Finite Group Databasebeta

← C2×C11×#2086 #14600856

Subgroups — C2×C11×#2086 #14600856

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#107C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C2×C11×#389C212yesmaximal
4C11×#2086C218yesmaximal, direct product factor
5C2×C11×#340C212yesmaximal
6C2×C11×#340C211yesmaximal, characteristic
7C23×C8×C11C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4—22no—
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C2×C11×#107—24no—
14C2×C11×#107C2214yes—
15C2×C11×C4⋊C8—24no—
16C2×C11×C4⋊C8C2214yes—
17C11×#389—24no—
18C11×#389C2218yes—
19C2×C11×#95—22no—
20C11×#340C2218yes—
21C11×#340C2214yes—
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C22×C8×C11—24no—
28C22×C8×C11—22no—
29C22×C8×C11—24no—
30C22×C8×C11D414yes—
31C22×C8×C11C2312yes—
32C22×C8×C11C2312yes—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—24no—
35C2×C11×C4⋊C4—24no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—28no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—48no—
40C2×C11×C4⋊C4Q818yes—
41C2×C11×C4⋊C4C2314yes—
42C2×C11×C4⋊C4C2314yes—
43C2×C42×C11—22no—
44C2×C42×C11—22no—
45C2×C42×C11D412yes—
46C2×C42×C11C2312yes—
47C11×#107—28no—
48C11×C4⋊C8—28no—
49C11×#95—28no—
50C2×#2086C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—28no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—24no—
59C22×C4×C11—44no—
60C22×C4×C11—44no—
61C22×C4×C11—44no—
62C22×C4×C11—44no—
63C22×C4×C11—44no—
64C22×C4×C11D814yes—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×Q814yes—
70C22×C4×C11#4112yes—
71C22×C4×C11#4114yes—
72C22×C4×C11C2411yescharacteristic
73C2×C8×C11—28no—
74C2×C8×C11—22no—
75C2×C8×C11—24no—
76C2×C8×C11—24no—
77C2×C8×C11—44no—
78C2×C8×C11C2×D414yes—
79C11×C4⋊C4—28no—
80C11×C4⋊C4—24no—
81C11×C4⋊C4—24no—
82C11×C4⋊C4—24no—
83C11×C4⋊C4—44no—
84C11×C4⋊C4—416no—
85C11×C4⋊C4C2×Q818yes—
86C42×C11—24no—
87C42×C11—22no—
88C42×C11—22no—
89C22×#107C2×C1111yescharacteristic
90C22×C4⋊C8C2×C1111yescharacteristic
91C2×#389C2×C1112yes—
92#2086C2×C1118yesdirect product factor
93C2×#340C2×C1112yes—
94C2×#340C2×C1111yescharacteristic
95C23×C11#12112yes—
96C23×C11C22⋊Q814yes—
97C23×C11C2×D812yes—
98C23×C11#13512yes—
99C23×C11#13714yes—
100C23×C11C22×D411yescharacteristic
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—28no—
104C2×C4×C11—22no—
105C2×C4×C11—28no—
106C2×C4×C11—24no—
107C2×C4×C11—44no—
108C2×C4×C11—44no—
109C2×C4×C11—44no—
110C2×C4×C11—416no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11—88no—
115C2×C4×C11#12112yes—
116C2×C4×C11C22⋊Q814yes—
117C2×C4×C11#12314yes—
118C2×C4×C11#12518yes—
119C2×C4×C11C4⋊Q814yes—
120C2×C4×C11C2×D814yes—
121C2×C4×C11C22×D411yescharacteristic
122C2×C4×C11C22×Q812yes—
123C2×C4×C11C2×#4112yes—
124C2×C4×C11C2×#4111yescharacteristic
125C8×C11—24no—
126C8×C11—42no—
127C23×C8C22×C1111yescharacteristic
128C23×C8C22×C1111yescharacteristic
129C22×C4⋊C4—22no—
130C22×C4⋊C4C22×C1112yes—
131C22×C4⋊C4C22×C1112yes—
132C22×C42C22×C1111yescharacteristic
133C2×#107—24no—
134C2×#107C22×C1114yes—
135C2×C4⋊C8—24no—
136C2×C4⋊C8C22×C1114yes—
137#389—24no—
138#389C22×C1118yes—
139C2×#95—22no—
140#340C22×C1118yes—
141#340C22×C1114yes—
142C22×C11#39814yes—
143C22×C11#46614yes—
144C22×C11#47014yes—
145C22×C11#47418yes—
146C22×C11#47918yes—
147C22×C11C2×#12111yescharacteristic
148C22×C11C2×C22⋊Q812yes—
149C22×C11C22×D811yescharacteristic
150C22×C11C2×#13511yescharacteristic
151C22×C11C2×#13712yes—
152C4×C11—24no—
153C4×C11—42no—
154C4×C11—48no—
155C4×C11—84no—
156C4×C11#39814yes—
157C4×C11C2×#12311yescharacteristic
158C4×C11C2×#12512yes—
159C4×C11C2×C4⋊Q811yescharacteristic
160C23×C4—22no—
161C23×C4—22no—
162C23×C4D4×C1111yescharacteristic
163C23×C4D4×C1111yescharacteristic
164C23×C4C23×C1111yescharacteristic
165C22×C8—24no—
166C22×C8—22no—
167C22×C8—24no—
168C22×C8D4×C1114yes—
169C22×C8C23×C1112yes—
170C22×C8C23×C1112yes—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—28no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—48no—
178C2×C4⋊C4Q8×C1118yes—
179C2×C4⋊C4C23×C1114yes—
180C2×C4⋊C4C23×C1114yes—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42D4×C1112yes—
184C2×C42C23×C1112yes—
185#107—28no—
186C4⋊C8—28no—
187#95—28no—
188C2×C11#208618yesdirect product factor
189C2×C11C2×#39811yescharacteristic
190C2×C11C2×#46611yescharacteristic
191C2×C11C2×#47011yescharacteristic
192C2×C11C2×#47412yes—
193C2×C11C2×#47912yes—
194C24C2×D4×C1111yescharacteristic
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—28no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—24no—
202C22×C4—44no—
203C22×C4—44no—
204C22×C4—44no—
205C22×C4—44no—
206C22×C4—44no—
207C22×C4C11×D814yes—
208C22×C4C2×D4×C1112yes—
209C22×C4C2×D4×C1112yes—
210C22×C4C2×D4×C1111yescharacteristic
211C22×C4C2×D4×C1112yes—
212C22×C4C2×Q8×C1114yes—
213C22×C4C11×#4112yes—
214C22×C4C11×#4114yes—
215C22×C4C24×C1111yescharacteristic
216C2×C8—28no—
217C2×C8—24no—
218C2×C8—22no—
219C2×C8—24no—
220C2×C8—44no—
221C2×C8C2×D4×C1114yes—
222C4⋊C4—28no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—24no—
226C4⋊C4—44no—
227C4⋊C4—416no—
228C4⋊C4C2×Q8×C1118yes—
229C42—24no—
230C42—22no—
231C42—22no—
232C11C2×#208611yescharacteristic, direct product factor, Sylow
233C23C11×#12112yes—
234C23C11×C22⋊Q814yes—
235C23C2×C11×D812yes—
236C23C11×#13512yes—
237C23C11×#13714yes—
238C23C22×D4×C1111yescharacteristic
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—28no—
242C2×C4—22no—
243C2×C4—28no—
244C2×C4—24no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—416no—
249C2×C4—44no—
250C2×C4—44no—
251C2×C4—44no—
252C2×C4—88no—
253C2×C4C11×#12112yes—
254C2×C4C11×C22⋊Q814yes—
255C2×C4C11×#12314yes—
256C2×C4C11×#12518yes—
257C2×C4C11×C4⋊Q814yes—
258C2×C4C2×C11×D814yes—
259C2×C4C22×D4×C1111yescharacteristic
260C2×C4C22×Q8×C1112yes—
261C2×C4C2×C11×#4112yes—
262C2×C4C2×C11×#4111yescharacteristic
263C8—24no—
264C8—42no—
265C22C11×#39814yes—
266C22C11×#46614yes—
267C22C11×#47014yes—
268C22C11×#47418yes—
269C22C11×#47918yes—
270C22C2×C11×#12111yescharacteristic
271C22C2×C11×C22⋊Q812yes—
272C22C22×C11×D811yescharacteristic
273C22C2×C11×#13511yescharacteristic
274C22C2×C11×#13712yes—
275C4—24no—
276C4—42no—
277C4—48no—
278C4—84no—
279C4C11×#39814yes—
280C4C2×C11×#12311yescharacteristic
281C4C2×C11×#12512yes—
282C4C2×C11×C4⋊Q811yescharacteristic
283C2C11×#208618yesdirect product factor
284C2C2×C11×#39811yescharacteristic
285C2C2×C11×#46611yescharacteristic
286C2C2×C11×#47011yescharacteristic
287C2C2×C11×#47412yes—
288C2C2×C11×#47912yes—
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2086C2direct (N × H)
50. C2×#2086C11direct (N × H)
92. #2086C2×C11direct (N × H)
188. C2×C11#2086direct (N × H)
232. C11C2×#2086direct (N × H)
283. C2C11×#2086direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C22×C11×C4⋊C82
C2×C11×#3892
C11×#20862
C2×C11×#3402
C2×#208611