Finite Group Databasebeta

← #14767697

Subgroups — #14767697

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079099C211yesmaximal, characteristic
2#13077531C211yesmaximal, characteristic, complemented
3#13077464C211yesmaximal, characteristic, complemented
4#13069525C211yesmaximal, characteristic, complemented
5#13069511C211yesmaximal, characteristic, complemented
6#13069149C211yesmaximal, characteristic, complemented
7#13069147C211yesmaximal, characteristic, complemented
8#13069142C211yesmaximal, characteristic, complemented
9#13069106C211yesmaximal, characteristic, complemented
10#13069101C211yesmaximal, characteristic, complemented
11#13069096C211yesmaximal, characteristic, complemented
12#13069093C211yesmaximal, characteristic, complemented
13#13068738C211yesmaximal, characteristic, complemented
14#13068370C211yesmaximal, characteristic, complemented
15C11×#1910C211yesmaximal, characteristic, complemented
16C11×#568C2211yescharacteristic
17C11×#535C2211yescharacteristic
18C2×#67003C2211yescharacteristic
19C2×#67002C2211yescharacteristic
20#10623329C2211yescharacteristic
21C2×#66985C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23#10623276C2211yescharacteristic
24#10623056C2211yescharacteristic
25#10623052C2211yescharacteristic
26C11×#418C2211yescharacteristic
27C11×#418C2211yescharacteristic
28C11×#410C2211yescharacteristic
29#10622849C2211yescharacteristic
30#10622849C2211yescharacteristic
31C2×#66897C2211yescharacteristic
32#10622758—22no—
33#10622757—22no—
34#10622752C2211yescharacteristic
35#10622744C2211yescharacteristic
36C2×#66887C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38#10622735C2211yescharacteristic
39#10622687C412yescomplemented
40#10622686C412yescomplemented
41#10622672C412yescomplemented
42#10622671C412yescomplemented
43#10622619C2211yescharacteristic
44#10622618C2211yescharacteristic
45#10622614C2211yescharacteristic
46#10622611C2211yescharacteristic
47#10622610C2211yescharacteristic
48#10622610C2211yescharacteristic
49#10622398—22no—
50#10622369—22no—
51C11×H(3,ℤ/4)C2211yescharacteristic
52C11×H(3,ℤ/4)C2211yescharacteristic
53C11⋊#338C2211yescharacteristic
54#10622197C2211yescharacteristic
55#10622171C2211yescharacteristic
56#10622169C2211yescharacteristic
57#10622169C2211yescharacteristic
58#10622169C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C2×#4339C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C11×#131—22no—
64C11×#131—41no—
65C2×C11×M16—41no—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C11×#127C2×C412yescomplemented
69C11×#124C2×C412yescomplemented
70C11×#121—41no—
71C11×#120—41no—
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C22⋊Dic11—41no—
76#67003—21no—
77#67003—21no—
78#67003—21no—
79#67003—21no—
80#67002—41no—
81#67002—41no—
82C2×#4326C2×C411yescharacteristic, complemented
83C2×#4325C2×C411yescharacteristic, complemented
84C2×#4325C2×C412yescomplemented
85D4×Dic11—22no—
86D4×Dic11—41no—
87C2×#4324C2×C411yescharacteristic, complemented
88C2×#4324C2×C412yescomplemented
89#66985—41no—
90#66985—41no—
91C2×#4323—21no—
92C2×#4323—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323C2×C412yes—
96C2×#4323C2×C412yes—
97C2×#4323C2×C411yescharacteristic, complemented
98C2×#4323C2×C412yescomplemented
99C2×#4323C2×C412yescomplemented
100#66979C2311yescharacteristic
101#66979C2311yescharacteristic
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66960—41no—
107M16×D11—41no—
108#66954—22no—
109#66948—41no—
110#66946—22no—
111#66935—41no—
112C22⋊C4×D11—41no—
113#66928C2×C412yescomplemented
114#66927C2×C412yescomplemented
115C4×D44—41no—
116C11×#102—22no—
117C11×#102—41no—
118C11×#99—41no—
119#66901—22no—
120#66901—41no—
121#66897—41no—
122#66889—22no—
123#66887—41no—
124#66886—21no—
125#66886—21no—
126#66885—22no—
127#66879D412yescomplemented
128C8×Dic11D412yescomplemented
129#66873—41no—
130#66872—21no—
131#66871—21no—
132#66870—41no—
133#66869—41no—
134#66867—21no—
135#66867C2×C412yescomplemented
136C4×C11⋊C8—21no—
137C4×C11⋊C8C2×C412yescomplemented
138#22286—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—42no—
153C2×D4×C11C22×C412yes—
154C2×D4×C11C22×C411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C22×Dic11—42no—
159#4339—21no—
160#4339—21no—
161#4339—21no—
162#4339—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—42no—
169C2×D44C22×C411yescharacteristic
170C2×D44C22×C412yes—
171C2×C4×D11—21no—
172C2×C4×D11—42no—
173C2×Dic22C22×C411yescharacteristic
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—21no—
178C11×M16—42no—
179C2×C8×C11—21no—
180C2×C8×C11—42no—
181C2×C8×C11C2×D412yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C22×C412yes—
192C22⋊Dic11—21no—
193C22⋊Dic11—21no—
194C22⋊Dic11—42no—
195#4326—21no—
196#4326—21no—
197#4325—21no—
198#4325—21no—
199#4325—42no—
200#4324—21no—
201#4324—21no—
202#4324—42no—
203#4323—22no—
204#4323—22no—
205#4323—22no—
206#4323—22no—
207#4323—21no—
208#4323—21no—
209#4323—42no—
210#4323—42no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—42no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11C2×D412yes—
217#4318—21no—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8C22×C412yes—
226C2×C11⋊C8C22×C411yescharacteristic
227C2×C11⋊C8C22×C411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8#4111yescharacteristic
231C2×C11⋊C8#4111yescharacteristic
232#4313—42no—
233C8×D11—42no—
234#3155—111no—
235#2957—111no—
236#2948—111no—
237#1978—111no—
238#1976—111no—
239#1911—111no—
240#1911—111no—
241#1910—111no—
242#1910D1111yescharacteristic, complemented
243#1904—111no—
244#1904—111no—
245#1903—111no—
246#1903—111no—
247#1833—111no—
248#1747—111no—
249C23×C11—22no—
250C23×C11—21no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—161no—
254C23×C11H(5,𝔽2)11yescharacteristic
255C22×D11—22no—
256C22×D11—21no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—161no—
260Q8×C11—21no—
261Q8×C11—21no—
262D4×C11—22no—
263D4×C11—21no—
264D4×C11—21no—
265D4×C11—22no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—162no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C22⋊D11—41no—
284C22⋊D11—41no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—162no—
289D44—22no—
290D44—21no—
291D44—21no—
292D44—22no—
293D44—41no—
294D44—41no—
295D44—162no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—162no—
299Dic22—21no—
300Dic22—21no—
301C8×C11—22no—
302C8×C11—41no—
303C11⋊C8—22no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C11⋊C8C4×D411yescharacteristic
307C11⋊C8C4×D411yescharacteristic
308C11⋊C8C4×D411yescharacteristic
309C11⋊C8C4×D411yescharacteristic
310C2×AGL(1,ℤ/8)—111no—
311C2×AGL(1,ℤ/8)—111no—
312C2×#135—111no—
313C22×D8—111no—
314#568—111no—
315#568C2×D1111yescharacteristic
316#535—111no—
317#535C2×D1111yescharacteristic
318#518—111no—
319#518—111no—
320#496—112no—
321#496—112no—
322#495—112no—
323#493—112no—
324#444—222no—
325#443—222no—
326#442—222no—
327C4×D8—222no—
328C2×#108—111no—
329#427—111no—
330#421—111no—
331#421—111no—
332#421—111no—
333#421—111no—
334#418—111no—
335#418—111no—
336#418C2×D1111yescharacteristic
337#418C2×D1111yescharacteristic
338C2×#100—111no—
339C2×#100—111no—
340#410—111no—
341#410C2×D1111yescharacteristic
342#405—111no—
343#405—111no—
344#405—111no—
345#344—111no—
346#344—111no—
347#338—111no—
348H(3,ℤ/4)—111no—
349H(3,ℤ/4)—111no—
350H(3,ℤ/4)—111no—
351H(3,ℤ/4)C2×D1111yescharacteristic
352H(3,ℤ/4)C2×D1111yescharacteristic
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—82no—
358C22×C11—82no—
359C22×C11—161no—
360C22×C11#51811yescharacteristic
361C22×C11#53511yescharacteristic
362C22×C11#54011yescharacteristic
363C2×D11—42no—
364C2×D11—41no—
365C2×D11—82no—
366C2×D11—82no—
367C2×D11—81no—
368C2×D11—161no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C2×C4×D411yescharacteristic
374C4×C11#51811yescharacteristic
375C4×C11#53511yescharacteristic
376C4×C11#54011yescharacteristic
377Dic11—42no—
378Dic11—41no—
379Dic11—81no—
380C2×#41—111no—
381C2×#41C22×D1111yescharacteristic
382C22×D4—111no—
383C22×D4C22×D1111yescharacteristic
384AGL(1,ℤ/8)—441no—
385AGL(1,ℤ/8)—441no—
386AGL(1,ℤ/8)—441no—
387AGL(1,ℤ/8)—441no—
388#135—221no—
389#135—221no—
390#135—221no—
391#135—221no—
392C2×Q16—111no—
393C2×SD16—111no—
394C2×SD16—111no—
395C2×SD16—112no—
396C2×SD16—112no—
397C2×D8—112no—
398C2×D8—112no—
399C2×D8—111no—
400C2×D8—112no—
401C2×D8—112no—
402C2×D8—221no—
403C2×D8—221no—
404C2×D8—221no—
405C2×D8—221no—
406#131—22no—
407#131—41no—
408#131—222no—
409#131—441no—
410C2×M16—41no—
411C2×M16—111no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—441no—
415C2×M16C22×D1111yescharacteristic
416C2×M16C22×D1111yescharacteristic
417C22×C8—111no—
418#127—112no—
419#127C4×D1112yescomplemented
420#124—112no—
421#124C4×D1112yescomplemented
422#121—41no—
423#121—441no—
424#120—41no—
425#120—441no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—441no—
429C4×D4—441no—
430#117—111no—
431#117—111no—
432#117C22×D1111yescharacteristic
433#117C22×D1111yescharacteristic
434#117C22×D1111yescharacteristic
435C2×C22⋊C4—441no—
436C2×C22⋊C4—441no—
437#108—221no—
438#108—221no—
439#107—221no—
440#106—221no—
441#104—222no—
442#104—222no—
443#104—441no—
444#104—441no—
445#102—22no—
446#102—41no—
447#102—222no—
448#102—441no—
449#100—441no—
450#100—441no—
451#99—41no—
452#99—441no—
453#97—112no—
454#97—112no—
455#97—221no—
456C4×C8—112no—
457C4×C8—112no—
458C4×C8—221no—
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—21no—
462C2×C11—81no—
463C2×C11—82no—
464C2×C11#232811yescharacteristic
465D11—81no—
466D11—82no—
467C24—21no—
468C24—221no—
469#41—21no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—221no—
474#41—221no—
475#41—221no—
476#41—221no—
477C2×Q8—111no—
478C2×Q8C2×C4×D1111yescharacteristic
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—112no—
487C2×D4—111no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—442no—
495C2×D4C2×C4×D1112yes—
496C2×D4C2×C4×D1111yescharacteristic
497C22×C4—21no—
498C22×C4—221no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4C23×D1111yescharacteristic
502Q16—221no—
503Q16—221no—
504SD16—221no—
505SD16—221no—
506SD16—221no—
507SD16—221no—
508SD16—442no—
509SD16—442no—
510D8—222no—
511D8—222no—
512D8—222no—
513D8—222no—
514D8—221no—
515D8—221no—
516D8—442no—
517D8—442no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—42no—
523M16—221no—
524M16—221no—
525M16—221no—
526M16—221no—
527M16—221no—
528M16—221no—
529M16—442no—
530C2×C8—21no—
531C2×C8—42no—
532C2×C8—111no—
533C2×C8—111no—
534C2×C8—111no—
535C2×C8—111no—
536C2×C8—111no—
537C2×C8—111no—
538C2×C8—112no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—442no—
542C2×C8D4×D1112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—42no—
552C22⋊C4—221no—
553C22⋊C4—221no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C42—21no—
558C42—21no—
559C42—112no—
560C42—221no—
561C42C2×C4×D1112yes—
562C11#2228611yescharacteristic, complemented, Sylow
563C23—22no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—161no—
568C23—222no—
569C23—221no—
570C23—441no—
571C23—441no—
572C23—1761no—
573C23#6703711yescharacteristic
574Q8—21no—
575Q8—21no—
576Q8—221no—
577Q8—221no—
578D4—22no—
579D4—21no—
580D4—21no—
581D4—22no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—162no—
587D4—222no—
588D4—221no—
589D4—221no—
590D4—222no—
591D4—441no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—1762no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—1762no—
608C2×C4—1762no—
609C2×C4C22×C4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4#6703711yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#6704211yescharacteristic
615C8—22no—
616C8—41no—
617C8—111no—
618C8—111no—
619C8—111no—
620C8—111no—
621C8—222no—
622C8—441no—
623C8—441no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—81no—
628C22—82no—
629C22—82no—
630C22—161no—
631C22—441no—
632C22—442no—
633C22—881no—
634C22—882no—
635C22—882no—
636C22—1761no—
637C22#1062301711yescharacteristic
638C22#1062313811yescharacteristic
639C22#1062314611yescharacteristic
640C4—42no—
641C4—41no—
642C4—81no—
643C4—81no—
644C4—442no—
645C4—441no—
646C4—881no—
647C4C4×D4×D1111yescharacteristic
648C4#1062307611yescharacteristic
649C4#1062312311yescharacteristic
650C4#1062319411yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—82no—
655C2—81no—
656C2—882no—
657C2—881no—
658C2#1307133711yescharacteristic
subgroupG/H
centerC2#13071337
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1910C2
socleC2×C11#2328
prime radical#13079099C2
cosocleC22×C4×C11C24
hypercenter#1910D11
hypocenterC11#22286
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1910

Complements

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

NH ≅ G/Ntype
2. #13077531C2semidirect
3. #13077464C2semidirect
4. #13069525C2semidirect
5. #13069511C2semidirect
6. #13069149C2semidirect
7. #13069147C2semidirect
8. #13069142C2semidirect
9. #13069106C2semidirect
10. #13069101C2semidirect
11. #13069096C2semidirect
12. #13069093C2semidirect
13. #13068738C2semidirect
14. #13068370C2semidirect
15. C11×#1910C2semidirect
39. #10622687C4semidirect
40. #10622686C4semidirect
41. #10622672C4semidirect
42. #10622671C4semidirect
68. C11×#127C2×C4semidirect
69. C11×#124C2×C4semidirect
82. C2×#4326C2×C4semidirect
83. C2×#4325C2×C4semidirect
84. C2×#4325C2×C4semidirect
87. C2×#4324C2×C4semidirect
88. C2×#4324C2×C4semidirect
97. C2×#4323C2×C4semidirect
98. C2×#4323C2×C4semidirect
99. C2×#4323C2×C4semidirect
113. #66928C2×C4semidirect
114. #66927C2×C4semidirect
127. #66879D4semidirect
128. C8×Dic11D4semidirect
135. #66867C2×C4semidirect
137. C4×C11⋊C8C2×C4semidirect
242. #1910D11semidirect
419. #127C4×D11semidirect
421. #124C4×D11semidirect
562. C11#22286semidirect

Maximal subgroups

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

subgroupindex
#130790992
#130775312
#130774642
#130695252
#130695112
#130691492
#130691472
#130691422
#130691062
#130691012
#130690962
#130690932
#130687382
#130683702
C11×#19102
#2228611