Finite Group Databasebeta

← #14767682

Subgroups — #14767682

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#13077533C211yesmaximal, characteristic, complemented
2#13077476C211yesmaximal, characteristic, complemented
3#13069521C211yesmaximal, characteristic, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069154C211yesmaximal, characteristic, complemented
6#13069149C211yesmaximal, characteristic, complemented
7#13069144C211yesmaximal, characteristic, complemented
8#13069139C211yesmaximal, characteristic, complemented
9#13069112C211yesmaximal, characteristic, complemented
10#13069105C211yesmaximal, characteristic, complemented
11#13069098C211yesmaximal, characteristic, complemented
12#13069091C211yesmaximal, characteristic, complemented
13#13068740C211yesmaximal, characteristic, complemented
14#13068371C211yesmaximal, characteristic, complemented
15C11×#3154C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C11×#135C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C11×#536C2211yescharacteristic
21C11×#535C2211yescharacteristic
22#10623350C2211yescharacteristic
23#10623350C2211yescharacteristic
24#10623343C2211yescharacteristic
25#10623329C2211yescharacteristic
26C11×#497C412yescomplemented
27C11×#496C412yescomplemented
28C11×#495C412yescomplemented
29C11×#492C412yescomplemented
30C11×#405C2211yescharacteristic
31#10622853C2211yescharacteristic
32#10622853C2211yescharacteristic
33#10622849C2211yescharacteristic
34#10622849C2211yescharacteristic
35#10622849C2211yescharacteristic
36#10622849C2211yescharacteristic
37C2×#66900C2211yescharacteristic
38#10622838C2211yescharacteristic
39#10622838C2211yescharacteristic
40C2×#66897C2211yescharacteristic
41#10622828C2211yescharacteristic
42#10622828C2211yescharacteristic
43#10622810—22no—
44#10622809—22no—
45#10622777—22no—
46SD16×Dic11—22no—
47C2×#66883C2211yescharacteristic
48#10622719C2211yescharacteristic
49#10622714C2211yescharacteristic
50#10622714C2211yescharacteristic
51C11⋊#338C2211yescharacteristic
52#10622195C2211yescharacteristic
53#10622194C2211yescharacteristic
54#10622194C2211yescharacteristic
55#10622169C2211yescharacteristic
56#10622169C2211yescharacteristic
57#10622169C2211yescharacteristic
58#10622169C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C2×C11×#41C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C11×#137—41no—
64C11×#137—41no—
65C11×AGL(1,ℤ/8)—41no—
66C11×AGL(1,ℤ/8)—41no—
67C11×#135—21no—
68C11×#135—21no—
69C11×#135—21no—
70C11×#135—21no—
71C2×C11×Q16C2×C411yescharacteristic, complemented
72C2×C11×Q16C2×C412yescomplemented
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16C2×C412yes—
78C2×C11×SD16C2×C412yes—
79C2×C11×SD16C2×C412yes—
80C2×C11×SD16C2×C411yescharacteristic, complemented
81C2×C11×SD16C2×C411yescharacteristic, complemented
82C2×C11×SD16C2×C412yescomplemented
83C2×C11×D8C2×C412yes—
84C2×C11×D8C2×C411yescharacteristic, complemented
85C2×C11×M16C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×C4⋊Q8C2×C412yescomplemented
88C11×#127C2×C412yes—
89C11×#124C2×C412yes—
90C11×#124C2×C412yescomplemented
91C11×#123—41no—
92C11×C22⋊Q8—41no—
93C11×#121—41no—
94C11×#120—41no—
95C11×#117C2311yescharacteristic
96C2×C22⋊Dic11—41no—
97#67001—22no—
98#67001—22no—
99#67001—41no—
100#67001—41no—
101Q8×Dic11—22no—
102Q8×Dic11—41no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105#66979—41no—
106#66979C2311yescharacteristic
107#66979C2311yescharacteristic
108#66979C2311yescharacteristic
109#66979C2311yescharacteristic
110C2×#4318—41no—
111C2×#4318—41no—
112C2×#4318C2311yescharacteristic
113C2×#4318C2311yescharacteristic
114C2×#4318C2311yescharacteristic
115C2×#4318C2311yescharacteristic
116C11×#97C2×C412yescomplemented
117C4×C8×C11C2×C412yescomplemented
118#66901—22no—
119#66901—22no—
120#66901—41no—
121#66901—41no—
122#66900—41no—
123#66899—22no—
124#66899—41no—
125#66898—41no—
126#66898—41no—
127#66897—41no—
128#66896—22no—
129#66896—41no—
130#66883—21no—
131#66883—21no—
132#66882—21no—
133#66881—21no—
134#66879—21no—
135#66879D412yescomplemented
136C8×Dic11—21no—
137C8×Dic11D412yescomplemented
138#22284—111nomaximal, Sylow
139C24×C11—21no—
140C11×#41—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C11×#41—21no—
146C11×#41—21no—
147C11×#41—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22×C411yescharacteristic
154C2×Q8×C11C22×C412yes—
155C2×Q8×C11C22×C411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11C22×C412yes—
165C2×D4×C11C22×C411yescharacteristic
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11C2411yescharacteristic
171C22×Dic11—42no—
172C11×Q16—21no—
173C11×Q16—21no—
174C11×Q16—42no—
175C11×SD16—22no—
176C11×SD16—22no—
177C11×SD16—22no—
178C11×SD16—22no—
179C11×SD16—21no—
180C11×SD16—21no—
181C11×SD16—21no—
182C11×SD16—21no—
183C11×SD16—42no—
184C11×SD16—42no—
185C11×D8—21no—
186C11×D8—21no—
187C11×D8—42no—
188C11×M16—21no—
189C11×M16—21no—
190C2×C8×C11C22×C412yes—
191C2×C8×C11C22×C411yescharacteristic
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C2×D411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11#4111yescharacteristic
196C2×C8×C11#4111yescharacteristic
197C11×C4⋊C4—21no—
198C11×C4⋊C4—42no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C42×C11C22×C412yes—
203C22⋊Dic11—21no—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—42no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—42no—
217C4×Dic11C2×D412yes—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—42no—
227#4318—42no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—42no—
232C2×C11⋊C8—42no—
233C2×C11⋊C8C2×D412yes—
234#3154D1111yescharacteristic
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#1905—111no—
244#1904—111no—
245#1903—111no—
246#1902—111no—
247#1833—111no—
248#1747—111no—
249C23×C11—21no—
250C23×C11—22no—
251C23×C11—21no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—161no—
255C23×C11H(5,𝔽2)11yescharacteristic
256Q8×C11—22no—
257Q8×C11—21no—
258Q8×C11—21no—
259Q8×C11—21no—
260Q8×C11—22no—
261Q8×C11—21no—
262Q8×C11—41no—
263Q8×C11—41no—
264D4×C11—21no—
265D4×C11—21no—
266D4×C11—22no—
267D4×C11—21no—
268D4×C11—22no—
269D4×C11—21no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—162no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11C23×C411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×Dic11—22no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—162no—
298C8×C11—22no—
299C8×C11C4×D411yescharacteristic
300C8×C11C4×D411yescharacteristic
301C8×C11C4×D411yescharacteristic
302C8×C11C4×D411yescharacteristic
303C11⋊C8—22no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C2×#137C2×D1111yescharacteristic
308C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
309C2×#135C2×D1111yescharacteristic
310C22×SD16C2×D1111yescharacteristic
311#568—111no—
312#568—111no—
313#536C2×D1111yescharacteristic
314#535C2×D1111yescharacteristic
315#519—111no—
316#518—111no—
317#497Dic1112yescomplemented
318#496Dic1112yescomplemented
319#495Dic1112yescomplemented
320#492Dic1112yescomplemented
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#421—111no—
331#419—111no—
332#419—111no—
333#418—111no—
334#418—111no—
335C2×#101—111no—
336C2×#100—111no—
337#410—111no—
338#410—111no—
339#405—111no—
340#405—111no—
341#405C2×D1111yescharacteristic
342#344—111no—
343#344—111no—
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)—111no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—42no—
354C22×C11—81no—
355C22×C11—82no—
356C22×C11—81no—
357C22×C11—82no—
358C22×C11—161no—
359C22×C11#51811yescharacteristic
360C22×C11#53511yescharacteristic
361C22×C11#54011yescharacteristic
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11C2×C4×D411yescharacteristic
367C4×C11#51811yescharacteristic
368C4×C11#53511yescharacteristic
369C4×C11#54011yescharacteristic
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C2×#41C22×D1111yescharacteristic
375C2×#41C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378#137—41no—
379#137—41no—
380AGL(1,ℤ/8)—41no—
381AGL(1,ℤ/8)—41no—
382#135—21no—
383#135—21no—
384#135—21no—
385#135—21no—
386C2×Q16C2×Dic1111yescharacteristic, complemented
387C2×Q16C2×Dic1112yescomplemented
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16C2×Dic1112yes—
393C2×SD16C2×Dic1112yes—
394C2×SD16C2×Dic1112yes—
395C2×SD16C2×Dic1111yescharacteristic, complemented
396C2×SD16C2×Dic1111yescharacteristic, complemented
397C2×SD16C2×Dic1112yescomplemented
398C2×D8C2×Dic1112yes—
399C2×D8C2×Dic1111yescharacteristic, complemented
400#131—222no—
401#131—222no—
402#131—441no—
403#131—441no—
404C2×M16—111no—
405C2×M16—111no—
406C2×M16—111no—
407C2×M16—111no—
408C2×M16—441no—
409C2×M16—441no—
410C2×M16C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C4⋊Q8C2×Dic1112yescomplemented
413#127C2×Dic1112yes—
414#124C2×Dic1112yes—
415#124C2×Dic1112yescomplemented
416#123—41no—
417C22⋊Q8—41no—
418#121—41no—
419#120—41no—
420C4×Q8—222no—
421C4×Q8—441no—
422C4×D4—222no—
423C4×D4—441no—
424#117—111no—
425#117—111no—
426#117—111no—
427#117—111no—
428#117—441no—
429#117C22×D1111yescharacteristic
430C2×C22⋊C4—441no—
431#108—221no—
432#108—221no—
433#107—221no—
434#106—221no—
435#104—222no—
436#104—222no—
437#104—441no—
438#104—441no—
439#103—222no—
440#103—441no—
441#102—222no—
442#102—441no—
443#101—441no—
444#100—441no—
445#99—441no—
446#99—441no—
447#97—112no—
448#97—221no—
449#97C2×Dic1112yescomplemented
450C4×C8—112no—
451C4×C8—221no—
452C4×C8C2×Dic1112yescomplemented
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—81no—
457C2×C11—81no—
458C2×C11—82no—
459C2×C11#232811yescharacteristic
460C24—21no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466#41—21no—
467#41—21no—
468#41—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8C22×Dic1111yescharacteristic
475C2×Q8C22×Dic1112yes—
476C2×Q8C22×Dic1111yescharacteristic
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4C22×Dic1112yes—
486C2×D4C22×Dic1111yescharacteristic
487C2×D4C22×Dic1111yescharacteristic
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—442no—
492C22×C4C23×D1111yescharacteristic
493Q16—21no—
494Q16—21no—
495Q16—42no—
496SD16—22no—
497SD16—22no—
498SD16—22no—
499SD16—22no—
500SD16—21no—
501SD16—21no—
502SD16—21no—
503SD16—21no—
504SD16—42no—
505SD16—42no—
506D8—21no—
507D8—21no—
508D8—42no—
509M16—21no—
510M16—21no—
511M16—221no—
512M16—221no—
513M16—221no—
514M16—221no—
515M16—221no—
516M16—221no—
517M16—221no—
518M16—221no—
519M16—442no—
520M16—442no—
521C2×C8—112no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—442no—
526C2×C8—442no—
527C2×C8D4×D1111yescharacteristic
528C2×C8D4×D1111yescharacteristic
529C2×C8#434111yescharacteristic
530C2×C8#434111yescharacteristic
531C2×C8C22×Dic1112yes—
532C2×C8C22×Dic1111yescharacteristic
533C2×C8C22×Dic1111yescharacteristic
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C22⋊C4—21no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—221no—
545C22⋊C4—221no—
546C22⋊C4—221no—
547C22⋊C4—221no—
548C22⋊C4—442no—
549C42—112no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—442no—
554C42C22×Dic1112yes—
555C11#2228411yescharacteristic, complemented, Sylow
556C23—21no—
557C23—22no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—161no—
562C23#6703711yescharacteristic
563Q8—22no—
564Q8—21no—
565Q8—21no—
566Q8—21no—
567Q8—22no—
568Q8—21no—
569Q8—41no—
570Q8—41no—
571D4—21no—
572D4—21no—
573D4—22no—
574D4—21no—
575D4—22no—
576D4—21no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—162no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—1762no—
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#6703711yescharacteristic
604C2×C4C23×Dic1111yescharacteristic
605C8—22no—
606C8—222no—
607C8—441no—
608C8—441no—
609C8—441no—
610C8D4×Dic1111yescharacteristic
611C8D4×Dic1111yescharacteristic
612C8D4×Dic1111yescharacteristic
613C8D4×Dic1111yescharacteristic
614C22—41no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—81no—
619C22—82no—
620C22—81no—
621C22—82no—
622C22—161no—
623C22#1062324611yescharacteristic
624C22#1062325011yescharacteristic
625C22#1062332911yescharacteristic
626C4—42no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—442no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062324611yescharacteristic
635C4#1062325011yescharacteristic
636C4C2×D4×Dic1111yescharacteristic
637C4#1062332911yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—82no—
642C2—81no—
643C2—81no—
644C2#1307134211yescharacteristic
subgroupG/H
centerC2#13071342
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3154C2
socleC2×C11#2328
cosocleC22×C4×C11C24
hypercenter#3154D11
hypocenterC11#22284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3154

Complements

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

NH ≅ G/Ntype
1. #13077533C2semidirect
2. #13077476C2semidirect
3. #13069521C2semidirect
4. #13069515C2semidirect
5. #13069154C2semidirect
6. #13069149C2semidirect
7. #13069144C2semidirect
8. #13069139C2semidirect
9. #13069112C2semidirect
10. #13069105C2semidirect
11. #13069098C2semidirect
12. #13069091C2semidirect
13. #13068740C2semidirect
14. #13068371C2semidirect
26. C11×#497C4semidirect
27. C11×#496C4semidirect
28. C11×#495C4semidirect
29. C11×#492C4semidirect
71. C2×C11×Q16C2×C4semidirect
72. C2×C11×Q16C2×C4semidirect
80. C2×C11×SD16C2×C4semidirect
81. C2×C11×SD16C2×C4semidirect
82. C2×C11×SD16C2×C4semidirect
84. C2×C11×D8C2×C4semidirect
87. C11×C4⋊Q8C2×C4semidirect
90. C11×#124C2×C4semidirect
116. C11×#97C2×C4semidirect
117. C4×C8×C11C2×C4semidirect
135. #66879D4semidirect
137. C8×Dic11D4semidirect
317. #497Dic11semidirect
318. #496Dic11semidirect
319. #495Dic11semidirect
320. #492Dic11semidirect
386. C2×Q16C2×Dic11semidirect
387. C2×Q16C2×Dic11semidirect
395. C2×SD16C2×Dic11semidirect
396. C2×SD16C2×Dic11semidirect
397. C2×SD16C2×Dic11semidirect
399. C2×D8C2×Dic11semidirect
412. C4⋊Q8C2×Dic11semidirect
415. #124C2×Dic11semidirect
449. #97C2×Dic11semidirect
452. C4×C8C2×Dic11semidirect
555. C11#22284semidirect

Maximal subgroups

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

subgroupindex
#130775332
#130774762
#130695212
#130695152
#130691542
#130691492
#130691442
#130691392
#130691122
#130691052
#130690982
#130690912
#130687402
#130683712
C11×#31542
#2228411