Finite Group Databasebeta

← #14804501

Subgroups — #14804501

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622784C212yesmaximal, complemented
2C2×#10622447C211yesmaximal, characteristic, complemented
3#13073570C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic
5#13069811C212yesmaximal, complemented
6#13069616C212yesmaximal, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069036C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#461C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999C2212yes—
16C2×#66999C2212yes—
17C2×#66991C2212yes—
18C2×#66983—21no—
19C22×C8×D11C2212yes—
20C2×C4×D44C2211yescharacteristic
21C11×#461—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622825—21no—
29#10622784—28no—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66881C2212yes—
32#10622605—22no—
33#10622601—21no—
34#10622600C2212yes—
35#10622589—21no—
36#10622574—22no—
37#10622548C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622447—24no—
41#10622189C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C22⋊D11—22no—
48C22×D44D411yescharacteristic
49C22×C4×D11C2312yes—
50C2×C11×SD16—24no—
51C2×C11×SD16—24no—
52C2×C11×SD16—42no—
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64#66999—24no—
65#66999—24no—
66#66999—42no—
67#66999—42no—
68#66991—24no—
69#66991—42no—
70#66983—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—22no—
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×#103—24no—
93#66899—24no—
94#66899—42no—
95#66896—22no—
96#66896D414yescomplemented
97C11⋊#95—21no—
98C11⋊#95—22no—
99(C2×D11)⋊C8—24no—
100#66881—24no—
101C4×C11⋊C8—22no—
102#25385—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11C2×D412yes—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—82no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11C2×D412yes—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44SD1614yescomplemented
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C11×SD16—48no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D414yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C22⋊C4—42no—
150C42×C11C2×D412yes—
151C42×C11#4112yes—
152C22⋊Dic11—44no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—44no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—42no—
163C4⋊Dic11—81no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11#4112yes—
166Dic11⋊C4—44no—
167Dic11⋊C4—44no—
168C4×Dic11—42no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8C2×D412yes—
175C8×D11—48no—
176C2×#465—112no—
177C2×#461D1111yescharacteristic, complemented
178C2×C8×D4—111no—
179#2542—111no—
180#2537—111no—
181#2035—112no—
182#2000—112no—
183#1956—111no—
184#1948—111no—
185#1892—112no—
186C4×#102—111no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11C2×SD1614yes—
202Q8×C11—42no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—42no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—84no—
219C2×C4×C11#12112yes—
220C2×C4×C11#12112yes—
221C2×C4×C11C2×SD1612yes—
222C2×C4×C11#13512yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C22⋊D11—88no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242D44—28no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—42no—
246C4×D11—42no—
247C8×C11—24no—
248C11⋊C8—22no—
249C11⋊C8—41no—
250C22×SD16C2×D1112yes—
251C23×C8—112no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4C2×D1111yescharacteristic
259#465—228no—
260#461—24no—
261C8×D4—224no—
262C2×#106—112no—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#103—112no—
265C2×#103—112no—
266C2×#103C2×D1112yes—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#399—222no—
272#394—222no—
273#390—221no—
274#384—111no—
275#384—221no—
276#380—112no—
277#380—221no—
278C4×C4⋊C4—111no—
279#340—112no—
280#340—111no—
281#340—111no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11C2×#12111yescharacteristic
290C22×C11D4211yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11C22×SD1611yescharacteristic
293C22×C11C2×#13511yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57811yescharacteristic
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—42no—
303C4×C11—22no—
304C4×C11—82no—
305C4×C11—81no—
306C4×C11#46514yescomplemented
307C4×C11#53211yescharacteristic
308C4×C11#54011yescharacteristic
309C4×C11D4211yescharacteristic
310C4×C11#55011yescharacteristic
311Dic11—42no—
312Dic11—42no—
313Dic11—42no—
314Dic11—82no—
315C22×Q8C22×D1112yes—
316C22×D4—111no—
317C22×D4—222no—
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—112no—
321C2×SD16—24no—
322C2×SD16—24no—
323C2×SD16—42no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—224no—
327C22×C8—224no—
328C22×C8—442no—
329C22×C8C22×D1112yes—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8C22⋊D1114yescomplemented
364#103—24no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369C22⋊C8—224no—
370C4×C8—222no—
371#95—222no—
372#95—221no—
373C2×C11—82no—
374C2×C11#242811yescharacteristic
375C2×C11C2×#46511yescharacteristic
376C2×C11#306311yescharacteristic
377C2×C11D4×SD1611yescharacteristic
378C2×C11#328311yescharacteristic
379C2×C11#329811yescharacteristic
380C2×C11#330311yescharacteristic
381D11—44no—
382C24—21no—
383C24—112no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—114no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—444no—
399C2×D4—444no—
400C2×D4—882no—
401C2×D4D4×D1112yes—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—112no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—48no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—112no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8—448no—
430C2×C8C2×C22⋊D1114yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4—112no—
436C4⋊C4—112no—
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—444no—
443C4⋊C4—444no—
444C4⋊C4—442no—
445C4⋊C4—881no—
446C22⋊C4—42no—
447C22⋊C4—224no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C42—442no—
453C42#434112yes—
454C42C2×C22⋊D1112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—114no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23C2×D4×D1111yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475D4—22no—
476D4—22no—
477D4—41no—
478D4—41no—
479D4—228no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—84no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4SD16×D1112yes—
507C2×C4#6696912yes—
508C2×C4#6699112yes—
509C2×C4#6699112yes—
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×#434111yescharacteristic
512C2×C4#6703711yescharacteristic
513C2×C4#41×D1111yescharacteristic
514C2×C4#6704211yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—24no—
517C8—222no—
518C8—441no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22#1062314011yescharacteristic
534C22#1062314311yescharacteristic
535C22C2×SD16×D1111yescharacteristic
536C22C2×#6696911yescharacteristic
537C22#1062330911yescharacteristic
538C22#1062331011yescharacteristic
539C22C2×#6699111yescharacteristic
540C4—22no—
541C4—82no—
542C4—81no—
543C4—442no—
544C4—442no—
545C4—442no—
546C4—882no—
547C4#1062278414yescomplemented
548C4#1062312711yescharacteristic
549C4#1062315011yescharacteristic
550C4D4×C22⋊D1111yescharacteristic
551C4#1062336511yescharacteristic
552C2—82no—
553C2—444no—
554C2#1307220011yescharacteristic
555C2C2×#1062278411yescharacteristic
556C2#1307830111yescharacteristic
557C2#1308031511yescharacteristic
558C2#1308033311yescharacteristic
559C2#1308048411yescharacteristic
560C2#1308054711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#461D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622784C2semidirect
2. C2×#10622447C2semidirect
3. #13073570C2semidirect
5. #13069811C2semidirect
6. #13069616C2semidirect
7. #13069419C2semidirect
8. #13069380C2semidirect
9. #13069036C2semidirect
10. C4×#66896C2semidirect
11. C2×C11×#461C2semidirect
91. C11×C4⋊C8D4semidirect
96. #66896D4semidirect
134. C2×D44SD16semidirect
177. C2×#461D11semidirect
306. C4×C11#465semidirect
363. C4⋊C8C22⋊D11semidirect
455. C11#25385semidirect
547. 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
#130735702
#130735292
#130698112
#130696162
#130694192
#130693802
#130690362
C4×#668962
C2×C11×#4612
#2538511