Finite Group Databasebeta

← #14767685

Subgroups — #14767685

Order 2816.

796 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
1#13079095C211yesmaximal, characteristic
2#13077529C211yesmaximal, characteristic, complemented
3#13077475C211yesmaximal, characteristic, complemented
4#13069518C211yesmaximal, characteristic, complemented
5#13069511C211yesmaximal, characteristic, complemented
6#13069153C211yesmaximal, characteristic, complemented
7#13069145C211yesmaximal, characteristic, complemented
8#13069141C211yesmaximal, characteristic, complemented
9#13069135C211yesmaximal, characteristic, complemented
10#13069104C211yesmaximal, characteristic, complemented
11#13069095C211yesmaximal, characteristic, complemented
12#13069091C211yesmaximal, characteristic, complemented
13#13068737C211yesmaximal, characteristic, complemented
14#13068370C211yesmaximal, characteristic, complemented
15C11×#1905C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C11×#519C2211yescharacteristic
18#10623361C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20#10623350C2211yescharacteristic
21#10623347C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66961C2211yescharacteristic
24#10623276C2211yescharacteristic
25#10623052C2211yescharacteristic
26C11×#421C2211yescharacteristic
27C11×#419C2211yescharacteristic
28C11×#410C2211yescharacteristic
29#10622849C2211yescharacteristic
30C2×#66900C2211yescharacteristic
31#10622838C2211yescharacteristic
32#10622804C412yescomplemented
33#10622803C412yescomplemented
34#10622789C412yescomplemented
35#10622788C412yescomplemented
36C2×#66887C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38#10622735C2211yescharacteristic
39#10622639—22no—
40C4×#4325—22no—
41#10622619C2211yescharacteristic
42#10622618C2211yescharacteristic
43#10622618C2211yescharacteristic
44#10622614C2211yescharacteristic
45#10622614C2211yescharacteristic
46#10622611C2211yescharacteristic
47#10622610C2211yescharacteristic
48#10622610C2211yescharacteristic
49#10622437—22no—
50#10622436—22no—
51C11×#344C2211yescharacteristic
52C11×H(3,ℤ/4)C2211yescharacteristic
53C11⋊#338C2211yescharacteristic
54#10622195C2211yescharacteristic
55#10622194C2211yescharacteristic
56#10622169C2211yescharacteristic
57#10622169C2211yescharacteristic
58#10622169C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C2×#4339C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C11×#137—41no—
64C11×#137—41no—
65C2×C11×Q16C2×C412yescomplemented
66C2×C11×SD16C2×C412yescomplemented
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C11×#117—41no—
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75#67003—21no—
76#67003—21no—
77#67003—21no—
78#67003—21no—
79#67001—22no—
80#67001—41no—
81#67000C2×C412yes—
82#67000C2×C412yescomplemented
83#66999—41no—
84#66997C2×C412yescomplemented
85C2×#4326C2×C411yescharacteristic, complemented
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325C2×C412yes—
91C2×#4325C2×C412yes—
92C2×#4325C2×C411yescharacteristic, complemented
93#66993C2×C412yes—
94#66990—41no—
95C2×#4324C2×C411yescharacteristic, complemented
96C2×#4323C2×C411yescharacteristic, complemented
97#66983—41no—
98#66982—41no—
99#66979C2311yescharacteristic
100#66979C2311yescharacteristic
101C2×#4318—41no—
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66961—41no—
107#66961—41no—
108#66960—22no—
109M16×D11—41no—
110C2×D88C2×C412yes—
111C2×#4314C2×C412yes—
112#66954—41no—
113#66946—41no—
114C22⋊C4×D11—41no—
115C4×D44—22no—
116C11×#104—22no—
117C11×#103—41no—
118C11×#99—41no—
119#66901—41no—
120#66900—41no—
121#66899—22no—
122#66887—41no—
123#66886—21no—
124#66886—21no—
125#66879C2×C412yescomplemented
126C8×Dic11C2×C412yescomplemented
127#66873—22no—
128#66873—41no—
129#66872—21no—
130#66871—21no—
131#66870—41no—
132#66869—22no—
133#66869—41no—
134#66867—21no—
135#66867D412yescomplemented
136C4×C11⋊C8—21no—
137C4×C11⋊C8D412yescomplemented
138#22284—111nomaximal, Sylow
139C23×D11—21no—
140C11×#41—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—21no—
157C2×C22⋊D11—42no—
158#4339—21no—
159#4339—21no—
160#4339—21no—
161#4339—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C22×C412yes—
168C2×D44C22×C411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—42no—
171C2×Dic22C22×C411yescharacteristic
172C11×Q16—42no—
173C11×SD16—42no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—21no—
178C2×C8×C11—21no—
179C2×C8×C11C22×C412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11C2×D412yes—
191C22⋊Dic11—21no—
192C22⋊Dic11—21no—
193#4326—21no—
194#4326—21no—
195#4325—22no—
196#4325—22no—
197#4325—22no—
198#4325—22no—
199#4325—21no—
200#4325—21no—
201#4324—21no—
202#4324—21no—
203#4323—21no—
204#4323—21no—
205(C2×D11)⋊C4—42no—
206(C2×D11)⋊C4—42no—
207(C2×D11)⋊C4—42no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11C22×C412yes—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218#4318—21no—
219#4318—42no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223C2×C11⋊C8C22×C411yescharacteristic
224C2×C11⋊C8C22×C411yescharacteristic
225C2×C11⋊C8C2×D412yes—
226C2×C11⋊C8C2×D411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228C2×C11⋊C8#4111yescharacteristic
229C2×C11⋊C8#4111yescharacteristic
230D88—42no—
231#4314—42no—
232#4313—42no—
233C8×D11—42no—
234#3154—111no—
235#2957—111no—
236#2949—111no—
237#1977—111no—
238#1976—111no—
239#1912—111no—
240#1911—111no—
241#1910—111no—
242#1909—111no—
243#1905D1111yescharacteristic, complemented
244#1904—111no—
245#1903—111no—
246#1902—111no—
247#1833—111no—
248#1747—111no—
249C23×C11—21no—
250C23×C11H(5,𝔽2)11yescharacteristic
251C22×D11—21no—
252C22×D11—22no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—161no—
256Q8×C11—22no—
257Q8×C11—21no—
258Q8×C11—22no—
259Q8×C11—21no—
260Q8×C11—41no—
261Q8×C11—41no—
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—41no—
265D4×C11—41no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C22⋊D11—41no—
282C22⋊D11—41no—
283C22⋊D11—162no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—41no—
287D44—21no—
288D44—22no—
289D44—22no—
290D44—21no—
291D44—41no—
292D44—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—162no—
296Dic22—21no—
297Dic22—21no—
298C8×C11—22no—
299C8×C11—41no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8C4×D411yescharacteristic
304C11⋊C8C4×D411yescharacteristic
305C11⋊C8C4×D411yescharacteristic
306C11⋊C8C4×D411yescharacteristic
307C2×#137C2×D1111yescharacteristic
308C2×AGL(1,ℤ/8)—111no—
309C2×#135—111no—
310C22×SD16—111no—
311#568—111no—
312#568—111no—
313#536—111no—
314#535—111no—
315#519C2×D1111yescharacteristic
316#518—111no—
317#497—112no—
318#496—112no—
319#495—112no—
320#492—112no—
321#444—222no—
322#443—222no—
323#440—222no—
324C4×SD16—222no—
325C2×#108—111no—
326#427—111no—
327#421—111no—
328#421—111no—
329#421—111no—
330#421C2×D1111yescharacteristic
331#419—111no—
332#419C2×D1111yescharacteristic
333#418—111no—
334#418—111no—
335C2×#101—111no—
336C2×#100—111no—
337#410—111no—
338#410C2×D1111yescharacteristic
339#405—111no—
340#405—111no—
341#405—111no—
342#344—111no—
343#344C2×D1111yescharacteristic
344#338—111no—
345H(3,ℤ/4)—111no—
346H(3,ℤ/4)—111no—
347H(3,ℤ/4)—111no—
348H(3,ℤ/4)—111no—
349H(3,ℤ/4)C2×D1111yescharacteristic
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—81no—
353C22×C11#51811yescharacteristic
354C22×C11#53511yescharacteristic
355C22×C11#54011yescharacteristic
356C2×D11—42no—
357C2×D11—41no—
358C2×D11—82no—
359C2×D11—81no—
360C2×D11—82no—
361C2×D11—161no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C2×C4×D411yescharacteristic
368C4×C11#51811yescharacteristic
369C4×C11#53511yescharacteristic
370C4×C11#54011yescharacteristic
371Dic11—42no—
372Dic11—41no—
373Dic11—81no—
374C2×#41—111no—
375C2×#41C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4—111no—
378#137—41no—
379#137—41no—
380AGL(1,ℤ/8)—441no—
381AGL(1,ℤ/8)—441no—
382#135—221no—
383#135—221no—
384#135—221no—
385#135—221no—
386C2×Q16—111no—
387C2×Q16C4×D1112yescomplemented
388C2×SD16—112no—
389C2×SD16—112no—
390C2×SD16—111no—
391C2×SD16—111no—
392C2×SD16—112no—
393C2×SD16—221no—
394C2×SD16—221no—
395C2×SD16—221no—
396C2×SD16—221no—
397C2×SD16C4×D1112yescomplemented
398C2×D8—111no—
399C2×D8—112no—
400#131—222no—
401#131—222no—
402#131—441no—
403#131—441no—
404C2×M16—111no—
405C2×M16—111no—
406C2×M16—111no—
407C2×M16—441no—
408C2×M16—441no—
409C2×M16C22×D1111yescharacteristic
410C2×M16C22×D1111yescharacteristic
411C22×C8—111no—
412C4⋊Q8—112no—
413#127—112no—
414#124—112no—
415#124—112no—
416#123—441no—
417C22⋊Q8—441no—
418#121—441no—
419#120—441no—
420C4×Q8—22no—
421C4×Q8—41no—
422C4×D4—222no—
423C4×D4—441no—
424#117—41no—
425#117—111no—
426#117—111no—
427#117C22×D1111yescharacteristic
428#117C22×D1111yescharacteristic
429#117C22×D1111yescharacteristic
430C2×C22⋊C4—441no—
431#108—221no—
432#108—221no—
433#107—221no—
434#106—221no—
435#104—22no—
436#104—222no—
437#104—441no—
438#104—441no—
439#103—41no—
440#103—222no—
441#102—222no—
442#102—441no—
443#101—441no—
444#100—441no—
445#99—41no—
446#99—441no—
447#97—112no—
448#97—112no—
449#97—221no—
450C4×C8—112no—
451C4×C8—112no—
452C4×C8—221no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—81no—
457C2×C11#232811yescharacteristic
458D11—81no—
459D11—82no—
460C24—221no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—221no—
466#41—221no—
467#41—221no—
468#41—221no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—111no—
475C2×Q8C2×C4×D1111yescharacteristic
476C2×Q8C2×C4×D1112yes—
477C2×D4—21no—
478C2×D4—111no—
479C2×D4—112no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—442no—
487C2×D4C2×C4×D1111yescharacteristic
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4C23×D1111yescharacteristic
493Q16—42no—
494Q16—221no—
495Q16—221no—
496SD16—42no—
497SD16—221no—
498SD16—221no—
499SD16—222no—
500SD16—222no—
501SD16—222no—
502SD16—222no—
503SD16—221no—
504SD16—221no—
505SD16—442no—
506D8—221no—
507D8—221no—
508D8—442no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16—21no—
513M16—221no—
514M16—221no—
515M16—221no—
516M16—221no—
517M16—221no—
518M16—221no—
519M16—442no—
520M16—442no—
521C2×C8—21no—
522C2×C8—111no—
523C2×C8—111no—
524C2×C8—111no—
525C2×C8—111no—
526C2×C8—111no—
527C2×C8—111no—
528C2×C8—112no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—442no—
532C2×C8—442no—
533C2×C8C2×C4×D1112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—221no—
545C22⋊C4—221no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—112no—
553C42—221no—
554C42D4×D1112yes—
555C11#2228411yescharacteristic, complemented, Sylow
556C23—21no—
557C23—221no—
558C23—222no—
559C23—441no—
560C23—441no—
561C23—1761no—
562C23#6703711yescharacteristic
563Q8—22no—
564Q8—21no—
565Q8—22no—
566Q8—21no—
567Q8—41no—
568Q8—41no—
569Q8—221no—
570Q8—221no—
571D4—21no—
572D4—21no—
573D4—41no—
574D4—41no—
575D4—221no—
576D4—222no—
577D4—221no—
578D4—222no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—1762no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—1762no—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704211yescharacteristic
605C8—22no—
606C8—41no—
607C8—111no—
608C8—111no—
609C8—111no—
610C8—111no—
611C8—222no—
612C8—441no—
613C8—441no—
614C22—41no—
615C22—41no—
616C22—81no—
617C22—441no—
618C22—442no—
619C22—882no—
620C22—881no—
621C22—882no—
622C22—1761no—
623C22#1062307611yescharacteristic
624C22#1062312311yescharacteristic
625C22#1062314611yescharacteristic
626C4—42no—
627C4—41no—
628C4—42no—
629C4—81no—
630C4—81no—
631C4—442no—
632C4—441no—
633C4—881no—
634C4#1062301711yescharacteristic
635C4C4×D4×D1111yescharacteristic
636C4#1062313811yescharacteristic
637C4#1062319411yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—81no—
642C2—882no—
643C2—881no—
644C2#1307133711yescharacteristic
subgroupG/H
centerC2#13071337
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1905C2
socleC2×C11#2328
prime radical#13079095C2
cosocleC22×C4×C11C24
hypercenter#1905D11
hypocenterC11#22284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1905

Complements

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

NH ≅ G/Ntype
2. #13077529C2semidirect
3. #13077475C2semidirect
4. #13069518C2semidirect
5. #13069511C2semidirect
6. #13069153C2semidirect
7. #13069145C2semidirect
8. #13069141C2semidirect
9. #13069135C2semidirect
10. #13069104C2semidirect
11. #13069095C2semidirect
12. #13069091C2semidirect
13. #13068737C2semidirect
14. #13068370C2semidirect
15. C11×#1905C2semidirect
32. #10622804C4semidirect
33. #10622803C4semidirect
34. #10622789C4semidirect
35. #10622788C4semidirect
65. C2×C11×Q16C2×C4semidirect
66. C2×C11×SD16C2×C4semidirect
82. #67000C2×C4semidirect
84. #66997C2×C4semidirect
85. C2×#4326C2×C4semidirect
92. C2×#4325C2×C4semidirect
95. C2×#4324C2×C4semidirect
96. C2×#4323C2×C4semidirect
125. #66879C2×C4semidirect
126. C8×Dic11C2×C4semidirect
135. #66867D4semidirect
137. C4×C11⋊C8D4semidirect
243. #1905D11semidirect
387. C2×Q16C4×D11semidirect
397. C2×SD16C4×D11semidirect
555. C11#22284semidirect

Maximal subgroups

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

subgroupindex
#130790952
#130775292
#130774752
#130695182
#130695112
#130691532
#130691452
#130691412
#130691352
#130691042
#130690952
#130690912
#130687372
#130683702
C11×#19052
#2228411