Finite Group Databasebeta

← #14807057

Subgroups — #14807057

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3C2×#10622670C211yesmaximal, characteristic, complemented
4#13069617C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068924C212yesmaximal, complemented
10#13068444C211yesmaximal, characteristic, complemented
11C11×#2540C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#124C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C2×#66983C2212yes—
20C22×C4⋊Dic11C2212yes—
21#10623086—24no—
22#10623086—24no—
23C2×#66950—21no—
24C2×#66939—22no—
25C2×C4×D44C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#399—21no—
28C11×#392—21no—
29C11×#390—22no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2212yes—
33C2×#66896C2211yescharacteristic
34C2×#66896C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622670—24no—
38#10622668—24no—
39C2×#66873C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11D411yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C23×Dic11—22no—
52C2×#4341—28no—
53C2×#4341—48no—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22—21no—
57C11×#124—22no—
58C11×#124—22no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—42no—
61C11×#121—24no—
62C11×#121—42no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4D412yes—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×#4325—22no—
76C2×#4325—42no—
77C2×#4323—22no—
78C2×#4323—42no—
79#66983—24no—
80#66983—24no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66950—28no—
93#66939—216no—
94C4×D44—22no—
95C4×D44D414yescomplemented
96#66922—22no—
97#66922D414yescomplemented
98C11×#95—21no—
99#66899—24no—
100#66899—22no—
101#66896—24no—
102#66896—22no—
103C22⋊(C11⋊C8)—42no—
104C22⋊(C11⋊C8)—42no—
105#66873—24no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#25577—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D412yes—
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—82no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—28no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—44no—
140C22×Dic11—28no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—44no—
144C22×Dic11—44no—
145#4341—432no—
146C2×D44—21no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44C2×D412yes—
150C2×C4×D11—24no—
151C2×C4×D11—44no—
152C2×Dic22—24no—
153C2×Dic22—44no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4#4114yescomplemented
158C11×C22⋊C4—24no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C42×C11—81no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166#4325—44no—
167#4323—44no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×D414yes—
175C4⋊Dic11C2×D412yes—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×#547—111no—
184C2×#489—111no—
185C2×#463—111no—
186#2540D1111yescharacteristic, complemented
187#2000—112no—
188#1999—112no—
189#1987—111no—
190#1955—111no—
191#1874—112no—
192#1872—112no—
193#1762—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11AGL(1,ℤ/8)14yes—
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—41no—
211C22×D11—41no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—42no—
215D4×C11—28no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—42no—
219D4×C11—88no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C22⋊D11—416no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—416no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248D44—22no—
249D44—22no—
250D44—42no—
251C4×D11—48no—
252Dic22—48no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256C22×#41—221no—
257C22×SD16—111no—
258C22×D8—111no—
259#547—224no—
260#547—224no—
261C2×C4⋊Q8—111no—
262C2×#124C2×D1111yescharacteristic
263C2×#123—222no—
264C2×C22⋊Q8—221no—
265C2×C22⋊Q8C2×D1112yes—
266C2×#121—112no—
267C2×#121C2×D1112yes—
268C2×C4×D4—111no—
269C2×C4×D4C2×D1111yescharacteristic
270C22×C4⋊C4—112no—
271#489—224no—
272#463—224no—
273C2×C4⋊C8—111no—
274C2×#103—112no—
275C2×#103—111no—
276C2×#102—112no—
277C2×#102—111no—
278C2×#102—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×#97—111no—
282#399—21no—
283#392—21no—
284#390—22no—
285C4×C4⋊C4C2×D1111yescharacteristic
286#340—112no—
287#340—112no—
288#340—112no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#54612yes—
303C22×C11C2×AGL(1,ℤ/8)12yes—
304C22×C11#57711yescharacteristic
305C22×C11#57811yescharacteristic
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—81no—
316C4×C11#53211yescharacteristic
317C4×C11#53511yescharacteristic
318C4×C11#55012yes—
319Dic11—44no—
320Dic11—42no—
321C2×#41—228no—
322C2×#41—448no—
323C22×Q8—221no—
324C22×Q8C22×D1111yescharacteristic
325C22×D4—22no—
326C22×D4—111no—
327C22×D4—222no—
328C22×D4C22⋊D1111yescharacteristic
329C22×D4C22×D1111yescharacteristic
330C23×C4—222no—
331C23×C4—221no—
332C23×C4C22×D1112yes—
333C2×SD16—222no—
334C2×SD16—442no—
335C2×D8—222no—
336C2×D8—442no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—112no—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342#124—22no—
343#124—22no—
344#123—2216no—
345C22⋊Q8—24no—
346C22⋊Q8—42no—
347C22⋊Q8—228no—
348#121—24no—
349#121—42no—
350#121—224no—
351#121—224no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—114no—
355C4×D4—222no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22×D1112yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4C22⋊D1112yes—
372C2×C42—21no—
373C2×C42C22×D1111yescharacteristic
374C4⋊C8—222no—
375#103—222no—
376#103—224no—
377#102—222no—
378#102—224no—
379#102—224no—
380C22⋊C8—442no—
381C22⋊C8—442no—
382#97—222no—
383#95—21no—
384C2×C11—44no—
385C2×C11—161no—
386C2×C11#243111yescharacteristic
387C2×C11#300311yescharacteristic
388C2×C11#301311yescharacteristic
389C2×C11#330612yes—
390C2×C11#330812yes—
391D11—82no—
392C24—21no—
393C24—221no—
394C24C2×C22⋊D1112yes—
395#41—4432no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—224no—
401C2×Q8—444no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—82no—
411C2×D4—112no—
412C2×D4—228no—
413C2×D4—221no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—444no—
417C2×D4—444no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—228no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—444no—
431C22×C4—444no—
432C22×C4—444no—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C23×D1111yescharacteristic
437SD16—444no—
438D8—444no—
439C2×C8—222no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—222no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C4⋊C4—112no—
450C4⋊C4—114no—
451C4⋊C4—228no—
452C4⋊C4—224no—
453C4⋊C4—221no—
454C4⋊C4—222no—
455C4⋊C4#434114yescomplemented
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C42—81no—
464C42D4×D1112yes—
465C42D4×D1112yes—
466C11#2557711yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—41no—
474C23—42no—
475C23—42no—
476C23—41no—
477C23—41no—
478C23—222no—
479C23—442no—
480C23—442no—
481C23—441no—
482C23—441no—
483C23#6700214yes—
484C23C22×C22⋊D1111yescharacteristic
485Q8—41no—
486Q8—41no—
487Q8—42no—
488Q8—448no—
489D4—28no—
490D4—41no—
491D4—41no—
492D4—42no—
493D4—88no—
494D4—222no—
495D4—222no—
496D4—4416no—
497D4—442no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—448no—
516C2×C4—4416no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4#6699012yes—
521C2×C4#6699012yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434112yes—
525C2×C4#6703712yes—
526C8—441no—
527C8—441no—
528C8—442no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—82no—
537C22—82no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—882no—
545C22—882no—
546C22C2×#6699011yescharacteristic
547C22#1062333712yes—
548C22C2×#6700212yes—
549C22#1062336711yescharacteristic
550C22#1062336911yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—81no—
556C4—442no—
557C4—444no—
558C4#1062324611yescharacteristic
559C4#1062324711yescharacteristic
560C4#1062324912yes—
561C2—44no—
562C2—161no—
563C2—882no—
564C2#1307223211yescharacteristic
565C2#1307784211yescharacteristic
566C2#1307792811yescharacteristic
567C2#1308057712yes—
568C2#1308060712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#25577
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10622668C2semidirect
3. C2×#10622670C2semidirect
4. #13069617C2semidirect
5. #13069612C2semidirect
6. #13069564C2semidirect
7. #13069415C2semidirect
8. #13068934C2semidirect
9. #13068924C2semidirect
10. #13068444C2semidirect
11. C11×#2540C2semidirect
95. C4×D44D4semidirect
97. #66922D4semidirect
157. C11×C4⋊C4#41semidirect
186. #2540D11semidirect
455. C4⋊C4#4341semidirect
466. C11#25577semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106226682
C2×#106226702
#130696172
#130696122
#130695642
#130694152
#130689342
#130689242
#130684442
C11×#25402
#2557711