Finite Group Databasebeta

← #14675662

Subgroups — #14675662

Order 2816.

2438 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3C2×#10622277C211yesmaximal, characteristic
4C2×#10622277C212yesmaximal
5#13066868C212yesmaximal, complemented
6#13066867C212yesmaximal, complemented
7#13066851C211yesmaximal, characteristic, complemented
8#13066849C211yesmaximal, characteristic, complemented
9#13066848C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal
11C11×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×C4⋊C4×D11—24no—
25C2×C4⋊C4×D11—24no—
26C2×C4⋊C4×D11C418yescomplemented
27C2×#66925—24no—
28C2×#66925—28no—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622277—24no—
41#10622277—28no—
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C22×C4×D11—24no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—24no—
57C22×C4×D11—24no—
58C22×C4×D11—24no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11C2×C414yes—
64C22×C4×D11C2×C414yes—
65C22×C4×D11C2×C414yes—
66C22×C4×D11D414yes—
67C22×C4×D11D414yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4C2×C414yes—
71C2×C42×C11—24no—
72C2×C42×C11—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4D418yes—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11C2×C414yes—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4C2×C414yes—
90C2×Dic11⋊C4C2×C414yes—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—24no—
93C4⋊C4×D11—232no—
94#66925—232no—
95C11×#95—24no—
96C11×#95—22no—
97C11×#95—24no—
98C11⋊#95—24no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106#13870—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11C22×C412yes—
113C23×D11C2×D412yes—
114C23×D11C2×D412yes—
115C23×D11C2×D414yes—
116C23×D11#4114yes—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11#4114yes—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11C22×C412yes—
169C22×Dic11C22×C412yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C2×D414yes—
172C22×Dic11C2×D412yes—
173C22×Dic11C2×D412yes—
174C22×Dic11#4114yes—
175C2×C4×D11—216no—
176C2×C4×D11—216no—
177C2×C4×D11—28no—
178C2×C4×D11—28no—
179C2×C4×D11—28no—
180C2×C4×D11—216no—
181C2×C4×D11—216no—
182C2×C4×D11—28no—
183C2×C4×D11—216no—
184C2×C4×D11—28no—
185C2×C4×D11—28no—
186C2×C4×D11—44no—
187C2×C4×D11—48no—
188C2×C4×D11—44no—
189C2×C4×D11C22⋊C4116yes—
190C11×C4⋊C4—28no—
191C42×C11—28no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—48no—
194C4⋊Dic11—28no—
195Dic11⋊C4—216no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198C4×Dic11—28no—
199C22×#117—111no—
200C23×C4⋊C4—111no—
201C2×#381—112no—
202C2×#381—111no—
203#1441—112no—
204#1441—112no—
205#1436—111no—
206#1436—111no—
207#1436—111no—
208#1436D1111yescharacteristic, complemented
209C22⋊#95—112no—
210C23×C11C23×C411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D412yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4112yes—
216C23×C11C2×#4112yes—
217C23×C112−1+412yes—
218C23×C112−1+412yes—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11C2×C22⋊C414yes—
236C22×D11C4×D418yes—
237C22×D11#12014yes—
238C22×D11#12118yes—
239C22×D11#12314yes—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11C2×C22⋊C414yes—
268C2×C4×C11#11714yescomplemented
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—41no—
283C2×Dic11—42no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11C2×C22⋊C414yes—
297C2×Dic11#11714yescomplemented
298C4×D11—232no—
299C4×D11—232no—
300C4×D11—416no—
301C24×C4—111no—
302C24×C4—111no—
303C24×C4—111no—
304C2×#117—228no—
305C2×#117—224no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—118no—
310C22×C4⋊C4—112no—
311C22×C4⋊C4—224no—
312C22×C4⋊C4—224no—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C42—111no—
317C22×C42C2×D1111yescharacteristic
318#381—228no—
319#381—224no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—111no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95C2×D1112yes—
329C2×#95C2×D1111yescharacteristic
330C2×#95C2×D1112yes—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11C2×#11711yescharacteristic
333C22×C11C2×#11711yescharacteristic
334C22×C11C2×C4×D412yes—
335C22×C11#51912yes—
336C22×C11C2×#12011yescharacteristic
337C22×C11C2×#12112yes—
338C22×C11C2×#12311yescharacteristic
339C22×C11#52512yes—
340C22×C11#52512yes—
341C22×C11#53611yescharacteristic
342C22×C11#53612yes—
343C22×C11#53611yescharacteristic
344C22×C11#54712yes—
345C22×C11#54712yes—
346C22×C11#54712yes—
347C22×C11#54712yes—
348C22×C11#55212yes—
349C22×C11#55212yes—
350C22×C11#55212yes—
351C22×C11#55212yes—
352C2×D11—24no—
353C2×D11—28no—
354C2×D11—28no—
355C2×D11—28no—
356C2×D11—28no—
357C2×D11—28no—
358C2×D11—28no—
359C2×D11—24no—
360C2×D11#38618yes—
361C4×C11—24no—
362C4×C11—24no—
363C4×C11—44no—
364C4×C11—42no—
365C4×C11—82no—
366Dic11—24no—
367Dic11—24no—
368Dic11—44no—
369Dic11—42no—
370Dic11—82no—
371C25—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—114no—
375C23×C4—114no—
376C23×C4—114no—
377C23×C4—112no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—114no—
381C23×C4—112no—
382C23×C4—224no—
383C23×C4—222no—
384C23×C4—222no—
385C23×C4—224no—
386C23×C4—224no—
387C23×C4—222no—
388C23×C4—222no—
389C23×C4—224no—
390C23×C4—224no—
391C23×C4—224no—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1112yes—
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397#117—2232no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—2232no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4C4×D1114yes—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—224no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—224no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—224no—
423C2×C42—222no—
424#95—24no—
425#95—24no—
426#95—22no—
427#95—224no—
428#95—224no—
429#95—224no—
430#95—224no—
431#95—224no—
432#95—224no—
433#95—224no—
434#95—222no—
435C2×C11#228011yescharacteristic
436C2×C11C2×#38611yescharacteristic
437C2×C11#231011yescharacteristic
438C2×C11#234412yes—
439C2×C11#234412yes—
440C2×C11#240612yes—
441C2×C11#241312yes—
442C2×C11#241312yes—
443C2×C11#248412yes—
444D11—28no—
445C24—112no—
446C24—114no—
447C24—112no—
448C24—112no—
449C24—114no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24C23×D1111yescharacteristic
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—1116no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—228no—
486C22×C4—228no—
487C22×C4—228no—
488C22×C4—2216no—
489C22×C4—2216no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—228no—
494C22×C4—2216no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—228no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—444no—
519C22×C4—448no—
520C22×C4—444no—
521C22×C4C2×C4×D1112yes—
522C22×C4C2×C4×D1112yes—
523C22×C4C2×C4×D1112yes—
524C22×C4#433914yes—
525C22×C4D4×D1114yes—
526C22×C4D4×D1112yes—
527C22×C4D4×D1112yes—
528C4⋊C4—28no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—2216no—
532C4⋊C4—228no—
533C22⋊C4—2216no—
534C22⋊C4—448no—
535C42—28no—
536C42—228no—
537C11#1387011yescharacteristic, complemented, Sylow
538C23—114no—
539C23—118no—
540C23—114no—
541C23—118no—
542C23—114no—
543C23—224no—
544C23—222no—
545C23—222no—
546C23—224no—
547C23—222no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—222no—
558C23—224no—
559C23C22×C4×D1111yescharacteristic
560C23C2×#433912yes—
561C23C2×D4×D1111yescharacteristic
562C23C2×D4×D1111yescharacteristic
563C23C2×D4×D1112yes—
564C23#6704012yes—
565C23#41×D1112yes—
566C23#41×D1112yes—
567C23#6704312yes—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—114no—
596C2×C4—114no—
597C2×C4—2232no—
598C2×C4—2232no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—4416no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4#6692514yescomplemented
628C2×C4C22⋊C4×D1114yes—
629C22—118no—
630C22—228no—
631C22—228no—
632C22—224no—
633C22—228no—
634C22—228no—
635C22—228no—
636C22—224no—
637C22—228no—
638C22C2×#6692511yescharacteristic
639C22C2×C22⋊C4×D1111yescharacteristic
640C22#1062303812yes—
641C22D11×#11711yescharacteristic
642C22#1062306012yes—
643C22C4×D4×D1112yes—
644C22#1062307812yes—
645C22#1062307812yes—
646C22#1062308212yes—
647C22#1062310312yes—
648C22#1062311212yes—
649C22D11×#12011yescharacteristic
650C22D11×#12112yes—
651C22#1062315912yes—
652C22#1062316212yes—
653C22D11×#12311yescharacteristic
654C22#1062318612yes—
655C22#1062320611yescharacteristic
656C22#1062322412yes—
657C22#1062323912yes—
658C22#1062325511yescharacteristic
659C4—24no—
660C4—24no—
661C4—44no—
662C4—42no—
663C4—82no—
664C4—224no—
665C4—224no—
666C4—444no—
667C4—442no—
668C4—882no—
669C2—228no—
670C2#1307099711yescharacteristic
671C2D11×#38611yescharacteristic
672C2#1307119911yescharacteristic
673C2#1307148112yes—
674C2#1307148212yes—
675C2#1307194912yes—
676C2#1307202012yes—
677C2#1307202212yes—
678C2#1307290112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13870
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
5. #13066868C2semidirect
6. #13066867C2semidirect
7. #13066851C2semidirect
8. #13066849C2semidirect
9. #13066848C2semidirect
11. C11×#1436C2semidirect
26. C2×C4⋊C4×D11C4semidirect
208. #1436D11semidirect
268. C2×C4×C11#117semidirect
297. C2×Dic11#117semidirect
537. C11#13870semidirect
627. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C22×C4⋊C4×D112
C2×#106222772
#130668682
#130668672
#130668512
#130668492
#130668482
(C2×D11)⋊#952
C11×#14362
#1387011