Finite Group Databasebeta

← C2×C11×#1989 #14598503

Subgroups — C2×C11×#1989 #14598503

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1989C218yesmaximal, direct product factor
5C2×C11×#340C212yesmaximal
6C2×C11×#340C212yesmaximal
7C23×C8×C11C2212yes—
8C2×C11×#125—22no—
9C2×C11×#125—24no—
10C2×C11×#125C418yescomplemented
11C2×C11×#125C2214yes—
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11—21no—
18C22×C42×C11C2211yescharacteristic
19C2×C11×C4⋊C8—24no—
20C2×C11×C4⋊C8C2214yes—
21C4×C11×C4⋊C4—22no—
22C4×C11×C4⋊C4C2214yes—
23C2×C11×#95—21no—
24C11×#340C2218yes—
25C11×#340C2218yes—
26C23×C4×C11—22no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—24no—
33C22×C8×C11—28no—
34C22×C8×C11C2314yes—
35C11×#125—216no—
36C11×#125—28no—
37C11×#125C2×C4116yescomplemented
38C2×C11×C4⋊C4—28no—
39C2×C11×C4⋊C4—28no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C11×C4⋊C4Q818yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C42×C11—24no—
55C2×C42×C11—44no—
56C2×C42×C11C2×C414yes—
57C2×C42×C11D412yes—
58C2×C42×C11D414yes—
59C2×C42×C11C2312yes—
60C11×C4⋊C8—28no—
61C11×#95—24no—
62C2×#1989C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—24no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—28no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—44no—
74C22×C4×C11—44no—
75C22×C4×C11—44no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C22⋊C414yes—
79C22×C4×C11C22⋊C414yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×Q814yes—
86C22×C4×C11#4114yes—
87C22×C4×C11C2411yescharacteristic
88C2×C8×C11—24no—
89C2×C8×C11—28no—
90C2×C8×C11—48no—
91C11×C4⋊C4—216no—
92C11×C4⋊C4—216no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4C22×C414yes—
100C11×C4⋊C4C22×C414yes—
101C11×C4⋊C4C2×Q818yes—
102C42×C11—48no—
103C42×C11C22⋊C418yes—
104C42×C11C22×C414yes—
105C42×C11C2×D414yes—
106C22×#125C2×C1111yescharacteristic
107C22×C4⋊C8C2×C1111yescharacteristic
108C2×C4×C4⋊C4C2×C1111yescharacteristic
109#1989C2×C1118yesdirect product factor
110C2×#340C2×C1112yes—
111C2×#340C2×C1112yes—
112C23×C11C2×C22⋊C412yes—
113C23×C11C22⋊Q814yes—
114C23×C11#13514yes—
115C23×C11AGL(1,ℤ/8)12yes—
116C23×C11#13712yes—
117C23×C11C22×D411yescharacteristic
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—28no—
122C2×C4×C11—28no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—28no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—48no—
132C2×C4×C11—48no—
133C2×C4×C11—416no—
134C2×C4×C11C2×C22⋊C414yes—
135C2×C4×C11C2×C22⋊C414yes—
136C2×C4×C11C2×C22⋊C412yes—
137C2×C4×C11C4×Q818yes—
138C2×C4×C11C22⋊Q814yes—
139C2×C4×C11#12414yes—
140C2×C4×C11C4⋊Q814yes—
141C2×C4×C11C23×C411yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×Q812yes—
144C2×C4×C11C2×#4112yes—
145C8×C11—44no—
146C23×C8C22×C1112yes—
147C2×#125—22no—
148C2×#125—24no—
149C2×#125C4×C1118yescomplemented
150C2×#125C22×C1114yes—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C22×C1111yescharacteristic
154C22×C4⋊C4C22×C1111yescharacteristic
155C22×C4⋊C4C22×C1112yes—
156C22×C42—21no—
157C22×C42C22×C1111yescharacteristic
158C2×C4⋊C8—24no—
159C2×C4⋊C8C22×C1114yes—
160C4×C4⋊C4—22no—
161C4×C4⋊C4C22×C1114yes—
162C2×#95—21no—
163#340C22×C1118yes—
164#340C22×C1118yes—
165C22×C11#39114yes—
166C22×C11#41614yes—
167C22×C11#41714yes—
168C22×C11#47818yes—
169C22×C11#47918yes—
170C22×C11C22×C22⋊C411yescharacteristic
171C22×C11C2×C22⋊Q812yes—
172C22×C11C2×#13512yes—
173C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
174C22×C11C2×#13711yescharacteristic
175C4×C11—24no—
176C4×C11—24no—
177C4×C11—48no—
178C4×C11—44no—
179C4×C11—44no—
180C4×C11#39114yes—
181C4×C11C2×C4×Q812yes—
182C4×C11C2×#12411yescharacteristic
183C4×C11C2×C4⋊Q811yescharacteristic
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4D4×C1111yescharacteristic
188C23×C4D4×C1111yescharacteristic
189C23×C4C23×C1111yescharacteristic
190C22×C8—24no—
191C22×C8—28no—
192C22×C8C23×C1114yes—
193#125—216no—
194#125—28no—
195#125C2×C4×C11116yescomplemented
196C2×C4⋊C4—28no—
197C2×C4⋊C4—28no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4C2×C4×C1114yes—
207C2×C4⋊C4C2×C4×C1114yes—
208C2×C4⋊C4Q8×C1118yes—
209C2×C4⋊C4C23×C1112yes—
210C2×C4⋊C4C23×C1112yes—
211C2×C4⋊C4C23×C1114yes—
212C2×C42—24no—
213C2×C42—44no—
214C2×C42C2×C4×C1114yes—
215C2×C42D4×C1112yes—
216C2×C42D4×C1114yes—
217C2×C42C23×C1112yes—
218C4⋊C8—28no—
219#95—24no—
220C2×C11#198918yesdirect product factor
221C2×C11C2×#39111yescharacteristic
222C2×C11C2×#41611yescharacteristic
223C2×C11C2×#41711yescharacteristic
224C2×C11C2×#47812yes—
225C2×C11C2×#47912yes—
226C24C2×D4×C1111yescharacteristic
227C22×C4—24no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—28no—
233C22×C4—24no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—44no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C11×C22⋊C414yes—
242C22×C4C11×C22⋊C414yes—
243C22×C4C22×C4×C1112yes—
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1112yes—
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C2×D4×C1112yes—
248C22×C4C2×Q8×C1114yes—
249C22×C4C11×#4114yes—
250C22×C4C24×C1111yescharacteristic
251C2×C8—24no—
252C2×C8—28no—
253C2×C8—48no—
254C4⋊C4—216no—
255C4⋊C4—216no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—28no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—24no—
262C4⋊C4C22×C4×C1114yes—
263C4⋊C4C22×C4×C1114yes—
264C4⋊C4C2×Q8×C1118yes—
265C42—48no—
266C42C11×C22⋊C418yes—
267C42C22×C4×C1114yes—
268C42C2×D4×C1114yes—
269C11C2×#198911yescharacteristic, direct product factor, Sylow
270C23C2×C11×C22⋊C412yes—
271C23C11×C22⋊Q814yes—
272C23C11×#13514yes—
273C23C11×AGL(1,ℤ/8)12yes—
274C23C11×#13712yes—
275C23C22×D4×C1111yescharacteristic
276C2×C4—28no—
277C2×C4—28no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—28no—
284C2×C4—48no—
285C2×C4—48no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—416no—
292C2×C4C2×C11×C22⋊C414yes—
293C2×C4C2×C11×C22⋊C414yes—
294C2×C4C2×C11×C22⋊C412yes—
295C2×C4C4×Q8×C1118yes—
296C2×C4C11×C22⋊Q814yes—
297C2×C4C11×#12414yes—
298C2×C4C11×C4⋊Q814yes—
299C2×C4C23×C4×C1111yescharacteristic
300C2×C4C22×D4×C1111yescharacteristic
301C2×C4C22×Q8×C1112yes—
302C2×C4C2×C11×#4112yes—
303C8—44no—
304C22C11×#39114yes—
305C22C11×#41614yes—
306C22C11×#41714yes—
307C22C11×#47818yes—
308C22C11×#47918yes—
309C22C22×C11×C22⋊C411yescharacteristic
310C22C2×C11×C22⋊Q812yes—
311C22C2×C11×#13512yes—
312C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
313C22C2×C11×#13711yescharacteristic
314C4—24no—
315C4—24no—
316C4—44no—
317C4—44no—
318C4—48no—
319C4C11×#39114yes—
320C4C2×C4×Q8×C1112yes—
321C4C2×C11×#12411yescharacteristic
322C4C2×C11×C4⋊Q811yescharacteristic
323C2C11×#198918yesdirect product factor
324C2C2×C11×#39111yescharacteristic
325C2C2×C11×#41611yescharacteristic
326C2C2×C11×#41711yescharacteristic
327C2C2×C11×#47812yes—
328C2C2×C11×#47912yes—
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×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×#1989C2direct (N × H)
10. C2×C11×#125C4semidirect
37. C11×#125C2×C4semidirect
62. C2×#1989C11direct (N × H)
109. #1989C2×C11direct (N × H)
149. C2×#125C4×C11semidirect
195. #125C2×C4×C11semidirect
220. C2×C11#1989direct (N × H)
269. C11C2×#1989direct (N × H)
323. C2C11×#1989direct (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×C4⋊C82
C2×C4×C11×C4⋊C42
C11×#19892
C2×C11×#3402
C2×#198911