Finite Group Databasebeta

← #14682919

Subgroups — #14682919

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2#13066864C212yesmaximal, complemented
3#13066864C212yesmaximal, complemented
4#13066856C212yesmaximal
5#13066854C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066848C211yesmaximal, characteristic, complemented
8#13066842C212yesmaximal, complemented
9C11×#1436C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622601C418yescomplemented
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×D44—24no—
42C22×D44—42no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C42×C11—42no—
50C2×C42×C11—41no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—42no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×(C2×D11)⋊C4C2×C418yes—
69C2×C4×Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—41no—
72C2×C4×Dic11C2×C414yes—
73C11×#95—24no—
74C11×#95—42no—
75C11×#95—41no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95—41no—
83#14503—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11C22×C414yes—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4114yes—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11C22×C414yes—
149C22×Dic11#4114yes—
150C2×D44—28no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—48no—
154C2×D44—48no—
155C11×C4⋊C4—44no—
156C42×C11—44no—
157(C2×D11)⋊C4—48no—
158(C2×D11)⋊C4—48no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163C4×Dic11—44no—
164C4×Dic11—44no—
165C2×#390—111no—
166#1440—112no—
167#1440—112no—
168#1438—112no—
169#1437—112no—
170#1437—112no—
171#1436—111no—
172#1436D1111yescharacteristic, complemented
173#1434—112no—
174C23×C11C23×C411yescharacteristic
175C23×C11C2×#4112yes—
176C23×C11C2×#4112yes—
177C23×C11C2×#4112yes—
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)12yes—
181C23×C11H(5,𝔽2)12yes—
182C23×C11H(5,𝔽2)12yes—
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11#11714yes—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268D44—416no—
269C23×D4—111no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C42—111no—
278C22×C42—111no—
279C22×C42C2×D1111yescharacteristic
280#390—118no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—111no—
288C2×#95C2×D1112yes—
289C2×#95C2×D1112yes—
290C2×#95C2×D1111yescharacteristic
291C22×C11C2×#11711yescharacteristic
292C22×C11C4×#4112yes—
293C22×C11#51811yescharacteristic
294C22×C11#51811yescharacteristic
295C22×C11#51812yes—
296C22×C11#53812yes—
297C22×C11#53812yes—
298C22×C11#53812yes—
299C22×C11#53812yes—
300C22×C11#54012yes—
301C22×C11#54012yes—
302C22×C11#55112yes—
303C22×C11#55312yes—
304C22×C11#55312yes—
305C22×C11#55511yescharacteristic
306C22×C11#55511yescharacteristic
307C22×C11#55912yes—
308C22×C11#55912yes—
309C22×C11#56011yescharacteristic
310C22×C11#56012yes—
311C22×C11#56011yescharacteristic
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C4×C11—24no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—44no—
331C4×C11—82no—
332Dic11—44no—
333Dic11—44no—
334Dic11—82no—
335C25—112no—
336C22×D4—114no—
337C22×D4—224no—
338C22×D4—441no—
339C22×D4—441no—
340C22×D4—442no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4C4×D1114yes—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—224no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—442no—
359C2×C22⋊C4—442no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4—442no—
362C2×C22⋊C4—442no—
363C2×C22⋊C4—442no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C42—42no—
371C2×C42—41no—
372C2×C42—114no—
373C2×C42—442no—
374C2×C42—441no—
375C2×C42—442no—
376#95—24no—
377#95—42no—
378#95—41no—
379#95—224no—
380#95—224no—
381#95—224no—
382#95—441no—
383#95—442no—
384#95—442no—
385#95—442no—
386C2×C11#231211yescharacteristic
387C2×C11#233312yes—
388C2×C11#235712yes—
389C2×C11#237211yescharacteristic
390C2×C11#238011yescharacteristic
391C2×C11#279712yes—
392C2×C11#279712yes—
393C2×C11#280312yes—
394C2×C11#280312yes—
395D11—84no—
396C24—114no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24—222no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24—222no—
411C24C23×D1111yescharacteristic
412C2×D4—228no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—448no—
416C2×D4—448no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
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×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4C2×C4×D1112yes—
463C22×C4C2×C4×D1112yes—
464C22×C4C2×C4×D1112yes—
465C22×C4#433914yes—
466C22×C4#434314yes—
467C4⋊C4—44no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C42—44no—
475C42—444no—
476C42—444no—
477C11#1450311yescharacteristic, complemented, Sylow
478C23—224no—
479C23—224no—
480C23—224no—
481C23—224no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23C22×C4×D1111yescharacteristic
514C23C2×#433912yes—
515C23#6703711yescharacteristic
516C23#6703711yescharacteristic
517C23#6703712yes—
518C23C2×#434312yes—
519C23#41×D1112yes—
520C23#6704212yes—
521C23#6704212yes—
522D4—4416no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4#6692514yes—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—444no—
580C22—882no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22—882no—
585C22—882no—
586C22—882no—
587C22—882no—
588C22C2×#6692511yescharacteristic
589C22#1062301711yescharacteristic
590C22#1062304512yes—
591C22#1062305211yescharacteristic
592C22#1062306112yes—
593C22#1062307612yes—
594C22#1062309012yes—
595C22#1062309112yes—
596C22#1062309112yes—
597C22C4×#434312yes—
598C22#1062311612yes—
599C22#1062312611yescharacteristic
600C22#1062315112yes—
601C22#1062316812yes—
602C22#1062317512yes—
603C22#1062319412yes—
604C22#1062319711yescharacteristic
605C22#1062320111yescharacteristic
606C22#1062322912yes—
607C22#1062323512yes—
608C22#1062326511yescharacteristic
609C4—24no—
610C4—42no—
611C4—42no—
612C4—44no—
613C4—82no—
614C4—444no—
615C4—444no—
616C4—882no—
617C2—884no—
618C2#1307121111yescharacteristic
619C2#1307138012yes—
620C2#1307158512yes—
621C2#1307172711yescharacteristic
622C2#1307179111yescharacteristic
623C2#1307647412yes—
624C2#1307647712yes—
625C2#1307654312yes—
626C2#1307654712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. #13066864C2semidirect
3. #13066864C2semidirect
5. #13066854C2semidirect
6. #13066852C2semidirect
7. #13066848C2semidirect
8. #13066842C2semidirect
9. C11×#1436C2semidirect
31. #10622601C4semidirect
172. #1436D11semidirect
477. C11#14503semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
#130668642
#130668562
#130668542
#130668522
#130668482
#130668422
C11×#14362
#1450311