Finite Group Databasebeta

← D11×#2223 #14908338

Subgroups — D11×#2223 #14908338

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×SD32C211yesmaximal, characteristic, complemented
2D11×#504C211yesmaximal, characteristic, complemented
3D11×#473C211yesmaximal, characteristic, complemented
4D11×#472C211yesmaximal, characteristic
5#13070749C211yesmaximal, characteristic, complemented
6#13070748C211yesmaximal, characteristic, complemented
7#13070747C211yesmaximal, characteristic, complemented
8#13070746C211yesmaximal, characteristic, complemented
9#13070745C211yesmaximal, characteristic, complemented
10#13070744C211yesmaximal, characteristic, complemented
11#13070743C211yesmaximal, characteristic, complemented
12D11×#368C211yesmaximal, characteristic, complemented
13D11×#362C211yesmaximal, characteristic, complemented
14D11×#361C211yesmaximal, characteristic, complemented
15C11×#2223C211yesmaximal, characteristic, complemented
16D11×#137—21no—
17D11×AGL(1,ℤ/8)—21no—
18C2×Q16×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20D11×#131C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic, complemented
22C11×#504C2211yescharacteristic, complemented
23C11×#473C2211yescharacteristic, complemented
24C11×#472C2211yescharacteristic
25#10622817—21no—
26#10622812—21no—
27#10622805C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic, complemented
29#10622773C2211yescharacteristic
30C2×#66891C2211yescharacteristic, complemented
31#10622756C2211yescharacteristic, complemented
32#10622755C2211yescharacteristic
33#10622753C2211yescharacteristic, complemented
34D11×SD32—21no—
35D11×SD32—21no—
36D11×SD32—21no—
37D11×SD32—21no—
38#10622520—21no—
39#10622520C2211yescharacteristic, complemented
40D11×M32—21no—
41D11×M32C2211yescharacteristic
42C2×#66864C2211yescharacteristic, complemented
43#10622514—21no—
44#10622514C2211yescharacteristic, complemented
45C2×C16×D11—21no—
46C2×C16×D11C2211yescharacteristic
47#10622510C2211yescharacteristic
48#10622509C2211yescharacteristic, complemented
49D11×#108C2211yescharacteristic
50D11×#108C2211yescharacteristic
51#10622368—21no—
52D11×#101—21no—
53#10622362—21no—
54D11×#100—21no—
55C11×#368C2211yescharacteristic, complemented
56C11×#362C2211yescharacteristic, complemented
57C11×#361C2211yescharacteristic, complemented
58#10622203C2211yescharacteristic, complemented
59#10622201C2211yescharacteristic, complemented
60#10622155C2211yescharacteristic, complemented
61#10622154C2211yescharacteristic, complemented
62#10622144C2211yescharacteristic, complemented
63#10622134C2211yescharacteristic, complemented
64#10622133C2211yescharacteristic, complemented
65#10622131C2211yescharacteristic, complemented
66#10622131C2211yescharacteristic, complemented
67#41×D11D411yescharacteristic
68C2×Q8×D11—21no—
69C2×D4×D11—21no—
70C11×#137—21no—
71C11×AGL(1,ℤ/8)—21no—
72C2×C11×Q16C2311yescharacteristic
73C2×C11×D8C2311yescharacteristic
74C11×#131C2311yescharacteristic
75#67004—21no—
76#67002—21no—
77#67001D411yescharacteristic
78C2×#4326—21no—
79#66995—21no—
80#66985—21no—
81C2×#4323—21no—
82#66971—41no—
83Q16×D11—21no—
84Q16×D11—21no—
85Q16×D11—21no—
86Q16×D11—21no—
87Q16×D11—41no—
88#66968—41no—
89#66967—41no—
90SD16×D11—41no—
91SD16×D11—41no—
92#66964—41no—
93D8×D11—21no—
94D8×D11—21no—
95D8×D11—21no—
96D8×D11—21no—
97D8×D11—41no—
98#66962—21no—
99#66961—21no—
100#66960—21no—
101#66960D411yescharacteristic
102M16×D11—21no—
103M16×D11—21no—
104M16×D11—21no—
105M16×D11D411yescharacteristic
106C2×Dic44C2311yescharacteristic
107C2×D88C2311yescharacteristic
108#66954—21no—
109#66954C2311yescharacteristic
110C2×C8×D11—21no—
111C2×C8×D11C2311yescharacteristic
112C11×SD32—21no—
113C11×SD32—21no—
114C11×M32—21no—
115C11×M32C2311yescharacteristic
116C2×C11×C16—21no—
117C2×C11×C16C2311yescharacteristic
118C11×#108C2311yescharacteristic
119C11×#108C2311yescharacteristic
120C11×#101—21no—
121C11×#100—21no—
122#66900—21no—
123#66897—21no—
124#66892—21no—
125#66892—21no—
126#66891—21no—
127#66891—21no—
128#66888—21no—
129#66888—21no—
130#66887—21no—
131#66887—21no—
132#66886—21no—
133#66886—21no—
134#66883C2311yescharacteristic
135#66883C2311yescharacteristic
136#66876—21no—
137#66876C2311yescharacteristic
138C2×C11⋊C16—21no—
139C2×C11⋊C16C2311yescharacteristic
140#66864—21no—
141#66864—21no—
142#66862—21no—
143#66862—21no—
144#66862—21no—
145C16×D11—21no—
146C16×D11—21no—
147C16×D11—21no—
148C16×D11D411yescharacteristic
149C16×D11D411yescharacteristic
150C16×D11D411yescharacteristic
151C16×D11D411yescharacteristic
152C2×#2223—111nomaximal, Sylow
153C23×D11—41no—
154C11×#41C2×D411yescharacteristic
155C2×Q8×C11—21no—
156C2×D4×C11—21no—
157C2×C22⋊D11—41no—
158#4343D811yescharacteristic
159Q8×D11—41no—
160Q8×D11—41no—
161Q8×D11—41no—
162Q8×D11—41no—
163Q8×D11D811yescharacteristic
164#4341—21no—
165#4341D811yescharacteristic
166D4×D11—21no—
167D4×D11—41no—
168D4×D11—41no—
169D4×D11—41no—
170D4×D11—41no—
171D4×D11D811yescharacteristic
172#4339—21no—
173#4339C2×D411yescharacteristic
174C2×D44—21no—
175C2×C4×D11—21no—
176C2×C4×D11—41no—
177C2×C4×D11C2×D411yescharacteristic
178C2×Dic22—21no—
179C2×Dic22—41no—
180C11×Q16—21no—
181C11×Q16—21no—
182C11×Q16—41no—
183C11×SD16—41no—
184C11×SD16—41no—
185C11×D8—21no—
186C11×D8—21no—
187C11×D8—41no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—21no—
191C11×M16C2×D411yescharacteristic
192C2×C8×C11—21no—
193C2×C8×C11C2411yescharacteristic
194#4326—41no—
195#4326—41no—
196#4326—41no—
197#4326—41no—
198#4325—41no—
199#4325—41no—
200#4324—41no—
201#4324—41no—
202#4323—41no—
203#4323—41no—
204#4323—41no—
205#4323—41no—
206#4318—21no—
207#4318—21no—
208#4318—21no—
209#4318C2×D411yescharacteristic
210C2×C11⋊C8—21no—
211C2×C11⋊C8C2×D411yescharacteristic
212Dic44—21no—
213Dic44—21no—
214Dic44—41no—
215D88—21no—
216D88—21no—
217D88—41no—
218#4314—41no—
219#4314—41no—
220#4313—21no—
221#4313—21no—
222#4313—21no—
223#4313—41no—
224#4313—41no—
225C8×D11—21no—
226C8×D11—21no—
227C8×D11—21no—
228C8×D11—41no—
229C8×D11—41no—
230C8×D11C2×D411yescharacteristic
231C8×D11C2×D411yescharacteristic
232C8×D11#4111yescharacteristic
233C8×D11#4111yescharacteristic
234C11×C16—21no—
235C11×C16C2×D411yescharacteristic
236C11×C16C2×D411yescharacteristic
237C11⋊C16—21no—
238C11⋊C16C2×D411yescharacteristic
239C11⋊C16C2×D411yescharacteristic
240C22×SD32—111no—
241C2×#504—111no—
242C2×#473—111no—
243C2×#472—111no—
244#2223—111no—
245#2223—111no—
246#2223—111no—
247#2223—111no—
248#2223—111no—
249#2223—111no—
250#2223—111no—
251#2223D1111yescharacteristic, direct product factor
252C2×#368—111no—
253C2×#362—111no—
254C2×#361—111no—
255C23×C11—41no—
256C22×D11—21no—
257C22×D11—41no—
258C22×D11—81no—
259C22×D11—81no—
260C22×D11—162no—
261C22×D11#13511yescharacteristic
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11C2×D811yescharacteristic
265D4×C11—21no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11C2×D811yescharacteristic
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11C22×D411yescharacteristic
272C22⋊D11—21no—
273C22⋊D11—21no—
274C22⋊D11—21no—
275C22⋊D11—81no—
276C22⋊D11—81no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11#13511yescharacteristic
280D44—21no—
281D44—41no—
282D44—41no—
283D44C2×D811yescharacteristic
284C4×D11—21no—
285C4×D11—21no—
286C4×D11—21no—
287C4×D11—81no—
288C4×D11—81no—
289C4×D11#12111yescharacteristic
290C4×D11#12111yescharacteristic
291C4×D11C2×D811yescharacteristic
292C4×D11C2×D811yescharacteristic
293Dic22—21no—
294Dic22—41no—
295Dic22—41no—
296Dic22—81no—
297Dic22—81no—
298Dic22C2×D811yescharacteristic
299C8×C11—21no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11C22×D411yescharacteristic
303C8×C11C2×#4111yescharacteristic
304C11⋊C8—21no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8#12111yescharacteristic
308C11⋊C8#12111yescharacteristic
309C2×#137—221no—
310C2×AGL(1,ℤ/8)—221no—
311C22×Q16—111no—
312C22×D8—111no—
313C2×#131—111no—
314C2×SD32—111no—
315C2×SD32—111no—
316C2×SD32—111no—
317C2×SD32—221no—
318C2×SD32—221no—
319C2×SD32—221no—
320C2×SD32—221no—
321C2×SD32C2×D1111yescharacteristic, complemented
322#504—111no—
323#504—111no—
324#504—111no—
325#504—221no—
326#504—221no—
327#504C2×D1111yescharacteristic, complemented
328C2×M32—111no—
329C2×M32—221no—
330C22×C16—111no—
331C22×C16—221no—
332#473—111no—
333#473—111no—
334#473—111no—
335#473—221no—
336#473—221no—
337#473C2×D1111yescharacteristic, complemented
338#472—111no—
339#472—111no—
340#472—111no—
341#472—221no—
342#472—221no—
343#472C2×D1111yescharacteristic
344C2×#108—111no—
345C2×#108—111no—
346C2×#101—221no—
347C2×#100—221no—
348#368—111no—
349#368—111no—
350#368—111no—
351#368C2×D1111yescharacteristic, complemented
352#362—111no—
353#362—111no—
354#362—111no—
355#362C2×D1111yescharacteristic, complemented
356#361—111no—
357#361—111no—
358#361—111no—
359#361C2×D1111yescharacteristic, complemented
360C22×C11—21no—
361C22×C11—81no—
362C22×C11—161no—
363C22×C11C2×#13511yescharacteristic
364C2×D11—22no—
365C2×D11—21no—
366C2×D11—42no—
367C2×D11—81no—
368C2×D11—162no—
369C2×D11—162no—
370C2×D11—161no—
371C2×D11#46611yescharacteristic
372C2×D11#46611yescharacteristic
373C4×C11—21no—
374C4×C11—81no—
375C4×C11C2×#12111yescharacteristic
376C4×C11C22×D811yescharacteristic
377Dic11—21no—
378Dic11—81no—
379Dic11#46611yescharacteristic
380Dic11#46611yescharacteristic
381C2×#41—111no—
382C22×Q8—221no—
383C22×D4—221no—
384#137—21no—
385#137—221no—
386#137—221no—
387#137—221no—
388#137—441no—
389#137—441no—
390AGL(1,ℤ/8)—21no—
391AGL(1,ℤ/8)—221no—
392AGL(1,ℤ/8)—221no—
393AGL(1,ℤ/8)—221no—
394AGL(1,ℤ/8)—441no—
395AGL(1,ℤ/8)—441no—
396C2×Q16—111no—
397C2×Q16—221no—
398C2×Q16—221no—
399C2×Q16—221no—
400C2×Q16—221no—
401C2×Q16—221no—
402C2×Q16—441no—
403C2×Q16C22×D1111yescharacteristic
404C2×SD16—441no—
405C2×SD16—441no—
406C2×D8—111no—
407C2×D8—221no—
408C2×D8—221no—
409C2×D8—221no—
410C2×D8—221no—
411C2×D8—221no—
412C2×D8—441no—
413C2×D8C22×D1111yescharacteristic
414#131—111no—
415#131—111no—
416#131—111no—
417#131—221no—
418#131—221no—
419#131C22×D1111yescharacteristic
420C2×M16—111no—
421C2×M16—221no—
422C2×M16—221no—
423C2×M16—221no—
424C22×C8—111no—
425C22×C8—221no—
426SD32—21no—
427SD32—21no—
428SD32—221no—
429SD32—221no—
430SD32—221no—
431SD32—221no—
432SD32—221no—
433SD32—221no—
434M32—21no—
435M32—111no—
436M32—221no—
437M32—221no—
438M32—221no—
439M32—221no—
440M32C22×D1111yescharacteristic
441C2×C16—21no—
442C2×C16—111no—
443C2×C16—111no—
444C2×C16—111no—
445C2×C16—111no—
446C2×C16—111no—
447C2×C16—221no—
448C2×C16—221no—
449C2×C16—221no—
450C2×C16—221no—
451C2×C16C22×D1111yescharacteristic
452#108—111no—
453#108—111no—
454#108—221no—
455#108—221no—
456#108C22×D1111yescharacteristic
457#108C22×D1111yescharacteristic
458#101—21no—
459#101—221no—
460#101—221no—
461#101—221no—
462#100—21no—
463#100—221no—
464#100—221no—
465#100—221no—
466C2×C11—21no—
467C2×C11—41no—
468C2×C11—161no—
469C2×C11C2×#46611yescharacteristic
470D11—21no—
471D11—41no—
472D11—161no—
473D11#222312yesdirect product factor
474C24—441no—
475#41—111no—
476#41—111no—
477#41—111no—
478#41—221no—
479#41—221no—
480#41D4×D1111yescharacteristic
481C2×Q8—21no—
482C2×Q8—111no—
483C2×Q8—221no—
484C2×Q8—441no—
485C2×Q8—441no—
486C2×Q8—441no—
487C2×Q8—441no—
488C2×Q8—441no—
489C2×D4—21no—
490C2×D4—111no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—441no—
494C2×D4—441no—
495C2×D4—441no—
496C2×D4—441no—
497C2×D4—441no—
498C22×C4—111no—
499C22×C4—221no—
500C22×C4—441no—
501Q16—21no—
502Q16—21no—
503Q16—41no—
504Q16—221no—
505Q16—221no—
506Q16—441no—
507Q16—441no—
508Q16—441no—
509Q16—441no—
510Q16—441no—
511SD16—41no—
512SD16—41no—
513SD16—441no—
514SD16—441no—
515SD16—441no—
516SD16—441no—
517SD16—441no—
518SD16—441no—
519D8—21no—
520D8—21no—
521D8—41no—
522D8—221no—
523D8—221no—
524D8—441no—
525D8—441no—
526D8—441no—
527D8—441no—
528D8—441no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—111no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—221no—
539M16—441no—
540M16—441no—
541M16D4×D1111yescharacteristic
542C2×C8—21no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—441no—
553C2×C8—441no—
554C2×C8C23×D1111yescharacteristic
555C16—21no—
556C16—111no—
557C16—111no—
558C16—221no—
559C16D4×D1111yescharacteristic
560C16D4×D1111yescharacteristic
561C11C2×#222311yescharacteristic, complemented, Sylow
562C23—41no—
563C23—111no—
564C23—221no—
565C23—441no—
566C23—881no—
567C23—881no—
568C23—1762no—
569Q8—41no—
570Q8—41no—
571Q8—111no—
572Q8—221no—
573Q8—441no—
574Q8—441no—
575Q8—881no—
576Q8—881no—
577Q8D8×D1111yescharacteristic
578D4—21no—
579D4—41no—
580D4—41no—
581D4—111no—
582D4—221no—
583D4—221no—
584D4—221no—
585D4—221no—
586D4—441no—
587D4—441no—
588D4—881no—
589D4—881no—
590D4D8×D1111yescharacteristic
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—111no—
594C2×C4—111no—
595C2×C4—111no—
596C2×C4—111no—
597C2×C4—111no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—441no—
603C2×C4—881no—
604C2×C4—881no—
605C2×C4C2×D4×D1111yescharacteristic
606C8—21no—
607C8—41no—
608C8—41no—
609C8—111no—
610C8—111no—
611C8—221no—
612C8—441no—
613C8—441no—
614C8C2×D4×D1111yescharacteristic
615C8#41×D1111yescharacteristic
616C22—21no—
617C22—81no—
618C22—111no—
619C22—111no—
620C22—161no—
621C22—222no—
622C22—221no—
623C22—442no—
624C22—881no—
625C22—1761no—
626C22—1762no—
627C22—1762no—
628C22D11×#13511yescharacteristic
629C4—21no—
630C4—81no—
631C4—111no—
632C4—111no—
633C4—221no—
634C4—881no—
635C4D11×#12111yescharacteristic
636C4C2×D8×D1111yescharacteristic
637C2—21no—
638C2—41no—
639C2—112no—
640C2—161no—
641C2—221no—
642C2—441no—
643C2—1761no—
644C2D11×#46611yescharacteristic
subgroupG/H
centerC2D11×#466
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2223C2
socleC2×C11C2×#466
prime radicalD11×#472C2
hypercenter#2223D11
hypocenterC11C2×#2223
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #2223

Complements

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

NH ≅ G/Ntype
1. C2×D11×SD32C2semidirect
2. D11×#504C2semidirect
3. D11×#473C2semidirect
5. #13070749C2semidirect
6. #13070748C2semidirect
7. #13070747C2semidirect
8. #13070746C2semidirect
9. #13070745C2semidirect
10. #13070744C2semidirect
11. #13070743C2semidirect
12. D11×#368C2semidirect
13. D11×#362C2semidirect
14. D11×#361C2semidirect
15. C11×#2223C2semidirect
21. C2×C11×SD32C22semidirect
22. C11×#504C22semidirect
23. C11×#473C22semidirect
27. #10622805C22semidirect
28. C2×#66892C22semidirect
30. C2×#66891C22semidirect
31. #10622756C22semidirect
33. #10622753C22semidirect
39. #10622520C22semidirect
42. C2×#66864C22semidirect
44. #10622514C22semidirect
48. #10622509C22semidirect
55. C11×#368C22semidirect
56. C11×#362C22semidirect
57. C11×#361C22semidirect
58. #10622203C22semidirect
59. #10622201C22semidirect
60. #10622155C22semidirect
61. #10622154C22semidirect
62. #10622144C22semidirect
63. #10622134C22semidirect
64. #10622133C22semidirect
65. #10622131C22semidirect
66. #10622131C22semidirect
251. #2223D11direct (N × H)
321. C2×SD32C2×D11semidirect
327. #504C2×D11semidirect
337. #473C2×D11semidirect
351. #368C2×D11semidirect
355. #362C2×D11semidirect
359. #361C2×D11semidirect
473. D11#2223direct (N × H)
561. C11C2×#2223semidirect

Maximal subgroups

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

subgroupindex
C2×D11×SD322
D11×#5042
D11×#4732
D11×#4722
#130707492
#130707482
#130707472
#130707462
#130707452
#130707442
#130707432
D11×#3682
D11×#3622
D11×#3612
C11×#22232
C2×#222311