Finite Group Databasebeta

← #14787711

Subgroups — #14787711

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic, complemented
5#13069804C212yesmaximal, complemented
6#13069620C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic, complemented
9#13068922C212yesmaximal, complemented
10#13068810C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991C2212yes—
15C22×#4324C2211yescharacteristic
16C2×#66977—21no—
17#10623082—24no—
18#10623082—24no—
19C2×#66950C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66936—22no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66881C2212yes—
32C2×#66880C2212yes—
33C4×#4324—24no—
34#10622607—22no—
35#10622601—21no—
36#10622600C2212yes—
37#10622598—21no—
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622464—24no—
42C11×#340C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C22⋊D11—22no—
48C2×#4339—28no—
49C2×#4339—44no—
50C2×#4339—44no—
51C22×D44D411yescharacteristic
52C22×C4×D11—22no—
53C22×C4×D11C2312yes—
54C22×Dic22—21no—
55C22×Dic22C2311yescharacteristic
56C22×C8×C11C2312yes—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66#66991—24no—
67#66991—24no—
68C2×#4324—22no—
69C2×#4324—22no—
70C2×#4324—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79#66977—28no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66950—24no—
86#66950—42no—
87C4⋊C4×D11—24no—
88C4⋊C4×D11—24no—
89#66936—216no—
90C4×D44—22no—
91C4×D44—22no—
92#66922—22no—
93#66922D414yes—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C11×C4⋊C8—22no—
97C11×#102—42no—
98#66896—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—42no—
102#66881—24no—
103#66880—24no—
104#66874—22no—
105#66872—22no—
106C4×C11⋊C8—22no—
107#24120—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11C2×D412yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—28no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11C2×D412yes—
131#4339—432no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44SD1614yescomplemented
135C2×C4×D11—28no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×Dic22—24no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22#4112yescomplemented
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4C2×D412yes—
162C11×C22⋊C4—24no—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165C22⋊Dic11—28no—
166#4324—28no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—82no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—44no—
176C4⋊Dic11C2×D414yes—
177Dic11⋊C4—28no—
178Dic11⋊C4—42no—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8#4112yescomplemented
186C2×#547—111no—
187C2×#475—111no—
188C2×C4×SD16—111no—
189#2538—111no—
190#2034—112no—
191#2000—112no—
192#1990—111no—
193#1954—111no—
194#1872—112no—
195#1853—112no—
196#1802D1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11C2×SD1614yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—41no—
215D4×C11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—48no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11C2×SD1612yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C22⋊D11—416no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—28no—
249C4×D11—416no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253C4×D11—42no—
254Dic22—22no—
255Dic22—22no—
256Dic22—41no—
257Dic22—41no—
258Dic22—48no—
259C8×C11—42no—
260C11⋊C8—22no—
261C11⋊C8—41no—
262C22×#41—221no—
263C22×SD16—111no—
264#547—224no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×#123—222no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—221no—
270C2×#121—112no—
271C2×C4×Q8—111no—
272C2×C4×D4—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275#475—224no—
276C4×SD16—224no—
277C2×#106—112no—
278C2×#106—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#103—112no—
281C2×#103—111no—
282C2×#102—111no—
283C2×#102C2×D1112yes—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C4×C8—111no—
287#396—222no—
288#390—221no—
289#389—221no—
290#384C2×D1111yescharacteristic
291#380—112no—
292#340—112no—
293#340—112no—
294#340C2×D1112yes—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—82no—
319C4×C11#45014yes—
320C4×C11#52511yescharacteristic
321C4×C11#53711yescharacteristic
322C4×C11#54811yescharacteristic
323C4×C11#55011yescharacteristic
324Dic11—42no—
325Dic11—42no—
326Dic11—44no—
327Dic11—81no—
328C2×#41—228no—
329C2×#41—444no—
330C2×#41—444no—
331C22×Q8—111no—
332C22×Q8—221no—
333C22×D4—111no—
334C22×D4—222no—
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—112no—
338C23×C4—222no—
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—222no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8C22×D1112yes—
345C4⋊Q8—114no—
346C4⋊Q8—222no—
347#123—2216no—
348C22⋊Q8—228no—
349C22⋊Q8—224no—
350C22⋊Q8—442no—
351#121—224no—
352#121—224no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×D4—22no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4D4414yes—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22×D1112yes—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#106—224no—
380#106—222no—
381C4⋊C8—22no—
382#103—224no—
383#103—222no—
384#102—42no—
385#102—222no—
386C22⋊C8—224no—
387C22⋊C8—442no—
388C4×C8—222no—
389#95—222no—
390C2×C11—82no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45011yescharacteristic
393C2×C11#301311yescharacteristic
394C2×C11#329811yescharacteristic
395C2×C11#333211yescharacteristic
396C2×C11#333511yescharacteristic
397C2×C11#335311yescharacteristic
398D11—44no—
399C24—21no—
400C24—112no—
401#41—4432no—
402C2×Q8—112no—
403C2×Q8—224no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—442no—
410C2×Q8—442no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—114no—
417C2×D4—228no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4C2×D4412yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—112no—
429C22×C4—228no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—444no—
440C22×C4—444no—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444SD16—228no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—112no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—114no—
460C4⋊C4—228no—
461C4⋊C4—222no—
462C4⋊C4—224no—
463C4⋊C4—222no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—444no—
467C4⋊C4—442no—
468C4⋊C4C2×D4412yes—
469C22⋊C4—24no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C22⋊C4—444no—
473C22⋊C4—882no—
474C42—442no—
475C42C2×D4412yes—
476C42D4×D1112yes—
477C11#2412011yescharacteristic, complemented, Sylow
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—114no—
486C23—222no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23—222no—
492C23C2×D4×D1111yescharacteristic
493Q8—222no—
494Q8—222no—
495Q8—441no—
496Q8—441no—
497Q8—448no—
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502D4—228no—
503D4—4416no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—48no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—4416no—
519C2×C4—441no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4#6693512yes—
531C2×C4#6693512yes—
532C2×C4#6696412yes—
533C2×C4SD16×D1112yes—
534C2×C4C22×D4411yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#6703711yescharacteristic
537C2×C4#6704011yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C8—42no—
541C8—222no—
542C8—441no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—224no—
551C22—224no—
552C22—224no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22C2×#6693511yescharacteristic
558C22#1062314311yescharacteristic
559C22#1062316211yescharacteristic
560C22C2×#6696411yescharacteristic
561C22C2×SD16×D1111yescharacteristic
562C22#1062330611yescharacteristic
563C22#1062331011yescharacteristic
564C4—22no—
565C4—42no—
566C4—82no—
567C4—444no—
568C4—442no—
569C4—442no—
570C4—881no—
571C4#1062238914yes—
572C4#1062304111yescharacteristic
573C4#1062305511yescharacteristic
574C4#1062313011yescharacteristic
575C4#1062316411yescharacteristic
576C2—82no—
577C2—444no—
578C2#1307196211yescharacteristic
579C2C2×#1062238911yescharacteristic
580C2#1307793311yescharacteristic
581C2#1308048411yescharacteristic
582C2#1308094611yescharacteristic
583C2#1308097011yescharacteristic
584C2#1308119711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenter#1802D11
hypocenterC11#24120
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×C4×#4324C2semidirect
4. #13073539C2semidirect
5. #13069804C2semidirect
6. #13069620C2semidirect
7. #13069576C2semidirect
8. #13069409C2semidirect
9. #13068922C2semidirect
10. #13068810C2semidirect
11. C11×#1802C2semidirect
134. C2×D44SD16semidirect
152. C2×Dic22#41semidirect
185. C2×C11⋊C8#41semidirect
196. #1802D11semidirect
477. C11#24120semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106224642
C2×C4×#43242
#130735392
#130698042
#130696202
#130695762
#130694092
#130689222
#130688102
C11×#18022
#2412011