Finite Group Databasebeta

← #14764943

Subgroups — #14764943

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622344C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic, complemented
3C2×#10622552C211yesmaximal, characteristic
4#13069470C212yesmaximal, complemented
5#13069299C212yesmaximal, complemented
6#13069244C212yesmaximal, complemented
7#13068970C212yesmaximal, complemented
8#13068921C211yesmaximal, characteristic, complemented
9#13068811C211yesmaximal, characteristic, complemented
10#13068548C211yesmaximal, characteristic
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×#4314C2212yes—
19C2×C4×Dic22C2211yescharacteristic, complemented
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2212yescomplemented
23#10622825C2211yescharacteristic
24#10622823—21no—
25C4×C22⋊Dic11—21no—
26C2×#66885C2212yes—
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×#66881C2212yescomplemented
30C2×#66880C2212yescomplemented
31#10622552—21no—
32#10622552—21no—
33#10622552C2212yes—
34#10622552C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic, complemented
36#10622546—21no—
37C4×Dic11⋊C4—21no—
38#10622542C2211yescharacteristic, complemented
39#10622541C2211yescharacteristic, complemented
40#10622344C418yescomplemented
41C11×#336C2212yescomplemented
42#10622189C2212yescomplemented
43#10622189C2212yescomplemented
44C24×D11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C22×D44C2312yes—
55C22×Dic22C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C2×C42×C11—42no—
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4—44no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—42no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77#66977—22no—
78#66977C2×C414yes—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×#4314—42no—
85C2×#4314—42no—
86C2×#4314C2×C418yescomplemented
87C4×Dic22—42no—
88C11×C22⋊C8—22no—
89C11×C22⋊C8C2×C414yes—
90C4×C8×C11—42no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96#66885—42no—
97#66885—42no—
98#66885C2×C418yescomplemented
99#66881—42no—
100#66880—42no—
101#22043—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C23×D11—24no—
104C23×D11—22no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11SD1614yescomplemented
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C2×D44—24no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—48no—
142C2×D44—42no—
143C2×D44—42no—
144C2×D44—48no—
145C2×D44C22×C414yes—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22C22×C412yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11C22×C414yes—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—41no—
159C42×C11—41no—
160C22⋊Dic11—24no—
161C22⋊Dic11—42no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—44no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—42no—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—24no—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176C4×Dic11—42no—
177C4×Dic11—42no—
178#4314—48no—
179C2×#450—111no—
180C4×C22⋊Q8—111no—
181C2×#390—111no—
182#1968—112no—
183#1934—112no—
184#1926—112no—
185#1880—112no—
186#1872—111no—
187#1853—111no—
188#1786—111no—
189C4×C22⋊C8D1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11C4×D412yes—
195C23×C11C2×SD1612yes—
196C23×C11#13512yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—24no—
199C22×D11—48no—
200C22×D11—48no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—48no—
208C22×D11—84no—
209C22×D11—84no—
210C22×D11—84no—
211C22×D11—84no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11C4×D412yes—
228C2×C4×C11C2×SD1612yes—
229C2×C4×C11C2×SD1612yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)12yes—
234C2×C4×C11H(5,𝔽2)12yes—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—84no—
251D44—24no—
252D44—24no—
253D44—48no—
254D44—42no—
255D44—42no—
256Dic22—24no—
257Dic22—42no—
258C8×C11—24no—
259C8×C11—42no—
260C23×D4—111no—
261C22×SD16—112no—
262C2×C22⋊Q8—111no—
263C2×C4×Q8—111no—
264C22×C4⋊C4—111no—
265C22×C22⋊C4—221no—
266C22×C22⋊C4—221no—
267C22×C42C2×D1111yescharacteristic
268#450—118no—
269C2×#106—112no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8C2×D1111yescharacteristic
275C2×C22⋊C8C2×D1111yescharacteristic
276C2×C4×C8C2×D1112yescomplemented
277#391—111no—
278#390—112no—
279#390—112no—
280#390—221no—
281#390—221no—
282#389—111no—
283#387—221no—
284#385—221no—
285#380—111no—
286C4×C4⋊C4—111no—
287C4×C4⋊C4—221no—
288C4×C22⋊C4—221no—
289#340—112no—
290#340—112no—
291#336C2×D1112yescomplemented
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11C4×SD1614yes—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11#53511yescharacteristic
302C22×C11C22×SD1611yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11#57511yescharacteristic
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—816no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—82no—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—41no—
319C4×C11#51812yes—
320C4×C11#53812yes—
321Dic11—42no—
322Dic11—42no—
323Dic11—81no—
324Dic11—82no—
325Dic11—81no—
326C25—221no—
327C22×Q8—111no—
328C22×D4—114no—
329C22×D4—112no—
330C22×D4—221no—
331C22×D4—222no—
332C22×D4—442no—
333C22×D4—442no—
334C23×C4—221no—
335C23×C4D4411yescharacteristic
336C23×C4D4411yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×SD16—118no—
339C2×SD16—442no—
340C2×SD16—442no—
341C22×C8C22×D1112yes—
342C22×C8C22×D1112yes—
343C22⋊Q8—114no—
344C22⋊Q8—222no—
345C4×Q8—442no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—442no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—444no—
362C2×C22⋊C4—444no—
363C2×C42—42no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42D4411yescharacteristic
367C2×C42D4411yescharacteristic
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370#106—442no—
371#103—442no—
372#102—118no—
373#102—442no—
374#102—442no—
375C22⋊C8—22no—
376C22⋊C8C4×D1114yes—
377C4×C8—42no—
378#95—221no—
379#95—221no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—24no—
384C2×C11#232111yescharacteristic
385C2×C11C2×C4×SD1611yescharacteristic
386C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
387C2×C11#318711yescharacteristic
388C2×C11#318811yescharacteristic
389C2×C11#320811yescharacteristic
390C2×C11#321111yescharacteristic
391D11—84no—
392C24—224no—
393C24—222no—
394C24—442no—
395C24—442no—
396C24—442no—
397C24—442no—
398C24—442no—
399C24—442no—
400C24C2×D4411yescharacteristic
401C2×Q8—112no—
402C2×Q8—221no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×D4—114no—
406C2×D4—224no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—448no—
413C2×D4—442no—
414C2×D4—442no—
415C2×D4—448no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4—442no—
431C22×C4#431414yescomplemented
432C22×C4C2×C4×D1112yes—
433C22×C4C2×D4411yescharacteristic
434C22×C4C2×D4411yescharacteristic
435C22×C4C2×D4411yescharacteristic
436C22×C4C2×D4411yescharacteristic
437C22×C4C2×D4411yescharacteristic
438C22×C4#433912yes—
439C22×C4C23×D1111yescharacteristic
440SD16—448no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8C2×C4×D1114yes—
447C4⋊C4—112no—
448C4⋊C4—224no—
449C4⋊C4—221no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—222no—
454C4⋊C4—442no—
455C4⋊C4—442no—
456C4⋊C4—442no—
457C22⋊C4—224no—
458C22⋊C4—444no—
459C22⋊C4—442no—
460C22⋊C4—444no—
461C22⋊C4—444no—
462C22⋊C4—444no—
463C42—22no—
464C42—22no—
465C42—41no—
466C42—41no—
467C42—442no—
468C42—442no—
469C11#2204311yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—224no—
475C23—448no—
476C23—448no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23—442no—
481C23—442no—
482C23—442no—
483C23—448no—
484C23—884no—
485C23—884no—
486C23—884no—
487C23—884no—
488C23C4×D4412yes—
489C23C2×#431412yes—
490C23#6695712yes—
491C23C22×D4411yescharacteristic
492Q8—224no—
493Q8—442no—
494D4—224no—
495D4—224no—
496D4—448no—
497D4—442no—
498D4—442no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—442no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—884no—
530C2×C4C4×D4412yes—
531C2×C4C2×#431412yes—
532C2×C4C2×#431412yes—
533C2×C4#6696112yes—
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×#433911yescharacteristic
536C2×C4#6703712yes—
537C2×C4#6704212yes—
538C8—24no—
539C8—42no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—444no—
547C22—444no—
548C22—444no—
549C22—8816no—
550C22—882no—
551C22—882no—
552C22—882no—
553C22—882no—
554C22C4×#431414yes—
555C22C2×C4×D4411yescharacteristic
556C22#1062302411yescharacteristic
557C22#1062305611yescharacteristic
558C22C22×#431411yescharacteristic
559C22C2×#6695711yescharacteristic
560C22C2×#6696111yescharacteristic
561C22#1062327911yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—442no—
568C4—442no—
569C4—882no—
570C4—881no—
571C4—881no—
572C4#1062307612yes—
573C4#1062309112yes—
574C2—24no—
575C2—884no—
576C2#1307127611yescharacteristic
577C2C2×C4×#431411yescharacteristic
578C2C4×#6696111yescharacteristic
579C2#1307937411yescharacteristic
580C2#1307938311yescharacteristic
581C2#1307955911yescharacteristic
582C2#1307958311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#66977C2semidirect
4. #13069470C2semidirect
5. #13069299C2semidirect
6. #13069244C2semidirect
7. #13068970C2semidirect
8. #13068921C2semidirect
9. #13068811C2semidirect
11. C4×C11×C22⋊C8C2semidirect
19. C2×C4×Dic22C22semidirect
22. C2×C4×C8×C11C22semidirect
29. C2×#66881C22semidirect
30. C2×#66880C22semidirect
35. C4×C4⋊Dic11C22semidirect
38. #10622542C22semidirect
39. #10622541C22semidirect
40. #10622344C4semidirect
41. C11×#336C22semidirect
42. #10622189C22semidirect
43. #10622189C22semidirect
86. C2×#4314C2×C4semidirect
98. #66885C2×C4semidirect
118. C22×C4×C11SD16semidirect
189. C4×C22⋊C8D11semidirect
276. C2×C4×C8C2×D11semidirect
291. #336C2×D11semidirect
431. C22×C4#4314semidirect
469. C11#22043semidirect

Maximal subgroups

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

subgroupindex
C2×#106223442
C4×#669772
C2×#106225522
#130694702
#130692992
#130692442
#130689702
#130689212
#130688112
#130685482
C4×C11×C22⋊C82
#2204311