Finite Group Databasebeta

← #14804251

Subgroups — #14804251

Order 2816.

1150 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×#10622776C212yesmaximal, complemented
2C2×#10622696C211yesmaximal, characteristic, complemented
3#13073563C211yesmaximal, characteristic
4#13071676C211yesmaximal, characteristic, complemented
5#13069929C212yesmaximal, complemented
6#13069702C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13068973C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C11×#492C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×Q8×Dic11C2212yes—
17C22×#4325C2212yes—
18C2×#66993C2212yes—
19C2×#66991—21no—
20C2×#66991—21no—
21C2×C4×D44C2211yescharacteristic
22C11×#492—24no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622843C2212yes—
25C2×#66899C2212yes—
26#10622836—22no—
27#10622834C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622776—28no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×Dic11⋊C8C2212yes—
34#10622696—24no—
35#10622598—21no—
36#10622594—22no—
37C4⋊C4×Dic11—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622188C2212yes—
44C22×Q8×C11C2312yes—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—24no—
55C2×C11×SD16—24no—
56C2×C11×SD16—42no—
57C2×C11×SD16—42no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yescomplemented
62C11×#127—22no—
63C11×#127—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69Q8×Dic11—24no—
70Q8×Dic11—42no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4325—42no—
74#66993—24no—
75#66993—42no—
76#66991—44no—
77#66991—44no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11C2312yes—
88C22×C11⋊C8C2312yes—
89C4×D44—22no—
90C4×D44—22no—
91C4×C8×C11—22no—
92#66899—24no—
93#66896—24no—
94#66896—42no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95D412yes—
99#66885—22no—
100#66885D414yescomplemented
101Dic11⋊C8—24no—
102C4⋊(C11⋊C8)—22no—
103#25366—111nomaximal, Sylow
104C24×C11—22no—
105C23×D11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D414yes—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—81no—
123C2×D4×C11—81no—
124C22×C4×C11—22no—
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—21no—
137C22×Dic11C2×D412yes—
138C22×Dic11C2×D412yes—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44C2×D412yes—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C11×SD16—48no—
149C11×SD16—48no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×D412yes—
155C2×C8×C11#4112yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C42×C11C2×D412yes—
159C42×C11#4112yes—
160C22⋊Dic11—44no—
161C22⋊Dic11—44no—
162#4325—48no—
163(C2×D11)⋊C4—42no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—44no—
171C4⋊Dic11SD1614yescomplemented
172C4⋊Dic11C2×D412yes—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—44no—
176C4×Dic11—42no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×#492D1111yescharacteristic, complemented
181C2×#460—112no—
182C2×#461—111no—
183#2541—111no—
184#2365—111no—
185#2055—112no—
186#2014—112no—
187#1982—111no—
188#1939—111no—
189#1880—112no—
190C4×#102—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—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
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—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11#12112yes—
222C2×C4×C11#12112yes—
223C2×C4×C11C2×SD1612yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C22⋊D11—88no—
232C22⋊D11—88no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11C2×SD1614yes—
248D44—22no—
249D44—22no—
250D44—41no—
251D44—41no—
252C4×D11—84no—
253C8×C11—22no—
254C8×C11—22no—
255C11⋊C8—42no—
256C22×SD16—112no—
257C22×SD16C2×D1112yes—
258C22×SD16C2×D1112yes—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#127—112no—
261C2×#127C2×D1111yescharacteristic
262C2×#121—221no—
263C2×#121—221no—
264C2×C4×Q8—112no—
265C2×C4×D4—111no—
266#492—24no—
267#461—224no—
268#460—228no—
269C2×C4⋊C8—112no—
270C2×C4⋊C8—111no—
271C2×#103—112no—
272C2×#102—111no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102—112no—
276C2×C4×C8C2×D1111yescharacteristic
277#392—222no—
278#391—112no—
279#390—112no—
280#389—221no—
281#387—222no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—111no—
284C4×C4⋊C4—221no—
285#340—111no—
286#340—111no—
287#336—112no—
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#55011yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57711yescharacteristic
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11#46014yescomplemented
312C4×C11#53211yescharacteristic
313C4×C11#54011yescharacteristic
314C4×C11D4211yescharacteristic
315C4×C11#54611yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—81no—
320Dic11—81no—
321C22×Q8C22×D1112yes—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—111no—
325C22×D4—222no—
326C22×D4—222no—
327C22×D4C22×D1112yes—
328C23×C4—221no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—42no—
334C2×SD16—42no—
335C2×SD16—224no—
336C2×SD16—224no—
337C2×SD16—442no—
338C22×C8—112no—
339C22×C8C22×D1111yescharacteristic
340C22×C8C22×D1111yescharacteristic
341C4⋊Q8—22no—
342C4⋊Q8C22⋊D1114yescomplemented
343#127—22no—
344#127—22no—
345#127—224no—
346#127—442no—
347#121—444no—
348#121—444no—
349C4×Q8—224no—
350C4×Q8—442no—
351C4×D4—222no—
352C4×D4—222no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—221no—
364C2×C42—112no—
365C2×C42—222no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—224no—
369C4⋊C8—222no—
370#103—224no—
371#102—114no—
372#102—224no—
373#102—222no—
374#102—442no—
375C4×C8—22no—
376#95—112no—
377#95—222no—
378#95—222no—
379#95—221no—
380C2×C11—162no—
381C2×C11#242811yescharacteristic
382C2×C11C2×#46011yescharacteristic
383C2×C11#304311yescharacteristic
384C2×C11#327211yescharacteristic
385C2×C11D4×SD1611yescharacteristic
386C2×C11#339211yescharacteristic
387C2×C11#339711yescharacteristic
388D11—82no—
389C24—22no—
390C24—221no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8C2×C22⋊D1114yes—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—81no—
408C2×D4—81no—
409C2×D4—112no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—444no—
418C2×D4—444no—
419C2×D4—882no—
420C2×D4—882no—
421C22×C4—22no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—48no—
434SD16—48no—
435SD16—448no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8D4×D1112yes—
444C2×C8#434112yes—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—114no—
448C4⋊C4—112no—
449C4⋊C4—222no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—444no—
456C22⋊C4—444no—
457C22⋊C4—444no—
458C22⋊C4—442no—
459C42—222no—
460C42—222no—
461C42—444no—
462C42—442no—
463C42#434112yes—
464C42C2×C22⋊D1112yes—
465C11#2536611yescharacteristic, complemented, Sylow
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—222no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23C2×D4×D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—84no—
490D4—84no—
491D4—222no—
492D4—222no—
493D4—441no—
494D4—441no—
495D4—888no—
496D4—888no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—114no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—884no—
518C2×C4SD16×D1112yes—
519C2×C4#6696712yes—
520C2×C4#6699212yes—
521C2×C4#6699212yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#6703711yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—22no—
529C8—22no—
530C8—442no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22#1062324811yescharacteristic
546C22#1062324911yescharacteristic
547C22C2×SD16×D1111yescharacteristic
548C22C2×#6696711yescharacteristic
549C22#1062329311yescharacteristic
550C22#1062329311yescharacteristic
551C22C2×#6699211yescharacteristic
552C4—22no—
553C4—44no—
554C4—224no—
555C4—442no—
556C4—442no—
557C4—881no—
558C4—881no—
559C4#1062277614yescomplemented
560C4#1062324711yescharacteristic
561C4#1062325011yescharacteristic
562C4D4×C22⋊D1111yescharacteristic
563C4#1062333711yescharacteristic
564C2—162no—
565C2—882no—
566C2#1307220711yescharacteristic
567C2C2×#1062277611yescharacteristic
568C2#1307813411yescharacteristic
569C2#1308021511yescharacteristic
570C2#1308031111yescharacteristic
571C2#1308159411yescharacteristic
572C2#1308164111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#492C2
socleC23×C11C22×D4
prime radical#13073563C2
hypercenterC2×#492D11
hypocenterC11#25366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. C2×#10622776C2semidirect
2. C2×#10622696C2semidirect
4. #13071676C2semidirect
5. #13069929C2semidirect
6. #13069702C2semidirect
7. #13069544C2semidirect
8. #13069334C2semidirect
9. #13068973C2semidirect
10. C4×#66885C2semidirect
11. C2×C11×#492C2semidirect
61. C11×C4⋊Q8D4semidirect
100. #66885D4semidirect
171. C4⋊Dic11SD16semidirect
180. C2×#492D11semidirect
311. C4×C11#460semidirect
342. C4⋊Q8C22⋊D11semidirect
465. C11#25366semidirect
559. C4#10622776semidirect

Maximal subgroups

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

subgroupindex
C2×#106227762
C2×#106226962
#130735632
#130716762
#130699292
#130697022
#130695442
#130693342
#130689732
C4×#668852
C2×C11×#4922
#2536611