Finite Group Databasebeta

← C2×C11×#2123 #14610539

Subgroups — C2×C11×#2123 #14610539

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#413C211yesmaximal, characteristic
3C2×C11×#410C211yesmaximal, characteristic
4C11×#2123C218yesmaximal, direct product factor
5C2×C11×#352C214yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C23×Q8×C11C411yescharacteristic, complemented
8C22×C11×M16—21no—
9C11×#536—22no—
10C11×#536—22no—
11C11×#536C414yescomplemented
12C11×#536C2214yes—
13C2×C11×C4⋊Q8—21no—
14C2×C11×#124—21no—
15C2×C11×#123C412yescomplemented
16C2×C11×#123C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#117—21no—
20C2×C11×#117C411yescharacteristic, complemented
21C11×#413—22no—
22C11×#413C2214yes—
23C2×C11×#101—21no—
24C2×C11×#100C2212yes—
25C11×#410—22no—
26C11×#410C2214yes—
27C2×C11×#99—21no—
28C2×C11×#99C2212yes—
29C11×#352C22116yescomplemented
30C2×C11×#41—41no—
31C2×C11×#41—41no—
32C2×C11×#41—42no—
33C2×C11×#41C2×C412yes—
34C2×C11×#41D412yes—
35C2×C11×#41D412yes—
36C2×C11×#41C2312yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—21no—
40C22×Q8×C11—42no—
41C22×Q8×C11—41no—
42C22×Q8×C11—41no—
43C22×Q8×C11C2×C414yescomplemented
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11C2×C411yescharacteristic
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C412yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—24no—
54C2×C11×M16—41no—
55C2×C11×M16—42no—
56C22×C8×C11—41no—
57C11×C4⋊Q8—24no—
58C11×C4⋊Q8—24no—
59C11×#124—24no—
60C11×#124—24no—
61C11×#123—24no—
62C11×#123—22no—
63C11×#123—22no—
64C11×#123C2×C414yes—
65C11×#123C2×C418yescomplemented
66C11×#123C2314yes—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×#117—22no—
72C11×#117—24no—
73C11×#117—42no—
74C11×#117C2×C414yescomplemented
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4C2×C412yes—
83C2×C42×C11—21no—
84C2×C42×C11—41no—
85C11×#101—24no—
86C11×#100—22no—
87C11×#100C2314yes—
88C11×#99—24no—
89C11×#99—22no—
90C11×#99C2314yes—
91C2×#2123C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C22⋊C411yescharacteristic
93C24×C11C22×C411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C11×#41—42no—
100C11×#41—42no—
101C11×#41—42no—
102C11×#41—42no—
103C2×Q8×C11—24no—
104C2×Q8×C11—24no—
105C2×Q8×C11—41no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11—44no—
112C2×Q8×C11—44no—
113C2×Q8×C11—42no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11C22⋊C412yes—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11C22⋊C412yes—
125C2×D4×C11C22⋊C412yes—
126C2×D4×C11C22×C411yescharacteristic
127C2×D4×C11C22×C412yes—
128C2×D4×C11C2×D411yescharacteristic
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D411yescharacteristic
131C2×D4×C11C2411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11C22⋊C411yescharacteristic
148C22×C4×C11C22⋊C411yescharacteristic
149C22×C4×C11C22⋊C412yes—
150C22×C4×C11C22⋊C412yes—
151C22×C4×C11C22⋊C412yes—
152C22×C4×C11C22⋊C411yescharacteristic
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C11×M16—24no—
159C11×M16—42no—
160C11×M16—44no—
161C2×C8×C11—42no—
162C2×C8×C11—44no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—44no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4C22×C414yes—
175C42×C11—24no—
176C42×C11—44no—
177C2×#536C2×C1111yescharacteristic
178C2×#413C2×C1111yescharacteristic
179C2×#410C2×C1111yescharacteristic
180#2123C2×C1118yesdirect product factor
181C2×#352C2×C1114yescomplemented
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11C2×C22⋊C411yescharacteristic
193C23×C11C2×C22⋊C412yes—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C23×C411yescharacteristic
196C23×C11C22×D411yescharacteristic
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—48no—
200Q8×C11—44no—
201Q8×C11—44no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—84no—
237C2×C4×C11#9912yes—
238C2×C4×C11#9911yescharacteristic
239C2×C4×C11#9911yescharacteristic
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C22×D411yescharacteristic
245C8×C11—44no—
246C22×#41C22×C1111yescharacteristic
247C23×Q8C4×C1111yescharacteristic, complemented
248C22×M16—21no—
249#536—22no—
250#536—22no—
251#536C4×C1114yescomplemented
252#536C22×C1114yes—
253C2×C4⋊Q8—21no—
254C2×#124—21no—
255C2×#123C4×C1112yescomplemented
256C2×#123C22×C1112yes—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×#117—21no—
260C2×#117C4×C1111yescharacteristic, complemented
261#413—22no—
262#413C22×C1114yes—
263C2×#101—21no—
264C2×#100C22×C1112yes—
265#410—22no—
266#410C22×C1114yes—
267C2×#99—21no—
268C2×#99C22×C1112yes—
269#352C22×C11116yescomplemented
270C22×C11—22no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—21no—
276C22×C11—41no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C2×#9911yescharacteristic
288C22×C11C2×#9911yescharacteristic
289C22×C11C22×C22⋊C411yescharacteristic
290C4×C11—21no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—44no—
295C4×C11—44no—
296C4×C11—84no—
297C4×C11C2×#9912yes—
298C4×C11C2×#9912yes—
299C2×#41—41no—
300C2×#41—41no—
301C2×#41—42no—
302C2×#41C2×C4×C1112yes—
303C2×#41D4×C1112yes—
304C2×#41D4×C1112yes—
305C2×#41C23×C1112yes—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8—22no—
309C22×Q8—42no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8C2×C4×C1114yescomplemented
313C22×Q8D4×C1111yescharacteristic
314C22×D4C2×C4×C1111yescharacteristic
315C22×D4D4×C1111yescharacteristic
316C22×D4C23×C1111yescharacteristic
317C23×C4C2×C4×C1111yescharacteristic
318C23×C4C2×C4×C1112yes—
319C23×C4D4×C1111yescharacteristic
320C23×C4D4×C1111yescharacteristic
321C2×M16—22no—
322C2×M16—24no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326C4⋊Q8—24no—
327C4⋊Q8—24no—
328#124—24no—
329#124—24no—
330#123—24no—
331#123—22no—
332#123—22no—
333#123C2×C4×C1114yes—
334#123C2×C4×C1118yescomplemented
335#123C23×C1114yes—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340#117—22no—
341#117—24no—
342#117—42no—
343#117C2×C4×C1114yescomplemented
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—41no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4C2×C4×C1112yes—
352C2×C42—21no—
353C2×C42—41no—
354#101—24no—
355#100—22no—
356#100C23×C1114yes—
357#99—24no—
358#99—22no—
359#99C23×C1114yes—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—41no—
363C2×C11—41no—
364C2×C11—41no—
365C2×C11—41no—
366C2×C11—42no—
367C2×C11#212312yesdirect product factor
368C2×C11C22×#9911yescharacteristic
369C24C11×C22⋊C411yescharacteristic
370C24C22×C4×C1111yescharacteristic
371C24C2×D4×C1111yescharacteristic
372#41—42no—
373#41—42no—
374#41—42no—
375#41—42no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—42no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8C11×C22⋊C412yes—
394C2×Q8C2×D4×C1112yes—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C11×C22⋊C412yes—
402C2×D4C11×C22⋊C412yes—
403C2×D4C22×C4×C1111yescharacteristic
404C2×D4C22×C4×C1112yes—
405C2×D4C2×D4×C1111yescharacteristic
406C2×D4C2×D4×C1112yes—
407C2×D4C2×D4×C1111yescharacteristic
408C2×D4C24×C1111yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C11×C22⋊C411yescharacteristic
425C22×C4C11×C22⋊C411yescharacteristic
426C22×C4C11×C22⋊C412yes—
427C22×C4C11×C22⋊C412yes—
428C22×C4C11×C22⋊C412yes—
429C22×C4C11×C22⋊C411yescharacteristic
430C22×C4C22×C4×C1112yes—
431C22×C4C22×C4×C1114yes—
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1112yes—
435M16—24no—
436M16—42no—
437M16—44no—
438C2×C8—42no—
439C2×C8—44no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—28no—
443C4⋊C4—24no—
444C4⋊C4—44no—
445C22⋊C4—24no—
446C22⋊C4—28no—
447C22⋊C4—22no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—42no—
451C22⋊C4C22×C4×C1114yes—
452C42—24no—
453C42—44no—
454C11C2×#212311yescharacteristic, direct product factor, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C2×C11×C22⋊C411yescharacteristic
465C23C2×C11×C22⋊C411yescharacteristic
466C23C2×C11×C22⋊C412yes—
467C23C2×C11×C22⋊C411yescharacteristic
468C23C23×C4×C1111yescharacteristic
469C23C22×D4×C1111yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—48no—
473Q8—44no—
474Q8—44no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—41no—
479D4—41no—
480D4—42no—
481D4—41no—
482D4—41no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—84no—
510C2×C4C11×#9912yes—
511C2×C4C11×#9911yescharacteristic
512C2×C4C11×#9911yescharacteristic
513C2×C4C2×C11×C22⋊C412yes—
514C2×C4C2×C11×C22⋊C412yes—
515C2×C4C2×C11×C22⋊C411yescharacteristic
516C2×C4C2×C11×C22⋊C412yes—
517C2×C4C22×D4×C1111yescharacteristic
518C8—44no—
519C22—22no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—41no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22C2×C11×#9911yescharacteristic
537C22C2×C11×#9911yescharacteristic
538C22C22×C11×C22⋊C411yescharacteristic
539C4—21no—
540C4—22no—
541C4—21no—
542C4—22no—
543C4—44no—
544C4—44no—
545C4—84no—
546C4C2×C11×#9912yes—
547C4C2×C11×#9912yes—
548C2—21no—
549C2—21no—
550C2—41no—
551C2—41no—
552C2—41no—
553C2—41no—
554C2—42no—
555C2C11×#212312yesdirect product factor
556C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC23C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C23 ▷ 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
4. C11×#2123C2direct (N × H)
5. C2×C11×#352C2semidirect
7. C23×Q8×C11C4semidirect
11. C11×#536C4semidirect
15. C2×C11×#123C4semidirect
20. C2×C11×#117C4semidirect
29. C11×#352C22semidirect
43. C22×Q8×C11C2×C4semidirect
65. C11×#123C2×C4semidirect
74. C11×#117C2×C4semidirect
91. C2×#2123C11direct (N × H)
180. #2123C2×C11direct (N × H)
181. C2×#352C2×C11semidirect
247. C23×Q8C4×C11semidirect
251. #536C4×C11semidirect
255. C2×#123C4×C11semidirect
260. C2×#117C4×C11semidirect
269. #352C22×C11semidirect
312. C22×Q8C2×C4×C11semidirect
334. #123C2×C4×C11semidirect
343. #117C2×C4×C11semidirect
367. C2×C11#2123direct (N × H)
454. C11C2×#2123direct (N × H)
555. C2C11×#2123direct (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×#4132
C2×C11×#4102
C11×#21232
C2×C11×#3522
C2×#212311