Finite Group Databasebeta

← D11×#2401 #14920068

Subgroups — D11×#2401 #14920068

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071919C211yesmaximal, characteristic, complemented
2#13071918C211yesmaximal, characteristic, complemented
3#13071917C213yesmaximal, complemented
4#13071916C213yesmaximal, complemented
5#13071915C213yesmaximal, complemented
6#13071914C211yesmaximal, characteristic, complemented
7#13071913C213yesmaximal, complemented
8D11×#401C211yesmaximal, characteristic, complemented
9D11×#400C213yesmaximal, complemented
10D11×#397C213yesmaximal
11D11×#396C211yesmaximal, characteristic
12C4×C4⋊C4×D11C213yesmaximal, complemented
13C4×C22⋊C4×D11C213yesmaximal
14D11×#376C211yesmaximal, characteristic, complemented
15C11×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2213yes—
18C2×C4⋊C4×D11C2213yes—
19C2×C22⋊C4×D11C2213yes—
20C2×C22⋊C4×D11C2213yes—
21C2×C42×D11C2213yes—
22C2×C42×D11C2213yes—
23C11×#401C2211yescharacteristic, complemented
24C11×#400C2213yescomplemented
25C11×#397C2213yes—
26C11×#396C2211yescharacteristic
27C4×C11×C4⋊C4C2213yescomplemented
28C4×C11×C22⋊C4C2213yes—
29C11×#376C2211yescharacteristic, complemented
30C4×C22⋊Dic11C2213yes—
31#10622607C2213yes—
32#10622606C2213yes—
33#10622599C2213yescomplemented
34#10622595C2213yescomplemented
35C4⋊C4×Dic11C2213yescomplemented
36C4⋊C4×Dic11C2213yescomplemented
37#10622566C2213yes—
38#10622565C2213yes—
39#10622565C2213yes—
40#10622561C2213yes—
41C22⋊C4×Dic11C2213yes—
42C22⋊C4×Dic11C2213yes—
43C4×(C2×D11)⋊C4C2213yes—
44C4×(C2×D11)⋊C4C2213yes—
45C4×C4⋊Dic11C2213yescomplemented
46#10622545C2213yescomplemented
47C4×Dic11⋊C4C2213yescomplemented
48C4×Dic11⋊C4C2213yescomplemented
49#10622289C2211yescharacteristic
50#10622288C2213yes—
51#10622288C2213yes—
52#10622287C2213yes—
53#10622279C2213yes—
54#10622279C2213yes—
55D11×#95C2211yescharacteristic
56D11×#95C2213yes—
57D11×#95C2213yes—
58D11×#95C2213yes—
59D11×#95C2213yes—
60D11×#95C2213yes—
61C11⋊#401C2213yescomplemented
62C11⋊#401C2211yescharacteristic, complemented
63C11⋊#401C2213yescomplemented
64#10622273C2213yescomplemented
65#10622273C2213yescomplemented
66#10622272C2213yescomplemented
67#10622271C2213yescomplemented
68#10622271C2213yescomplemented
69#10622262C2213yescomplemented
70#10622262C2213yescomplemented
71#10622261C2213yescomplemented
72#10622261C2211yescharacteristic, complemented
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×C4×D11—212no—
77C22×C4×D11C2313yes—
78C22×C4×D11C2313yes—
79C22×C4×D11C2313yes—
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2313yes—
84C22×C4×D11C2311yescharacteristic
85C2×C11×C4⋊C4C2313yes—
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C42×C11C2313yes—
90C2×C42×C11C2313yes—
91C2×C22⋊Dic11C2313yes—
92C2×C22⋊Dic11C2313yes—
93C2×(C2×D11)⋊C4C2313yes—
94C2×(C2×D11)⋊C4C2313yes—
95C2×(C2×D11)⋊C4C2313yes—
96C2×(C2×D11)⋊C4C2313yes—
97C2×C4⋊Dic11C2313yes—
98C2×C4⋊Dic11C2313yes—
99C2×Dic11⋊C4C2313yes—
100C2×Dic11⋊C4C2313yes—
101C2×Dic11⋊C4C2313yes—
102C2×Dic11⋊C4C2313yes—
103C2×C4×Dic11C2313yes—
104C2×C4×Dic11C2313yes—
105C2×C4×Dic11C2313yes—
106C2×C4×Dic11C2313yes—
107C2×C4×Dic11C2313yes—
108C2×C4×Dic11C2313yes—
109C4⋊C4×D11—212no—
110C4⋊C4×D11—212no—
111C22⋊C4×D11—212no—
112C22⋊C4×D11—212no—
113C42×D11—212no—
114C42×D11—212no—
115C11×#95C2313yes—
116C11×#95C2311yescharacteristic
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11⋊#95C2313yes—
122C11⋊#95C2313yes—
123C11⋊#95C2313yes—
124C11⋊#95C2313yes—
125C11⋊#95C2313yes—
126C11⋊#95C2313yes—
127C11⋊#95C2313yes—
128C11⋊#95C2313yes—
129C11⋊#95C2313yes—
130C11⋊#95C2313yes—
131C11⋊#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137C2×#2401—111nomaximal, Sylow
138C24×C11C2411yescharacteristic
139C23×D11—26no—
140C23×D11—26no—
141C23×D11#4114yes—
142C23×D11C2411yescharacteristic
143C23×D11C2411yescharacteristic
144C22×C4×C11—26no—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2413yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2413yes—
149C22×C4×C11C2413yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—26no—
152C22×Dic11C2411yescharacteristic
153C22×Dic11C2413yes—
154C22×Dic11C2413yes—
155C22×Dic11C2413yes—
156C22×Dic11C2413yes—
157C22×Dic11C2411yescharacteristic
158C2×C4×D11—26no—
159C2×C4×D11—26no—
160C2×C4×D11—26no—
161C2×C4×D11—26no—
162C2×C4×D11—26no—
163C2×C4×D11—26no—
164C2×C4×D11—26no—
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—416no—
173C2×C4×D11#41112yes—
174C2×C4×D11#41112yes—
175C11×C4⋊C4—26no—
176C11×C4⋊C4—26no—
177C11×C22⋊C4—26no—
178C11×C22⋊C4—26no—
179C42×C11—26no—
180C42×C11—26no—
181C22⋊Dic11—26no—
182C22⋊Dic11—26no—
183(C2×D11)⋊C4—26no—
184(C2×D11)⋊C4—26no—
185(C2×D11)⋊C4—26no—
186(C2×D11)⋊C4—26no—
187C4⋊Dic11—26no—
188C4⋊Dic11—26no—
189Dic11⋊C4—26no—
190Dic11⋊C4—26no—
191Dic11⋊C4—26no—
192Dic11⋊C4—26no—
193C4×Dic11—26no—
194C4×Dic11—26no—
195C4×Dic11—26no—
196C4×Dic11—26no—
197C4×Dic11—26no—
198C4×Dic11—26no—
199#2401—111no—
200#2401—113no—
201#2401—113no—
202#2401—111no—
203#2401—113no—
204#2401—113no—
205#2401—111no—
206#2401D1111yescharacteristic, direct product factor
207C2×#401—111no—
208C2×#400—113no—
209C2×#397—113no—
210C2×#396—111no—
211C2×C4×C4⋊C4—113no—
212C2×C4×C22⋊C4—113no—
213C2×#376—111no—
214C23×C11—23no—
215C23×C11—23no—
216C23×C11C2×#4112yes—
217C23×C11C2511yescharacteristic
218C22×D11—23no—
219C22×D11—23no—
220C22×D11—224no—
221C22×D11—44no—
222C22×D11—412no—
223C22×D11C2×#4112yes—
224C22×D11C2×#4116yes—
225C22×D11C2×#4112yes—
226C22×D11C2×#4116yes—
227C2×C4×C11—23no—
228C2×C4×C11—23no—
229C2×C4×C11—23no—
230C2×C4×C11—23no—
231C2×C4×C11—23no—
232C2×C4×C11—23no—
233C2×C4×C11—23no—
234C2×C4×C11—23no—
235C2×C4×C11—23no—
236C2×C4×C11—23no—
237C2×C4×C11—23no—
238C2×C4×C11—23no—
239C2×C4×C11—44no—
240C2×C4×C11C2×#4116yes—
241C2×C4×C11C2×#4116yes—
242C2×Dic11—23no—
243C2×Dic11—23no—
244C2×Dic11—23no—
245C2×Dic11—23no—
246C2×Dic11—23no—
247C2×Dic11—23no—
248C2×Dic11—23no—
249C2×Dic11—23no—
250C2×Dic11—23no—
251C2×Dic11—23no—
252C2×Dic11—23no—
253C2×Dic11—23no—
254C2×Dic11—44no—
255C2×Dic11C2×#4116yes—
256C2×Dic11C2×#4116yes—
257C4×D11—224no—
258C4×D11—44no—
259C4×D11—412no—
260C4×D11—412no—
261C4×D11—412no—
262C4×D11—44no—
263C4×D11—44no—
264C4×D11#126116yes—
265C24×C4—111no—
266C22×C4⋊C4—113no—
267C22×C4⋊C4—113no—
268C22×C22⋊C4—113no—
269C22×C22⋊C4—113no—
270C22×C42—113no—
271C22×C42—113no—
272#401—113no—
273#401—113no—
274#401—111no—
275#401C2×D1111yescharacteristic, complemented
276#400—113no—
277#400—113no—
278#400—113no—
279#400—113no—
280#400—113no—
281#400—113no—
282#400—113no—
283#400C2×D1113yescomplemented
284#397—113no—
285#397—113no—
286#397—113no—
287#397—113no—
288#397—113no—
289#397—113no—
290#397—113no—
291#397C2×D1113yes—
292#396—113no—
293#396—113no—
294#396—111no—
295#396C2×D1111yescharacteristic
296C4×C4⋊C4—113no—
297C4×C4⋊C4—113no—
298C4×C4⋊C4—113no—
299C4×C4⋊C4—113no—
300C4×C4⋊C4—113no—
301C4×C4⋊C4—113no—
302C4×C4⋊C4—113no—
303C4×C4⋊C4C2×D1113yescomplemented
304C4×C22⋊C4—113no—
305C4×C22⋊C4—113no—
306C4×C22⋊C4—113no—
307C4×C22⋊C4—113no—
308C4×C22⋊C4—113no—
309C4×C22⋊C4—113no—
310C4×C22⋊C4—113no—
311C4×C22⋊C4C2×D1113yes—
312#376—113no—
313#376—113no—
314#376—111no—
315#376C2×D1111yescharacteristic, complemented
316C2×#95—111no—
317C2×#95—113no—
318C2×#95—113no—
319C2×#95—113no—
320C2×#95—113no—
321C2×#95—113no—
322C22×C11—26no—
323C22×C11—41no—
324C22×C11—43no—
325C22×C11C22×#4113yes—
326C22×C11C22×#4111yescharacteristic
327C22×C11C22×#4113yes—
328C2×D11—26no—
329C2×D11—41no—
330C2×D11—43no—
331C2×D11—416no—
332C2×D11C2×#12614yes—
333C2×D11#529112yes—
334C2×D11#529112yes—
335C4×C11—26no—
336C4×C11—41no—
337C4×C11—43no—
338C4×C11—43no—
339C4×C11—43no—
340C4×C11C2×#12614yes—
341Dic11—26no—
342Dic11—41no—
343Dic11—43no—
344Dic11—43no—
345Dic11—43no—
346Dic11C2×#12614yes—
347C25—111no—
348C23×C4—111no—
349C23×C4—113no—
350C23×C4—111no—
351C23×C4—113no—
352C23×C4—113no—
353C23×C4—113no—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—2212no—
358C23×C4C22×D1111yescharacteristic
359C2×C4⋊C4—113no—
360C2×C4⋊C4—113no—
361C2×C4⋊C4—113no—
362C2×C4⋊C4—113no—
363C2×C4⋊C4—113no—
364C2×C4⋊C4—113no—
365C2×C4⋊C4—2212no—
366C2×C4⋊C4—2212no—
367C2×C4⋊C4C22×D1113yes—
368C2×C4⋊C4C22×D1113yes—
369C2×C22⋊C4—113no—
370C2×C22⋊C4—113no—
371C2×C22⋊C4—113no—
372C2×C22⋊C4—113no—
373C2×C22⋊C4—113no—
374C2×C22⋊C4—113no—
375C2×C22⋊C4—2212no—
376C2×C22⋊C4—2212no—
377C2×C22⋊C4C22×D1113yes—
378C2×C22⋊C4C22×D1113yes—
379C2×C42—113no—
380C2×C42—113no—
381C2×C42—113no—
382C2×C42—113no—
383C2×C42—113no—
384C2×C42—113no—
385C2×C42—2212no—
386C2×C42—2212no—
387C2×C42C22×D1113yes—
388C2×C42C22×D1113yes—
389#95—113no—
390#95—113no—
391#95—113no—
392#95—113no—
393#95—113no—
394#95—113no—
395#95—113no—
396#95—113no—
397#95—113no—
398#95—113no—
399#95—113no—
400#95—113no—
401#95—113no—
402#95—113no—
403#95—113no—
404#95—113no—
405#95C22×D1111yescharacteristic
406#95C22×D1113yes—
407#95C22×D1113yes—
408#95C22×D1113yes—
409#95C22×D1113yes—
410#95C22×D1113yes—
411C2×C11—42no—
412C2×C11C22×#12611yescharacteristic
413C2×C11C2×#52913yes—
414C2×C11C2×#52913yes—
415D11—42no—
416D11#240118yesdirect product factor
417C24—111no—
418C24—114no—
419C24—111no—
420C24—226no—
421C24—226no—
422C24C23×D1111yescharacteristic
423C22×C4—26no—
424C22×C4—111no—
425C22×C4—1112no—
426C22×C4—113no—
427C22×C4—1112no—
428C22×C4—111no—
429C22×C4—113no—
430C22×C4—113no—
431C22×C4—113no—
432C22×C4—226no—
433C22×C4—226no—
434C22×C4—226no—
435C22×C4—226no—
436C22×C4—226no—
437C22×C4—226no—
438C22×C4—226no—
439C22×C4—226no—
440C22×C4—226no—
441C22×C4—226no—
442C22×C4—226no—
443C22×C4—226no—
444C22×C4—226no—
445C22×C4—226no—
446C22×C4—226no—
447C22×C4—4416no—
448C22×C4C23×D1111yescharacteristic
449C22×C4C23×D1113yes—
450C22×C4C23×D1113yes—
451C22×C4C23×D1113yes—
452C22×C4C23×D1113yes—
453C22×C4C23×D1111yescharacteristic
454C4⋊C4—26no—
455C4⋊C4—26no—
456C4⋊C4—226no—
457C4⋊C4—226no—
458C4⋊C4—226no—
459C4⋊C4—226no—
460C4⋊C4—226no—
461C4⋊C4—226no—
462C22⋊C4—26no—
463C22⋊C4—26no—
464C22⋊C4—226no—
465C22⋊C4—226no—
466C22⋊C4—226no—
467C22⋊C4—226no—
468C22⋊C4—226no—
469C22⋊C4—226no—
470C42—26no—
471C42—26no—
472C42—226no—
473C42—226no—
474C42—226no—
475C42—226no—
476C42—226no—
477C42—226no—
478C11C2×#240111yescharacteristic, complemented, Sylow
479C23—23no—
480C23—23no—
481C23—116no—
482C23—116no—
483C23—112no—
484C23—112no—
485C23—2224no—
486C23—223no—
487C23—223no—
488C23—444no—
489C23—4412no—
490C23#41×D1112yes—
491C23C24×D1111yescharacteristic
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—44no—
505C2×C4—116no—
506C2×C4—1116no—
507C2×C4—116no—
508C2×C4—2224no—
509C2×C4—223no—
510C2×C4—223no—
511C2×C4—223no—
512C2×C4—223no—
513C2×C4—223no—
514C2×C4—223no—
515C2×C4—223no—
516C2×C4—223no—
517C2×C4—223no—
518C2×C4—223no—
519C2×C4—223no—
520C2×C4—223no—
521C2×C4—444no—
522C2×C4—444no—
523C2×C4—4412no—
524C2×C4—4412no—
525C2×C4—4412no—
526C2×C4—444no—
527C2×C4—444no—
528C2×C4#41×D1116yes—
529C2×C4#41×D1116yes—
530C22—26no—
531C22—41no—
532C22—43no—
533C22—114no—
534C22—1112no—
535C22—1112no—
536C22—226no—
537C22—4416no—
538C22—441no—
539C22—443no—
540C22C2×#41×D1113yes—
541C22C2×#41×D1111yescharacteristic
542C22C2×#41×D1113yes—
543C4—26no—
544C4—41no—
545C4—43no—
546C4—43no—
547C4—43no—
548C4—114no—
549C4—226no—
550C4—441no—
551C4—443no—
552C4—443no—
553C4—443no—
554C4D11×#12614yes—
555C2—42no—
556C2—118no—
557C2—442no—
558C2C2×D11×#12611yescharacteristic
559C2D11×#52913yes—
560C2D11×#52913yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2401C2
prime radicalC24×D11C23
hypercenter#2401D11
hypocenterC11C2×#2401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #13071919C2semidirect
2. #13071918C2semidirect
3. #13071917C2semidirect
4. #13071916C2semidirect
5. #13071915C2semidirect
6. #13071914C2semidirect
7. #13071913C2semidirect
8. D11×#401C2semidirect
9. D11×#400C2semidirect
12. C4×C4⋊C4×D11C2semidirect
14. D11×#376C2semidirect
15. C11×#2401C2semidirect
23. C11×#401C22semidirect
24. C11×#400C22semidirect
27. C4×C11×C4⋊C4C22semidirect
29. C11×#376C22semidirect
33. #10622599C22semidirect
34. #10622595C22semidirect
35. C4⋊C4×Dic11C22semidirect
36. C4⋊C4×Dic11C22semidirect
45. C4×C4⋊Dic11C22semidirect
46. #10622545C22semidirect
47. C4×Dic11⋊C4C22semidirect
48. C4×Dic11⋊C4C22semidirect
61. C11⋊#401C22semidirect
62. C11⋊#401C22semidirect
63. C11⋊#401C22semidirect
64. #10622273C22semidirect
65. #10622273C22semidirect
66. #10622272C22semidirect
67. #10622271C22semidirect
68. #10622271C22semidirect
69. #10622262C22semidirect
70. #10622262C22semidirect
71. #10622261C22semidirect
72. #10622261C22semidirect
206. #2401D11direct (N × H)
275. #401C2×D11semidirect
283. #400C2×D11semidirect
303. C4×C4⋊C4C2×D11semidirect
315. #376C2×D11semidirect
416. D11#2401direct (N × H)
478. C11C2×#2401semidirect

Maximal subgroups

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

subgroupindex
#130719192
#130719182
#130719172
#130719162
#130719152
#130719142
#130719132
D11×#4012
D11×#4002
D11×#3972
D11×#3962
C4×C4⋊C4×D112
C4×C22⋊C4×D112
D11×#3762
C11×#24012
C2×#240111