Finite Group Databasebeta

← #14780588

Subgroups — #14780588

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623347C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5C2×#10622723C211yesmaximal, characteristic, complemented
6#13069616C218yesmaximal, complemented
7#13068333C211yesmaximal, characteristic, complemented
8C23×C11×SD16C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16—24no—
15C22×C11×SD16C2214yes—
16C23×C8×C11C2211yescharacteristic
17C2×#67006—22no—
18#10623347—24no—
19#10623347—24no—
20C2×#67000—21no—
21C2×#66999C2214yescomplemented
22C2×#66997—21no—
23#10623336—24no—
24#10623336—24no—
25C2×#66993—21no—
26C2×#66991C2214yes—
27C2×#66989—21no—
28C2×#66982—22no—
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622838—24no—
33C2×#66899C2214yescomplemented
34#10622828—24no—
35C2×#66896C2214yes—
36#10622723—24no—
37C2×(C2×D11)⋊C8C2214yescomplemented
38#10622189C2214yescomplemented
39C25×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11D414yescomplemented
47C22×Q8×C11C2312yes—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D414yes—
55C22×D4×C11C2312yes—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11D412yes—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C22×D44D411yescharacteristic
67C22×C4×D11C2312yes—
68C22×Dic22D411yescharacteristic
69C2×C11×SD16—232no—
70C2×C11×SD16—28no—
71C2×C11×SD16—28no—
72C2×C11×SD16—28no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11D414yescomplemented
76C22×C8×C11C2312yes—
77#67006—216no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—24no—
81#67000—28no—
82#66999—28no—
83#66999—28no—
84#66997—28no—
85#66993—28no—
86#66991—28no—
87#66991—28no—
88#66989—28no—
89#66982—216no—
90C2×(C2×D11)⋊C4—24no—
91#66979—22no—
92#66979—22no—
93#66979D414yes—
94#66979D414yescomplemented
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—24no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318—22no—
103C22×C11⋊C8C2312yes—
104#66899—28no—
105#66896—28no—
106(C2×D11)⋊C8—28no—
107#23388—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—84no—
113C24×C11C2×D411yescharacteristic
114C23×D11C2×D412yes—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11—44no—
126C2×Q8×C11—44no—
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—28no—
129C2×D4×C11—24no—
130C2×D4×C11—28no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—216no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—88no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11C2×D412yes—
161#4339—44no—
162#4339—44no—
163#4339—44no—
164#4339—44no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C11×SD16—232no—
178C2×C8×C11—28no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11C2×D414yes—
182C22⋊Dic11—216no—
183C22⋊Dic11—24no—
184C22⋊Dic11—24no—
185(C2×D11)⋊C4—216no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2×D414yes—
190Dic11⋊C4—216no—
191C4×Dic11—24no—
192C4×Dic11—24no—
193#4318—44no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C23×SD16D1111yescharacteristic, complemented
198C2×#536—111no—
199C2×#535—111no—
200C2×#419—111no—
201C2×#418—111no—
202C2×#408—111no—
203#2000—118no—
204#1735—111no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—88no—
212C23×C11—88no—
213C23×C11—88no—
214C23×C11#12012yes—
215C23×C11#12012yes—
216C23×C11#12112yes—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—28no—
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—48no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—48no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—48no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12012yes—
238C2×C4×C11#12014yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12114yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12714yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—48no—
250C22⋊D11—816no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258D44—44no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263Dic22—44no—
264C8×C11—24no—
265C11⋊C8—42no—
266C22×#41—111no—
267C23×Q8C2×D1111yescharacteristic
268C23×D4C2×D1111yescharacteristic
269C22×SD16—24no—
270C22×SD16—24no—
271C22×SD16—24no—
272C22×SD16C2×D1114yes—
273C22×M16—111no—
274C23×C8C2×D1111yescharacteristic
275#536—224no—
276#536—224no—
277#535—224no—
278#535—224no—
279C2×C4⋊Q8—221no—
280C2×#127—221no—
281C2×#124—221no—
282C2×#124—221no—
283C2×#123—222no—
284C2×C22⋊Q8—114no—
285C2×#121—114no—
286C2×#120—222no—
287C2×#117—111no—
288C2×#117—111no—
289#419—224no—
290#418—224no—
291C2×#103—114no—
292C2×#102—114no—
293#408—224no—
294C2×C22⋊C8—114no—
295#340—114no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—816no—
302C22×C11—84no—
303C22×C11—84no—
304C22×C11#39214yes—
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12111yescharacteristic
308C22×C11#57714yes—
309C2×D11—42no—
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—44no—
313C4×C11—44no—
314C4×C11#39214yes—
315C4×C11C2×#12011yescharacteristic
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12711yescharacteristic
319Dic11—42no—
320Dic11—44no—
321Dic11—44no—
322C25—21no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—111no—
336C22×Q8C22⋊D1114yescomplemented
337C22×Q8C22×D1112yes—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—112no—
345C22×D4—111no—
346C22×D4—224no—
347C22×D4C22⋊D1114yes—
348C22×D4C22×D1112yes—
349C23×C4—21no—
350C23×C4—112no—
351C23×C4C22×D1111yescharacteristic
352C2×SD16—232no—
353C2×SD16—28no—
354C2×SD16—28no—
355C2×SD16—28no—
356C2×M16—222no—
357C2×M16—222no—
358C2×M16—222no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—112no—
362C22×C8C22⋊D1114yescomplemented
363C22×C8C22×D1112yes—
364C4⋊Q8—228no—
365#127—228no—
366#124—228no—
367#124—228no—
368#123—2216no—
369C22⋊Q8—228no—
370C22⋊Q8—228no—
371#121—228no—
372#121—228no—
373#120—2216no—
374#117—114no—
375#117—114no—
376#117—222no—
377#117—222no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C42—221no—
386C2×C42—221no—
387#103—228no—
388#102—228no—
389C22⋊C8—228no—
390C2×C11—24no—
391C2×C11—84no—
392C2×C11C2×#39211yescharacteristic
393C2×C11#300912yes—
394C2×C11#301012yes—
395C2×C11#305712yes—
396D11—82no—
397C24—22no—
398C24—24no—
399C24—42no—
400C24—42no—
401C24—84no—
402C24—112no—
403C24D4×D1111yescharacteristic
404#41—444no—
405#41—444no—
406#41—444no—
407#41—444no—
408C2×Q8—24no—
409C2×Q8—22no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8C2×C22⋊D1114yes—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—224no—
439C2×D4—2216no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—888no—
444C2×D4C2×C22⋊D1114yes—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—112no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1112yes—
460C22×C4D4×D1112yes—
461C22×C4#434112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C23×D1111yescharacteristic
466SD16—232no—
467M16—444no—
468C2×C8—28no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—222no—
474C2×C8C2×C22⋊D1114yes—
475C4⋊C4—114no—
476C4⋊C4—114no—
477C4⋊C4—2216no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C22⋊C4—2216no—
481C22⋊C4—2216no—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C42—224no—
485C42—224no—
486C11#2338811yescharacteristic, complemented, Sylow
487C23—24no—
488C23—24no—
489C23—48no—
490C23—42no—
491C23—42no—
492C23—48no—
493C23—88no—
494C23—88no—
495C23—88no—
496C23—228no—
497C23—222no—
498C23—222no—
499C23—222no—
500C23#6699012yes—
501C23#6699012yes—
502C23#6699112yes—
503C23C2×D4×D1111yescharacteristic
504Q8—24no—
505Q8—24no—
506Q8—42no—
507Q8—42no—
508Q8—48no—
509Q8—444no—
510D4—24no—
511D4—24no—
512D4—42no—
513D4—42no—
514D4—48no—
515D4—448no—
516D4—444no—
517D4—8816no—
518C2×C4—24no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—48no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—444no—
528C2×C4—444no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4#6699012yes—
534C2×C4#6699012yes—
535C2×C4#6699112yes—
536C2×C4#6699214yes—
537C2×C4#6699214yes—
538C2×C4#6699314yes—
539C2×C4#6700614yes—
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—24no—
547C8—442no—
548C22—24no—
549C22—24no—
550C22—24no—
551C22—48no—
552C22—44no—
553C22—816no—
554C22—84no—
555C22—84no—
556C22—444no—
557C22—444no—
558C22—442no—
559C22—444no—
560C22#1062283614yes—
561C22#1062329314yes—
562C22C2×#6699011yescharacteristic
563C22C2×#6699011yescharacteristic
564C22C2×#6699111yescharacteristic
565C4—44no—
566C4—444no—
567C4—444no—
568C4—442no—
569C4#1062283614yes—
570C4C2×#6699211yescharacteristic
571C4C2×#6699211yescharacteristic
572C4C2×#6699311yescharacteristic
573C4C2×#6700611yescharacteristic
574C2—24no—
575C2—84no—
576C2—882no—
577C2C2×#1062283611yescharacteristic
578C2#1307788912yes—
579C2#1307789812yes—
580C2#1307825112yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
hypercenterC23×SD16D11
hypocenterC11#23388
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623347C2semidirect
3. C2×#10622838C2semidirect
4. C2×#10622828C2semidirect
5. C2×#10622723C2semidirect
6. #13069616C2semidirect
7. #13068333C2semidirect
8. C23×C11×SD16C2semidirect
21. C2×#66999C22semidirect
33. C2×#66899C22semidirect
37. C2×(C2×D11)⋊C8C22semidirect
38. #10622189C22semidirect
46. C22×Q8×C11D4semidirect
75. C22×C8×C11D4semidirect
94. #66979D4semidirect
197. C23×SD16D11semidirect
336. C22×Q8C22⋊D11semidirect
362. C22×C8C22⋊D11semidirect
486. C11#23388semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
C2×#106233362
C2×#106228382
C2×#106228282
C2×#106227232
#130696162
#130683332
C23×C11×SD162
#2338811