Finite Group Databasebeta

← #14675475

Subgroups — #14675475

Order 2816.

1814 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5C2×#10622545C211yesmaximal, characteristic, complemented
6#13066877C212yesmaximal, complemented
7#13066874C212yesmaximal, complemented
8#13066864C212yesmaximal
9#13066860C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4—24no—
36C4×(C2×D11)⋊C4—24no—
37C4×(C2×D11)⋊C4C418yescomplemented
38#10622545—24no—
39C4×Dic11⋊C4—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4C2×C414yes—
76C2×(C2×D11)⋊C4C2×C414yes—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2×C414yes—
87C2×C4×Dic11D414yes—
88C2×C4×Dic11D414yes—
89C11×#95—24no—
90C11×#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95C2×C414yes—
99C11⋊#95C2×C414yes—
100#13842—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
102C23×D11—21no—
103C23×D11—21no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11C22×C412yes—
112C23×D11#4114yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
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×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4114yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
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—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11C22×C412yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C22×C412yes—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11#4114yes—
175C2×C4×D11—28no—
176C2×C4×D11—28no—
177C2×C4×D11—28no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×C4×D11—44no—
182C42×C11—28no—
183C42×C11—44no—
184C42×C11—44no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189Dic11⋊C4—216no—
190C4×Dic11—28no—
191C4×Dic11—28no—
192C4×Dic11—28no—
193C2×C4×C4⋊C4—111no—
194C2×C4×C22⋊C4—111no—
195C2×C4×C22⋊C4—111no—
196C2×C4×C22⋊C4—111no—
197C2×#376—111no—
198#1443—112no—
199#1442—112no—
200#1440—112no—
201#1439—112no—
202C4×#95—111no—
203C4×#95D1111yescharacteristic, complemented
204C23×C11C23×C411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11C2×#4111yescharacteristic
212C23×C11C2×#4111yescharacteristic
213C23×C11C2×#4112yes—
214C23×C11C2×#4112yes—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—42no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11#11714yes—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
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#11714yes—
263C2×C4×C11C4×D414yes—
264C2×C4×C11C4×D414yes—
265C2×C4×C11#12114yes—
266C2×C4×C11#12314yes—
267C2×C4×C11#12414yes—
268C2×C4×C11#12614yes—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11#11714yes—
300C4×D11—416no—
301C24×C4—111no—
302C22×C4⋊C4—112no—
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C42—111no—
308C22×C42—111no—
309C22×C42—111no—
310C22×C42C2×D1111yescharacteristic
311C22×C42C2×D1111yescharacteristic
312C22×C42C2×D1111yescharacteristic
313C4×C4⋊C4—224no—
314C4×C22⋊C4—118no—
315C4×C22⋊C4—224no—
316C4×C22⋊C4—224no—
317#376—224no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95C2×D1112yes—
328C2×#95C2×D1112yes—
329C22×C11C2×#11711yescharacteristic
330C22×C11C2×#11711yescharacteristic
331C22×C11C2×#11711yescharacteristic
332C22×C11C2×C4×D411yescharacteristic
333C22×C11C2×C4×D411yescharacteristic
334C22×C11C4×#4111yescharacteristic
335C22×C11C4×#4111yescharacteristic
336C22×C11C2×#12111yescharacteristic
337C22×C11C2×#12311yescharacteristic
338C22×C11#52512yes—
339C22×C11#52512yes—
340C22×C11#52512yes—
341C22×C11C2×#12411yescharacteristic
342C22×C11C2×#12611yescharacteristic
343C22×C11#52912yes—
344C22×C11#52912yes—
345C22×C11#52912yes—
346C22×C11#52912yes—
347C22×C11#52912yes—
348C22×C11#52912yes—
349C22×C11#52912yes—
350C22×C11#52912yes—
351C22×C11#53212yes—
352C2×D11—24no—
353C2×D11—24no—
354C2×D11—24no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C4×C11—44no—
364C4×C11—44no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11#38818yes—
368Dic11—24no—
369Dic11—44no—
370Dic11—44no—
371Dic11—42no—
372Dic11—42no—
373C25—111no—
374C23×C4—111no—
375C23×C4—112no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—222no—
381C23×C4—222no—
382C23×C4—222no—
383C23×C4—222no—
384C23×C4—222no—
385C23×C4—222no—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1112yes—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C2×C4⋊C4—224no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—114no—
413C2×C42—114no—
414C2×C42—114no—
415C2×C42—222no—
416C2×C42—222no—
417C2×C42—222no—
418C2×C42—222no—
419C2×C42—222no—
420C2×C42—222no—
421C2×C42C4×D1114yes—
422#95—24no—
423#95—24no—
424#95—114no—
425#95—114no—
426#95—224no—
427#95—224no—
428#95—224no—
429#95—224no—
430#95—224no—
431#95—224no—
432#95—224no—
433C2×C11#228311yescharacteristic
434C2×C11C2×#38811yescharacteristic
435C2×C11#229011yescharacteristic
436C2×C11#229011yescharacteristic
437C2×C11#229011yescharacteristic
438C2×C11#229311yescharacteristic
439C2×C11#229811yescharacteristic
440C2×C11#239212yes—
441C2×C11#239512yes—
442C2×C11#239812yes—
443C2×C11#240112yes—
444D11—44no—
445C24—112no—
446C24—114no—
447C24—222no—
448C24—222no—
449C24—221no—
450C24—221no—
451C24—221no—
452C24—221no—
453C24—221no—
454C24—221no—
455C24—222no—
456C24C23×D1111yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
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—114no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—222no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—228no—
509C22×C4—228no—
510C22×C4—228no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—444no—
514C22×C4—444no—
515C22×C4C2×C4×D1112yes—
516C22×C4C2×C4×D1112yes—
517C22×C4C2×C4×D1112yes—
518C22×C4#433914yes—
519C22×C4#433914yes—
520C22×C4#433912yes—
521C22×C4#433912yes—
522C22×C4D4×D1112yes—
523C22×C4D4×D1112yes—
524C22×C4#434112yes—
525C22×C4#434312yes—
526C4⋊C4—2216no—
527C22⋊C4—228no—
528C22⋊C4—228no—
529C22⋊C4—2216no—
530C22⋊C4—2216no—
531C42—28no—
532C42—44no—
533C42—44no—
534C42—228no—
535C42—228no—
536C42—228no—
537C11#1384211yescharacteristic, complemented, Sylow
538C23—114no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—222no—
543C23—222no—
544C23—222no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—442no—
552C23—442no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—442no—
558C23—442no—
559C23—442no—
560C23—442no—
561C23C22×C4×D1111yescharacteristic
562C23C2×#433911yescharacteristic
563C23C2×#433911yescharacteristic
564C23C2×#433912yes—
565C23C2×#433912yes—
566C23C2×D4×D1111yescharacteristic
567C23C2×D4×D1111yescharacteristic
568C23C2×#434111yescharacteristic
569C23C2×#434311yescharacteristic
570C23#41×D1112yes—
571C23#41×D1112yes—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—114no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
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—4416no—
628C2×C4#6692514yes—
629C2×C4(C22⋊D11)⋊C414yes—
630C2×C4#6693714yes—
631C2×C4#6693814yes—
632C2×C4#6694614yes—
633C2×C4#6694714yes—
634C2×C4#6695114yes—
635C22—224no—
636C22—224no—
637C22—224no—
638C22—444no—
639C22—442no—
640C22—444no—
641C22—444no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—444no—
646C22C2×#6692511yescharacteristic
647C22C4×#433911yescharacteristic
648C22C4×#433911yescharacteristic
649C22#1062301012yes—
650C22#1062301012yes—
651C22C2×(C22⋊D11)⋊C411yescharacteristic
652C22C2×#6693711yescharacteristic
653C22C2×#6693811yescharacteristic
654C22C2×#6694611yescharacteristic
655C22C2×#6694711yescharacteristic
656C22C2×#6695111yescharacteristic
657C22D11×#11711yescharacteristic
658C22D11×#11711yescharacteristic
659C22#1062305912yes—
660C22#1062305912yes—
661C22#1062306912yes—
662C22#1062307812yes—
663C22#1062307812yes—
664C22#1062307812yes—
665C22#1062307912yes—
666C22#1062308812yes—
667C22#1062311112yes—
668C22#1062311112yes—
669C4—44no—
670C4—42no—
671C4—42no—
672C4—44no—
673C4—224no—
674C4—444no—
675C4—442no—
676C4—442no—
677C4—444no—
678C4#1062228218yes—
679C2—444no—
680C2#1307100811yescharacteristic
681C2C2×#1062228211yescharacteristic
682C2#1307105711yescharacteristic
683C2#1307105711yescharacteristic
684C2#1307106211yescharacteristic
685C2#1307107911yescharacteristic
686C2#1307111311yescharacteristic
687C2#1307186012yes—
688C2#1307187912yes—
689C2#1307190312yes—
690C2#1307191712yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#13842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic11⋊C4C2semidirect
5. C2×#10622545C2semidirect
6. #13066877C2semidirect
7. #13066874C2semidirect
10. C4×C11⋊#95C2semidirect
11. C4×C11×#95C2semidirect
37. C4×(C2×D11)⋊C4C4semidirect
203. C4×#95D11semidirect
537. C11#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic11⋊C42
C2×C4×(C2×D11)⋊C42
C2×#106225452
#130668772
#130668742
#130668642
#130668602
C4×C11⋊#952
C4×C11×#952
#1384211