Finite Group Databasebeta

← #14780864

Subgroups — #14780864

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C23×#4324C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13071200C211yesmaximal, characteristic, complemented
6#13069710C214yesmaximal, complemented
7#13069704C214yesmaximal, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C2×C11×#535C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C11×#535—24no—
14C11×#535—24no—
15C2×C11×#127C2212yes—
16C2×C11×#124C2212yes—
17C2×C11×#121—22no—
18C2×C11×#120—22no—
19C2×C11×#117C2211yescharacteristic
20C2×#67004—24no—
21C2×#67004—24no—
22C2×#67004—24no—
23C22×#4326C2212yescomplemented
24C22×#4324—24no—
25C22×#4324—24no—
26C22×#4324—24no—
27C22×#4324C2214yes—
28C22×#4324C2212yescomplemented
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C23×C11⋊C8C2211yescharacteristic
32#10622846—24no—
33C2×#66899C2212yescomplemented
34#10622828—24no—
35C2×#66896C2214yes—
36C2×#66896C2212yescomplemented
37#10622587—22no—
38#10622556—22no—
39#10622542C2214yescomplemented
40#10622162C2214yescomplemented
41C25×C11—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—24no—
56C22×D4×C11—22no—
57C22×D4×C11D414yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22D414yescomplemented
70C22×Dic22C2312yes—
71C11×#127—24no—
72C11×#127—24no—
73C11×#124—24no—
74C11×#124—24no—
75C11×#121—216no—
76C11×#120—216no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11C2312yes—
83C2×C22⋊Dic11—21no—
84#67004—232no—
85C2×#4326—24no—
86C2×#4326—24no—
87C2×#4326—24no—
88C2×#4324—232no—
89C2×#4324—28no—
90C2×#4324—24no—
91C2×#4324—28no—
92C2×#4324—24no—
93C2×#4324—28no—
94C2×#4324—24no—
95#66979—22no—
96#66979—22no—
97C2×C4⋊Dic11C2312yes—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318D414yescomplemented
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8D414yescomplemented
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2312yes—
107#66899—24no—
108#66896—28no—
109#66896—24no—
110C11⋊#95—28no—
111#23423—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—24no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—84no—
118C24×C11C2×D411yescharacteristic
119C11×#41—28no—
120C11×#41—28no—
121C11×#41—44no—
122C11×#41—44no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—24no—
130C2×D4×C11—216no—
131C2×D4×C11—28no—
132C2×D4×C11—24no—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—88no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D412yes—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C2×Dic22—28no—
172C2×Dic22—28no—
173C2×Dic22—24no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—42no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—42no—
183C2×Dic22C2×D414yes—
184C11×C4⋊C4—24no—
185C11×C22⋊C4—216no—
186C11×C22⋊C4—24no—
187C42×C11—22no—
188C42×C11—22no—
189C22⋊Dic11—42no—
190#4326—216no—
191#4324—232no—
192#4324—216no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4×Dic11—42no—
196#4318—28no—
197C2×C11⋊C8—28no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8C2×D414yes—
203C2×C11⋊C8C2×D414yes—
204C22×#137—111no—
205C23×SD16—111no—
206C2×#535D1111yescharacteristic
207C2×#418—111no—
208C2×#416—111no—
209#2310—111no—
210#2015—114no—
211#2014—114no—
212#1729—111no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—88no—
224C23×C11—88no—
225C23×C11—88no—
226C23×C11#12012yes—
227C23×C11#12112yes—
228C23×C11#12712yes—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—24no—
235D4×C11—22no—
236D4×C11—24no—
237D4×C11—22no—
238D4×C11—48no—
239D4×C11—42no—
240D4×C11—41no—
241D4×C11—42no—
242D4×C11—41no—
243D4×C11—48no—
244D4×C11—816no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—28no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—48no—
251C2×C4×C11#12014yes—
252C2×C4×C11#12014yes—
253C2×C4×C11#12012yes—
254C2×C4×C11#12112yes—
255C2×C4×C11#12114yes—
256C2×C4×C11#12114yes—
257C2×C4×C11#12712yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—48no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270Dic22—24no—
271Dic22—24no—
272Dic22—42no—
273Dic22—42no—
274Dic22—48no—
275C11⋊C8—24no—
276C11⋊C8—24no—
277C22×#41C2×D1111yescharacteristic
278C23×Q8—111no—
279C23×D4C2×D1111yescharacteristic
280C2×#137—224no—
281C2×#137—224no—
282C2×#137—224no—
283C22×Q16—112no—
284C22×SD16—114no—
285C22×SD16—112no—
286C22×SD16—224no—
287C22×SD16—224no—
288C22×SD16—224no—
289C22×M16—111no—
290C23×C8—111no—
291#535—24no—
292#535—24no—
293C2×#127C2×D1112yes—
294C2×#124C2×D1112yes—
295C2×#121—22no—
296C2×#120—22no—
297C2×#117—111no—
298C2×#117C2×D1111yescharacteristic
299#418—224no—
300#416—224no—
301C2×#103—112no—
302C2×#102—112no—
303C2×#102—114no—
304#391—114no—
305#391—222no—
306#381—222no—
307#336—114no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—48no—
315C22×C11—816no—
316C22×C11—82no—
317C22×C11—84no—
318C22×C11—82no—
319C22×C11—84no—
320C22×C11#39214yes—
321C22×C11C2×#12011yescharacteristic
322C22×C11C2×#12111yescharacteristic
323C22×C11C2×#12711yescharacteristic
324C22×C11#57714yes—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11#39214yes—
328C4×C11C2×#12011yescharacteristic
329C4×C11C2×#12011yescharacteristic
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×#12111yescharacteristic
332Dic11—44no—
333Dic11—82no—
334C25—21no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41C22⋊D1114yes—
341C22×Q8—114no—
342C22×Q8—112no—
343C22×Q8—222no—
344C22×Q8—221no—
345C22×Q8—222no—
346C22×Q8—222no—
347C22×Q8—222no—
348C22×Q8—222no—
349C22×Q8C22×D1111yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4C22⋊D1114yes—
359C22×D4C22×D1112yes—
360C22×D4C22×D1111yescharacteristic
361C23×C4—21no—
362C23×C4—221no—
363C23×C4C22×D1111yescharacteristic
364#137—2232no—
365C2×Q16—224no—
366C2×Q16—224no—
367C2×Q16—224no—
368C2×SD16—228no—
369C2×SD16—224no—
370C2×SD16—228no—
371C2×SD16—224no—
372C2×SD16—2232no—
373C2×SD16—228no—
374C2×SD16—224no—
375C2×M16—114no—
376C2×M16—222no—
377C2×M16—222no—
378C22×C8—114no—
379C22×C8—112no—
380C22×C8—112no—
381C22×C8—222no—
382C22×C8—222no—
383#127—24no—
384#127—24no—
385#124—24no—
386#124—24no—
387#121—216no—
388#120—216no—
389#117—22no—
390#117—22no—
391#117—222no—
392#117—222no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4C22⋊D1112yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4C22⋊D1112yes—
398C2×C42—221no—
399C2×C42C22×D1112yes—
400#103—224no—
401#102—224no—
402#102—228no—
403#95—228no—
404C2×C11—24no—
405C2×C11—82no—
406C2×C11—84no—
407C2×C11C2×#39211yescharacteristic
408C2×C11#300912yes—
409C2×C11#304312yes—
410C2×C11#315412yes—
411C24—22no—
412C24—21no—
413C24—24no—
414C24—42no—
415C24—42no—
416C24—84no—
417C24C2×C22⋊D1111yescharacteristic
418#41—28no—
419#41—28no—
420#41—44no—
421#41—44no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—114no—
428C2×Q8—224no—
429C2×Q8—222no—
430C2×Q8—228no—
431C2×Q8—228no—
432C2×Q8—222no—
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8—222no—
436C2×Q8—444no—
437C2×Q8—444no—
438C2×Q8—442no—
439C2×Q8—442no—
440C2×Q8C2×C22⋊D1112yes—
441C2×D4—24no—
442C2×D4—216no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—44no—
459C2×D4—42no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—88no—
463C2×D4C2×C22⋊D1114yes—
464C2×D4C2×C22⋊D1112yes—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—224no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4D4×D1112yes—
475C22×C4D4×D1112yes—
476C22×C4D4×D1112yes—
477C22×C4#434112yes—
478C22×C4C2×C22⋊D1114yes—
479C22×C4C2×C22⋊D1112yes—
480C22×C4C2×C22⋊D1112yes—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483Q16—2216no—
484SD16—2232no—
485SD16—2216no—
486M16—228no—
487C2×C8—114no—
488C2×C8—114no—
489C2×C8—228no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—222no—
493C2×C8—222no—
494C4⋊C4—24no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C22⋊C4—216no—
498C22⋊C4—24no—
499C22⋊C4—442no—
500C42—22no—
501C42—22no—
502C42—442no—
503C11#2342311yescharacteristic, complemented, Sylow
504C23—24no—
505C23—24no—
506C23—22no—
507C23—41no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—48no—
512C23—44no—
513C23—48no—
514C23—88no—
515C23—88no—
516C23—88no—
517C23#6699112yes—
518C23#6699312yes—
519C23#6700612yes—
520C23C22×C22⋊D1111yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525Q8—224no—
526Q8—224no—
527Q8—442no—
528Q8—442no—
529Q8—448no—
530D4—24no—
531D4—22no—
532D4—24no—
533D4—22no—
534D4—48no—
535D4—42no—
536D4—41no—
537D4—42no—
538D4—41no—
539D4—48no—
540D4—816no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—48no—
547C2×C4—224no—
548C2×C4—442no—
549C2×C4—448no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4#6699014yes—
554C2×C4#6699014yes—
555C2×C4#6699112yes—
556C2×C4#6699214yes—
557C2×C4#6699214yes—
558C2×C4#6699312yes—
559C2×C4#6700612yes—
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×#434111yescharacteristic
564C2×C4C22×C22⋊D1111yescharacteristic
565C2×C4C22×C22⋊D1111yescharacteristic
566C8—224no—
567C8—224no—
568C22—24no—
569C22—24no—
570C22—24no—
571C22—44no—
572C22—48no—
573C22—42no—
574C22—44no—
575C22—816no—
576C22—84no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22#1062283614yes—
581C22C2×#6699111yescharacteristic
582C22C2×#6699311yescharacteristic
583C22#1062336714yes—
584C22C2×#6700611yescharacteristic
585C4—44no—
586C4—42no—
587C4—444no—
588C4—882no—
589C4#1062283614yes—
590C4C2×#6699011yescharacteristic
591C4C2×#6699011yescharacteristic
592C4C2×#6699211yescharacteristic
593C4C2×#6699211yescharacteristic
594C2—24no—
595C2—84no—
596C2—82no—
597C2C2×#1062283611yescharacteristic
598C2#1307789312yes—
599C2#1307813312yes—
600C2#1307908812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11#23423
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C23×#4324C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622846C2semidirect
5. #13071200C2semidirect
6. #13069710C2semidirect
7. #13069704C2semidirect
8. #13068313C2semidirect
23. C22×#4326C22semidirect
28. C22×#4324C22semidirect
33. C2×#66899C22semidirect
36. C2×#66896C22semidirect
39. #10622542C22semidirect
40. #10622162C22semidirect
69. C22×Dic22D4semidirect
101. C2×#4318D4semidirect
104. C22×C11⋊C8D4semidirect
503. C11#23423semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C23×#43242
C2×#106228282
C2×#106228462
#130712002
#130697102
#130697042
#130683132
C2×C11×#5352
#2342311