Finite Group Databasebeta

← #14810426

Subgroups — #14810426

Order 2816.

1320 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×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3#13076912C211yesmaximal, characteristic
4#13069755C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069589C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal
9#13068920C212yesmaximal, complemented
10#13068379C211yesmaximal, characteristic, complemented
11C2×C11×#489C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×#66999C2211yescharacteristic
16C2×#66997—21no—
17C2×#66991C2211yescharacteristic
18D11×C4⋊Q8—24no—
19D11×C4⋊Q8—24no—
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66941—21no—
23C2×#66941C2212yes—
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#489—24no—
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#97C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2212yes—
32#10622834C2211yescharacteristic
33C2×#66896C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35#10622668—24no—
36#10622569—21no—
37#10622569—21no—
38#10622557—21no—
39#10622557—21no—
40#10622549C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C2×Q8×D11—28no—
52C2×Q8×D11—44no—
53C2×Q8×D11—44no—
54C22×C4×D11—22no—
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yescomplemented
63C11×#124—22no—
64C11×#124—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73#66999—24no—
74#66997—28no—
75#66991—24no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C4⋊C4×D11—28no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—24no—
91#66941—28no—
92#66941—24no—
93#66941—24no—
94C42×D11—22no—
95C42×D11—22no—
96#66922—22no—
97#66922D414yescomplemented
98C11×#103—24no—
99C11×#102—24no—
100C11×#97—22no—
101#66899—24no—
102#66896—24no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107(C2×D11)⋊C8—24no—
108#66867—22no—
109#25908—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—24no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—42no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—42no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137Q8×D11—432no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—28no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—22no—
148C2×C4×D11—44no—
149C2×C4×D11—44no—
150C2×C4×D11#4114yes—
151C2×Dic22—28no—
152C2×Dic22—24no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—44no—
156C2×Dic22—44no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D414yes—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—42no—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—42no—
170(C2×D11)⋊C4—42no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C2×D414yes—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—42no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C22×C4⋊Q8—111no—
187C2×#489—111no—
188C2×#489D1111yescharacteristic, complemented
189#2850—111no—
190#2024—112no—
191#2023—112no—
192#1993—111no—
193#1993—111no—
194#1874—112no—
195#1872—112no—
196#1749—111no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C22×D411yescharacteristic
205C22×D11—21no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11#12412yes—
210C22×D11AGL(1,ℤ/8)12yes—
211C22×D11#13712yes—
212Q8×C11—48no—
213Q8×C11—42no—
214Q8×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4112yes—
232C2×C4×C112−1+412yes—
233C22⋊D11—84no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—24no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11#12412yes—
250C2×Dic11AGL(1,ℤ/8)12yes—
251C2×Dic11#13712yes—
252C4×D11—28no—
253C4×D11—28no—
254C4×D11—24no—
255C4×D11—24no—
256C4×D11—416no—
257Dic22—416no—
258Dic22—48no—
259C8×C11—42no—
260C11⋊C8—42no—
261C23×Q8—221no—
262C2×C4⋊Q8—112no—
263C2×C4⋊Q8—111no—
264C2×C4⋊Q8—221no—
265C2×C4⋊Q8—221no—
266C2×C4⋊Q8—224no—
267C2×C4⋊Q8—224no—
268C2×C4⋊Q8C2×D1111yescharacteristic
269C2×#124C2×D1111yescharacteristic
270C2×C22⋊Q8—111no—
271C2×#121—111no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—221no—
274C22×C42—111no—
275#489—24no—
276#489—224no—
277C2×#103—112no—
278C2×#103C2×D1112yes—
279C2×#102—112no—
280C2×#102C2×D1112yes—
281C2×C22⋊C8—112no—
282C2×#97—111no—
283C2×#97C2×D1111yescharacteristic
284#391—111no—
285#390—111no—
286#388—221no—
287#388—221no—
288#386—221no—
289#386—221no—
290#382—111no—
291#340—112no—
292#340—112no—
293#340—112no—
294#340—112no—
295#336—112no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11C2×#12011yescharacteristic
304C22×C11C2×#12411yescharacteristic
305C22×C11#53611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11#48914yescomplemented
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—44no—
320C4×C11—81no—
321C4×C11#54812yes—
322C4×C11#54812yes—
323Dic11—22no—
324Dic11—22no—
325Dic11—22no—
326Dic11—44no—
327Dic11—81no—
328Dic11—81no—
329C22×Q8—21no—
330C22×Q8—222no—
331C22×Q8—228no—
332C22×Q8—221no—
333C22×Q8—444no—
334C22×Q8—444no—
335C22×Q8C22×D1111yescharacteristic
336C22×D4—221no—
337C22×D4C22×D1111yescharacteristic
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—222no—
342C22×C8—112no—
343C22×C8C22×D1112yes—
344C4⋊Q8—22no—
345C4⋊Q8—114no—
346C4⋊Q8—224no—
347C4⋊Q8—228no—
348C4⋊Q8—228no—
349C4⋊Q8—224no—
350C4⋊Q8—222no—
351C4⋊Q8C22⋊D1114yescomplemented
352#124—22no—
353#124—22no—
354C22⋊Q8—224no—
355#121—224no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—222no—
378C2×C42—222no—
379C2×C42C22×D1111yescharacteristic
380#103—24no—
381#103—224no—
382#102—24no—
383#102—224no—
384C22⋊C8—224no—
385#97—22no—
386#97—222no—
387#95—221no—
388#95—221no—
389#95—221no—
390#95—221no—
391C2×C11—161no—
392C2×C11#243611yescharacteristic
393C2×C11#300311yescharacteristic
394C2×C11#300411yescharacteristic
395C2×C11C2×#48911yescharacteristic
396C2×C11#314111yescharacteristic
397C2×C11#323811yescharacteristic
398C2×C11#323911yescharacteristic
399D11—24no—
400C24—21no—
401C24—111no—
402C2×Q8—24no—
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8—228no—
410C2×Q8—224no—
411C2×Q8—442no—
412C2×Q8—442no—
413C2×Q8—444no—
414C2×Q8—444no—
415C2×Q8—4432no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—442no—
421C2×D4—442no—
422C2×D4—442no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—114no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—228no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—222no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—114no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—224no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—442no—
463C4⋊C4C2×C22⋊D1114yes—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C22⋊C4—442no—
469C22⋊C4—442no—
470C42—222no—
471C42—222no—
472C42—221no—
473C42—221no—
474C42D4×D1112yes—
475C42C2×C22⋊D1112yes—
476C11#2590811yescharacteristic, complemented, Sylow
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—112no—
485C23—112no—
486C23—112no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23C2×D4×D1111yescharacteristic
492Q8—48no—
493Q8—42no—
494Q8—42no—
495Q8—448no—
496Q8—4416no—
497D4—42no—
498D4—42no—
499D4—884no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—112no—
511C2×C4—112no—
512C2×C4—112no—
513C2×C4—228no—
514C2×C4—228no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—4416no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4#6699012yes—
534C2×C4#6699012yes—
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#41×D1112yes—
537C2×C4#6704312yes—
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—42no—
540C8—442no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—114no—
549C22—222no—
550C22—222no—
551C22—222no—
552C22—222no—
553C22—222no—
554C22—222no—
555C22D11×#12411yescharacteristic
556C22#1062320611yescharacteristic
557C22D11×AGL(1,ℤ/8)11yescharacteristic
558C22D11×AGL(1,ℤ/8)11yescharacteristic
559C22D11×#13711yescharacteristic
560C22D11×#13711yescharacteristic
561C22C2×#6699011yescharacteristic
562C4—22no—
563C4—22no—
564C4—44no—
565C4—81no—
566C4—222no—
567C4—222no—
568C4—222no—
569C4—444no—
570C4—881no—
571C4—881no—
572C4#1062320812yes—
573C4#1062336212yes—
574C2—161no—
575C2—224no—
576C2#1307227111yescharacteristic
577C2#1307784111yescharacteristic
578C2#1307784811yescharacteristic
579C2D11×#48911yescharacteristic
580C2#1307900811yescharacteristic
581C2#1307983311yescharacteristic
582C2#1307984211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#489D11
hypocenterC11#25908
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622668C2semidirect
4. #13069755C2semidirect
5. #13069750C2semidirect
6. #13069590C2semidirect
7. #13069589C2semidirect
9. #13068920C2semidirect
10. #13068379C2semidirect
11. C2×C11×#489C2semidirect
62. C11×C4⋊Q8D4semidirect
97. #66922D4semidirect
188. C2×#489D11semidirect
316. C2×D11#489semidirect
351. C4⋊Q8C22⋊D11semidirect
476. C11#25908semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106226682
#130769122
#130697552
#130697502
#130695902
#130695892
#130689302
#130689202
#130683792
C2×C11×#4892
#2590811