Finite Group Databasebeta

← #14804523

Subgroups — #14804523

Order 2816.

1154 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×#10622784C212yesmaximal, complemented
2C2×#10622447C211yesmaximal, characteristic, complemented
3#13073563C211yesmaximal, characteristic
4#13073534C211yesmaximal, characteristic, complemented
5#13069804C212yesmaximal, complemented
6#13069616C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069041C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#460C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999C2212yes—
16C2×#66993—21no—
17C2×#66991C2212yes—
18C2×#66991C2212yes—
19C22×C8×D11C2212yes—
20C2×C4×D44C2211yescharacteristic
21C11×#460—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26#10622836—22no—
27#10622834—21no—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622784—28no—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66881C2212yes—
33#10622607—22no—
34#10622600C2212yes—
35#10622552—21no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38#10622541—21no—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622447—24no—
41#10622189C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×D44D411yescharacteristic
51C22×C4×D11C2312yes—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—42no—
55C22×C8×C11C2312yes—
56C11×#127—22no—
57C11×#127—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66#66999—24no—
67#66999—42no—
68#66993—44no—
69#66991—24no—
70#66991—24no—
71#66991—42no—
72#66991—42no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4D412yes—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C2×C8×D11—24no—
87C2×C8×D11—24no—
88C2×C8×D11—42no—
89C4×D44—22no—
90C4×D44—22no—
91C11×C4⋊C8D414yescomplemented
92C11×#102—24no—
93#66899—22no—
94#66899D414yescomplemented
95#66896—24no—
96#66896—42no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99(C2×D11)⋊C8—24no—
100#66881—24no—
101C4×C11⋊C8—22no—
102#25387—111nomaximal, Sylow
103C24×C11—22no—
104C23×D11C2×D412yes—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—81no—
122C2×D4×C11—81no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—44no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—82no—
133C2×C22⋊D11—82no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11C2×D412yes—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44SD1614yescomplemented
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C11×SD16—48no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11C2×D414yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—42no—
154C42×C11—42no—
155C42×C11C2×D412yes—
156C42×C11#4112yes—
157C22⋊Dic11—44no—
158C22⋊Dic11—44no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—44no—
161(C2×D11)⋊C4—82no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—81no—
169C4⋊Dic11C2×D412yes—
170C4⋊Dic11#4112yes—
171Dic11⋊C4—44no—
172C4×Dic11—42no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8C2×D412yes—
179C8×D11—48no—
180C2×#465—112no—
181C2×#460D1111yescharacteristic, complemented
182C2×C8×D4—111no—
183#2541—111no—
184#2538—111no—
185#2034—112no—
186#2000—112no—
187#1957—111no—
188#1948—111no—
189#1893—112no—
190C4×#103—111no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C22×D411yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11C2×SD1614yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—84no—
215D4×C11—84no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13512yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C22⋊D11—88no—
235C22⋊D11—88no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248D44—28no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253C8×C11—24no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C22×SD16C2×D1112yes—
257C23×C8—112no—
258C2×#127—221no—
259C2×#127C2×D1111yescharacteristic
260C2×C22⋊Q8—112no—
261C2×#121—112no—
262C2×#121—112no—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×D4—111no—
265#465—228no—
266#460—24no—
267C8×D4—224no—
268C2×#106—112no—
269C2×C4⋊C8C2×D1111yescharacteristic
270C2×#103—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102C2×D1112yes—
275C2×C22⋊C8—112no—
276C2×C4×C8—111no—
277#396—222no—
278#392—222no—
279#390—221no—
280#390—221no—
281#389—221no—
282#384—111no—
283#380—112no—
284C4×C4⋊C4—111no—
285#340—112no—
286#340—111no—
287#340—111no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11C2×#12111yescharacteristic
296C22×C11D4211yescharacteristic
297C22×C11#54611yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—81no—
312C4×C11#46514yescomplemented
313C4×C11#53211yescharacteristic
314C4×C11#54011yescharacteristic
315C4×C11D4211yescharacteristic
316C4×C11#55011yescharacteristic
317Dic11—42no—
318Dic11—42no—
319Dic11—42no—
320Dic11—82no—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—111no—
325C22×D4—222no—
326C22×D4—222no—
327C22×D4C22×D1112yes—
328C23×C4—112no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—42no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8—224no—
335C22×C8—224no—
336C22×C8—442no—
337C22×C8C22×D1112yes—
338#127—22no—
339#127—22no—
340#127—444no—
341C22⋊Q8—224no—
342C22⋊Q8—442no—
343#121—224no—
344#121—224no—
345#121—442no—
346#121—442no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—222no—
350C4×D4—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4—112no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C42—21no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#106—224no—
369C4⋊C8C22⋊D1114yescomplemented
370#103—114no—
371#103—222no—
372#102—24no—
373#102—224no—
374#102—442no—
375C22⋊C8—224no—
376C4×C8—222no—
377#95—222no—
378#95—221no—
379C2×C11—162no—
380C2×C11#242811yescharacteristic
381C2×C11C2×#46511yescharacteristic
382C2×C11#306211yescharacteristic
383C2×C11D4×SD1611yescharacteristic
384C2×C11#328711yescharacteristic
385C2×C11#329511yescharacteristic
386C2×C11#330411yescharacteristic
387D11—44no—
388C24—22no—
389C24—112no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8D4×D1112yes—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—81no—
407C2×D4—81no—
408C2×D4—114no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—444no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—882no—
416C2×D4—882no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—112no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—48no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—448no—
442C2×C8C2×C22⋊D1114yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—112no—
447C4⋊C4—112no—
448C4⋊C4—222no—
449C4⋊C4—221no—
450C4⋊C4—221no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—444no—
454C4⋊C4—442no—
455C4⋊C4—881no—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—882no—
461C42—42no—
462C42—442no—
463C42#434112yes—
464C42C2×C22⋊D1112yes—
465C11#2538711yescharacteristic, complemented, Sylow
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—114no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23C2×D4×D1111yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—41no—
484Q8—41no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—84no—
490D4—84no—
491D4—228no—
492D4—888no—
493D4—888no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4SD16×D1112yes—
519C2×C4#6696912yes—
520C2×C4#6699112yes—
521C2×C4#6699112yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4#6703711yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—24no—
529C8—222no—
530C8—441no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—224no—
539C22—224no—
540C22—224no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22#1062314011yescharacteristic
546C22#1062314311yescharacteristic
547C22C2×SD16×D1111yescharacteristic
548C22C2×#6696911yescharacteristic
549C22#1062330511yescharacteristic
550C22#1062330611yescharacteristic
551C22C2×#6699111yescharacteristic
552C4—22no—
553C4—42no—
554C4—81no—
555C4—442no—
556C4—442no—
557C4—442no—
558C4—882no—
559C4#1062278414yescomplemented
560C4#1062312711yescharacteristic
561C4#1062315011yescharacteristic
562C4D4×C22⋊D1111yescharacteristic
563C4#1062336511yescharacteristic
564C2—162no—
565C2—444no—
566C2#1307220011yescharacteristic
567C2C2×#1062278411yescharacteristic
568C2#1307829011yescharacteristic
569C2#1308030711yescharacteristic
570C2#1308037111yescharacteristic
571C2#1308044311yescharacteristic
572C2#1308055811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radical#13073563C2
hypercenterC2×#460D11
hypocenterC11#25387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10622784C2semidirect
2. C2×#10622447C2semidirect
4. #13073534C2semidirect
5. #13069804C2semidirect
6. #13069616C2semidirect
7. #13069423C2semidirect
8. #13069380C2semidirect
9. #13069041C2semidirect
10. C4×#66899C2semidirect
11. C2×C11×#460C2semidirect
91. C11×C4⋊C8D4semidirect
94. #66899D4semidirect
140. C2×D44SD16semidirect
181. C2×#460D11semidirect
312. C4×C11#465semidirect
369. C4⋊C8C22⋊D11semidirect
465. C11#25387semidirect
559. C4#10622784semidirect

Maximal subgroups

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

subgroupindex
C2×#106227842
C2×#106224472
#130735632
#130735342
#130698042
#130696162
#130694232
#130693802
#130690412
C4×#668992
C2×C11×#4602
#2538711