Finite Group Databasebeta

← C2×C11×#2026 #14600643

Subgroups — C2×C11×#2026 #14600643

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C22×C11×#103C212yesmaximal
3C2×C11×#391C211yesmaximal, characteristic
4C11×#2026C218yesmaximal, direct product factor
5C2×C11×#340C212yesmaximal
6C2×C11×#336C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C23×C8×C11C2212yes—
9C2×C11×#125—28no—
10C2×C11×#125—22no—
11C2×C11×#125C2214yes—
12C22×C11×C4⋊C4—22no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11C2211yescharacteristic
16C2×C11×#103—28no—
17C2×C11×#103C2218yes—
18C11×#391—22no—
19C11×#391C2214yes—
20C2×C11×#95—22no—
21C11×#340C2218yes—
22C11×#336C2214yes—
23C22×Q8×C11—21no—
24C22×Q8×C11—22no—
25C22×Q8×C11—24no—
26C22×Q8×C11—24no—
27C22×Q8×C11Q814yes—
28C22×Q8×C11C2312yes—
29C23×C4×C11—21no—
30C23×C4×C11—22no—
31C23×C4×C11—21no—
32C23×C4×C11D412yes—
33C23×C4×C11C2311yescharacteristic
34C22×C8×C11—24no—
35C22×C8×C11—24no—
36C22×C8×C11—24no—
37C22×C8×C11C2314yes—
38C11×#125—216no—
39C11×#125—216no—
40C2×C11×C4⋊C4—216no—
41C2×C11×C4⋊C4—28no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D418yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2314yes—
49C2×C42×C11—24no—
50C2×C42×C11D412yes—
51C2×C42×C11C2312yes—
52C11×#103—216no—
53C11×#95—28no—
54C2×#2026C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11C2×D411yescharacteristic
56C2×Q8×C11—24no—
57C2×Q8×C11—22no—
58C2×Q8×C11—216no—
59C2×Q8×C11—24no—
60C2×Q8×C11—24no—
61C2×Q8×C11—42no—
62C2×Q8×C11—42no—
63C2×Q8×C11—48no—
64C2×Q8×C11C2×Q814yes—
65C22×C4×C11—24no—
66C22×C4×C11—28no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—22no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—44no—
76C22×C4×C11—44no—
77C22×C4×C11—42no—
78C22×C4×C11—44no—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D414yes—
82C22×C4×C11C2×Q812yes—
83C22×C4×C11#4114yes—
84C22×C4×C11#4112yes—
85C22×C4×C11C2411yescharacteristic
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C2×C8×C11—24no—
89C2×C8×C11—48no—
90C11×C4⋊C4—232no—
91C11×C4⋊C4—28no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4C2×D418yes—
96C42×C11—24no—
97C42×C11—24no—
98C22×#125C2×C1111yescharacteristic
99C22×#103C2×C1112yes—
100C2×#391C2×C1111yescharacteristic
101#2026C2×C1118yesdirect product factor
102C2×#340C2×C1112yes—
103C2×#336C2×C1111yescharacteristic
104C23×C11#12012yes—
105C23×C11C22⋊Q812yes—
106C23×C11#12412yes—
107C23×C11#13514yes—
108C23×C11#13714yes—
109C23×C11C22×D411yescharacteristic
110Q8×C11—28no—
111Q8×C11—44no—
112Q8×C11—48no—
113C2×C4×C11—24no—
114C2×C4×C11—28no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—48no—
123C2×C4×C11—48no—
124C2×C4×C11—416no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—84no—
128C2×C4×C11#12012yes—
129C2×C4×C11C22⋊Q818yes—
130C2×C4×C11C22⋊Q812yes—
131C2×C4×C11#12418yes—
132C2×C4×C11#12412yes—
133C2×C4×C11C22×D412yes—
134C2×C4×C11C22×Q811yescharacteristic
135C2×C4×C11C2×#4112yes—
136C2×C4×C11C2×#4111yescharacteristic
137C8×C11—44no—
138C23×Q8C22×C1111yescharacteristic
139C23×C8C22×C1112yes—
140C2×#125—28no—
141C2×#125—22no—
142C2×#125C22×C1114yes—
143C22×C4⋊C4—22no—
144C22×C4⋊C4C22×C1111yescharacteristic
145C22×C4⋊C4C22×C1112yes—
146C22×C42C22×C1111yescharacteristic
147C2×#103—28no—
148C2×#103C22×C1118yes—
149#391—22no—
150#391C22×C1114yes—
151C2×#95—22no—
152#340C22×C1118yes—
153#336C22×C1114yes—
154C22×C11#39314yes—
155C22×C11#45218yes—
156C22×C11#47918yes—
157C22×C11#48814yes—
158C22×C11#49114yes—
159C22×C11C2×#12011yescharacteristic
160C22×C11C2×C22⋊Q811yescharacteristic
161C22×C11C2×#12411yescharacteristic
162C22×C11C2×#13512yes—
163C22×C11C2×#13712yes—
164C4×C11—44no—
165C4×C11—44no—
166C4×C11—48no—
167C4×C11—82no—
168C4×C11#39314yes—
169C4×C11C2×C22⋊Q812yes—
170C4×C11C2×#12412yes—
171C22×Q8—21no—
172C22×Q8—22no—
173C22×Q8—24no—
174C22×Q8—24no—
175C22×Q8Q8×C1114yes—
176C22×Q8C23×C1112yes—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4D4×C1112yes—
181C23×C4C23×C1111yescharacteristic
182C22×C8—24no—
183C22×C8—24no—
184C22×C8—24no—
185C22×C8C23×C1114yes—
186#125—216no—
187#125—216no—
188C2×C4⋊C4—216no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4D4×C1118yes—
195C2×C4⋊C4C23×C1112yes—
196C2×C4⋊C4C23×C1114yes—
197C2×C42—24no—
198C2×C42D4×C1112yes—
199C2×C42C23×C1112yes—
200#103—216no—
201#95—28no—
202C2×C11#202618yesdirect product factor
203C2×C11C2×#39311yescharacteristic
204C2×C11C2×#45212yes—
205C2×C11C2×#47912yes—
206C2×C11C2×#48811yescharacteristic
207C2×C11C2×#49111yescharacteristic
208C24C2×D4×C1111yescharacteristic
209C2×Q8—24no—
210C2×Q8—22no—
211C2×Q8—216no—
212C2×Q8—24no—
213C2×Q8—24no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—48no—
217C2×Q8C2×Q8×C1114yes—
218C22×C4—24no—
219C22×C4—28no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—44no—
229C22×C4—44no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4C2×D4×C1114yes—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1114yes—
235C22×C4C2×Q8×C1112yes—
236C22×C4C11×#4114yes—
237C22×C4C11×#4112yes—
238C22×C4C24×C1111yescharacteristic
239C2×C8—24no—
240C2×C8—24no—
241C2×C8—24no—
242C2×C8—48no—
243C4⋊C4—232no—
244C4⋊C4—28no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—42no—
248C4⋊C4C2×D4×C1118yes—
249C42—24no—
250C42—24no—
251C11C2×#202611yescharacteristic, direct product factor, Sylow
252C23C11×#12012yes—
253C23C11×C22⋊Q812yes—
254C23C11×#12412yes—
255C23C11×#13514yes—
256C23C11×#13714yes—
257C23C22×D4×C1111yescharacteristic
258Q8—28no—
259Q8—44no—
260Q8—48no—
261C2×C4—24no—
262C2×C4—28no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—48no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—48no—
272C2×C4—416no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—84no—
276C2×C4C11×#12012yes—
277C2×C4C11×C22⋊Q818yes—
278C2×C4C11×C22⋊Q812yes—
279C2×C4C11×#12418yes—
280C2×C4C11×#12412yes—
281C2×C4C22×D4×C1112yes—
282C2×C4C22×Q8×C1111yescharacteristic
283C2×C4C2×C11×#4112yes—
284C2×C4C2×C11×#4111yescharacteristic
285C8—44no—
286C22C11×#39314yes—
287C22C11×#45218yes—
288C22C11×#47918yes—
289C22C11×#48814yes—
290C22C11×#49114yes—
291C22C2×C11×#12011yescharacteristic
292C22C2×C11×C22⋊Q811yescharacteristic
293C22C2×C11×#12411yescharacteristic
294C22C2×C11×#13512yes—
295C22C2×C11×#13712yes—
296C4—44no—
297C4—44no—
298C4—48no—
299C4—82no—
300C4C11×#39314yes—
301C4C2×C11×C22⋊Q812yes—
302C4C2×C11×#12412yes—
303C2C11×#202618yesdirect product factor
304C2C2×C11×#39311yescharacteristic
305C2C2×C11×#45212yes—
306C2C2×C11×#47912yes—
307C2C2×C11×#48811yescharacteristic
308C2C2×C11×#49111yescharacteristic
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×#2026C2direct (N × H)
54. C2×#2026C11direct (N × H)
101. #2026C2×C11direct (N × H)
202. C2×C11#2026direct (N × H)
251. C11C2×#2026direct (N × H)
303. C2C11×#2026direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C22×C11×#1032
C2×C11×#3912
C11×#20262
C2×C11×#3402
C2×C11×#3362
C2×#202611