Finite Group Databasebeta

← C2×C11×#2060 #14600751

Subgroups — C2×C11×#2060 #14600751

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C2×C11×#428C212yesmaximal
3C2×C11×#384C211yesmaximal, characteristic
4C11×#2060C218yesmaximal, direct product factor
5C2×C11×#343C211yesmaximal, characteristic
6C2×C11×#339C212yesmaximal
7C22×C11×M16C2212yes—
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#117C2212yes—
15C22×C11×C4⋊C4—22no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#428—24no—
20C11×#428C2218yes—
21C2×C11×#107—22no—
22C2×C11×#106—22no—
23C11×#384—22no—
24C11×#384C2214yes—
25C11×#343C2214yes—
26C11×#339C2218yes—
27C22×Q8×C11—22no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11D412yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—22no—
33C2×C11×M16—24no—
34C2×C11×M16Q818yescomplemented
35C2×C11×M16C2314yes—
36C22×C8×C11—22no—
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8—28no—
39C11×#125—28no—
40C11×#125—28no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—28no—
43C11×#117—22no—
44C11×#117—22no—
45C11×#117D414yes—
46C11×#117C2314yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—28no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—48no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11Q814yescomplemented
66C2×C42×C11C2312yes—
67C11×#107—28no—
68C11×#106—28no—
69C2×#2060C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11C2×D411yescharacteristic
71C2×Q8×C11—28no—
72C2×Q8×C11—84no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—44no—
83C22×C4×C11—44no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×Q814yes—
91C22×C4×C11C2×Q812yes—
92C22×C4×C11#4112yes—
93C22×C4×C11C2411yescharacteristic
94C11×M16—28no—
95C11×M16—24no—
96C11×M16C2×Q818yescomplemented
97C2×C8×C11—28no—
98C2×C8×C11—24no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—216no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—416no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4C2×D414yes—
109C11×C4⋊C4C2×D414yes—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—24no—
112C42×C11—24no—
113C42×C11—24no—
114C42×C11—24no—
115C42×C11—22no—
116C42×C11C2×Q814yescomplemented
117C2×#544C2×C1111yescharacteristic
118C2×#428C2×C1112yes—
119C2×#384C2×C1111yescharacteristic
120#2060C2×C1118yesdirect product factor
121C2×#343C2×C1111yescharacteristic
122C2×#339C2×C1112yes—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11#12011yescharacteristic
126C23×C11#12011yescharacteristic
127C23×C11C22⋊Q812yes—
128C23×C11C4⋊Q812yes—
129C23×C11C22×D411yescharacteristic
130Q8×C11—88no—
131C2×C4×C11—24no—
132C2×C4×C11—216no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11—82no—
147C2×C4×C11#12012yes—
148C2×C4×C11C22⋊Q814yes—
149C2×C4×C11C22⋊Q814yes—
150C2×C4×C11C22⋊Q812yes—
151C2×C4×C11C4⋊Q814yes—
152C2×C4×C11C4⋊Q814yes—
153C2×C4×C11C4⋊Q812yes—
154C2×C4×C11C22×D412yes—
155C2×C4×C11C22×Q812yes—
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C8×C11—28no—
159C22×M16C22×C1112yes—
160#544—24no—
161#544—22no—
162#544C22×C1114yes—
163C2×C4⋊Q8—22no—
164C2×#125—22no—
165C2×C22⋊Q8—22no—
166C2×#117C22×C1112yes—
167C22×C4⋊C4—22no—
168C22×C4⋊C4C22×C1111yescharacteristic
169C22×C4⋊C4C22×C1111yescharacteristic
170C22×C42C22×C1111yescharacteristic
171#428—24no—
172#428C22×C1118yes—
173C2×#107—22no—
174C2×#106—22no—
175#384—22no—
176#384C22×C1114yes—
177#343C22×C1114yes—
178#339C22×C1118yes—
179C22×C11—24no—
180C22×C11—24no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#39512yes—
186C22×C11#39512yes—
187C22×C11#45312yes—
188C22×C11#45612yes—
189C22×C11C2×#12011yescharacteristic
190C22×C11C2×C22⋊Q811yescharacteristic
191C22×C11C2×C4⋊Q811yescharacteristic
192C4×C11—28no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11—44no—
196C4×C11—82no—
197C4×C11#39514yes—
198C4×C11C2×C22⋊Q812yes—
199C4×C11C2×C4⋊Q812yes—
200C22×Q8—22no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4D4×C1112yes—
204C23×C4C23×C1111yescharacteristic
205C2×M16—22no—
206C2×M16—24no—
207C2×M16Q8×C1118yescomplemented
208C2×M16C23×C1114yes—
209C22×C8—22no—
210C4⋊Q8—28no—
211C4⋊Q8—28no—
212#125—28no—
213#125—28no—
214C22⋊Q8—28no—
215C22⋊Q8—28no—
216#117—22no—
217#117—22no—
218#117D4×C1114yes—
219#117C23×C1114yes—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—48no—
229C2×C4⋊C4D4×C1112yes—
230C2×C4⋊C4D4×C1112yes—
231C2×C4⋊C4D4×C1112yes—
232C2×C4⋊C4C23×C1112yes—
233C2×C4⋊C4C23×C1112yes—
234C2×C22⋊C4—22no—
235C2×C42—22no—
236C2×C42—21no—
237C2×C42—22no—
238C2×C42Q8×C1114yescomplemented
239C2×C42C23×C1112yes—
240#107—28no—
241#106—28no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—22no—
245C2×C11#206014yesdirect product factor
246C2×C11C2×#39511yescharacteristic
247C2×C11C2×#45311yescharacteristic
248C2×C11C2×#45611yescharacteristic
249C24C2×D4×C1111yescharacteristic
250C2×Q8—28no—
251C2×Q8—84no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C1114yes—
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1112yes—
268C22×C4C2×D4×C1112yes—
269C22×C4C2×Q8×C1114yes—
270C22×C4C2×Q8×C1112yes—
271C22×C4C11×#4112yes—
272C22×C4C24×C1111yescharacteristic
273M16—28no—
274M16—24no—
275M16C2×Q8×C1118yescomplemented
276C2×C8—28no—
277C2×C8—24no—
278C4⋊C4—28no—
279C4⋊C4—216no—
280C4⋊C4—24no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—416no—
286C4⋊C4—42no—
287C4⋊C4C2×D4×C1114yes—
288C4⋊C4C2×D4×C1114yes—
289C22⋊C4—24no—
290C22⋊C4—24no—
291C42—24no—
292C42—24no—
293C42—24no—
294C42—22no—
295C42C2×Q8×C1114yescomplemented
296C11C2×#206011yescharacteristic, direct product factor, Sylow
297C23—22no—
298C23—22no—
299C23C11×#12011yescharacteristic
300C23C11×#12011yescharacteristic
301C23C11×C22⋊Q812yes—
302C23C11×C4⋊Q812yes—
303C23C22×D4×C1111yescharacteristic
304Q8—88no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—216no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4C11×#12012yes—
322C2×C4C11×C22⋊Q814yes—
323C2×C4C11×C22⋊Q814yes—
324C2×C4C11×C22⋊Q812yes—
325C2×C4C11×C4⋊Q814yes—
326C2×C4C11×C4⋊Q814yes—
327C2×C4C11×C4⋊Q812yes—
328C2×C4C22×D4×C1112yes—
329C2×C4C22×Q8×C1112yes—
330C2×C4C22×Q8×C1111yescharacteristic
331C2×C4C2×C11×#4111yescharacteristic
332C8—28no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—24no—
338C22—24no—
339C22C11×#39512yes—
340C22C11×#39512yes—
341C22C11×#45312yes—
342C22C11×#45612yes—
343C22C2×C11×#12011yescharacteristic
344C22C2×C11×C22⋊Q811yescharacteristic
345C22C2×C11×C4⋊Q811yescharacteristic
346C4—28no—
347C4—44no—
348C4—44no—
349C4—44no—
350C4—82no—
351C4C11×#39514yes—
352C4C2×C11×C22⋊Q812yes—
353C4C2×C11×C4⋊Q812yes—
354C2—21no—
355C2—21no—
356C2—22no—
357C2C11×#206014yesdirect product factor
358C2C2×C11×#39511yescharacteristic
359C2C2×C11×#45311yescharacteristic
360C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2060C2direct (N × H)
34. C2×C11×M16Q8semidirect
65. C2×C42×C11Q8semidirect
69. C2×#2060C11direct (N × H)
96. C11×M16C2×Q8semidirect
116. C42×C11C2×Q8semidirect
120. #2060C2×C11direct (N × H)
207. C2×M16Q8×C11semidirect
238. C2×C42Q8×C11semidirect
245. C2×C11#2060direct (N × H)
275. M16C2×Q8×C11semidirect
295. C42C2×Q8×C11semidirect
296. C11C2×#2060direct (N × H)
357. C2C11×#2060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4282
C2×C11×#3842
C11×#20602
C2×C11×#3432
C2×C11×#3392
C2×#206011