Finite Group Databasebeta

← #14788526

Subgroups — #14788526

Order 2816.

1214 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×#10622685C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069693C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068877C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C11×#559C211yesmaximal, characteristic, complemented
12C11×#559—24no—
13C11×#559—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124C2212yes—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2212yes—
22C2×#66999—21no—
23C22×#4325C2211yescharacteristic
24C22×#4323C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622685—24no—
32C4×#4325—24no—
33#10622607—22no—
34#10622600—21no—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622552C2212yes—
38#10622548C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C23×C4×C11—22no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C11×#127—22no—
54C11×#127D414yes—
55C11×#124—28no—
56C11×#124—24no—
57C11×#124—24no—
58C11×#123—216no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C4×D4×C11—28no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—44no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—22no—
80C2×#4323—24no—
81C2×#4323—24no—
82C2×#4323—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44—22no—
96#66899—22no—
97#66899—42no—
98#66896—24no—
99#66896—24no—
100#66896—42no—
101C11⋊#95—22no—
102#66873—22no—
103#66872—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24186—111nomaximal, Sylow
107C24×C11—22no—
108C23×D11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—81no—
128C2×D4×C11—81no—
129C2×D4×C11C2×D414yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—28no—
133C22×C4×C11—82no—
134C22×C4×C11—82no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—22no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44#4112yes—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—28no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4325—28no—
165#4323—48no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—82no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175Dic11⋊C4—44no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8#4112yes—
185C2×#559D1111yescharacteristic, complemented
186C2×#459—111no—
187C2×C4×SD16—111no—
188#2538—111no—
189#2042—112no—
190#2012—112no—
191#1984—111no—
192#1957—111no—
193#1879—112no—
194#1864—112no—
195#1803—111no—
196C23×C11—24no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C22×D411yescharacteristic
204C22×D11—22no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211Q8×C11—22no—
212Q8×C11—22no—
213Q8×C11—41no—
214Q8×C11—41no—
215Q8×C11—44no—
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—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—88no—
237C2×C4×C11#12012yes—
238C2×C4×C11#12012yes—
239C2×C4×C11#13512yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253D44—22no—
254D44—22no—
255D44—41no—
256D44—41no—
257C4×D11—84no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C11⋊C8—42no—
261C22×SD16—111no—
262C22×D8—112no—
263#559—24no—
264#559—24no—
265C2×#127C2×D1111yescharacteristic
266C2×#124—21no—
267C2×#124C2×D1112yes—
268C2×#123—22no—
269C2×C22⋊Q8—221no—
270C2×C4×Q8C2×D1111yescharacteristic
271C2×C4×Q8C2×D1111yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4—111no—
274C2×C4×D4C2×D1112yes—
275#459—224no—
276C4×SD16—224no—
277C2×#106—111no—
278C2×C4⋊C8—111no—
279C2×#103—111no—
280C2×#103—112no—
281C2×#102—112no—
282C2×#102—112no—
283C2×#102—111no—
284C2×#102—112no—
285C2×C4×C8—111no—
286#396—222no—
287#390—112no—
288#389—112no—
289#384—111no—
290#380—221no—
291#340—112no—
292#336—112no—
293#336—112no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#54811yescharacteristic
303C22×C11#55011yescharacteristic
304C22×C11C2×#13511yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11#57611yescharacteristic
307C22×C11#57711yescharacteristic
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11#44914yes—
321C4×C11#52511yescharacteristic
322C4×C11#53711yescharacteristic
323C4×C11#54611yescharacteristic
324C4×C11#54711yescharacteristic
325Dic11—82no—
326Dic11—81no—
327C22×Q8C22⋊D1111yescharacteristic
328C22×Q8C22×D1111yescharacteristic
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—111no—
332C22×D4C22×D1112yes—
333C23×C4—22no—
334C23×C4—221no—
335C2×SD16—222no—
336C2×SD16—222no—
337C2×SD16—222no—
338C2×D8—224no—
339C2×D8—224no—
340C2×D8—442no—
341C22×C8—111no—
342C22×C8—112no—
343C22×C8—111no—
344#127—22no—
345#127C22⋊D1114yes—
346#124—28no—
347#124—24no—
348#124—24no—
349#123—216no—
350C22⋊Q8—444no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8C22⋊D1114yes—
355C4×D4—28no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—222no—
359C4×D4—222no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1112yes—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375C2×C42—21no—
376C2×C42C22×D1112yes—
377C2×C42C22×D1111yescharacteristic
378#106—222no—
379C4⋊C8—222no—
380#103—222no—
381#103—442no—
382#102—224no—
383#102—224no—
384#102—222no—
385#102—442no—
386C4×C8—222no—
387#95—222no—
388C2×C11—84no—
389C2×C11#240711yescharacteristic
390C2×C11C2×#44911yescharacteristic
391C2×C11#301211yescharacteristic
392C2×C11#336111yescharacteristic
393C2×C11#337311yescharacteristic
394C2×C11#339411yescharacteristic
395C2×C11#339911yescharacteristic
396D11—82no—
397C24—22no—
398C24—221no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8C2×C22⋊D1112yes—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—81no—
418C2×D4—81no—
419C2×D4—112no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4C2×C22⋊D1114yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—28no—
429C22×C4—82no—
430C22×C4—82no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441SD16—228no—
442D8—448no—
443C2×C8—112no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—222no—
447C2×C8—221no—
448C2×C8—222no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—222no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—444no—
461C4⋊C4—442no—
462C4⋊C4—881no—
463C4⋊C4C2×C22⋊D1112yes—
464C22⋊C4—28no—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—444no—
468C22⋊C4—442no—
469C22⋊C4—882no—
470C42—24no—
471C42—22no—
472C42—22no—
473C42C2×C22⋊D1112yes—
474C42C2×C22⋊D1112yes—
475C11#2418611yescharacteristic, complemented, Sylow
476C23—24no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—222no—
484C23—441no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23C22×C22⋊D1111yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—41no—
494Q8—41no—
495Q8—44no—
496D4—24no—
497D4—24no—
498D4—42no—
499D4—48no—
500D4—42no—
501D4—84no—
502D4—222no—
503D4—222no—
504D4—441no—
505D4—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—88no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—884no—
528C2×C4#6700212yes—
529C2×C4#6700312yes—
530C2×C4#6700612yes—
531C2×C4#6700612yes—
532C2×C4#41×D1111yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4#6704311yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C8—222no—
539C8—442no—
540C8—441no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—82no—
545C22—82no—
546C22—82no—
547C22—82no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22C2×#6700211yescharacteristic
556C22C2×#6700311yescharacteristic
557C22#1062336211yescharacteristic
558C22#1062336511yescharacteristic
559C22#1062336611yescharacteristic
560C22#1062336711yescharacteristic
561C22C2×#6700611yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—882no—
568C4—881no—
569C4#1062285114yes—
570C4#1062335511yescharacteristic
571C4#1062335911yescharacteristic
572C4#1062336011yescharacteristic
573C4#1062336411yescharacteristic
574C2—84no—
575C2—882no—
576C2#1307195511yescharacteristic
577C2C2×#1062285111yescharacteristic
578C2#1307792011yescharacteristic
579C2#1308127211yescharacteristic
580C2#1308140411yescharacteristic
581C2#1308160811yescharacteristic
582C2#1308165411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#559D11
hypocenterC11#24186
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. #13073534C2semidirect
4. #13069852C2semidirect
5. #13069693C2semidirect
6. #13069553C2semidirect
7. #13069423C2semidirect
8. #13068964C2semidirect
9. #13068877C2semidirect
10. #13068621C2semidirect
11. C2×C11×#559C2semidirect
185. C2×#559D11semidirect
475. C11#24186semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×C4×#43252
#130735342
#130698522
#130696932
#130695532
#130694232
#130689642
#130688772
#130686212
C2×C11×#5592
#2418611