Finite Group Databasebeta

← #14769232

Subgroups — #14769232

Order 2816.

1490 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×#10623082C211yesmaximal, characteristic
2C2×#10622726C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic, complemented
4#13069538C211yesmaximal, characteristic, complemented
5#13069418C211yesmaximal, characteristic, complemented
6#13069039C212yesmaximal, complemented
7#13068926C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9#13068557C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C23×C8×C11C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66991—21no—
16C2×#66979C2212yes—
17C2×#66977C2212yes—
18#10623082—24no—
19#10623082C418yescomplemented
20C2×C4⋊C4×D11—21no—
21C2×#66936—22no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C8×D4×C11—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28#10622834—21no—
29#10622825C2212yes—
30#10622726—28no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66885C2211yescharacteristic
34C2×#66880C2212yes—
35C2×#66880C2212yes—
36C2×#66880C2212yes—
37C2×#66880C2212yes—
38C4⋊C4×Dic11—21no—
39#10622564—22no—
40#10622548C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2211yescharacteristic
44#10622189C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C2×#4339—24no—
49C2×#4339—24no—
50C2×#4339—24no—
51C2×#4339—42no—
52C2×#4339—42no—
53C2×#4339C2×C418yes—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11—22no—
57C22×Dic22C2312yes—
58C22×C8×C11—24no—
59C22×C8×C11—24no—
60C22×C8×C11—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11C2×C414yes—
65C4×D4×C11D414yes—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72#66991—28no—
73C2×(C2×D11)⋊C4—21no—
74#66979—24no—
75#66979—42no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84#66977—24no—
85#66977C2×C418yes—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—22no—
89C4⋊C4×D11—28no—
90#66936—216no—
91C4×D44—22no—
92C4×D44C2×C414yes—
93#66922—22no—
94#66922C2×C414yes—
95C11×C4⋊C8—22no—
96C11×C22⋊C8—24no—
97C4×C8×C11—22no—
98C11⋊#95—21no—
99C11⋊#95—22no—
100#66885—24no—
101#66885—22no—
102#66885D414yescomplemented
103#66880—24no—
104#66880—24no—
105#66880—42no—
106#66880—42no—
107#22417—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—44no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131#4339—216no—
132#4339—48no—
133#4339—48no—
134#4339—48no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44C22×C412yes—
139C2×D44C2×D412yes—
140C2×D44#4112yes—
141C2×C4×D11—24no—
142C2×C4×D11—28no—
143C2×C4×D11—44no—
144C2×C4×D11—44no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22C22×C414yes—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—48no—
162C2×C8×C11C2×D412yes—
163C11×C4⋊C4C22⋊C414yes—
164C11×C22⋊C4C22⋊C418yes—
165C42×C11C22×C412yes—
166C42×C11C2×D412yes—
167C22⋊Dic11—28no—
168C22⋊Dic11—44no—
169C22⋊Dic11—82no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11C22×C412yes—
182C4⋊Dic11C2×D412yes—
183Dic11⋊C4—28no—
184C4×Dic11—44no—
185C4×Dic11—42no—
186C2×#547—111no—
187C2×C8×D4D1111yescharacteristic, complemented
188C2×#416—112no—
189#2354—111no—
190#1981—111no—
191#1956—111no—
192#1892—112no—
193#1873—112no—
194#1802—111no—
195#1788—112no—
196C4×#102—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11C2×C22⋊C414yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212D4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11#13512yes—
225C2×C4×C11#13512yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C22⋊D11—416no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248D44—22no—
249D44—22no—
250D44—22no—
251D44C4×D414yes—
252C4×D11—416no—
253C4×D11—48no—
254Dic22—24no—
255Dic22—24no—
256Dic22—42no—
257Dic22—42no—
258C8×C11—22no—
259C8×C11—42no—
260C8×C11—41no—
261C22×#41—112no—
262C23×C8C2×D1112yes—
263#547—118no—
264#547—224no—
265C2×C4⋊Q8—111no—
266C2×#123—222no—
267C2×C22⋊Q8—112no—
268C2×#121—221no—
269C2×C4×D4—111no—
270C2×C4×D4C2×D1111yescharacteristic
271C2×#117—112no—
272C22×C4⋊C4—221no—
273C8×D4—24no—
274C2×C4⋊C8C2×D1111yescharacteristic
275#416—228no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#102—111no—
281C2×#102—112no—
282C2×#102—111no—
283C2×C22⋊C8C2×D1112yes—
284C2×C4×C8C2×D1111yescharacteristic
285#390—221no—
286#388—222no—
287#384—111no—
288#380—112no—
289C4×C4⋊C4—111no—
290C4×C4⋊C4—221no—
291#340—112no—
292#340—111no—
293#340—111no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11D4211yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11C2×#13511yescharacteristic
305C22×C11C2×#13511yescharacteristic
306C22×C11#57711yescharacteristic
307C22×C11#57811yescharacteristic
308C2×D11—24no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—24no—
316C4×C11—22no—
317C4×C11#41614yescomplemented
318C4×C11C2×C4×D411yescharacteristic
319C4×C11#51811yescharacteristic
320C4×C11D4211yescharacteristic
321C4×C11#54611yescharacteristic
322Dic11—44no—
323Dic11—42no—
324Dic11—42no—
325Dic11—82no—
326Dic11—81no—
327C2×#41—118no—
328C2×#41—224no—
329C2×#41—224no—
330C2×#41—224no—
331C2×#41—442no—
332C2×#41—442no—
333C22×Q8—112no—
334C22×D4—111no—
335C22×D4—222no—
336C22×D4D4411yescharacteristic
337C23×C4—221no—
338C23×C4—222no—
339C23×C4C22×D1112yes—
340C22×C8—24no—
341C22×C8—24no—
342C22×C8—42no—
343C22×C8C22×D1112yes—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4⋊Q8—114no—
347C4⋊Q8—222no—
348#123—2216no—
349C22⋊Q8—118no—
350C22⋊Q8—224no—
351#121—228no—
352C4×D4—114no—
353C4×D4—222no—
354C4×D4C4×D1114yes—
355C4×D4C22⋊D1114yes—
356#117—224no—
357#117—442no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4D4411yescharacteristic
369C2×C22⋊C4—222no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4D4412yes—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377C4⋊C8—22no—
378#103—224no—
379#103—224no—
380#103—442no—
381#103—442no—
382#102—114no—
383#102—222no—
384#102—224no—
385C22⋊C8—24no—
386C4×C8—22no—
387#95—221no—
388#95—222no—
389C2×C11—44no—
390C2×C11D4×C22⋊C411yescharacteristic
391C2×C11C2×#41611yescharacteristic
392C2×C11#289811yescharacteristic
393C2×C11#328311yescharacteristic
394C2×C11#328411yescharacteristic
395C2×C11#330211yescharacteristic
396C2×C11#330311yescharacteristic
397D11—44no—
398C24—221no—
399C24C2×D4412yes—
400#41—2216no—
401#41—448no—
402#41—448no—
403#41—448no—
404C2×Q8—114no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—112no—
413C2×D4—112no—
414C2×D4—112no—
415C2×D4—228no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4(C2×D11)⋊C414yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—228no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4C2×C4×D1114yes—
438C22×C4C2×D4412yes—
439C22×C4C2×D4411yescharacteristic
440C22×C4C2×D4411yescharacteristic
441C22×C4C2×C22⋊D1114yes—
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—48no—
452C2×C8D4×D1112yes—
453C4⋊C4—112no—
454C4⋊C4—112no—
455C4⋊C4—224no—
456C4⋊C4—228no—
457C4⋊C4—224no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—222no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—222no—
464C4⋊C4—442no—
465C4⋊C4—881no—
466C4⋊C4(C2×D11)⋊C414yes—
467C22⋊C4—228no—
468C22⋊C4—224no—
469C22⋊C4—444no—
470C22⋊C4—882no—
471C22⋊C4(C2×D11)⋊C418yes—
472C42—444no—
473C42—442no—
474C42C2×C4×D1112yes—
475C42C2×C22⋊D1112yes—
476C11#2241711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23C2×(C2×D11)⋊C414yes—
491C23C22×D4411yescharacteristic
492Q8—224no—
493Q8—224no—
494Q8—442no—
495Q8—442no—
496D4—28no—
497D4—114no—
498D4—222no—
499D4—222no—
500D4—222no—
501D4—4416no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—4416no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—448no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4#6695712yes—
528C2×C4#6695712yes—
529C2×C4C2×(C2×D11)⋊C412yes—
530C2×C4C2×(C2×D11)⋊C414yes—
531C2×C4C2×(C2×D11)⋊C412yes—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#6703711yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C2×C4#6704211yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C8—22no—
539C8—42no—
540C8—41no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—224no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22D4×D4411yescharacteristic
556C22#1062308511yescharacteristic
557C22C2×#6695711yescharacteristic
558C22C2×#6695711yescharacteristic
559C22#1062328211yescharacteristic
560C22#1062328411yescharacteristic
561C22C22×(C2×D11)⋊C411yescharacteristic
562C4—24no—
563C4—22no—
564C4—442no—
565C4—444no—
566C4—442no—
567C4—882no—
568C4—881no—
569C4#1062272614yescomplemented
570C4C4×D4×D1111yescharacteristic
571C4#1062307611yescharacteristic
572C4D4×C22⋊D1111yescharacteristic
573C4#1062336011yescharacteristic
574C2—44no—
575C2—444no—
576C2D4×(C2×D11)⋊C411yescharacteristic
577C2C2×#1062272611yescharacteristic
578C2#1307715011yescharacteristic
579C2#1308033811yescharacteristic
580C2#1308034811yescharacteristic
581C2#1308053411yescharacteristic
582C2#1308054511yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
cosocleC22×C4×C11C24
hypercenterC2×C8×D4D11
hypocenterC11#22417
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622726C2semidirect
3. #13071565C2semidirect
4. #13069538C2semidirect
5. #13069418C2semidirect
6. #13069039C2semidirect
7. #13068926C2semidirect
8. #13068617C2semidirect
9. #13068557C2semidirect
10. C4×#66885C2semidirect
11. C2×C8×D4×C11C2semidirect
19. #10623082C4semidirect
102. #66885D4semidirect
187. C2×C8×D4D11semidirect
317. C4×C11#416semidirect
476. C11#22417semidirect
569. C4#10622726semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106227262
#130715652
#130695382
#130694182
#130690392
#130689262
#130686172
#130685572
C4×#668852
C2×C8×D4×C112
#2241711