Finite Group Databasebeta

← #14769245

Subgroups — #14769245

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623249C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic, complemented
3C2×#10622385C212yesmaximal, complemented
4#13071563C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069041C212yesmaximal, complemented
7#13068935C212yesmaximal, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068553C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1982C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×#66993—21no—
15C2×#66992—22no—
16C2×#66991C2212yes—
17C2×D4×Dic11—21no—
18C22×C8×D11C2212yes—
19#10623249—24no—
20#10623249C418yescomplemented
21C2×#66945C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32#10622600C2212yes—
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35#10622552—21no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11—21no—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622447—24no—
40#10622385—28no—
41#10622283—22no—
42#10622189C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C23×Dic11—22no—
51C2×#4341—24no—
52C2×#4341—24no—
53C2×#4341—24no—
54C2×#4341—42no—
55C2×#4341—42no—
56C2×#4341C2×C418yes—
57C22×D44D411yescharacteristic
58C22×C4×D11C2312yes—
59C22×Dic22C2311yescharacteristic
60C22×C8×C11C2312yes—
61C11×#127—22no—
62C11×#127C2×C414yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68#66993—28no—
69#66992—216no—
70#66991—24no—
71#66991C2×C418yes—
72D4×Dic11—28no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4D412yes—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C2×C8×D11—24no—
87C2×C8×D11—24no—
88C2×C8×D11—42no—
89#66945—24no—
90#66945—42no—
91C4×D44C2×C414yes—
92C4×D44D414yes—
93C4×Dic22—22no—
94C4×Dic22C2×C414yes—
95C11×C4⋊C8—22no—
96C11×#102—24no—
97C11×#102—42no—
98C11×#95—21no—
99#66896—24no—
100#66896—42no—
101C11⋊#95—22no—
102(C2×D11)⋊C8—24no—
103#66880—24no—
104#66874—22no—
105#66874D414yescomplemented
106C4×C11⋊C8—22no—
107#22418—111nomaximal, Sylow
108C24×C11—22no—
109C23×D11C2×D412yes—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—81no—
120C2×D4×C11—81no—
121C2×D4×C11C22×C414yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—28no—
128C2×C22⋊D11—28no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—82no—
132C2×C22⋊D11—82no—
133C22×Dic11—28no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—44no—
138C22×Dic11—44no—
139C22×Dic11C2×D412yes—
140#4341—216no—
141#4341—48no—
142#4341—48no—
143#4341—48no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44C22⋊C414yes—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11C22×C414yes—
152C2×C4×D11C2×D414yes—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C2×Dic22C2×D412yes—
158C2×Dic22#4112yes—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D412yes—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—28no—
170(C2×D11)⋊C4—44no—
171(C2×D11)⋊C4—82no—
172(C2×D11)⋊C4C22⋊C418yes—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—81no—
178C4⋊Dic11C22⋊C414yes—
179C4⋊Dic11C22×C412yes—
180Dic11⋊C4—24no—
181C4×Dic11—24no—
182C4×Dic11—44no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8C2×D412yes—
189C8×D11—48no—
190C2×#550—111no—
191C2×C8×D4—111no—
192C2×#416—112no—
193#2354—111no—
194#1982D1111yescharacteristic, complemented
195#1957—111no—
196#1893—112no—
197#1875—112no—
198#1803—111no—
199#1788—112no—
200C4×#103—111no—
201C23×C11—24no—
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—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11C2×C22⋊C414yes—
216D4×C11—24no—
217D4×C11—24no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—48no—
221D4×C11—84no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11#13512yes—
233C2×C4×C11#13512yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C22⋊D11—416no—
241C22⋊D11—88no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—416no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11C2×C22⋊C414yes—
255D44—28no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—24no—
260Dic22—22no—
261Dic22—22no—
262Dic22—22no—
263Dic22C4×D414yes—
264C8×C11—42no—
265C11⋊C8—22no—
266C11⋊C8—41no—
267C22×#41—112no—
268C23×C8—112no—
269#550—118no—
270#550—224no—
271C2×#127—221no—
272C2×#127C2×D1111yescharacteristic
273C2×#121—112no—
274C2×#121—222no—
275C2×C4×Q8—111no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—112no—
279C8×D4—224no—
280C2×C4⋊C8C2×D1111yescharacteristic
281#416—228no—
282C2×#103—111no—
283C2×#103—112no—
284C2×#103—111no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102C2×D1112yes—
288C2×#102C2×D1112yes—
289C2×C22⋊C8—112no—
290C2×C4×C8—111no—
291#390—221no—
292#388—222no—
293#384—111no—
294#380—112no—
295C4×C4⋊C4—221no—
296C4×C4⋊C4C2×D1111yescharacteristic
297#340—112no—
298#340—111no—
299#340—111no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11D4211yescharacteristic
309C22×C11#54611yescharacteristic
310C22×C11C2×#13511yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—81no—
324C4×C11#41614yescomplemented
325C4×C11C2×C4×D411yescharacteristic
326C4×C11#51811yescharacteristic
327C4×C11D4211yescharacteristic
328C4×C11#54611yescharacteristic
329Dic11—24no—
330Dic11—24no—
331Dic11—42no—
332Dic11—82no—
333C2×#41—118no—
334C2×#41—224no—
335C2×#41—224no—
336C2×#41—224no—
337C2×#41—442no—
338C2×#41—442no—
339C22×Q8—111no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—111no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4C22×D1112yes—
346C23×C4—112no—
347C23×C4—222no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—224no—
351C22×C8—224no—
352C22×C8—442no—
353C22×C8C22×D1112yes—
354#127—22no—
355#127—228no—
356#127C4×D1114yes—
357#121—118no—
358#121—2216no—
359#121—224no—
360C4×Q8—114no—
361C4×Q8—222no—
362C4×D4—114no—
363C4×D4—114no—
364C4×D4—228no—
365#117—224no—
366#117—442no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—112no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C42—21no—
380C2×C42—221no—
381C2×C42—222no—
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—22no—
384#103—114no—
385#103—222no—
386#103—224no—
387#102—24no—
388#102—42no—
389#102—224no—
390#102—442no—
391C22⋊C8—224no—
392C4×C8—222no—
393#95—21no—
394#95—222no—
395C2×C11—84no—
396C2×C11D4×C22⋊C411yescharacteristic
397C2×C11C2×#41611yescharacteristic
398C2×C11#289711yescharacteristic
399C2×C11#328411yescharacteristic
400C2×C11#328711yescharacteristic
401C2×C11#330411yescharacteristic
402C2×C11#330511yescharacteristic
403D11—44no—
404C24—22no—
405C24—112no—
406#41—2216no—
407#41—448no—
408#41—448no—
409#41—448no—
410C2×Q8—112no—
411C2×Q8—112no—
412C2×Q8—112no—
413C2×Q8—221no—
414C2×Q8—221no—
415C2×Q8—221no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—882no—
435C2×D4—882no—
436C2×D4C2×C4×D1114yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—228no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—112no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—448no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—114no—
469C4⋊C4—112no—
470C4⋊C4—224no—
471C4⋊C4—221no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4D4×D1112yes—
477C22⋊C4—118no—
478C22⋊C4—228no—
479C22⋊C4—444no—
480C22⋊C4—882no—
481C42—42no—
482C42—224no—
483C42—444no—
484C42C2×C4×D1112yes—
485C42D4×D1112yes—
486C11#2241811yescharacteristic, complemented, Sylow
487C23—24no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—114no—
495C23—222no—
496C23—222no—
497C23—222no—
498C23—222no—
499C23—222no—
500C23—222no—
501C23C2×D4×D1111yescharacteristic
502Q8—114no—
503Q8—222no—
504Q8—222no—
505Q8—222no—
506D4—24no—
507D4—24no—
508D4—42no—
509D4—48no—
510D4—42no—
511D4—84no—
512D4—228no—
513D4—4416no—
514D4—888no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—114no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—4416no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4C22⋊C4×D1112yes—
541C2×C4C22⋊C4×D1112yes—
542C2×C4#6696512yes—
543C2×C4#6696912yes—
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4#6703711yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704211yescharacteristic
550C8—42no—
551C8—222no—
552C8—441no—
553C22—44no—
554C22—44no—
555C22—44no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—82no—
560C22—224no—
561C22—224no—
562C22—224no—
563C22—442no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22C2×C22⋊C4×D1111yescharacteristic
568C22#1062314011yescharacteristic
569C22#1062314311yescharacteristic
570C22C2×#6696511yescharacteristic
571C22C2×#6696911yescharacteristic
572C22#1062330511yescharacteristic
573C22#1062330611yescharacteristic
574C4—22no—
575C4—42no—
576C4—81no—
577C4—224no—
578C4—224no—
579C4—442no—
580C4—882no—
581C4#1062238514yescomplemented
582C4C4×D4×D1111yescharacteristic
583C4#1062307611yescharacteristic
584C4#1062320711yescharacteristic
585C4#1062324811yescharacteristic
586C2—84no—
587C2—444no—
588C2#1307143711yescharacteristic
589C2C2×#1062238511yescharacteristic
590C2#1307714111yescharacteristic
591C2#1308034911yescharacteristic
592C2#1308037111yescharacteristic
593C2#1308055811yescharacteristic
594C2#1308056911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1982C2
socleC23×C11C22×D4
prime radicalC2×#10623249C2
cosocleC22×C4×C11C24
hypercenter#1982D11
hypocenterC11#22418
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#10622447C2semidirect
3. C2×#10622385C2semidirect
4. #13071563C2semidirect
5. #13069423C2semidirect
6. #13069041C2semidirect
7. #13068935C2semidirect
8. #13068622C2semidirect
9. #13068553C2semidirect
10. C4×#66874C2semidirect
11. C11×#1982C2semidirect
20. #10623249C4semidirect
105. #66874D4semidirect
194. #1982D11semidirect
324. C4×C11#416semidirect
486. C11#22418semidirect
581. C4#10622385semidirect

Maximal subgroups

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

subgroupindex
C2×#106232492
C2×#106224472
C2×#106223852
#130715632
#130694232
#130690412
#130689352
#130686222
#130685532
C4×#668742
C11×#19822
#2241811