Finite Group Databasebeta

← #14804490

Subgroups — #14804490

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622770C212yesmaximal, complemented
2C2×#10622447C211yesmaximal, characteristic, complemented
3#13073563C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic, complemented
5#13069797C212yesmaximal, complemented
6#13069611C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069041C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66993—21no—
16C2×#66991C2212yes—
17C2×#66991C2212yes—
18C2×#66991C2212yes—
19C2×#66983—21no—
20C22×C8×D11C2212yes—
21C2×C4×D44C2211yescharacteristic
22C11×#459—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2212yes—
25#10622836—22no—
26#10622834—21no—
27C2×#66896C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32#10622770—28no—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66882C2212yes—
35#10622600C2212yes—
36#10622574—22no—
37#10622548C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622447—24no—
41#10622189C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—22no—
52C22×D44D411yescharacteristic
53C22×C4×D11C2312yes—
54C2×C11×D8—24no—
55C2×C11×D8—24no—
56C2×C11×D8—42no—
57C22×C8×C11C2312yes—
58C11×#127—22no—
59C11×#127—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66993—44no—
69#66991—24no—
70#66991—24no—
71#66991—24no—
72#66991—42no—
73#66991—42no—
74#66991—42no—
75#66983—44no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4D412yes—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C2×C8×D11—24no—
88C2×C8×D11—24no—
89C2×C8×D11—42no—
90C4×D44—22no—
91C4×D44—22no—
92C11×C4⋊C8D414yescomplemented
93C11×#102—24no—
94#66896—22no—
95#66896—24no—
96#66896—42no—
97#66896D414yescomplemented
98C11⋊#95—21no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101#66882—24no—
102C4×C11⋊C8—22no—
103#25384—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C23×D11C2×D412yes—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—81no—
123C2×D4×C11—81no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—21no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—82no—
139C2×C22⋊D11—82no—
140C2×C22⋊D11—82no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11C2×D412yes—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44D814yescomplemented
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C11×D8—48no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C2×D414yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C22⋊C4—42no—
161C42×C11C2×D412yes—
162C42×C11#4112yes—
163C22⋊Dic11—44no—
164C22⋊Dic11—44no—
165C22⋊Dic11—44no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—44no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175C4⋊Dic11C2×D412yes—
176C4⋊Dic11#4112yes—
177C4×Dic11—42no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8C2×D412yes—
184C8×D11—48no—
185C2×#466—112no—
186C2×#459D1111yescharacteristic, complemented
187C2×C8×D4—111no—
188#2541—111no—
189#2537—111no—
190#2033—112no—
191#1999—112no—
192#1957—111no—
193#1947—111no—
194#1893—112no—
195C4×#102—111no—
196C23×C11—22no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11C2×D814yes—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—42no—
221D4×C11—41no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—41no—
225D4×C11—42no—
226D4×C11—84no—
227D4×C11—84no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—84no—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11C2×D812yes—
237C2×C4×C11#13512yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C22⋊D11—88no—
245C22⋊D11—88no—
246C22⋊D11—88no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259D44—28no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—42no—
264C8×C11—24no—
265C11⋊C8—22no—
266C11⋊C8—41no—
267C22×D8C2×D1112yes—
268C23×C8—112no—
269C2×#127—221no—
270C2×#127C2×D1111yescharacteristic
271C2×#121—112no—
272C2×#121—112no—
273C2×#121—112no—
274C2×#121—221no—
275C2×C4×D4—111no—
276C2×C4×D4C2×D1111yescharacteristic
277#466—228no—
278#459—24no—
279C8×D4—224no—
280C2×#107—112no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—112no—
284C2×#102—111no—
285C2×#102—112no—
286C2×#102C2×D1112yes—
287C2×C22⋊C8—112no—
288C2×C4×C8—111no—
289#394—222no—
290#392—222no—
291#390—221no—
292#384—111no—
293#380—112no—
294#380—221no—
295C4×C4⋊C4—111no—
296#340—112no—
297#340—111no—
298#340—111no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11C2×#12111yescharacteristic
314C22×C11D4211yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11C22×D811yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C4×C11—22no—
328C4×C11—81no—
329C4×C11#46614yescomplemented
330C4×C11#53211yescharacteristic
331C4×C11#54011yescharacteristic
332C4×C11D4211yescharacteristic
333C4×C11#55011yescharacteristic
334Dic11—42no—
335Dic11—42no—
336Dic11—42no—
337Dic11—82no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—111no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4C22×D1112yes—
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C23×C4—112no—
348C2×D8—24no—
349C2×D8—24no—
350C2×D8—42no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—224no—
354C22×C8—224no—
355C22×C8—442no—
356C22×C8C22×D1112yes—
357#127—22no—
358#127—22no—
359#127—444no—
360#121—224no—
361#121—224no—
362#121—224no—
363#121—442no—
364#121—442no—
365#121—442no—
366#121—444no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—222no—
370C4×D4—222no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—224no—
387C4⋊C8C22⋊D1114yescomplemented
388#102—24no—
389#102—114no—
390#102—222no—
391#102—224no—
392#102—442no—
393C22⋊C8—224no—
394C4×C8—222no—
395#95—222no—
396#95—221no—
397C2×C11—82no—
398C2×C11—162no—
399C2×C11#242811yescharacteristic
400C2×C11C2×#46611yescharacteristic
401C2×C11#306211yescharacteristic
402C2×C11D4×D811yescharacteristic
403C2×C11#328411yescharacteristic
404C2×C11#329411yescharacteristic
405C2×C11#330511yescharacteristic
406D11—44no—
407C24—21no—
408C24—22no—
409C24—112no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—114no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—882no—
437C2×D4—882no—
438C2×D4—882no—
439C2×D4D4×D1112yes—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—112no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—48no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—448no—
467C2×C8C2×C22⋊D1114yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C22⋊C4—42no—
480C22⋊C4—224no—
481C22⋊C4—444no—
482C22⋊C4—444no—
483C22⋊C4—444no—
484C22⋊C4—444no—
485C42—442no—
486C42#434112yes—
487C42C2×C22⋊D1112yes—
488C11#2538411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—114no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23C2×D4×D1111yescharacteristic
511D4—22no—
512D4—22no—
513D4—42no—
514D4—41no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—42no—
519D4—84no—
520D4—84no—
521D4—228no—
522D4—888no—
523D4—888no—
524D4—888no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—84no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4D8×D1112yes—
548C2×C4#6696512yes—
549C2×C4#6699112yes—
550C2×C4#6699112yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4C2×#434111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704211yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—24no—
558C8—222no—
559C8—441no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22—224no—
575C22—224no—
576C22—224no—
577C22—442no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22#1062314011yescharacteristic
582C22#1062314311yescharacteristic
583C22C2×D8×D1111yescharacteristic
584C22C2×#6696511yescharacteristic
585C22#1062330511yescharacteristic
586C22#1062330611yescharacteristic
587C22C2×#6699111yescharacteristic
588C4—22no—
589C4—81no—
590C4—442no—
591C4—442no—
592C4—442no—
593C4—882no—
594C4#1062277014yescomplemented
595C4#1062312711yescharacteristic
596C4#1062315011yescharacteristic
597C4D4×C22⋊D1111yescharacteristic
598C4#1062336511yescharacteristic
599C2—82no—
600C2—162no—
601C2—444no—
602C2#1307220011yescharacteristic
603C2C2×#1062277011yescharacteristic
604C2#1307829011yescharacteristic
605C2#1308028811yescharacteristic
606C2#1308034911yescharacteristic
607C2#1308043211yescharacteristic
608C2#1308056911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11#25384
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622770C2semidirect
2. C2×#10622447C2semidirect
3. #13073563C2semidirect
4. #13073529C2semidirect
5. #13069797C2semidirect
6. #13069611C2semidirect
7. #13069423C2semidirect
8. #13069375C2semidirect
9. #13069041C2semidirect
10. C4×#66896C2semidirect
11. C2×C11×#459C2semidirect
92. C11×C4⋊C8D4semidirect
97. #66896D4semidirect
147. C2×D44D8semidirect
186. C2×#459D11semidirect
329. C4×C11#466semidirect
387. C4⋊C8C22⋊D11semidirect
488. C11#25384semidirect
594. C4#10622770semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
C2×#106224472
#130735632
#130735292
#130697972
#130696112
#130694232
#130693752
#130690412
C4×#668962
C2×C11×#4592
#2538411