Finite Group Databasebeta

← C2×C11×#2127 #14610548

Subgroups — C2×C11×#2127 #14610548

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C22×C11×#99C212yesmaximal, complemented
3C11×#2127C218yesmaximal, direct product factor
4C2×C11×#354C212yesmaximal, complemented
5C2×C11×#353C212yesmaximal, complemented
6C22×C11×#41C411yescharacteristic, complemented
7C23×D4×C11C2211yescharacteristic
8C11×#535—24no—
9C11×#535C414yescomplemented
10C11×#535C2214yes—
11C2×C11×#127C411yescharacteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C411yescharacteristic, complemented
14C2×C11×#124C2211yescharacteristic
15C2×C11×#121—22no—
16C2×C11×#120—22no—
17C2×C11×#117C411yescharacteristic, complemented
18C22×C11×C22⋊C4—22no—
19C2×C11×#99—24no—
20C2×C11×#99—22no—
21C2×C11×#99C2214yes—
22C2×C11×#99C2218yescomplemented
23C11×#354C2218yescomplemented
24C11×#353C2218yescomplemented
25C25×C11D412yes—
26C2×C11×#41—22no—
27C2×C11×#41—42no—
28C2×C11×#41—42no—
29C2×C11×#41C2×C414yescomplemented
30C22×Q8×C11C2×C411yescharacteristic, complemented
31C22×D4×C11—21no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—42no—
35C22×D4×C11—42no—
36C22×D4×C11C2×C411yescharacteristic
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic, complemented
39C22×D4×C11D412yes—
40C22×D4×C11D414yes—
41C22×D4×C11C2311yescharacteristic
42C22×D4×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11—42no—
45C23×C4×C11C2×C411yescharacteristic
46C11×#127—22no—
47C11×#127—22no—
48C11×#127C2×C414yescomplemented
49C11×#127C2×C412yescomplemented
50C11×#127C2312yes—
51C11×#124—22no—
52C11×#124—22no—
53C11×#124C2×C414yescomplemented
54C11×#124C2×C412yescomplemented
55C11×#124C2312yes—
56C11×#121—28no—
57C11×#121—28no—
58C11×#120—28no—
59C11×#120—28no—
60C11×#117—22no—
61C11×#117C2×C414yescomplemented
62C2×C11×C4⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—44no—
69C2×C11×C22⋊C4—42no—
70C2×C42×C11C2×C411yescharacteristic, complemented
71C2×C42×C11C2×C411yescharacteristic, complemented
72C11×#99—24no—
73C11×#99—28no—
74C11×#99C2318yes—
75C2×#2127C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—22no—
77C24×C11—24no—
78C24×C11—22no—
79C24×C11—21no—
80C24×C11—84no—
81C24×C11C22⋊C412yes—
82C24×C11C22⋊C414yes—
83C24×C11C22⋊C411yescharacteristic
84C24×C11C2×D412yes—
85C24×C11C2×D414yes—
86C11×#41—48no—
87C11×#41—48no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11C22×C412yescomplemented
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C2×D4×C11—44no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C2×D4×C11—42no—
104C2×D4×C11—41no—
105C2×D4×C11—44no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—84no—
112C2×D4×C11—84no—
113C2×D4×C11C22⋊C414yes—
114C2×D4×C11C22⋊C412yes—
115C2×D4×C11C22×C412yes—
116C2×D4×C11C22×C411yescharacteristic
117C2×D4×C11C22×C412yescomplemented
118C2×D4×C11C2×D414yes—
119C2×D4×C11C2×D412yes—
120C2×D4×C11C2411yescharacteristic
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—48no—
130C22×C4×C11—44no—
131C22×C4×C11—88no—
132C22×C4×C11C22⋊C411yescharacteristic
133C22×C4×C11C22⋊C412yes—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C11×C4⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—28no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—48no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11C22×C412yescomplemented
147C42×C11C22×C412yescomplemented
148C2×#535C2×C1111yescharacteristic
149C22×#99C2×C1112yescomplemented
150#2127C2×C1118yesdirect product factor
151C2×#354C2×C1112yescomplemented
152C2×#353C2×C1112yescomplemented
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—22no—
160C23×C11—24no—
161C23×C11—22no—
162C23×C11—42no—
163C23×C11—48no—
164C23×C11—44no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—84no—
170C23×C11—84no—
171C23×C11—84no—
172C23×C11—88no—
173C23×C11#9912yes—
174C23×C11#9912yes—
175C23×C11C2×C22⋊C411yescharacteristic
176C23×C11C2×C22⋊C412yes—
177C23×C11C2×C22⋊C414yes—
178C23×C11C2×C22⋊C412yes—
179C23×C11C22×D412yes—
180Q8×C11—42no—
181Q8×C11—42no—
182D4×C11—44no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—41no—
186D4×C11—44no—
187D4×C11—42no—
188D4×C11—41no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—48no—
192D4×C11—88no—
193D4×C11—84no—
194D4×C11—84no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—48no—
210C2×C4×C11—816no—
211C2×C4×C11—88no—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C23×C411yescharacteristic
215C22×#41C4×C1111yescharacteristic, complemented
216C23×D4C22×C1111yescharacteristic
217#535—24no—
218#535C4×C1114yescomplemented
219#535C22×C1114yes—
220C2×#127C4×C1111yescharacteristic, complemented
221C2×#127C22×C1111yescharacteristic
222C2×#124C4×C1111yescharacteristic, complemented
223C2×#124C22×C1111yescharacteristic
224C2×#121—22no—
225C2×#120—22no—
226C2×#117C4×C1111yescharacteristic, complemented
227C22×C22⋊C4—22no—
228C2×#99—24no—
229C2×#99—22no—
230C2×#99C22×C1114yes—
231C2×#99C22×C1118yescomplemented
232#354C22×C1118yescomplemented
233#353C22×C1118yescomplemented
234C22×C11—22no—
235C22×C11—24no—
236C22×C11—22no—
237C22×C11—24no—
238C22×C11—22no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—44no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—48no—
245C22×C11—48no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—84no—
253C22×C11—84no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11C2×#9911yescharacteristic
257C22×C11C2×#9914yes—
258C22×C11C2×#9911yescharacteristic
259C22×C11C22×C22⋊C411yescharacteristic
260C4×C11—22no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—88no—
267C25D4×C1112yes—
268C2×#41—22no—
269C2×#41—42no—
270C2×#41—42no—
271C2×#41C2×C4×C1114yescomplemented
272C22×Q8C2×C4×C1111yescharacteristic, complemented
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4C2×C4×C1111yescharacteristic
279C22×D4C2×C4×C1112yes—
280C22×D4C2×C4×C1111yescharacteristic, complemented
281C22×D4D4×C1112yes—
282C22×D4D4×C1114yes—
283C22×D4C23×C1111yescharacteristic
284C22×D4C23×C1112yes—
285C23×C4—21no—
286C23×C4—42no—
287C23×C4C2×C4×C1111yescharacteristic
288#127—22no—
289#127—22no—
290#127C2×C4×C1114yescomplemented
291#127C2×C4×C1112yescomplemented
292#127C23×C1112yes—
293#124—22no—
294#124—22no—
295#124C2×C4×C1114yescomplemented
296#124C2×C4×C1112yescomplemented
297#124C23×C1112yes—
298#121—28no—
299#121—28no—
300#120—28no—
301#120—28no—
302#117—22no—
303#117C2×C4×C1114yescomplemented
304C2×C4⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—42no—
312C2×C42C2×C4×C1111yescharacteristic, complemented
313C2×C42C2×C4×C1111yescharacteristic, complemented
314#99—24no—
315#99—28no—
316#99C23×C1118yes—
317C2×C11—21no—
318C2×C11—24no—
319C2×C11—21no—
320C2×C11—42no—
321C2×C11—44no—
322C2×C11—42no—
323C2×C11—82no—
324C2×C11#212712yesdirect product factor
325C2×C11C22×#9911yescharacteristic
326C24—22no—
327C24—22no—
328C24—24no—
329C24—21no—
330C24—84no—
331C24C11×C22⋊C412yes—
332C24C11×C22⋊C414yes—
333C24C11×C22⋊C411yescharacteristic
334C24C2×D4×C1112yes—
335C24C2×D4×C1114yes—
336#41—48no—
337#41—48no—
338C2×Q8—21no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8C22×C4×C1112yescomplemented
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—28no—
345C2×D4—24no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—44no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—44no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—84no—
362C2×D4—84no—
363C2×D4C11×C22⋊C414yes—
364C2×D4C11×C22⋊C412yes—
365C2×D4C22×C4×C1112yes—
366C2×D4C22×C4×C1111yescharacteristic
367C2×D4C22×C4×C1112yescomplemented
368C2×D4C2×D4×C1114yes—
369C2×D4C2×D4×C1112yes—
370C2×D4C24×C1111yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—44no—
380C22×C4—48no—
381C22×C4—88no—
382C22×C4C11×C22⋊C411yescharacteristic
383C22×C4C11×C22⋊C412yes—
384C22×C4C22×C4×C1111yescharacteristic
385C22×C4C22×C4×C1112yes—
386C4⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—28no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—28no—
392C22⋊C4—44no—
393C22⋊C4—48no—
394C42—21no—
395C42—21no—
396C42C22×C4×C1112yescomplemented
397C42C22×C4×C1112yescomplemented
398C11C2×#212711yescharacteristic, direct product factor, Sylow
399C23—24no—
400C23—22no—
401C23—24no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—22no—
406C23—24no—
407C23—22no—
408C23—42no—
409C23—48no—
410C23—44no—
411C23—44no—
412C23—44no—
413C23—41no—
414C23—41no—
415C23—84no—
416C23—84no—
417C23—84no—
418C23—88no—
419C23C11×#9912yes—
420C23C11×#9912yes—
421C23C2×C11×C22⋊C411yescharacteristic
422C23C2×C11×C22⋊C412yes—
423C23C2×C11×C22⋊C414yes—
424C23C2×C11×C22⋊C412yes—
425C23C22×D4×C1112yes—
426Q8—42no—
427Q8—42no—
428D4—44no—
429D4—42no—
430D4—42no—
431D4—41no—
432D4—44no—
433D4—42no—
434D4—41no—
435D4—42no—
436D4—42no—
437D4—48no—
438D4—88no—
439D4—84no—
440D4—84no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—48no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—48no—
456C2×C4—816no—
457C2×C4—88no—
458C2×C4C2×C11×C22⋊C411yescharacteristic
459C2×C4C2×C11×C22⋊C412yes—
460C2×C4C23×C4×C1111yescharacteristic
461C22—22no—
462C22—24no—
463C22—22no—
464C22—24no—
465C22—22no—
466C22—42no—
467C22—42no—
468C22—44no—
469C22—42no—
470C22—42no—
471C22—48no—
472C22—48no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—42no—
477C22—82no—
478C22—82no—
479C22—84no—
480C22—84no—
481C22—82no—
482C22—82no—
483C22C2×C11×#9911yescharacteristic
484C22C2×C11×#9914yes—
485C22C2×C11×#9911yescharacteristic
486C22C22×C11×C22⋊C411yescharacteristic
487C4—22no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—88no—
494C2—21no—
495C2—24no—
496C2—21no—
497C2—42no—
498C2—44no—
499C2—42no—
500C2—82no—
501C2C11×#212712yesdirect product factor
502C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C23×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C11×#2127C2direct (N × H)
4. C2×C11×#354C2semidirect
5. C2×C11×#353C2semidirect
6. C22×C11×#41C4semidirect
9. C11×#535C4semidirect
11. C2×C11×#127C4semidirect
13. C2×C11×#124C4semidirect
17. C2×C11×#117C4semidirect
22. C2×C11×#99C22semidirect
23. C11×#354C22semidirect
24. C11×#353C22semidirect
29. C2×C11×#41C2×C4semidirect
30. C22×Q8×C11C2×C4semidirect
38. C22×D4×C11C2×C4semidirect
48. C11×#127C2×C4semidirect
49. C11×#127C2×C4semidirect
53. C11×#124C2×C4semidirect
54. C11×#124C2×C4semidirect
61. C11×#117C2×C4semidirect
70. C2×C42×C11C2×C4semidirect
71. C2×C42×C11C2×C4semidirect
75. C2×#2127C11direct (N × H)
91. C2×Q8×C11C22×C4semidirect
117. C2×D4×C11C22×C4semidirect
146. C42×C11C22×C4semidirect
147. C42×C11C22×C4semidirect
149. C22×#99C2×C11semidirect
150. #2127C2×C11direct (N × H)
151. C2×#354C2×C11semidirect
152. C2×#353C2×C11semidirect
215. C22×#41C4×C11semidirect
218. #535C4×C11semidirect
220. C2×#127C4×C11semidirect
222. C2×#124C4×C11semidirect
226. C2×#117C4×C11semidirect
231. C2×#99C22×C11semidirect
232. #354C22×C11semidirect
233. #353C22×C11semidirect
271. C2×#41C2×C4×C11semidirect
272. C22×Q8C2×C4×C11semidirect
280. C22×D4C2×C4×C11semidirect
290. #127C2×C4×C11semidirect
291. #127C2×C4×C11semidirect
295. #124C2×C4×C11semidirect
296. #124C2×C4×C11semidirect
303. #117C2×C4×C11semidirect
312. C2×C42C2×C4×C11semidirect
313. C2×C42C2×C4×C11semidirect
324. C2×C11#2127direct (N × H)
341. C2×Q8C22×C4×C11semidirect
367. C2×D4C22×C4×C11semidirect
396. C42C22×C4×C11semidirect
397. C42C22×C4×C11semidirect
398. C11C2×#2127direct (N × H)
501. C2C11×#2127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C22×C11×#992
C11×#21272
C2×C11×#3542
C2×C11×#3532
C2×#212711