Finite Group Databasebeta

← #14781151

Subgroups — #14781151

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2#13077135C211yesmaximal, characteristic
3#13071208C211yesmaximal, characteristic
4#13069775C214yesmaximal, complemented
5#13069770C214yesmaximal, complemented
6C2×#10622192C211yesmaximal, characteristic, complemented
7#13068327C211yesmaximal, characteristic, complemented
8#13068325C211yesmaximal, characteristic, complemented
9C11×#2896C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623050—22no—
18#10623050—22no—
19#10623050—22no—
20#10623050C2214yes—
21C2×#66943—21no—
22C2×#66941—21no—
23C2×#66931—22no—
24C2×#66923—21no—
25C2×#66922—21no—
26C11×#419C2212yes—
27C11×#418C2212yes—
28C11×#417—21no—
29C11×#417—21no—
30C11×#416—22no—
31#10622846—22no—
32#10622845—21no—
33#10622845—21no—
34#10622843C2212yes—
35#10622838C2212yes—
36#10622834C2212yes—
37#10622833—22no—
38#10622828C2212yes—
39#10622825—22no—
40#10622193C2214yes—
41#10622192C2214yes—
42#10622170C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41Q814yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11D412yes—
57C22×Dic22—22no—
58C2×C11×M16—21no—
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C2×C11×M16C2312yes—
62C22×C8×C11—21no—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117D412yes—
66C11×#117C2312yes—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—24no—
74#66979—21no—
75#66979—21no—
76#66979—22no—
77#66979—22no—
78#66979D412yes—
79#66979C2312yes—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D412yes—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2312yes—
94C2×#4318—21no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318C2312yes—
98C22×C11⋊C8—21no—
99#66943—24no—
100#66943—24no—
101#66941—24no—
102#66941—24no—
103#66931—28no—
104#66931—28no—
105#66923—24no—
106#66923—24no—
107#66922—24no—
108#66922—24no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102—22no—
113#66899—22no—
114#66899—22no—
115#66896—22no—
116#66896—22no—
117C11⋊#95—24no—
118#23462—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—24no—
124C11×#41—24no—
125C11×#41—42no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41—42no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11C2×Q812yescomplemented
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—42no—
144C2×D4×C11C2×Q812yescomplemented
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×Q812yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—82no—
168C22×Dic11C2×D414yes—
169C2×Dic22—28no—
170C2×Dic22—84no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—42no—
174C2×C8×C11—22no—
175C2×C8×C11—42no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C42×C11—22no—
183C42×C11—22no—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
186C22⋊Dic11—42no—
187C22⋊Dic11—84no—
188C4⋊Dic11—28no—
189C4⋊Dic11—21no—
190C4⋊Dic11—22no—
191C4⋊Dic11—21no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—42no—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11C2×D412yes—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—22no—
203C4×Dic11—22no—
204#4318—22no—
205#4318—22no—
206#4318—42no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—42no—
209C2×#544—111no—
210#2896—111no—
211#2896D1111yescharacteristic
212#2311—111no—
213#2028—114no—
214#2027—114no—
215C2×#343—111no—
216#1733—111no—
217#1733—111no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11#12011yescharacteristic
226C23×C11#12011yescharacteristic
227C23×C11C22⋊Q812yes—
228C23×C11#12412yes—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—44no—
237D4×C11—44no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C22⋊Q812yes—
252C2×C4×C11C22⋊Q812yes—
253C2×C4×C11C22⋊Q812yes—
254C2×C4×C11C22⋊Q812yes—
255C2×C4×C11C22⋊Q812yes—
256C2×C4×C11#12412yes—
257C2×C4×C11#12412yes—
258C2×C4×C11#12412yes—
259C2×C4×C11#12412yes—
260C2×C4×C11#12412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C2×Dic11—44no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—82no—
278Dic22—88no—
279C8×C11—42no—
280C11⋊C8—42no—
281C22×#41C2×D1111yescharacteristic
282C22×M16—111no—
283C22×M16C2×D1111yescharacteristic
284#544—114no—
285#544—222no—
286#544—222no—
287#544—222no—
288C2×C4⋊Q8—221no—
289C2×C4⋊Q8—221no—
290C2×#125—221no—
291C2×#125—221no—
292C2×C22⋊Q8—222no—
293C2×#117—111no—
294C2×#117—111no—
295C2×#117C2×D1111yescharacteristic
296C22×C4⋊C4—111no—
297#419—112no—
298#419C2×D1112yes—
299#418—112no—
300#418C2×D1112yes—
301#417—21no—
302#417—21no—
303#417—221no—
304#417—221no—
305#416—22no—
306#416—222no—
307#391—112no—
308#390—112no—
309#386—222no—
310#380—222no—
311#343—114no—
312#339—114no—
313#339—114no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#39312yes—
328C22×C11#39312yes—
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11C2×#12411yescharacteristic
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11#39312yes—
336C4×C11#39312yes—
337C4×C11C2×C22⋊Q811yescharacteristic
338C4×C11C2×C22⋊Q811yescharacteristic
339C4×C11C2×#12411yescharacteristic
340C4×C11C2×#12411yescharacteristic
341Dic11—42no—
342Dic11—44no—
343Dic11—42no—
344Dic11—82no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—22no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41Dic2214yescomplemented
353C22×Q8—222no—
354C22×Q8C22×D1111yescharacteristic
355C22×D4—21no—
356C22×D4C22×D1111yescharacteristic
357C23×C4—21no—
358C23×C4—112no—
359C23×C4C22×D1111yescharacteristic
360C2×M16—21no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—112no—
364C2×M16—221no—
365C2×M16—222no—
366C2×M16—222no—
367C2×M16C22×D1112yes—
368C22×C8—21no—
369C22×C8—221no—
370C4⋊Q8—224no—
371C4⋊Q8—224no—
372C4⋊Q8—224no—
373C4⋊Q8—224no—
374#125—224no—
375#125—224no—
376#125—224no—
377#125—224no—
378C22⋊Q8—228no—
379C22⋊Q8—228no—
380#117—21no—
381#117—21no—
382#117—112no—
383#117—112no—
384#117—221no—
385#117—221no—
386#117—222no—
387#117—222no—
388#117C22⋊D1112yes—
389#117C22×D1112yes—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1111yescharacteristic
403C2×C4⋊C4C22⋊D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—224no—
408C2×C42—21no—
409C2×C42—112no—
410C2×C42—221no—
411#103—22no—
412#103—22no—
413#103—222no—
414#103—222no—
415#102—22no—
416#102—22no—
417#102—222no—
418#102—222no—
419#95—224no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—22no—
423C2×C11—22no—
424C2×C11—82no—
425C2×C11C2×#39311yescharacteristic
426C2×C11#301911yescharacteristic
427C2×C11#302011yescharacteristic
428C24—21no—
429C24D4×D1111yescharacteristic
430#41—24no—
431#41—24no—
432#41—24no—
433#41—24no—
434#41—42no—
435#41—42no—
436#41—42no—
437#41—42no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—228no—
444C2×Q8—884no—
445C2×Q8C2×Dic2212yescomplemented
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×Dic2212yescomplemented
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—42no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—114no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—882no—
470C22×C4C2×Dic2212yes—
471C22×C4#433912yes—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4#434112yes—
476C22×C4#434112yes—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480M16—22no—
481M16—22no—
482M16—42no—
483M16—222no—
484M16—222no—
485M16—442no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—222no—
489C2×C8—442no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—112no—
493C4⋊C4—112no—
494C4⋊C4—228no—
495C4⋊C4—228no—
496C4⋊C4—228no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—442no—
504C4⋊C4C2×C22⋊D1112yes—
505C4⋊C4C2×C22⋊D1112yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—442no—
511C22⋊C4—884no—
512C42—22no—
513C42—22no—
514C42—222no—
515C42—222no—
516C42—222no—
517C42—222no—
518C11#2346211yescharacteristic, complemented, Sylow
519C23—22no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23—41no—
525C23—41no—
526C23#6693112yes—
527C23#6693812yes—
528C23#6699011yescharacteristic
529C23#6699011yescharacteristic
530C23C2×D4×D1111yescharacteristic
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—888no—
536D4—22no—
537D4—22no—
538D4—44no—
539D4—44no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—224no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—444no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—882no—
562C2×C4#6693112yes—
563C2×C4#6693112yes—
564C2×C4#6693112yes—
565C2×C4#6693812yes—
566C2×C4#6693812yes—
567C2×C4#6693812yes—
568C2×C4#6697712yes—
569C2×C4#6697712yes—
570C2×C4#6698912yes—
571C2×C4#6698912yes—
572C2×C4#6699011yescharacteristic
573C2×C4#6699011yescharacteristic
574C2×C4C22×Dic2211yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—42no—
581C8—442no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—42no—
592C22—82no—
593C22—81no—
594C22—81no—
595C22#1062256012yes—
596C22#1062256012yes—
597C22C2×#6693111yescharacteristic
598C22C2×#6693811yescharacteristic
599C22C2×#6699011yescharacteristic
600C4—42no—
601C4—42no—
602C4—42no—
603C4—444no—
604C4—442no—
605C4—442no—
606C4—882no—
607C4#1062256012yes—
608C4#1062256012yes—
609C4C2×#6693111yescharacteristic
610C4C2×#6693811yescharacteristic
611C4C2×#6697711yescharacteristic
612C4C2×#6698911yescharacteristic
613C2—21no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—82no—
618C2C2×#1062256011yescharacteristic
619C2#1307797111yescharacteristic
620C2#1307797811yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2896C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
hypercenter#2896D11
hypocenterC11#23462
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
4. #13069775C2semidirect
5. #13069770C2semidirect
6. C2×#10622192C2semidirect
7. #13068327C2semidirect
8. #13068325C2semidirect
50. C2×C11×#41Q8semidirect
134. C2×Q8×C11C2×Q8semidirect
144. C2×D4×C11C2×Q8semidirect
352. C2×#41Dic22semidirect
445. C2×Q8C2×Dic22semidirect
455. C2×D4C2×Dic22semidirect
518. C11#23462semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
#130771352
#130712082
#130697752
#130697702
C2×#106221922
#130683272
#130683252
C11×#28962
#2346211