Finite Group Databasebeta

← C2×C11×#1659 #14596172

Subgroups — C2×C11×#1659 #14596172

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×H(3,𝔽4)C211yesmaximal, characteristic
2C2×C11×#497C211yesmaximal, characteristic, complemented
3C2×C11×#489C212yesmaximal, complemented
4C11×#1659C218yesmaximal, direct product factor
5C2×C11×#329C211yesmaximal, characteristic, complemented
6C2×C11×#329C212yesmaximal, complemented
7C22×C11×Q16—21no—
8C22×C11×SD16—21no—
9C11×H(3,𝔽4)—24no—
10C11×H(3,𝔽4)—22no—
11C11×H(3,𝔽4)C2214yes—
12C2×C11×C4⋊Q8C2211yescharacteristic, complemented
13C2×C11×#124—22no—
14C2×C11×#124—21no—
15C2×C11×#124C2211yescharacteristic
16C2×C11×#124C2212yes—
17C2×C11×#120—22no—
18C2×C11×#120—21no—
19C11×#497—22no—
20C11×#497C2214yescomplemented
21C11×#489—24no—
22C11×#489C2218yescomplemented
23C2×C11×#103—22no—
24C2×C11×#102—22no—
25C2×C11×#97C2211yescharacteristic, complemented
26C2×C11×#97C2212yescomplemented
27C11×#329C2214yescomplemented
28C11×#329C2218yescomplemented
29C25×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D412yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11D412yes—
36C22×D4×C11D411yescharacteristic
37C2×C11×Q16—24no—
38C2×C11×Q16—44no—
39C2×C11×SD16—24no—
40C2×C11×SD16—44no—
41C22×C8×C11—21no—
42C22×C8×C11—22no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yescomplemented
46C11×#124—28no—
47C11×#124—24no—
48C11×#124—28no—
49C11×#124—24no—
50C11×#124—22no—
51C11×#124—22no—
52C11×#124—22no—
53C11×#124D414yes—
54C11×#124D412yes—
55C11×#124C2314yes—
56C11×#124C2312yes—
57C11×#120—28no—
58C11×#120—24no—
59C11×#120—28no—
60C11×#120—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C11×#103—28no—
70C11×#102—28no—
71C11×#97—22no—
72C11×#97—21no—
73C11×#97C2314yescomplemented
74C11×#97C2312yescomplemented
75C2×#1659C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—24no—
77C24×C11—21no—
78C24×C11—22no—
79C24×C11—82no—
80C24×C11—84no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—42no—
85C2×Q8×C11—44no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—41no—
89C2×Q8×C11C2×D414yes—
90C2×Q8×C11C2×D412yes—
91C2×D4×C11—24no—
92C2×D4×C11—28no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—42no—
96C2×D4×C11—44no—
97C2×D4×C11—82no—
98C2×D4×C11—84no—
99C2×D4×C11C2×D414yes—
100C2×D4×C11C2×D412yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C11×Q16—48no—
107C11×SD16—48no—
108C2×C8×C11—24no—
109C2×C8×C11—22no—
110C2×C8×C11—24no—
111C2×C8×C11—44no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—42no—
114C11×C22⋊C4—28no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C42×C11—24no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D412yes—
125C42×C11C2411yescharacteristic
126C2×H(3,𝔽4)C2×C1111yescharacteristic
127C2×#497C2×C1111yescharacteristic, complemented
128C2×#489C2×C1112yescomplemented
129#1659C2×C1118yesdirect product factor
130C2×#329C2×C1112yescomplemented
131C2×#329C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—24no—
134C23×C11—42no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11—44no—
138C23×C11—44no—
139C23×C11—84no—
140C23×C11—88no—
141C23×C11—816no—
142C23×C11#12011yescharacteristic
143Q8×C11—42no—
144Q8×C11—44no—
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—81no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—42no—
151D4×C11—44no—
152D4×C11—81no—
153D4×C11—82no—
154D4×C11—84no—
155D4×C11—88no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11#12012yes—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11C22×D412yes—
167C2×C4×C11C22×D411yescharacteristic
168C8×C11—24no—
169C8×C11—44no—
170C22×Q16—21no—
171C22×SD16—21no—
172H(3,𝔽4)—24no—
173H(3,𝔽4)—22no—
174H(3,𝔽4)C22×C1114yes—
175C2×C4⋊Q8C22×C1111yescharacteristic, complemented
176C2×#124—21no—
177C2×#124—22no—
178C2×#124C22×C1112yes—
179C2×#124C22×C1111yescharacteristic
180C2×#120—21no—
181C2×#120—22no—
182#497—22no—
183#497C22×C1114yescomplemented
184#489—24no—
185#489C22×C1118yescomplemented
186C2×#103—22no—
187C2×#102—22no—
188C2×#97C22×C1112yescomplemented
189C2×#97C22×C1111yescharacteristic, complemented
190#329C22×C1114yescomplemented
191#329C22×C1118yescomplemented
192C22×C11—42no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—44no—
196C22×C11—44no—
197C22×C11—816no—
198C22×C11—84no—
199C22×C11—88no—
200C22×C11#45312yes—
201C22×C11#45514yes—
202C22×C11C2×#12011yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—42no—
208C4×C11—44no—
209C4×C11—82no—
210C25—21no—
211C22×Q8—21no—
212C22×Q8D4×C1111yescharacteristic
213C22×Q8D4×C1112yes—
214C22×D4—21no—
215C22×D4—22no—
216C22×D4D4×C1111yescharacteristic
217C22×D4D4×C1112yes—
218C2×Q16—24no—
219C2×Q16—44no—
220C2×SD16—24no—
221C2×SD16—44no—
222C22×C8—21no—
223C22×C8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—21no—
226C4⋊Q8C23×C1112yescomplemented
227#124—28no—
228#124—24no—
229#124—28no—
230#124—24no—
231#124—22no—
232#124—22no—
233#124—22no—
234#124D4×C1114yes—
235#124D4×C1112yes—
236#124C23×C1114yes—
237#124C23×C1112yes—
238#120—28no—
239#120—24no—
240#120—28no—
241#120—24no—
242C2×C4⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C42—21no—
249C2×C42C23×C1111yescharacteristic
250#103—28no—
251#102—28no—
252#97—22no—
253#97—21no—
254#97C23×C1114yescomplemented
255#97C23×C1112yescomplemented
256C2×C11—82no—
257C2×C11—84no—
258C2×C11#165914yesdirect product factor
259C2×C11C2×#45311yescharacteristic
260C2×C11C2×#45512yes—
261C24—24no—
262C24—21no—
263C24—22no—
264C24—82no—
265C24—84no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—42no—
270C2×Q8—44no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8C2×D4×C1114yes—
275C2×Q8C2×D4×C1112yes—
276C2×D4—24no—
277C2×D4—28no—
278C2×D4—22no—
279C2×D4—21no—
280C2×D4—42no—
281C2×D4—44no—
282C2×D4—82no—
283C2×D4—84no—
284C2×D4C2×D4×C1114yes—
285C2×D4C2×D4×C1112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4C2×D4×C1112yes—
290C22×C4C2×D4×C1111yescharacteristic
291Q16—48no—
292SD16—48no—
293C2×C8—24no—
294C2×C8—22no—
295C2×C8—24no—
296C2×C8—44no—
297C4⋊C4—24no—
298C4⋊C4—42no—
299C22⋊C4—28no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C42—24no—
308C42C2×D4×C1111yescharacteristic
309C42C2×D4×C1112yes—
310C42C24×C1111yescharacteristic
311C11C2×#165911yescharacteristic, direct product factor, Sylow
312C23—22no—
313C23—24no—
314C23—42no—
315C23—44no—
316C23—44no—
317C23—44no—
318C23—44no—
319C23—84no—
320C23—88no—
321C23—816no—
322C23C11×#12011yescharacteristic
323Q8—42no—
324Q8—44no—
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—82no—
329Q8—82no—
330D4—42no—
331D4—44no—
332D4—81no—
333D4—82no—
334D4—84no—
335D4—88no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4C11×#12012yes—
345C2×C4C11×#12011yescharacteristic
346C2×C4C22×D4×C1112yes—
347C2×C4C22×D4×C1111yescharacteristic
348C8—24no—
349C8—44no—
350C22—42no—
351C22—44no—
352C22—44no—
353C22—44no—
354C22—44no—
355C22—816no—
356C22—84no—
357C22—88no—
358C22C11×#45312yes—
359C22C11×#45514yes—
360C22C2×C11×#12011yescharacteristic
361C4—21no—
362C4—21no—
363C4—22no—
364C4—22no—
365C4—42no—
366C4—44no—
367C4—82no—
368C2—82no—
369C2—84no—
370C2C11×#165914yesdirect product factor
371C2C2×C11×#45311yescharacteristic
372C2C2×C11×#45512yes—
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×H(3,𝔽4)C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#497C2semidirect
3. C2×C11×#489C2semidirect
4. C11×#1659C2direct (N × H)
5. C2×C11×#329C2semidirect
6. C2×C11×#329C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
20. C11×#497C22semidirect
22. C11×#489C22semidirect
25. C2×C11×#97C22semidirect
26. C2×C11×#97C22semidirect
27. C11×#329C22semidirect
28. C11×#329C22semidirect
45. C11×C4⋊Q8C23semidirect
73. C11×#97C23semidirect
74. C11×#97C23semidirect
75. C2×#1659C11direct (N × H)
127. C2×#497C2×C11semidirect
128. C2×#489C2×C11semidirect
129. #1659C2×C11direct (N × H)
130. C2×#329C2×C11semidirect
131. C2×#329C2×C11semidirect
175. C2×C4⋊Q8C22×C11semidirect
183. #497C22×C11semidirect
185. #489C22×C11semidirect
188. C2×#97C22×C11semidirect
189. C2×#97C22×C11semidirect
190. #329C22×C11semidirect
191. #329C22×C11semidirect
226. C4⋊Q8C23×C11semidirect
254. #97C23×C11semidirect
255. #97C23×C11semidirect
258. C2×C11#1659direct (N × H)
311. C11C2×#1659direct (N × H)
370. C2C11×#1659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×H(3,𝔽4)2
C2×C11×#4972
C2×C11×#4892
C11×#16592
C2×C11×#3292
C2×#165911