Finite Group Databasebeta

← #14788652

Subgroups — #14788652

Order 2816.

1428 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069687C212yesmaximal, complemented
6#13069557C211yesmaximal, characteristic, complemented
7#13069441C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068877C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C11×#550—24no—
14C11×#550—24no—
15C2×C11×#127C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4323C2212yes—
24C2×C4×D44C2211yescharacteristic
25#10622844—21no—
26C2×#66896C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622685—24no—
32#10622627—24no—
33#10622605—21no—
34#10622602—22no—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622552C2212yes—
38#10622549C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—48no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11C2312yes—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11—21no—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C11×#127—24no—
59C11×#127—24no—
60C11×#127—22no—
61C11×#127D414yes—
62C11×#121—28no—
63C11×#121—216no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11D414yes—
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C2×#4323—22no—
78C2×#4323—22no—
79C2×#4323—24no—
80C2×#4323—24no—
81C2×#4323—22no—
82C2×#4323—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—22no—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2311yescharacteristic
92C4×D44—22no—
93C4×D44—22no—
94#66896—22no—
95#66896—24no—
96#66896—24no—
97#66896—42no—
98#66896—42no—
99C11⋊#95—22no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102#66873—22no—
103#66872—22no—
104C4⋊(C11⋊C8)—22no—
105#66867—22no—
106#24196—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—21no—
109C23×D11—21no—
110C11×#41—432no—
111C2×Q8×C11—22no—
112C2×Q8×C11—24no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11—82no—
133C2×D4×C11C2×D414yes—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—28no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44#4112yescomplemented
154C2×C4×D11—42no—
155C2×C4×D11—82no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166#4323—28no—
167#4323—48no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—44no—
170(C2×D11)⋊C4—82no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175Dic11⋊C4—82no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8#4112yescomplemented
185C2×#550D1111yescharacteristic, complemented
186C2×#459—111no—
187C2×#442—111no—
188#2580—111no—
189#2041—112no—
190#2011—112no—
191#1985—111no—
192#1961—111no—
193#1879—112no—
194#1864—112no—
195#1804—111no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—42no—
213C22×D11—42no—
214Q8×C11—28no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—48no—
220D4×C11—416no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—84no—
226D4×C11—88no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—48no—
236C2×C4×C11—416no—
237C2×C4×C11—42no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12012yes—
240C2×C4×C11AGL(1,ℤ/8)14yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252D44—22no—
253D44—22no—
254D44—41no—
255D44—41no—
256C4×D11—84no—
257C11⋊C8—22no—
258C11⋊C8—41no—
259C11⋊C8—42no—
260C22×#41—21no—
261C22×D8—111no—
262C22×D8—112no—
263#550—24no—
264#550—24no—
265C2×#127C2×D1112yes—
266C2×#127C2×D1111yescharacteristic
267C2×#121—22no—
268C2×#121—21no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4C2×D1112yes—
272C2×C4×D4C2×D1111yescharacteristic
273#459—224no—
274#442—224no—
275C2×#106—111no—
276C2×C4⋊C8—111no—
277C2×#102—112no—
278C2×#102—112no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—112no—
282C2×#102—112no—
283C2×#97—111no—
284#399—221no—
285#393—221no—
286#390—112no—
287#389—112no—
288#385—222no—
289#382—111no—
290#340—112no—
291#336—112no—
292#336—112no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11C2×#12011yescharacteristic
306C22×C11#54811yescharacteristic
307C22×C11#55011yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)12yes—
309C22×C11#57612yes—
310C2×D11—44no—
311C2×D11—42no—
312C2×D11—82no—
313C2×D11—81no—
314C2×D11—81no—
315C4×C11—22no—
316C4×C11—24no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11#52511yescharacteristic
321C4×C11#53711yescharacteristic
322C4×C11#54611yescharacteristic
323C4×C11#54711yescharacteristic
324Dic11—82no—
325Dic11—81no—
326C2×#41—28no—
327C2×#41—48no—
328C22×Q8C22⋊D1111yescharacteristic
329C22×D4—22no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—111no—
334C22×D4C22×D1112yes—
335C22×D4C22×D1111yescharacteristic
336C23×C4—22no—
337C23×C4—21no—
338C23×C4—221no—
339C2×D8—222no—
340C2×D8—222no—
341C2×D8—222no—
342C2×D8—224no—
343C2×D8—224no—
344C2×D8—442no—
345C22×C8—111no—
346C22×C8—112no—
347C22×C8—111no—
348#127—24no—
349#127—24no—
350#127—22no—
351#127C22⋊D1114yes—
352#121—28no—
353#121—216no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—22no—
359C4×D4—222no—
360C4×D4—222no—
361C4×D4C22⋊D1114yes—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4C22⋊D1112yes—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C42C22×D1112yes—
374C2×C42C22×D1111yescharacteristic
375#106—222no—
376C4⋊C8—222no—
377#102—224no—
378#102—222no—
379#102—224no—
380#102—222no—
381#102—442no—
382#102—442no—
383#97—222no—
384#95—221no—
385#95—221no—
386#95—222no—
387C2×C11—82no—
388C2×C11—84no—
389C2×C11#240711yescharacteristic
390C2×C11#300311yescharacteristic
391C2×C11#300811yescharacteristic
392C2×C11#336612yes—
393C2×C11#339912yes—
394D11—82no—
395C24—22no—
396C24—21no—
397C24—221no—
398#41—432no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×D4—28no—
402C2×D4—28no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4—82no—
421C2×D4—112no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4C2×C22⋊D1114yes—
428C2×D4C2×C22⋊D1112yes—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—442no—
438C22×C4—882no—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444D8—228no—
445D8—448no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—222no—
450C2×C8—221no—
451C2×C8—222no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—222no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—882no—
463C4⋊C4C2×C22⋊D1112yes—
464C22⋊C4—28no—
465C22⋊C4—24no—
466C22⋊C4—444no—
467C22⋊C4—442no—
468C22⋊C4—882no—
469C42—22no—
470C42—22no—
471C42C2×C22⋊D1112yes—
472C42C2×C22⋊D1112yes—
473C11#2419611yescharacteristic, complemented, Sylow
474C23—24no—
475C23—22no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—222no—
487C23—442no—
488C23—441no—
489C23—442no—
490C23—441no—
491C23C22×C22⋊D1111yescharacteristic
492Q8—28no—
493D4—24no—
494D4—22no—
495D4—24no—
496D4—22no—
497D4—416no—
498D4—48no—
499D4—41no—
500D4—42no—
501D4—41no—
502D4—42no—
503D4—84no—
504D4—88no—
505D4—222no—
506D4—222no—
507D4—441no—
508D4—441no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—416no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—441no—
525C2×C4—884no—
526C2×C4#6698514yes—
527C2×C4#6700612yes—
528C2×C4#6700612yes—
529C2×C4#41×D1111yescharacteristic
530C2×C4#41×D1111yescharacteristic
531C2×C4#6704211yescharacteristic
532C2×C4#6704311yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—222no—
536C8—442no—
537C8—441no—
538C22—44no—
539C22—42no—
540C22—44no—
541C22—42no—
542C22—44no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—442no—
551C22—444no—
552C22—882no—
553C22—881no—
554C22—881no—
555C22C2×#6698512yes—
556C22#1062336211yescharacteristic
557C22#1062336511yescharacteristic
558C22#1062336612yes—
559C22C2×#6700611yescharacteristic
560C4—24no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—42no—
565C4—882no—
566C4—881no—
567C4#1062335511yescharacteristic
568C4#1062335911yescharacteristic
569C4#1062336011yescharacteristic
570C4#1062336411yescharacteristic
571C2—84no—
572C2—82no—
573C2—882no—
574C2#1307195511yescharacteristic
575C2#1307784311yescharacteristic
576C2#1307788411yescharacteristic
577C2#1308131912yes—
578C2#1308165812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#24196
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622685C2semidirect
2. C2×#10622627C2semidirect
3. #13073974C2semidirect
4. #13069847C2semidirect
5. #13069687C2semidirect
6. #13069557C2semidirect
7. #13069441C2semidirect
8. #13068964C2semidirect
9. #13068877C2semidirect
10. #13068626C2semidirect
11. C2×C11×#550C2semidirect
153. C2×D44#41semidirect
184. C2×C11⋊C8#41semidirect
185. C2×#550D11semidirect
473. C11#24196semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×#106226272
#130739742
#130698472
#130696872
#130695572
#130694412
#130689642
#130688772
#130686262
C2×C11×#5502
#2419611