Finite Group Databasebeta

← #14767680

Subgroups — #14767680

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#13079093C211yesmaximal, characteristic
2#13077477C211yesmaximal, characteristic, complemented
3#13069517C211yesmaximal, characteristic, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069150C211yesmaximal, characteristic, complemented
6#13069145C211yesmaximal, characteristic, complemented
7#13069143C211yesmaximal, characteristic, complemented
8#13069138C211yesmaximal, characteristic, complemented
9#13069107C211yesmaximal, characteristic, complemented
10#13069100C211yesmaximal, characteristic, complemented
11#13069096C211yesmaximal, characteristic, complemented
12#13069089C211yesmaximal, characteristic, complemented
13#13068741C211yesmaximal, characteristic, complemented
14#13068371C211yesmaximal, characteristic, complemented
15C11×#2957C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C11×#568C2211yescharacteristic
18C11×#568C2211yescharacteristic
19#10623361C2211yescharacteristic
20#10623356C2211yescharacteristic
21C2×#67004C2211yescharacteristic
22C2×#67002C2211yescharacteristic
23C22×#4314C2211yescharacteristic
24#10623052C2211yescharacteristic
25#10623047C2211yescharacteristic
26C11×#444—22no—
27C11×#443—22no—
28C2×C11×#108C2211yescharacteristic
29C11×#421C2211yescharacteristic
30C11×#421C2211yescharacteristic
31C11×#405C2211yescharacteristic
32#10622853C2211yescharacteristic
33#10622853C2211yescharacteristic
34#10622849C2211yescharacteristic
35#10622849C2211yescharacteristic
36#10622803C412yescomplemented
37#10622788C412yescomplemented
38#10622781C412yescomplemented
39#10622767C412yescomplemented
40C2×#66888C2211yescharacteristic
41#10622744C2211yescharacteristic
42#10622744C2211yescharacteristic
43C2×#66887C2211yescharacteristic
44#10622733C2211yescharacteristic
45#10622733C2211yescharacteristic
46#10622719C2211yescharacteristic
47#10622714C2211yescharacteristic
48#10622714C2211yescharacteristic
49#10622323—22no—
50C4×#4314—22no—
51C11⋊#338C2211yescharacteristic
52#10622197C2211yescharacteristic
53#10622197C2211yescharacteristic
54#10622195C2211yescharacteristic
55#10622195C2211yescharacteristic
56#10622195C2211yescharacteristic
57#10622169C2211yescharacteristic
58#10622169C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C2×C11×#41C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C11×#135—21no—
64C11×#135—21no—
65C11×#135—21no—
66C11×#135—21no—
67C2×C11×Q16C2×C411yescharacteristic, complemented
68C2×C11×SD16C2×C411yescharacteristic, complemented
69C2×C11×SD16C2×C411yescharacteristic, complemented
70C2×C11×D8C2×C411yescharacteristic, complemented
71C11×#131—22no—
72C11×#131—22no—
73C11×#131—41no—
74C11×#131—41no—
75C2×C11×M16—41no—
76C2×C11×M16—41no—
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#117C2311yescharacteristic
82#67004—41no—
83#67004—41no—
84#67002—41no—
85#67002—41no—
86#67000C2×C412yes—
87#66997C2×C412yescomplemented
88C2×#4326C2×C412yescomplemented
89C2×#4325C2×C412yes—
90#66993C2×C412yes—
91#66990—41no—
92#66989C2×C412yescomplemented
93#66988—41no—
94C2×#4324C2×C412yescomplemented
95C2×#4323C2×C412yes—
96#66983—41no—
97#66979C2311yescharacteristic
98#66979C2311yescharacteristic
99#66979C2311yescharacteristic
100#66979C2311yescharacteristic
101#66977—41no—
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4314—21no—
105C2×#4314—21no—
106C2×#4314—21no—
107C2×#4314—21no—
108C2×#4314C2×C412yes—
109C2×#4314C2×C412yes—
110#66946—41no—
111#66940—41no—
112C22⋊C4×D11—41no—
113#66930—41no—
114C4×D44—22no—
115C4×Dic22—22no—
116C11×#108—21no—
117C11×#108—21no—
118C11×#104—22no—
119C11×#104—22no—
120C11×#97D412yescomplemented
121C4×C8×C11D412yescomplemented
122#66901—41no—
123#66901—41no—
124#66898—41no—
125#66898—41no—
126#66888—41no—
127#66887—41no—
128#66885—22no—
129#66885—41no—
130#66882—21no—
131#66881—21no—
132#66880—22no—
133#66880—41no—
134#66879—21no—
135#66879C2×C412yescomplemented
136C8×Dic11—21no—
137C8×Dic11C2×C412yescomplemented
138#22284—111nomaximal, Sylow
139C23×D11—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×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—42no—
158C22×Dic11—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22×C412yes—
165C2×C4×D11—42no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C412yes—
172C11×Q16—21no—
173C11×Q16—21no—
174C11×SD16—21no—
175C11×SD16—21no—
176C11×SD16—21no—
177C11×SD16—21no—
178C11×D8—21no—
179C11×D8—21no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—42no—
187C11×M16—42no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—42no—
191C2×C8×C11—42no—
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D412yes—
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C2×C8×C11#4111yescharacteristic
198C2×C8×C11#4111yescharacteristic
199C11×C4⋊C4—21no—
200C11×C22⋊C4—21no—
201C42×C11C2×D412yes—
202C22⋊Dic11—21no—
203C22⋊Dic11—21no—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—42no—
207#4326—42no—
208#4325—42no—
209#4324—42no—
210#4323—42no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—42no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—42no—
223C4×Dic11C22×C412yes—
224#4318—21no—
225#4318—21no—
226#4318—21no—
227#4318—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8C22×C412yes—
230#4314—22no—
231#4314—22no—
232#4314—22no—
233#4314—22no—
234#3154—111no—
235#2957D1111yescharacteristic, complemented
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—21no—
251C23×C11H(5,𝔽2)11yescharacteristic
252C22×D11—22no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—161no—
256Q8×C11—21no—
257Q8×C11—21no—
258Q8×C11—21no—
259Q8×C11—21no—
260D4×C11—21no—
261D4×C11—21no—
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
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—162no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—41no—
292D44—41no—
293C4×D11—162no—
294Dic22—22no—
295Dic22—22no—
296Dic22—41no—
297Dic22—41no—
298C8×C11—22no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11C4×D411yescharacteristic
302C8×C11C4×D411yescharacteristic
303C8×C11C4×D411yescharacteristic
304C8×C11C4×D411yescharacteristic
305C11⋊C8—22no—
306C11⋊C8—41no—
307C2×#137—111no—
308C2×AGL(1,ℤ/8)—111no—
309C2×#135C2×D1111yescharacteristic
310C22×SD16—111no—
311#568C2×D1111yescharacteristic
312#568C2×D1111yescharacteristic
313#536—111no—
314#535—111no—
315#519—111no—
316#518—111no—
317#497—112no—
318#496—112no—
319#495—112no—
320#492—112no—
321#444—22no—
322#443—22no—
323#440—222no—
324C4×SD16—222no—
325C2×#108C2×D1111yescharacteristic
326#427—111no—
327#421—111no—
328#421—111no—
329#421C2×D1111yescharacteristic
330#421C2×D1111yescharacteristic
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—81no—
354C22×C11—81no—
355C22×C11#51811yescharacteristic
356C22×C11#53511yescharacteristic
357C22×C11#54011yescharacteristic
358C2×D11—42no—
359C2×D11—82no—
360C2×D11—82no—
361C2×D11—161no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11C2×C4×D411yescharacteristic
366C4×C11#51811yescharacteristic
367C4×C11#53511yescharacteristic
368C4×C11#54011yescharacteristic
369Dic11—42no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C2×#41C22×D1111yescharacteristic
375C2×#41C22×D1111yescharacteristic
376C22×Q8—111no—
377C22×D4—111no—
378#137—441no—
379#137—441no—
380AGL(1,ℤ/8)—441no—
381AGL(1,ℤ/8)—441no—
382#135—21no—
383#135—21no—
384#135—21no—
385#135—21no—
386C2×Q16—112no—
387C2×Q16C4×D1111yescharacteristic, complemented
388C2×SD16—112no—
389C2×SD16—112no—
390C2×SD16—112no—
391C2×SD16—112no—
392C2×SD16—221no—
393C2×SD16—221no—
394C2×SD16—221no—
395C2×SD16—221no—
396C2×SD16C4×D1111yescharacteristic, complemented
397C2×SD16C4×D1111yescharacteristic, complemented
398C2×D8—112no—
399C2×D8C4×D1111yescharacteristic, complemented
400#131—22no—
401#131—22no—
402#131—41no—
403#131—41no—
404C2×M16—41no—
405C2×M16—41no—
406C2×M16—111no—
407C2×M16—111no—
408C2×M16C22×D1111yescharacteristic
409C2×M16C22×D1111yescharacteristic
410C2×M16C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
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—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—21no—
432#108—21no—
433#107—221no—
434#106—221no—
435#104—22no—
436#104—22no—
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#97C22⋊D1112yescomplemented
450C4×C8—112no—
451C4×C8—221no—
452C4×C8C22⋊D1112yescomplemented
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—81no—
457C2×C11—81no—
458C2×C11#232811yescharacteristic
459D11—82no—
460C24—221no—
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—112no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8C2×C4×D1111yescharacteristic
476C2×Q8C2×C4×D1111yescharacteristic
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—112no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—442no—
486C2×D4C2×C4×D1111yescharacteristic
487C2×D4C2×C4×D1111yescharacteristic
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4C23×D1111yescharacteristic
493Q16—21no—
494Q16—21no—
495Q16—442no—
496SD16—21no—
497SD16—21no—
498SD16—21no—
499SD16—21no—
500SD16—222no—
501SD16—222no—
502SD16—222no—
503SD16—222no—
504SD16—442no—
505SD16—442no—
506D8—21no—
507D8—21no—
508D8—442no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16—21no—
513M16—21no—
514M16—21no—
515M16—42no—
516M16—42no—
517M16—221no—
518M16—221no—
519M16—221no—
520M16—221no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—42no—
524C2×C8—42no—
525C2×C8—112no—
526C2×C8—221no—
527C2×C8C2×C4×D1111yescharacteristic
528C2×C8C2×C4×D1111yescharacteristic
529C2×C8#433911yescharacteristic
530C2×C8#433911yescharacteristic
531C2×C8C2×C22⋊D1112yes—
532C2×C8C2×C22⋊D1111yescharacteristic
533C2×C8C2×C22⋊D1111yescharacteristic
534C4⋊C4—21no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C22⋊C4—21no—
542C22⋊C4—221no—
543C22⋊C4—221no—
544C22⋊C4—221no—
545C22⋊C4—221no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C42—112no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—442no—
554C42C2×C22⋊D1112yes—
555C11#2228411yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—222no—
559C23—441no—
560C23—441no—
561C23—1761no—
562C23#6704211yescharacteristic
563Q8—21no—
564Q8—21no—
565Q8—21no—
566Q8—21no—
567Q8—222no—
568Q8—222no—
569Q8—441no—
570Q8—441no—
571D4—21no—
572D4—21no—
573D4—21no—
574D4—21no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—222no—
580D4—222no—
581D4—441no—
582D4—441no—
583D4—1762no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—1762no—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#433911yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#6704211yescharacteristic
604C2×C4C22×C22⋊D1111yescharacteristic
605C8—22no—
606C8—41no—
607C8—41no—
608C8—222no—
609C8—441no—
610C8C4×C22⋊D1111yescharacteristic
611C8C4×C22⋊D1111yescharacteristic
612C8C4×C22⋊D1111yescharacteristic
613C8C4×C22⋊D1111yescharacteristic
614C22—41no—
615C22—41no—
616C22—41no—
617C22—81no—
618C22—81no—
619C22—442no—
620C22—882no—
621C22—882no—
622C22—1761no—
623C22#1062307611yescharacteristic
624C22#1062309311yescharacteristic
625C22#1062336111yescharacteristic
626C4—42no—
627C4—41no—
628C4—41no—
629C4—442no—
630C4—442no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062307611yescharacteristic
635C4#1062309311yescharacteristic
636C4C2×C4×C22⋊D1111yescharacteristic
637C4#1062333611yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—81no—
642C2—81no—
643C2—882no—
644C2#1307133811yescharacteristic
subgroupG/H
centerC2#13071338
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2957C2
socleC2×C11#2328
prime radical#13079093C2
cosocleC22×C4×C11C24
hypercenter#2957D11
hypocenterC11#22284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #13077477C2semidirect
3. #13069517C2semidirect
4. #13069515C2semidirect
5. #13069150C2semidirect
6. #13069145C2semidirect
7. #13069143C2semidirect
8. #13069138C2semidirect
9. #13069107C2semidirect
10. #13069100C2semidirect
11. #13069096C2semidirect
12. #13069089C2semidirect
13. #13068741C2semidirect
14. #13068371C2semidirect
15. C11×#2957C2semidirect
36. #10622803C4semidirect
37. #10622788C4semidirect
38. #10622781C4semidirect
39. #10622767C4semidirect
67. C2×C11×Q16C2×C4semidirect
68. C2×C11×SD16C2×C4semidirect
69. C2×C11×SD16C2×C4semidirect
70. C2×C11×D8C2×C4semidirect
87. #66997C2×C4semidirect
88. C2×#4326C2×C4semidirect
92. #66989C2×C4semidirect
94. C2×#4324C2×C4semidirect
120. C11×#97D4semidirect
121. C4×C8×C11D4semidirect
135. #66879C2×C4semidirect
137. C8×Dic11C2×C4semidirect
235. #2957D11semidirect
387. C2×Q16C4×D11semidirect
396. C2×SD16C4×D11semidirect
397. C2×SD16C4×D11semidirect
399. C2×D8C4×D11semidirect
449. #97C22⋊D11semidirect
452. C4×C8C22⋊D11semidirect
555. C11#22284semidirect

Maximal subgroups

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

subgroupindex
#130790932
#130774772
#130695172
#130695152
#130691502
#130691452
#130691432
#130691382
#130691072
#130691002
#130690962
#130690892
#130687412
#130683712
C11×#29572
#2228411