Finite Group Databasebeta

← C2×C11×#2129 #14610550

Subgroups — C2×C11×#2129 #14610550

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal
3C11×#2129C218yesmaximal, direct product factor
4C2×C11×#354C214yesmaximal, complemented
5C22×C11×#41C2211yescharacteristic
6C23×Q8×C11C411yescharacteristic, complemented
7C11×#536—24no—
8C11×#536C414yescomplemented
9C11×#536C2214yes—
10C2×C11×C4⋊Q8C412yescomplemented
11C2×C11×#124C2212yes—
12C2×C11×#123—22no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#117—22no—
15C2×C11×#117C411yescharacteristic, complemented
16C11×#410—24no—
17C11×#410C2218yes—
18C2×C11×#99—22no—
19C2×C11×#99C2214yes—
20C11×#354C22116yescomplemented
21C2×C11×#41—42no—
22C2×C11×#41—42no—
23C2×C11×#41C2×C412yes—
24C2×C11×#41D414yes—
25C2×C11×#41C2312yes—
26C22×Q8×C11—22no—
27C22×Q8×C11—21no—
28C22×Q8×C11—42no—
29C22×Q8×C11—42no—
30C22×Q8×C11C2×C412yes—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11C2×C414yescomplemented
33C22×D4×C11D412yes—
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11D412yes—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8C2×C418yescomplemented
40C11×#124—24no—
41C11×#124C2×C414yes—
42C11×#124C2314yes—
43C11×#123—28no—
44C11×#123—28no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—28no—
47C11×#117—22no—
48C11×#117—28no—
49C11×#117—44no—
50C11×#117C2×C414yescomplemented
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—24no—
57C2×C42×C11—42no—
58C2×C42×C11C2×C412yes—
59C11×#99—28no—
60C11×#99—24no—
61C11×#99C2318yes—
62C2×#2129C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C2×D412yes—
65C11×#41—44no—
66C11×#41—44no—
67C11×#41—44no—
68C11×#41—44no—
69C2×Q8×C11—24no—
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—48no—
74C2×Q8×C11—48no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11C22⋊C412yes—
80C2×Q8×C11C22×C414yes—
81C2×Q8×C11C22×C412yes—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11C22⋊C414yes—
87C2×D4×C11C22×C411yescharacteristic
88C2×D4×C11C2×D414yes—
89C2×D4×C11C2×D412yes—
90C2×D4×C11C2411yescharacteristic
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—44no—
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C412yes—
104C22×C4×C11C22⋊C414yes—
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D414yes—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—216no—
111C11×C4⋊C4—48no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—28no—
114C11×C22⋊C4—28no—
115C11×C22⋊C4—28no—
116C11×C22⋊C4—44no—
117C42×C11—22no—
118C42×C11—48no—
119C42×C11C22×C414yes—
120C2×#536C2×C1111yescharacteristic
121C2×#410C2×C1112yes—
122#2129C2×C1118yesdirect product factor
123C2×#354C2×C1114yescomplemented
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—42no—
129C23×C11—44no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11C2×C22⋊C412yes—
132C23×C11C2×C22⋊C412yes—
133C23×C11C22×D412yes—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—44no—
137Q8×C11—44no—
138Q8×C11—48no—
139D4×C11—44no—
140D4×C11—41no—
141D4×C11—44no—
142D4×C11—42no—
143D4×C11—41no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—44no—
157C2×C4×C11—48no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—48no—
161C2×C4×C11—88no—
162C2×C4×C11#9912yes—
163C2×C4×C11#9912yes—
164C2×C4×C11C2×C22⋊C411yescharacteristic
165C2×C4×C11C2×C22⋊C414yes—
166C2×C4×C11C2×C22⋊C412yes—
167C2×C4×C11C23×C411yescharacteristic
168C22×#41C22×C1111yescharacteristic
169C23×Q8C4×C1111yescharacteristic, complemented
170#536—24no—
171#536C4×C1114yescomplemented
172#536C22×C1114yes—
173C2×C4⋊Q8C4×C1112yescomplemented
174C2×#124C22×C1112yes—
175C2×#123—22no—
176C2×C22⋊Q8—22no—
177C2×#117—22no—
178C2×#117C4×C1111yescharacteristic, complemented
179#410—24no—
180#410C22×C1118yes—
181C2×#99—22no—
182C2×#99C22×C1114yes—
183#354C22×C11116yescomplemented
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—44no—
193C22×C11—42no—
194C22×C11—82no—
195C22×C11C2×#9911yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11C22×C22⋊C411yescharacteristic
198C4×C11—24no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—44no—
202C4×C11—44no—
203C4×C11—88no—
204C4×C11C2×#9914yes—
205C2×#41—42no—
206C2×#41—42no—
207C2×#41C2×C4×C1112yes—
208C2×#41D4×C1114yes—
209C2×#41C23×C1112yes—
210C22×Q8—21no—
211C22×Q8—22no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8C2×C4×C1112yes—
215C22×Q8C2×C4×C1111yescharacteristic
216C22×Q8C2×C4×C1114yescomplemented
217C22×D4D4×C1112yes—
218C22×D4C23×C1111yescharacteristic
219C23×C4—21no—
220C23×C4C2×C4×C1111yescharacteristic
221C23×C4D4×C1112yes—
222C4⋊Q8—24no—
223C4⋊Q8C2×C4×C1118yescomplemented
224#124—24no—
225#124C2×C4×C1114yes—
226#124C23×C1114yes—
227#123—28no—
228#123—28no—
229C22⋊Q8—28no—
230C22⋊Q8—28no—
231#117—22no—
232#117—28no—
233#117—44no—
234#117C2×C4×C1114yescomplemented
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—42no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—24no—
241C2×C42—42no—
242C2×C42C2×C4×C1112yes—
243#99—28no—
244#99—24no—
245#99C23×C1118yes—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11—42no—
250C2×C11—42no—
251C2×C11#212912yesdirect product factor
252C2×C11C22×#9911yescharacteristic
253C24C11×C22⋊C411yescharacteristic
254C24C2×D4×C1112yes—
255#41—44no—
256#41—44no—
257#41—44no—
258#41—44no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—48no—
264C2×Q8—48no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8C11×C22⋊C412yes—
270C2×Q8C22×C4×C1114yes—
271C2×Q8C22×C4×C1112yes—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4C11×C22⋊C414yes—
277C2×D4C22×C4×C1111yescharacteristic
278C2×D4C2×D4×C1114yes—
279C2×D4C2×D4×C1112yes—
280C2×D4C24×C1111yescharacteristic
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—44no—
292C22×C4C11×C22⋊C412yes—
293C22×C4C11×C22⋊C412yes—
294C22×C4C11×C22⋊C414yes—
295C22×C4C11×C22⋊C411yescharacteristic
296C22×C4C22×C4×C1111yescharacteristic
297C22×C4C22×C4×C1112yes—
298C22×C4C2×D4×C1114yes—
299C4⋊C4—24no—
300C4⋊C4—216no—
301C4⋊C4—48no—
302C22⋊C4—24no—
303C22⋊C4—28no—
304C22⋊C4—28no—
305C22⋊C4—28no—
306C22⋊C4—44no—
307C42—22no—
308C42—48no—
309C42C22×C4×C1114yes—
310C11C2×#212911yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—42no—
316C23—44no—
317C23C2×C11×C22⋊C411yescharacteristic
318C23C2×C11×C22⋊C412yes—
319C23C2×C11×C22⋊C412yes—
320C23C22×D4×C1112yes—
321Q8—42no—
322Q8—42no—
323Q8—44no—
324Q8—44no—
325Q8—48no—
326D4—44no—
327D4—41no—
328D4—42no—
329D4—44no—
330D4—41no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—44no—
344C2×C4—48no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—88no—
349C2×C4C11×#9912yes—
350C2×C4C11×#9912yes—
351C2×C4C2×C11×C22⋊C411yescharacteristic
352C2×C4C2×C11×C22⋊C414yes—
353C2×C4C2×C11×C22⋊C412yes—
354C2×C4C23×C4×C1111yescharacteristic
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—44no—
364C22—42no—
365C22—82no—
366C22C2×C11×#9911yescharacteristic
367C22C2×C11×#9911yescharacteristic
368C22C22×C11×C22⋊C411yescharacteristic
369C4—21no—
370C4—24no—
371C4—21no—
372C4—44no—
373C4—44no—
374C4—88no—
375C4C2×C11×#9914yes—
376C2—21no—
377C2—21no—
378C2—42no—
379C2—42no—
380C2—42no—
381C2C11×#212912yesdirect product factor
382C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2129C2direct (N × H)
4. C2×C11×#354C2semidirect
6. C23×Q8×C11C4semidirect
8. C11×#536C4semidirect
10. C2×C11×C4⋊Q8C4semidirect
15. C2×C11×#117C4semidirect
20. C11×#354C22semidirect
32. C22×Q8×C11C2×C4semidirect
39. C11×C4⋊Q8C2×C4semidirect
50. C11×#117C2×C4semidirect
62. C2×#2129C11direct (N × H)
122. #2129C2×C11direct (N × H)
123. C2×#354C2×C11semidirect
169. C23×Q8C4×C11semidirect
171. #536C4×C11semidirect
173. C2×C4⋊Q8C4×C11semidirect
178. C2×#117C4×C11semidirect
183. #354C22×C11semidirect
216. C22×Q8C2×C4×C11semidirect
223. C4⋊Q8C2×C4×C11semidirect
234. #117C2×C4×C11semidirect
251. C2×C11#2129direct (N × H)
310. C11C2×#2129direct (N × H)
381. C2C11×#2129direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4102
C11×#21292
C2×C11×#3542
C2×#212911