Finite Group Databasebeta

← #14769233

Subgroups — #14769233

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×#10623086C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic, complemented
3C2×#10622385C212yesmaximal, complemented
4#13071563C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069418C211yesmaximal, characteristic, complemented
7#13069038C212yesmaximal, complemented
8#13068927C212yesmaximal, complemented
9#13068616C211yesmaximal, characteristic, complemented
10#13068553C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66983—21no—
15C22×C4⋊Dic11—21no—
16C22×C8×D11C2212yes—
17#10623086—24no—
18#10623086C418yescomplemented
19C2×#66950C2212yes—
20C2×#66945C2212yes—
21C2×#66939—22no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66896C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×#66880C2212yes—
32#10622600C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35#10622552—21no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622385—28no—
40C8×D44—24no—
41#10622283—22no—
42C11×#340C2211yescharacteristic
43C11×#340C2211yescharacteristic
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C22⋊D11—22no—
48C23×Dic11—22no—
49C2×#4341—24no—
50C2×#4341—24no—
51C2×#4341—24no—
52C2×#4341—42no—
53C2×#4341—42no—
54C2×#4341C2×C418yes—
55C22×D44D411yescharacteristic
56C22×C4×D11C2312yes—
57C22×Dic22C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C4×D4×C11—22no—
61C4×D4×C11C2×C414yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#66983—28no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—28no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×C4×Dic11—22no—
82C22×C11⋊C8C2312yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11—42no—
86#66950—24no—
87#66950C2×C418yes—
88#66945—24no—
89#66945—42no—
90#66939—216no—
91C4×D44C2×C414yes—
92C4×D44D414yes—
93#66922—22no—
94#66922C2×C414yes—
95C11×#102—22no—
96C11×#102D414yescomplemented
97C4×C8×C11—22no—
98C11×#95—21no—
99#66896—24no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102#66880—24no—
103#66880—42no—
104#66874—24no—
105#66874—42no—
106C4⋊(C11⋊C8)—22no—
107#22417—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11C2×D412yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C22×C412yes—
114C2×D4×C11C2×D412yes—
115C2×D4×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—28no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C22×Dic11—28no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—44no—
132C22×Dic11—44no—
133C22×Dic11C2×D412yes—
134#4341—216no—
135#4341—48no—
136#4341—48no—
137#4341—48no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44C22⋊C414yes—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11C22×C414yes—
146C2×C4×D11C2×D414yes—
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—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C22×C412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×D412yes—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—44no—
171(C2×D11)⋊C4—82no—
172(C2×D11)⋊C4C22⋊C418yes—
173C4⋊Dic11—28no—
174C4⋊Dic11—24no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—42no—
179C4⋊Dic11—81no—
180C4⋊Dic11C22⋊C414yes—
181C4×Dic11—44no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C8×D11—48no—
186C2×#547—111no—
187C2×C8×D4—111no—
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×#102D1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
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×C22⋊C414yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11C4×D414yes—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—48no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11#13512yes—
231C2×C4×C11#13512yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C22⋊D11—416no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—416no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11C2×C22⋊C414yes—
249D44—28no—
250C4×D11—24no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254Dic22—24no—
255Dic22—24no—
256Dic22—42no—
257Dic22—42no—
258C8×C11—22no—
259C8×C11—41no—
260C11⋊C8—42no—
261C22×#41—112no—
262C23×C8—112no—
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—224no—
274C2×C4⋊C8—111no—
275#416—228no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#102—112no—
281C2×#102C2×D1111yescharacteristic
282C2×#102C2×D1111yescharacteristic
283C2×C22⋊C8—112no—
284C2×C4×C8C2×D1111yescharacteristic
285#390—221no—
286#388—222no—
287#384—111no—
288#380—112no—
289C4×C4⋊C4—221no—
290C4×C4⋊C4C2×D1111yescharacteristic
291#340—112no—
292#340C2×D1111yescharacteristic
293#340C2×D1111yescharacteristic
294C22×C11—24no—
295C22×C11—42no—
296C22×C11—42no—
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—24no—
310C2×D11—24no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—81no—
319C4×C11#41614yescomplemented
320C4×C11C2×C4×D411yescharacteristic
321C4×C11#51811yescharacteristic
322C4×C11D4211yescharacteristic
323C4×C11#54611yescharacteristic
324Dic11—24no—
325Dic11—44no—
326Dic11—82no—
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×D4C22×D1111yescharacteristic
337C23×C4—21no—
338C23×C4—112no—
339C23×C4—222no—
340C22×C8—112no—
341C22×C8—224no—
342C22×C8—224no—
343C22×C8—442no—
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—22no—
353C4×D4—114no—
354C4×D4—114no—
355C4×D4C4×D1114yes—
356#117—224no—
357#117—442no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—21no—
375C2×C42—222no—
376C2×C42C22×D1111yescharacteristic
377C4⋊C8—222no—
378#103—224no—
379#103—224no—
380#103—442no—
381#103—442no—
382#102—22no—
383#102—224no—
384#102D4414yescomplemented
385C22⋊C8—224no—
386C4×C8—22no—
387#95—21no—
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—21no—
399C24—112no—
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—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—114no—
414C2×D4—228no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—444no—
418C2×D4—444no—
419C2×D4C2×C4×D1112yes—
420C2×D4C2×D4412yes—
421C2×D4#433912yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—228no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—444no—
439C22×C4—444no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—448no—
452C2×C8C2×D4412yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—114no—
458C4⋊C4—228no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—442no—
464C4⋊C4—881no—
465C4⋊C4C2×C4×D1112yes—
466C4⋊C4C2×D4412yes—
467C22⋊C4—24no—
468C22⋊C4—118no—
469C22⋊C4—228no—
470C22⋊C4—444no—
471C22⋊C4—882no—
472C42—42no—
473C42—444no—
474C42C2×C4×D1112yes—
475C42D4×D1112yes—
476C11#2241711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—114no—
485C23—222no—
486C23—222no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23C2×D4×D1111yescharacteristic
492Q8—224no—
493Q8—224no—
494Q8—442no—
495Q8—442no—
496D4—22no—
497D4—22no—
498D4—22no—
499D4—228no—
500D4—4416no—
501D4C4×D4414yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—48no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—114no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—4416no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4C22⋊C4×D1112yes—
529C2×C4C22⋊C4×D1112yes—
530C2×C4#6696512yes—
531C2×C4#6696912yes—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C22×D4411yescharacteristic
534C2×C4C2×#433911yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#6704211yescharacteristic
537C2×C4#6704211yescharacteristic
538C8—22no—
539C8—41no—
540C8—442no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—224no—
549C22—224no—
550C22—224no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22C2×C22⋊C4×D1111yescharacteristic
556C22D4×D4411yescharacteristic
557C22#1062308111yescharacteristic
558C22C2×#6696511yescharacteristic
559C22C2×#6696911yescharacteristic
560C22#1062330111yescharacteristic
561C22#1062330211yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—224no—
567C4—444no—
568C4—882no—
569C4#1062238514yescomplemented
570C4C2×C4×D4411yescharacteristic
571C4#1062305211yescharacteristic
572C4D4×D4411yescharacteristic
573C4#1062308111yescharacteristic
574C2—44no—
575C2—444no—
576C2C22⋊C4×D4411yescharacteristic
577C2C2×#1062238511yescharacteristic
578C2#1307714511yescharacteristic
579C2#1308033711yescharacteristic
580C2#1308034711yescharacteristic
581C2#1308053511yescharacteristic
582C2#1308054611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22417
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×D44C2semidirect
3. C2×#10622385C2semidirect
4. #13071563C2semidirect
5. #13069539C2semidirect
6. #13069418C2semidirect
7. #13069038C2semidirect
8. #13068927C2semidirect
9. #13068616C2semidirect
10. #13068553C2semidirect
11. C4×C11×#102C2semidirect
18. #10623086C4semidirect
96. C11×#102D4semidirect
196. C4×#102D11semidirect
319. C4×C11#416semidirect
384. #102D44semidirect
476. C11#22417semidirect
569. C4#10622385semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×C8×D442
C2×#106223852
#130715632
#130695392
#130694182
#130690382
#130689272
#130686162
#130685532
C4×C11×#1022
#2241711