Finite Group Databasebeta

← C4×D11×#126 #14912250

Subgroups — C4×D11×#126 #14912250

Order 2816.

2838 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#126C211yesmaximal, characteristic
2#13071170C213yesmaximal, complemented
3C4×#66951C213yesmaximal, complemented
4#126×Dic11C211yesmaximal, characteristic, complemented
5C4×#66929C211yesmaximal, characteristic, complemented
6#13071166C213yesmaximal, complemented
7C4×#66932C213yesmaximal, complemented
8#13071164C211yesmaximal, characteristic, complemented
9D11×#388C213yesmaximal
10D11×#387C213yesmaximal, complemented
11D11×#383C211yesmaximal, characteristic, complemented
12C4×C4⋊C4×D11C213yesmaximal, complemented
13C4×C22⋊C4×D11C213yesmaximal
14C43×D11C211yesmaximal, characteristic, complemented
15C4×C11×#126C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C11×#126C2211yescharacteristic
18D11×#126C4116yesdirect product factor
19C2×#66951C2213yes—
20C2×C4⋊C4×D11C2213yes—
21C2×C4⋊C4×D11C2213yes—
22C2×C22⋊C4×D11C2213yes—
23C2×C22⋊C4×D11C2213yes—
24C2×#66932C2213yes—
25C2×#66929C2211yescharacteristic
26C2×C42×D11C2213yes—
27C2×C42×D11C2213yes—
28C2×C42×D11C2213yes—
29C2×C42×D11C2211yescharacteristic
30C11×#388C2213yes—
31C11×#387C2213yescomplemented
32C11×#383C2211yescharacteristic, complemented
33C4×C11×C4⋊C4C2213yescomplemented
34C4×C11×C22⋊C4C2213yes—
35C43×C11C2211yescharacteristic, complemented
36C4×C22⋊Dic11C2213yes—
37#10622603C2213yes—
38#10622594C2213yescomplemented
39#10622591C2213yescomplemented
40C4⋊C4×Dic11C2213yescomplemented
41C4⋊C4×Dic11C2213yescomplemented
42#10622564C2213yes—
43#10622558C2213yes—
44#10622557C2213yes—
45C22⋊C4×Dic11C2213yes—
46C22⋊C4×Dic11C2213yes—
47#10622553C2213yes—
48C4×(C2×D11)⋊C4C2213yes—
49C4×(C2×D11)⋊C4C2213yes—
50#10622550C2211yescharacteristic, complemented
51C4×C4⋊Dic11C2213yescomplemented
52#10622546C2213yescomplemented
53C4×Dic11⋊C4C2213yescomplemented
54C4×Dic11⋊C4C2213yescomplemented
55C42×Dic11C2211yescharacteristic, complemented
56C42×Dic11C2213yescomplemented
57C42×Dic11C2213yescomplemented
58#10622283C2213yes—
59#10622282C2213yes—
60#10622279C2213yes—
61#10622279C2213yes—
62D11×#95C2213yes—
63D11×#95C2213yes—
64D11×#95C2213yes—
65D11×#95C2213yes—
66#10622268C2213yescomplemented
67#10622267C2213yescomplemented
68#10622266C2213yescomplemented
69#10622265C2213yescomplemented
70#10622264C2213yescomplemented
71#10622264C2213yescomplemented
72#10622262C2213yescomplemented
73#10622262C2213yescomplemented
74C24×D11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—212no—
78C22×C4×D11C2313yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C22×C4×D11C2313yes—
83C22×C4×D11C2313yes—
84C22×C4×D11C2313yes—
85C22×C4×D11C2311yescharacteristic
86C11×#126C2×C418yescomplemented
87C2×C11×C4⋊C4C2313yes—
88C2×C11×C4⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C42×C11C2313yes—
92C2×C42×C11C2313yes—
93C2×C42×C11C2313yes—
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11C2313yes—
96C2×C22⋊Dic11C2313yes—
97C2×(C2×D11)⋊C4C2313yes—
98C2×(C2×D11)⋊C4C2313yes—
99C2×(C2×D11)⋊C4C2313yes—
100C2×(C2×D11)⋊C4C2313yes—
101C2×C4⋊Dic11C2313yes—
102C2×C4⋊Dic11C2313yes—
103C2×Dic11⋊C4C2313yes—
104C2×Dic11⋊C4C2313yes—
105C2×Dic11⋊C4C2313yes—
106C2×Dic11⋊C4C2313yes—
107C2×C4×Dic11C2313yes—
108C2×C4×Dic11C2313yes—
109C2×C4×Dic11C2313yes—
110C2×C4×Dic11C2313yes—
111C2×C4×Dic11C2313yes—
112C2×C4×Dic11C2313yes—
113C2×C4×Dic11C2313yes—
114C2×C4×Dic11C2313yes—
115C2×C4×Dic11C2313yes—
116C2×C4×Dic11C2313yes—
117#66951C2×C4124yescomplemented
118C4⋊C4×D11—212no—
119C4⋊C4×D11C2×C4124yescomplemented
120C22⋊C4×D11—212no—
121C22⋊C4×D11C2×C4124yes—
122#66932C2×C4124yescomplemented
123#66929C2×C418yescomplemented
124C42×D11—212no—
125C42×D11—212no—
126C42×D11—212no—
127C42×D11C2×C418yescomplemented
128C11×#95C2313yes—
129C11×#95C2313yes—
130C11×#95C2313yes—
131C11×#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137C11⋊#95C2313yes—
138C11⋊#95C2313yes—
139C11⋊#95C2313yes—
140C11⋊#95C2313yes—
141C11⋊#95C2313yes—
142C11⋊#95C2313yes—
143C11⋊#95C2313yes—
144C2×C4×#126—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—26no—
147C23×D11—26no—
148C23×D11C22×C414yes—
149C23×D11C2411yescharacteristic
150C23×D11C2411yescharacteristic
151C22×C4×C11—26no—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2413yes—
154C22×C4×C11C2413yes—
155C22×C4×C11C2413yes—
156C22×C4×C11C2413yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—26no—
159C22×Dic11C2411yescharacteristic
160C22×Dic11C2413yes—
161C22×Dic11C2413yes—
162C22×Dic11C2413yes—
163C22×Dic11C2413yes—
164C22×Dic11C2411yescharacteristic
165C2×C4×D11—26no—
166C2×C4×D11—26no—
167C2×C4×D11—26no—
168C2×C4×D11—26no—
169C2×C4×D11—26no—
170C2×C4×D11—26no—
171C2×C4×D11—26no—
172C2×C4×D11—26no—
173C2×C4×D11—26no—
174C2×C4×D11—26no—
175C2×C4×D11—26no—
176C2×C4×D11—26no—
177C2×C4×D11—416no—
178C2×C4×D11C22×C4112yes—
179C2×C4×D11C22×C4112yes—
180C2×C4×D11#41112yes—
181C2×C4×D11#41112yes—
182C11×C4⋊C4—26no—
183C11×C4⋊C4C22×C4112yescomplemented
184C11×C22⋊C4—26no—
185C11×C22⋊C4C22×C4112yes—
186C42×C11—26no—
187C42×C11—26no—
188C42×C11—26no—
189C42×C11C22×C414yescomplemented
190C22⋊Dic11—26no—
191C22⋊Dic11C22×C4112yes—
192(C2×D11)⋊C4—26no—
193(C2×D11)⋊C4—26no—
194(C2×D11)⋊C4C22×C4112yes—
195(C2×D11)⋊C4C22×C4112yes—
196C4⋊Dic11—26no—
197C4⋊Dic11C22×C4112yescomplemented
198Dic11⋊C4—26no—
199Dic11⋊C4—26no—
200Dic11⋊C4C22×C4112yescomplemented
201Dic11⋊C4C22×C4112yescomplemented
202C4×Dic11—26no—
203C4×Dic11—26no—
204C4×Dic11—26no—
205C4×Dic11—26no—
206C4×Dic11—26no—
207C4×Dic11—26no—
208C4×Dic11—26no—
209C4×Dic11—26no—
210C4×Dic11—26no—
211C4×Dic11C22×C4112yescomplemented
212C22×#126—111no—
213C4×#126—113no—
214C4×#126—113no—
215C4×#126—111no—
216C4×#126—113no—
217C4×#126—113no—
218C4×#126—111no—
219C4×#126—111no—
220C4×#126D1111yescharacteristic, direct product factor
221C2×#388—113no—
222C2×#387—113no—
223C2×#383—111no—
224C2×C4×C4⋊C4—113no—
225C2×C4×C22⋊C4—113no—
226C2×C43—111no—
227C23×C11—23no—
228C23×C11—23no—
229C23×C11C23×C412yes—
230C23×C11C2511yescharacteristic
231C22×D11—23no—
232C22×D11—23no—
233C22×D11—224no—
234C22×D11—44no—
235C22×D11—412no—
236C22×D11C23×C412yes—
237C22×D11C23×C412yes—
238C22×D11C2×#4116yes—
239C22×D11C2×#4116yes—
240C2×C4×C11—23no—
241C2×C4×C11—23no—
242C2×C4×C11—23no—
243C2×C4×C11—23no—
244C2×C4×C11—23no—
245C2×C4×C11—23no—
246C2×C4×C11—23no—
247C2×C4×C11—23no—
248C2×C4×C11—23no—
249C2×C4×C11—23no—
250C2×C4×C11—44no—
251C2×C4×C11C23×C416yes—
252C2×C4×C11C23×C416yes—
253C2×C4×C11C2×#4116yes—
254C2×C4×C11C2×#4116yes—
255C2×Dic11—23no—
256C2×Dic11—23no—
257C2×Dic11—23no—
258C2×Dic11—23no—
259C2×Dic11—23no—
260C2×Dic11—23no—
261C2×Dic11—23no—
262C2×Dic11—23no—
263C2×Dic11—23no—
264C2×Dic11—23no—
265C2×Dic11—44no—
266C2×Dic11C23×C416yes—
267C2×Dic11C23×C416yes—
268C2×Dic11C2×#4116yes—
269C2×Dic11C2×#4116yes—
270C4×D11—224no—
271C4×D11—224no—
272C4×D11—224no—
273C4×D11—44no—
274C4×D11—412no—
275C4×D11—44no—
276C4×D11—44no—
277C4×D11#126116yesdirect product factor
278C24×C4—111no—
279C2×#126—1116no—
280C2×#126—113no—
281C2×#126—113no—
282C2×#126—111no—
283C2×#126C2×D1111yescharacteristic
284C22×C4⋊C4—113no—
285C22×C4⋊C4—113no—
286C22×C22⋊C4—113no—
287C22×C22⋊C4—113no—
288C22×C42—111no—
289C22×C42—113no—
290C22×C42—113no—
291C22×C42—113no—
292#388—113no—
293#388—113no—
294#388—113no—
295#388—113no—
296#388—113no—
297#388—113no—
298#388—113no—
299#388C2×D1113yes—
300#387—113no—
301#387—113no—
302#387—113no—
303#387—113no—
304#387—113no—
305#387—113no—
306#387—113no—
307#387C2×D1113yescomplemented
308#383—111no—
309#383—113no—
310#383—113no—
311#383C2×D1111yescharacteristic, complemented
312C4×C4⋊C4—113no—
313C4×C4⋊C4—113no—
314C4×C4⋊C4—113no—
315C4×C4⋊C4—113no—
316C4×C4⋊C4—113no—
317C4×C4⋊C4—113no—
318C4×C4⋊C4—113no—
319C4×C4⋊C4C2×D1113yescomplemented
320C4×C22⋊C4—113no—
321C4×C22⋊C4—113no—
322C4×C22⋊C4—113no—
323C4×C22⋊C4—113no—
324C4×C22⋊C4—113no—
325C4×C22⋊C4—113no—
326C4×C22⋊C4—113no—
327C4×C22⋊C4C2×D1113yes—
328C2×#95—113no—
329C2×#95—113no—
330C2×#95—113no—
331C2×#95—113no—
332C43—113no—
333C43—113no—
334C43—111no—
335C43C2×D1111yescharacteristic, complemented
336C22×C11—26no—
337C22×C11—41no—
338C22×C11—43no—
339C22×C11C24×C411yescharacteristic
340C22×C11C22×#4113yes—
341C22×C11C22×#4113yes—
342C2×D11—26no—
343C2×D11—41no—
344C2×D11—43no—
345C2×D11—416no—
346C2×D11C4×#41112yes—
347C2×D11C2×#12614yes—
348C2×D11#529112yes—
349C4×C11—26no—
350C4×C11—26no—
351C4×C11—26no—
352C4×C11—41no—
353C4×C11—43no—
354C4×C11C2×#12614yescomplemented
355Dic11—26no—
356Dic11—26no—
357Dic11—26no—
358Dic11—41no—
359Dic11—43no—
360Dic11C2×#12614yescomplemented
361C25—111no—
362C23×C4—111no—
363C23×C4—113no—
364C23×C4—113no—
365C23×C4—113no—
366C23×C4—111no—
367C23×C4—113no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—2212no—
372C23×C4C22×D1111yescharacteristic
373#126—1124no—
374#126—1124no—
375#126—118no—
376#126C4×D1118yesdirect product factor
377C2×C4⋊C4—113no—
378C2×C4⋊C4—113no—
379C2×C4⋊C4—113no—
380C2×C4⋊C4—1124no—
381C2×C4⋊C4—113no—
382C2×C4⋊C4—113no—
383C2×C4⋊C4—113no—
384C2×C4⋊C4—2212no—
385C2×C4⋊C4C22×D1113yes—
386C2×C4⋊C4C22×D1113yes—
387C2×C22⋊C4—113no—
388C2×C22⋊C4—113no—
389C2×C22⋊C4—113no—
390C2×C22⋊C4—1124no—
391C2×C22⋊C4—113no—
392C2×C22⋊C4—113no—
393C2×C22⋊C4—113no—
394C2×C22⋊C4—2212no—
395C2×C22⋊C4C22×D1113yes—
396C2×C22⋊C4C22×D1113yes—
397C2×C42—113no—
398C2×C42—118no—
399C2×C42—113no—
400C2×C42—113no—
401C2×C42—113no—
402C2×C42—113no—
403C2×C42—113no—
404C2×C42—113no—
405C2×C42—113no—
406C2×C42—113no—
407C2×C42—113no—
408C2×C42—2212no—
409C2×C42—2212no—
410C2×C42—2212no—
411C2×C42C22×D1113yes—
412C2×C42C22×D1113yes—
413C2×C42C22×D1113yes—
414C2×C42C22×D1111yescharacteristic
415#95—113no—
416#95—113no—
417#95—113no—
418#95—113no—
419#95—113no—
420#95—113no—
421#95—113no—
422#95—113no—
423#95—113no—
424#95—113no—
425#95—113no—
426#95—113no—
427#95C22×D1113yes—
428#95C22×D1113yes—
429#95C22×D1113yes—
430#95C22×D1113yes—
431C2×C11—42no—
432C2×C11C2×C4×#4113yes—
433C2×C11C22×#12611yescharacteristic
434C2×C11C2×#52913yes—
435D11—42no—
436D11C4×#12618yesdirect product factor
437C24—111no—
438C24—114no—
439C24—111no—
440C24—226no—
441C24—226no—
442C24C23×D1111yescharacteristic
443C22×C4—26no—
444C22×C4—111no—
445C22×C4—1112no—
446C22×C4—113no—
447C22×C4—113no—
448C22×C4—113no—
449C22×C4—1112no—
450C22×C4—1112no—
451C22×C4—1112no—
452C22×C4—111no—
453C22×C4—113no—
454C22×C4—226no—
455C22×C4—226no—
456C22×C4—226no—
457C22×C4—226no—
458C22×C4—226no—
459C22×C4—226no—
460C22×C4—226no—
461C22×C4—226no—
462C22×C4—226no—
463C22×C4—226no—
464C22×C4—226no—
465C22×C4—226no—
466C22×C4—226no—
467C22×C4—4416no—
468C22×C4C23×D1111yescharacteristic
469C22×C4C23×D1113yes—
470C22×C4C23×D1113yes—
471C22×C4C23×D1113yes—
472C22×C4C23×D1113yes—
473C22×C4C23×D1111yescharacteristic
474C4⋊C4—26no—
475C4⋊C4—1112no—
476C4⋊C4—1112no—
477C4⋊C4—1112no—
478C4⋊C4—226no—
479C4⋊C4—226no—
480C4⋊C4—226no—
481C4⋊C4C2×C4×D11112yescomplemented
482C22⋊C4—26no—
483C22⋊C4—1112no—
484C22⋊C4—1112no—
485C22⋊C4—1112no—
486C22⋊C4—226no—
487C22⋊C4—226no—
488C22⋊C4—226no—
489C22⋊C4C2×C4×D11112yes—
490C42—26no—
491C42—26no—
492C42—26no—
493C42—1112no—
494C42—226no—
495C42—226no—
496C42—226no—
497C42—226no—
498C42—226no—
499C42—226no—
500C42—226no—
501C42—226no—
502C42—226no—
503C42C2×C4×D1114yescomplemented
504C11C2×C4×#12611yescharacteristic, complemented, Sylow
505C23—23no—
506C23—23no—
507C23—112no—
508C23—116no—
509C23—116no—
510C23—112no—
511C23—2224no—
512C23—223no—
513C23—223no—
514C23—444no—
515C23—4412no—
516C23C22×C4×D1112yes—
517C23C24×D1111yescharacteristic
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—23no—
525C2×C4—23no—
526C2×C4—23no—
527C2×C4—23no—
528C2×C4—44no—
529C2×C4—116no—
530C2×C4—1116no—
531C2×C4—116no—
532C2×C4—116no—
533C2×C4—116no—
534C2×C4—2224no—
535C2×C4—2224no—
536C2×C4—2224no—
537C2×C4—223no—
538C2×C4—223no—
539C2×C4—223no—
540C2×C4—223no—
541C2×C4—223no—
542C2×C4—223no—
543C2×C4—223no—
544C2×C4—223no—
545C2×C4—223no—
546C2×C4—223no—
547C2×C4—444no—
548C2×C4—444no—
549C2×C4—4412no—
550C2×C4—444no—
551C2×C4—444no—
552C2×C4C22×C4×D1116yes—
553C2×C4C22×C4×D1116yes—
554C2×C4#41×D1116yes—
555C2×C4#41×D1116yes—
556C22—26no—
557C22—41no—
558C22—43no—
559C22—114no—
560C22—1112no—
561C22—1112no—
562C22—226no—
563C22—4416no—
564C22—441no—
565C22—443no—
566C22C23×C4×D1111yescharacteristic
567C22C2×#41×D1113yes—
568C22C2×#41×D1113yes—
569C4—26no—
570C4—26no—
571C4—26no—
572C4—41no—
573C4—43no—
574C4—114no—
575C4—226no—
576C4—226no—
577C4—226no—
578C4—441no—
579C4—443no—
580C4D11×#12614yesdirect product factor
581C2—42no—
582C2—118no—
583C2—442no—
584C2C4×#41×D1113yes—
585C2C2×D11×#12611yescharacteristic
586C2D11×#52913yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#126C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenterC4×#126D11
hypocenterC11C2×C4×#126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #13071170C2semidirect
3. C4×#66951C2semidirect
4. #126×Dic11C2semidirect
5. C4×#66929C2semidirect
6. #13071166C2semidirect
7. C4×#66932C2semidirect
8. #13071164C2semidirect
10. D11×#387C2semidirect
11. D11×#383C2semidirect
12. C4×C4⋊C4×D11C2semidirect
14. C43×D11C2semidirect
15. C4×C11×#126C2semidirect
18. D11×#126C4direct (N × H)
31. C11×#387C22semidirect
32. C11×#383C22semidirect
33. C4×C11×C4⋊C4C22semidirect
35. C43×C11C22semidirect
38. #10622594C22semidirect
39. #10622591C22semidirect
40. C4⋊C4×Dic11C22semidirect
41. C4⋊C4×Dic11C22semidirect
50. #10622550C22semidirect
51. C4×C4⋊Dic11C22semidirect
52. #10622546C22semidirect
53. C4×Dic11⋊C4C22semidirect
54. C4×Dic11⋊C4C22semidirect
55. C42×Dic11C22semidirect
56. C42×Dic11C22semidirect
57. C42×Dic11C22semidirect
66. #10622268C22semidirect
67. #10622267C22semidirect
68. #10622266C22semidirect
69. #10622265C22semidirect
70. #10622264C22semidirect
71. #10622264C22semidirect
72. #10622262C22semidirect
73. #10622262C22semidirect
86. C11×#126C2×C4semidirect
117. #66951C2×C4semidirect
119. C4⋊C4×D11C2×C4semidirect
122. #66932C2×C4semidirect
123. #66929C2×C4semidirect
127. C42×D11C2×C4semidirect
183. C11×C4⋊C4C22×C4semidirect
189. C42×C11C22×C4semidirect
197. C4⋊Dic11C22×C4semidirect
200. Dic11⋊C4C22×C4semidirect
201. Dic11⋊C4C22×C4semidirect
211. C4×Dic11C22×C4semidirect
220. C4×#126D11direct (N × H)
277. C4×D11#126direct (N × H)
307. #387C2×D11semidirect
311. #383C2×D11semidirect
319. C4×C4⋊C4C2×D11semidirect
335. C43C2×D11semidirect
354. C4×C11C2×#126semidirect
360. Dic11C2×#126semidirect
376. #126C4×D11direct (N × H)
436. D11C4×#126direct (N × H)
481. C4⋊C4C2×C4×D11semidirect
503. C42C2×C4×D11semidirect
504. C11C2×C4×#126semidirect
580. C4D11×#126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×#1262
#130711702
C4×#669512
#126×Dic112
C4×#669292
#130711662
C4×#669322
#130711642
D11×#3882
D11×#3872
D11×#3832
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C43×D112
C4×C11×#1262
C2×C4×#12611