Finite Group Databasebeta

← #14682235

Subgroups — #14682235

Order 2816.

1758 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622553C212yesmaximal, complemented
3C2×#10622282C212yesmaximal, complemented
4#13066860C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066856C212yesmaximal
7#13066848C211yesmaximal, characteristic, complemented
8Dic11⋊#95C212yesmaximal, 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×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622601C418yescomplemented
32#10622553—28no—
33#10622282—28no—
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—24no—
44C22×D44—42no—
45C22×D44—41no—
46C22×D44—41no—
47C22×D44C2×C414yes—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C42×C11—24no—
52C2×C42×C11—41no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4C2×C418yes—
70C2×(C2×D11)⋊C4C2×C418yes—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—42no—
73C2×Dic11⋊C4—42no—
74C2×Dic11⋊C4—42no—
75C2×Dic11⋊C4—42no—
76C2×Dic11⋊C4D418yescomplemented
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—41no—
80C2×C4×Dic11C2×C414yes—
81C11×#95—24no—
82C11×#95—24no—
83C11×#95—41no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—41no—
89#14445—111nomaximal, Sylow
90C24×C11C2411yescharacteristic
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×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11C22×C414yes—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
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—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11#4114yes—
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×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11C22×C414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×D414yes—
155C22×Dic11#4114yes—
156C2×D44—28no—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—48no—
160C2×D44—48no—
161C11×C4⋊C4—44no—
162C42×C11—44no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169Dic11⋊C4—48no—
170Dic11⋊C4—48no—
171C4×Dic11—44no—
172C4×Dic11—44no—
173C2×#390—111no—
174C2×#388—112no—
175C2×#388—112no—
176#1439—112no—
177#1439—112no—
178#1438—112no—
179#1436—111no—
180#1436D1111yescharacteristic, complemented
181C4⋊#95—112no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D412yes—
184C23×C11C2×#4112yes—
185C23×C11C2×#4112yes—
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)12yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C112−1+412yes—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
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—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11#11714yes—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11C4×D418yes—
276D44—416no—
277C23×D4—111no—
278C22×C4⋊C4—112no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4C2×D1111yescharacteristic
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C42—111no—
288C22×C42—111no—
289C22×C42C2×D1111yescharacteristic
290#390—118no—
291#388—228no—
292#388—228no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—111no—
298C2×#95C2×D1112yes—
299C2×#95C2×D1112yes—
300C2×#95C2×D1111yescharacteristic
301C22×C11C2×#11711yescharacteristic
302C22×C11C2×C4×D412yes—
303C22×C11#51811yescharacteristic
304C22×C11#51811yescharacteristic
305C22×C11#52012yes—
306C22×C11#53412yes—
307C22×C11#53712yes—
308C22×C11#53812yes—
309C22×C11#53812yes—
310C22×C11#53812yes—
311C22×C11#53912yes—
312C22×C11D4211yescharacteristic
313C22×C11#54712yes—
314C22×C11#55012yes—
315C22×C11#55012yes—
316C22×C11#55512yes—
317C22×C11#55612yes—
318C22×C11#55911yescharacteristic
319C22×C11H(3,𝔽4)11yescharacteristic
320C22×C11#56212yes—
321C22×C11#56311yescharacteristic
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C4×C11—24no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—82no—
342Dic11—28no—
343Dic11—44no—
344Dic11—82no—
345C25—112no—
346C22×D4—114no—
347C22×D4—224no—
348C22×D4—441no—
349C22×D4—441no—
350C22×D4—442no—
351C23×C4—112no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C23×C4C22×D1111yescharacteristic
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—442no—
364C2×C4⋊C4—442no—
365C2×C4⋊C4—442no—
366C2×C4⋊C4—442no—
367C2×C4⋊C4C4×D1114yes—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C42—24no—
387C2×C42—41no—
388C2×C42—114no—
389C2×C42—224no—
390C2×C42—442no—
391C2×C42—441no—
392#95—24no—
393#95—24no—
394#95—41no—
395#95—224no—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—441no—
400C2×C11#231211yescharacteristic
401C2×C11#232512yes—
402C2×C11#235412yes—
403C2×C11#236611yescharacteristic
404C2×C11#237911yescharacteristic
405C2×C11#268212yes—
406C2×C11#272712yes—
407C2×C11#273312yes—
408C2×C11#280812yes—
409D11—84no—
410C24—114no—
411C24—222no—
412C24—222no—
413C24—222no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24C23×D1111yescharacteristic
426C2×D4—228no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—448no—
430C2×D4—448no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4C2×C4×D1112yes—
477C22×C4C2×C4×D1112yes—
478C22×C4C2×C4×D1112yes—
479C22×C4#433914yes—
480C22×C4D4×D1114yes—
481C4⋊C4—44no—
482C4⋊C4—448no—
483C4⋊C4—448no—
484C22⋊C4—2216no—
485C22⋊C4—2216no—
486C22⋊C4—448no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C22⋊C4—448no—
490C42—44no—
491C42—444no—
492C42—444no—
493C11#1444511yescharacteristic, complemented, Sylow
494C23—224no—
495C23—224no—
496C23—224no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23C22×C4×D1111yescharacteristic
530C23C2×#433912yes—
531C23C2×D4×D1112yes—
532C23#6703711yescharacteristic
533C23#6703711yescharacteristic
534C23#6704012yes—
535C23#41×D1112yes—
536C23#6704212yes—
537C23#6704212yes—
538D4—4416no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—118no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4#6692514yes—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—882no—
597C22—882no—
598C22—882no—
599C22—882no—
600C22—882no—
601C22—882no—
602C22—882no—
603C22—882no—
604C22C2×#6692511yescharacteristic
605C22#1062301711yescharacteristic
606C22#1062303812yes—
607C22#1062305211yescharacteristic
608C22#1062306312yes—
609C22C4×D4×D1112yes—
610C22#1062308412yes—
611C22#1062309112yes—
612C22#1062309112yes—
613C22#1062309912yes—
614C22#1062310512yes—
615C22#1062312111yescharacteristic
616C22#1062313012yes—
617C22#1062316012yes—
618C22#1062317812yes—
619C22#1062318412yes—
620C22#1062319511yescharacteristic
621C22#1062321411yescharacteristic
622C22#1062322312yes—
623C22#1062323512yes—
624C22#1062326611yescharacteristic
625C4—24no—
626C4—44no—
627C4—42no—
628C4—42no—
629C4—82no—
630C4—228no—
631C4—444no—
632C4—882no—
633C2—884no—
634C2#1307121111yescharacteristic
635C2#1307131512yes—
636C2#1307156112yes—
637C2#1307167911yescharacteristic
638C2#1307178811yescharacteristic
639C2#1307498212yes—
640C2#1307557812yes—
641C2#1307564312yes—
642C2#1307659212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622282C2semidirect
4. #13066860C2semidirect
5. #13066860C2semidirect
7. #13066848C2semidirect
8. Dic11⋊#95C2semidirect
9. C11×#1436C2semidirect
31. #10622601C4semidirect
76. C2×Dic11⋊C4D4semidirect
180. #1436D11semidirect
493. C11#14445semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106225532
C2×#106222822
#130668602
#130668562
#130668482
Dic11⋊#952
C11×#14362
#1444511