396C2218yes—
20C4×C11×C4⋊C4C22124yescomplemented
21C4×C11×C22⋊C4C22124yes—
22C11×#376C2218yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2213yes—
25C2×C11×#95C2213yes—
26C2×C11×#95C2213yes—
27C2×C11×#95C2213yes—
28C2×C11×#95C2213yes—
29C25×C11C2311yescharacteristic
30C23×C4×C11—212no—
31C23×C4×C11C2313yes—
32C23×C4×C11C2313yes—
33C23×C4×C11C2313yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2314yes—
36C23×C4×C11C2313yes—
37C23×C4×C11C2311yescharacteristic
38C2×C11×C4⋊C4—212no—
39C2×C11×C4⋊C4—212no—
40C2×C11×C4⋊C4C23112yes—
41C2×C11×C4⋊C4C23112yes—
42C2×C11×C22⋊C4—212no—
43C2×C11×C22⋊C4—212no—
44C2×C11×C22⋊C4C23112yes—
45C2×C11×C22⋊C4C23112yes—
46C2×C42×C11—212no—
47C2×C42×C11—212no—
48C2×C42×C11C23112yes—
49C2×C42×C11C23112yes—
50C11×#95C2314yes—
51C11×#95C23112yes—
52C11×#95C23112yes—
53C11×#95C23112yes—
54C11×#95C23112yes—
55C11×#95C23112yes—
56C2×#2401C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11—26no—
58C24×C11—26no—
59C24×C11#4114yes—
60C24×C11C2412yes—
61C24×C11C2411yescharacteristic
62C22×C4×C11—26no—
63C22×C4×C11—26no—
64C22×C4×C11—26no—
65C22×C4×C11—26no—
66C22×C4×C11—26no—
67C22×C4×C11—26no—
68C22×C4×C11—26no—
69C22×C4×C11—26no—
70C22×C4×C11—26no—
71C22×C4×C11—26no—
72C22×C4×C11—26no—
73C22×C4×C11—26no—
74C22×C4×C11—224no—
75C22×C4×C11—416no—
76C22×C4×C11#41112yes—
77C22×C4×C11#41112yes—
78C22×C4×C11C2412yes—
79C22×C4×C11C2416yes—
80C22×C4×C11C2416yes—
81C22×C4×C11C2416yes—
82C22×C4×C11C2416yes—
83C22×C4×C11C2412yes—
84C11×C4⋊C4—224no—
85C11×C4⋊C4—224no—
86C11×C22⋊C4—224no—
87C11×C22⋊C4—224no—
88C42×C11—224no—
89C42×C11—224no—
90#2401C2×C11116yesdirect product factor
91C2×#401C2×C1111yescharacteristic, complemented
92C2×#400C2×C1113yescomplemented
93C2×#397C2×C1113yes—
94C2×#396C2×C1111yescharacteristic
95C2×C4×C4⋊C4C2×C1113yescomplemented
96C2×C4×C22⋊C4C2×C1113yes—
97C2×#376C2×C1111yescharacteristic, complemented
98C23×C11—224no—
99C23×C11—26no—
100C23×C11—26no—
101C23×C11—44no—
102C23×C11—412no—
103C23×C11C2×#4114yes—
104C23×C11C2×#4116yes—
105C23×C11C2×#4112yes—
106C23×C11C2×#4116yes—
107C23×C11C2511yescharacteristic
108C2×C4×C11—224no—
109C2×C4×C11—26no—
110C2×C4×C11—26no—
111C2×C4×C11—26no—
112C2×C4×C11—26no—
113C2×C4×C11—26no—
114C2×C4×C11—26no—
115C2×C4×C11—26no—
116C2×C4×C11—26no—
117C2×C4×C11—26no—
118C2×C4×C11—26no—
119C2×C4×C11—26no—
120C2×C4×C11—26no—
121C2×C4×C11—44no—
122C2×C4×C11—412no—
123C2×C4×C11—412no—
124C2×C4×C11—412no—
125C2×C4×C11—416no—
126C2×C4×C11#126116yes—
127C2×C4×C11C2×#41112yes—
128C2×C4×C11C2×#41112yes—
129C24×C4C22×C1111yescharacteristic
130C22×C4⋊C4C22×C1113yes—
131C22×C4⋊C4C22×C1113yes—
132C22×C22⋊C4C22×C1113yes—
133C22×C22⋊C4C22×C1113yes—
134C22×C42C22×C1113yes—
135C22×C42C22×C1113yes—
136#401C22×C1118yescomplemented
137#400C22×C11124yescomplemented
138#397C22×C11124yes—
139#396C22×C1118yes—
140C4×C4⋊C4C22×C11124yescomplemented
141C4×C22⋊C4C22×C11124yes—
142#376C22×C1118yescomplemented
143C2×#95C22×C1111yescharacteristic
144C2×#95C22×C1113yes—
145C2×#95C22×C1113yes—
146C2×#95C22×C1113yes—
147C2×#95C22×C1113yes—
148C2×#95C22×C1113yes—
149C22×C11—212no—
150C22×C11—416no—
151C22×C11—42no—
152C22×C11—46no—
153C22×C11C2×#12614yes—
154C22×C11#529112yes—
155C22×C11#529112yes—
156C22×C11C22×#4113yes—
157C22×C11C22×#4111yescharacteristic
158C22×C11C22×#4113yes—
159C4×C11—212no—
160C4×C11—42no—
161C4×C11—46no—
162C4×C11—46no—
163C4×C11—46no—
164C4×C11C2×#12618yes—
165C25C23×C1111yescharacteristic
166C23×C4—212no—
167C23×C4C23×C1113yes—
168C23×C4C23×C1113yes—
169C23×C4C23×C1113yes—
170C23×C4C23×C1111yescharacteristic
171C23×C4C23×C1114yes—
172C23×C4C23×C1113yes—
173C23×C4C23×C1111yescharacteristic
174C2×C4⋊C4—212no—
175C2×C4⋊C4—212no—
176C2×C4⋊C4C23×C11112yes—
177C2×C4⋊C4C23×C11112yes—
178C2×C22⋊C4—212no—
179C2×C22⋊C4—212no—
180C2×C22⋊C4C23×C11112yes—
181C2×C22⋊C4C23×C11112yes—
182C2×C42—212no—
183C2×C42—212no—
184C2×C42C23×C11112yes—
185C2×C42C23×C11112yes—
186#95C23×C1114yes—
187#95C23×C11112yes—
188#95C23×C11112yes—
189#95C23×C11112yes—
190#95C23×C11112yes—
191#95C23×C11112yes—
192C2×C11—44no—
193C2×C11#240118yesdirect product factor
194C2×C11C22×#12611yescharacteristic
195C2×C11C2×#52913yes—
196C2×C11C2×#52913yes—
197C24—26no—
198C24—26no—
199C24C11×#4114yes—
200C24C24×C1112yes—
201C24C24×C1111yescharacteristic
202C22×C4—26no—
203C22×C4—26no—
204C22×C4—26no—
205C22×C4—26no—
206C22×C4—26no—
207C22×C4—26no—
208C22×C4—26no—
209C22×C4—26no—
210C22×C4—26no—
211C22×C4—26no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—224no—
215C22×C4—416no—
216C22×C4C11×#41112yes—
217C22×C4C11×#41112yes—
218C22×C4C24×C1112yes—
219C22×C4C24×C1116yes—
220C22×C4C24×C1116yes—
221C22×C4C24×C1116yes—
222C22×C4C24×C1116yes—
223C22×C4C24×C1112yes—
224C4⋊C4—224no—
225C4⋊C4—224no—
226C22⋊C4—224no—
227C22⋊C4—224no—
228C42—224no—
229C42—224no—
230C11C2×#240111yescharacteristic, direct product factor, Sylow
231C23—224no—
232C23—26no—
233C23—26no—
234C23—44no—
235C23—412no—
236C23C2×C11×#4114yes—
237C23C2×C11×#4116yes—
238C23C2×C11×#4112yes—
239C23C2×C11×#4116yes—
240C23C25×C1111yescharacteristic
241C2×C4—224no—
242C2×C4—26no—
243C2×C4—26no—
244C2×C4—26no—
245C2×C4—26no—
246C2×C4—26no—
247C2×C4—26no—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—26no—
252C2×C4—26no—
253C2×C4—26no—
254C2×C4—44no—
255C2×C4—412no—
256C2×C4—412no—
257C2×C4—412no—
258C2×C4—416no—
259C2×C4C11×#126116yes—
260C2×C4C2×C11×#41112yes—
261C2×C4C2×C11×#41112yes—
262C22—212no—
263C22—416no—
264C22—42no—
265C22—46no—
266C22C2×C11×#12614yes—
267C22C11×#529112yes—
268C22C11×#529112yes—
269C22C22×C11×#4113yes—
270C22C22×C11×#4111yescharacteristic
271C22C22×C11×#4113yes—
272C4—212no—
273C4—42no—
274C4—46no—
275C4—46no—
276C4—46no—
277C4C2×C11×#12618yes—
278C2—44no—
279C2C11×#240118yesdirect product factor
280C2C22×C11×#12611yescharacteristic
281C2C2×C11×#52913yes—
282C2C2×C11×#52913yes—
subgroupG/H
centerC23×C4×C11C23
commutator, Frattini, cosocleC23C25×C11
socleC24×C11C24
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2401C2direct (N × H)
2. C2×C11×#401C2semidirect
3. C2×C11×#400C2semidirect
6. C2×C4×C11×C4⋊C4C2semidirect
8. C2×C11×#376C2semidirect
16. C11×#401C22semidirect
17. C11×#400C22semidirect
20. C4×C11×C4⋊C4C22semidirect
22. C11×#376C22semidirect
56. C2×#2401C11direct (N × H)
90. #2401C2×C11direct (N × H)
91. C2×#401C2×C11semidirect
92. C2×#400C2×C11semidirect
95. C2×C4×C4⋊C4C2×C11semidirect
97. C2×#376C2×C11semidirect
136. #401C22×C11semidirect
137. #400C22×C11semidirect
140. C4×C4⋊C4C22×C11semidirect
142. #376C22×C11semidirect
193. C2×C11#2401direct (N × H)
230. C11C2×#2401direct (N × H)
279. C2C11×#2401direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24012
C2×C11×#4012
C2×C11×#4002
C2×C11×#3972
C2×C11×#3962
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C2×C11×#3762
C2×#240111