Finite Group Databasebeta

← #14787808

Subgroups — #14787808

Order 2816.

1400 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic, complemented
3#13073517C211yesmaximal, characteristic, complemented
4#13069802C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068933C212yesmaximal, complemented
9#13068809C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#547C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C11×#547—24no—
14C11×#547—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×#4323C2211yescharacteristic
23C2×#66983C2212yes—
24C2×C4×D44C2211yescharacteristic
25#10622836—21no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622697—24no—
32#10622627—24no—
33#10622606—21no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2212yes—
38#10622569—22no—
39#10622549C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—48no—
47C22×Q8×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11C2312yes—
54C22×C22⋊D11—22no—
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yescomplemented
59C11×#123—216no—
60C11×C22⋊Q8—28no—
61C11×#121—24no—
62C11×#121—24no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11D414yescomplemented
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×#4323—22no—
80C2×#4323—22no—
81C2×#4323—22no—
82#66983—24no—
83#66983—42no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×D44—22no—
92C4×D44—22no—
93#66896—22no—
94#66896—42no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66873—22no—
101#66873—24no—
102#66872—22no—
103#66872—24no—
104C4⋊(C11⋊C8)—22no—
105#66867—22no—
106#24128—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C23×D11—21no—
110C11×#41—432no—
111C2×Q8×C11—24no—
112C2×Q8×C11—44no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—28no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—44no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—44no—
142C2×C22⋊D11—44no—
143C2×C22⋊D11—82no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44#4112yescomplemented
152C2×C4×D11—42no—
153C2×C4×D11—82no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D414yes—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—82no—
167#4323—28no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—42no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8#4112yescomplemented
183C2×#547D1111yescharacteristic, complemented
184C2×#476—111no—
185C2×#442—111no—
186#2535—111no—
187#2034—112no—
188#1999—112no—
189#1993—111no—
190#1955—111no—
191#1874—112no—
192#1853—112no—
193#1804—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11AGL(1,ℤ/8)14yes—
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—42no—
211C22×D11—42no—
212Q8×C11—48no—
213D4×C11—28no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—416no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—48no—
227C2×C4×C11—416no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C22⋊D11—88no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—22no—
250D44—22no—
251D44—41no—
252D44—41no—
253C4×D11—84no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—42no—
257C22×#41—21no—
258C22×D8—111no—
259#547—24no—
260#547—24no—
261C2×C4⋊Q8C2×D1111yescharacteristic
262C2×#123—22no—
263C2×C22⋊Q8—21no—
264C2×#121—112no—
265C2×#121C2×D1112yes—
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×C4×D4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1112yes—
270#476—224no—
271#442—224no—
272C2×#106—111no—
273C2×#106—112no—
274C2×C4⋊C8—111no—
275C2×#102—111no—
276C2×#102—111no—
277C2×#102—112no—
278C2×#102—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×#97—111no—
282#397—221no—
283#392—221no—
284#386—222no—
285#382—111no—
286#380—112no—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)12yes—
306C22×C11#57712yes—
307C2×D11—42no—
308C2×D11—44no—
309C2×D11—82no—
310C2×D11—81no—
311C2×D11—81no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11#52511yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54811yescharacteristic
320C4×C11#55011yescharacteristic
321Dic11—81no—
322Dic11—82no—
323C2×#41—28no—
324C2×#41—48no—
325C22×Q8—21no—
326C22×D4—22no—
327C22×D4—111no—
328C22×D4—222no—
329C22×D4C22⋊D1111yescharacteristic
330C22×D4C22×D1111yescharacteristic
331C23×C4—22no—
332C23×C4—21no—
333C23×C4—221no—
334C23×C4C22×D1112yes—
335C2×D8—222no—
336C2×D8—222no—
337C2×D8—222no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—112no—
341C4⋊Q8—22no—
342C4⋊Q8C22⋊D1114yescomplemented
343#123—216no—
344C22⋊Q8—28no—
345#121—24no—
346#121—24no—
347#121—224no—
348#121—442no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—222no—
353C4×D4—222no—
354C4×D4C22⋊D1114yescomplemented
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4C22⋊D1112yes—
370C2×C42C22×D1111yescharacteristic
371#106—222no—
372#106—224no—
373C4⋊C8—222no—
374#102—222no—
375#102—222no—
376#102—224no—
377#102—442no—
378C22⋊C8—224no—
379C22⋊C8—442no—
380#97—222no—
381#95—222no—
382#95—221no—
383#95—221no—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11#240711yescharacteristic
387C2×C11#300311yescharacteristic
388C2×C11#301011yescharacteristic
389C2×C11#330612yes—
390C2×C11#334512yes—
391D11—82no—
392C24—21no—
393C24—221no—
394C24C2×C22⋊D1112yes—
395#41—432no—
396C2×Q8—24no—
397C2×Q8—44no—
398C2×D4—24no—
399C2×D4—28no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—112no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4—882no—
417C2×D4C2×C22⋊D1112yes—
418C22×C4—28no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—442no—
434C22×C4—882no—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439D8—228no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—222no—
444C2×C8—221no—
445C2×C8—222no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—222no—
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—222no—
455C4⋊C4—222no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4C2×C22⋊D1112yes—
459C4⋊C4C2×C22⋊D1114yes—
460C22⋊C4—28no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—444no—
464C22⋊C4—442no—
465C22⋊C4—882no—
466C42C2×C22⋊D1112yes—
467C42C2×C22⋊D1112yes—
468C11#2412811yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—222no—
481C23—442no—
482C23—441no—
483C23—442no—
484C23—441no—
485C23#6698514yes—
486C23C22×C22⋊D1111yescharacteristic
487Q8—48no—
488D4—28no—
489D4—22no—
490D4—22no—
491D4—416no—
492D4—41no—
493D4—41no—
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498D4—888no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—884no—
521C2×C4#6700612yes—
522C2×C4#6700612yes—
523C2×C4#41×D1111yescharacteristic
524C2×C4#41×D1111yescharacteristic
525C2×C4#6704211yescharacteristic
526C2×C4#6704311yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—222no—
530C8—441no—
531C8—442no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—82no—
543C22—82no—
544C22—442no—
545C22—444no—
546C22—881no—
547C22—881no—
548C22—882no—
549C22C2×#6698512yes—
550C22#1062335511yescharacteristic
551C22#1062336011yescharacteristic
552C22#1062336812yes—
553C22C2×#6700611yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—44no—
559C4—881no—
560C4—882no—
561C4#1062335911yescharacteristic
562C4#1062336211yescharacteristic
563C4#1062336411yescharacteristic
564C4#1062336511yescharacteristic
565C2—44no—
566C2—82no—
567C2—882no—
568C2#1307195511yescharacteristic
569C2#1307784311yescharacteristic
570C2#1307790211yescharacteristic
571C2#1308057112yes—
572C2#1308108612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11#24128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
2. C2×#10622627C2semidirect
3. #13073517C2semidirect
4. #13069802C2semidirect
5. #13069612C2semidirect
6. #13069590C2semidirect
7. #13069415C2semidirect
8. #13068933C2semidirect
9. #13068809C2semidirect
10. #13068626C2semidirect
11. C2×C11×#547C2semidirect
58. C11×C4⋊Q8D4semidirect
66. C4×D4×C11D4semidirect
151. C2×D44#41semidirect
182. C2×C11⋊C8#41semidirect
183. C2×#547D11semidirect
342. C4⋊Q8C22⋊D11semidirect
354. C4×D4C22⋊D11semidirect
468. C11#24128semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106226272
#130735172
#130698022
#130696122
#130695902
#130694152
#130689332
#130688092
#130686262
C2×C11×#5472
#2412811