Finite Group Databasebeta

← #14690466

Subgroups — #14690466

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C2×#10622574C214yesmaximal, complemented
3C2×#10622834C211yesmaximal, characteristic, complemented
4C2×#10622552C211yesmaximal, characteristic, complemented
5C2×#10622601C211yesmaximal, characteristic, complemented
6C2×#10622598C211yesmaximal, characteristic, complemented
7#13066855C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C23×C22⋊D11C2212yes—
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2214yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2214yes—
18C2×#66993—24no—
19C2×#66993—24no—
20C2×#66993—24no—
21C22×(C2×D11)⋊C4C2214yes—
22C22×(C2×D11)⋊C4C2214yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C11×#390—24no—
28#10622834—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622601—24no—
33#10622598—24no—
34#10622574—216no—
35#10622552—24no—
36C25×C11C2312yes—
37C24×D11C2312yes—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11D414yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—24no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—28no—
55C22×C22⋊D11—28no—
56C22×C22⋊D11—44no—
57C22×C22⋊D11—44no—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44D414yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D414yescomplemented
72C2×C11×C22⋊C4—28no—
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4—44no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—44no—
81#66993—232no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—28no—
92C2×C4⋊Dic11—24no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11D414yes—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95D418yescomplemented
102#15140—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—24no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11C2×D414yes—
114C24×C11C2411yescharacteristic
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11C2×D414yes—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—216no—
154C2×C22⋊D11—416no—
155C2×C22⋊D11—416no—
156C2×C22⋊D11—416no—
157C2×C22⋊D11—416no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11C2×D414yes—
180C22×Dic11C2×D412yes—
181C22×Dic11C2×D414yes—
182C22×Dic11C2×D412yes—
183C22×Dic11#4114yes—
184C2×D44—28no—
185C2×D44—28no—
186C2×D44—28no—
187C2×D44—44no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44—44no—
191C11×C4⋊C4—28no—
192C11×C22⋊C4—416no—
193C42×C11—44no—
194C22⋊Dic11—416no—
195(C2×D11)⋊C4—416no—
196(C2×D11)⋊C4—416no—
197C4⋊Dic11—48no—
198C4⋊Dic11—44no—
199C4×Dic11—28no—
200C4×Dic11—44no—
201C22×#127—111no—
202C2×#394—114no—
203C2×#390—111no—
204C2×#390—111no—
205C2×#390—111no—
206C2×#390D1111yescharacteristic, complemented
207C2×#389—111no—
208#1438—114no—
209C4×#95—111no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—28no—
214C23×C11—28no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—44no—
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D412yes—
237C23×C11C22×D411yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4112yes—
242C23×C11H(5,𝔽2)12yes—
243C23×C11H(5,𝔽2)12yes—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—28no—
248C22×D11—28no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—44no—
256C22×D11—44no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—44no—
260C22×D11—44no—
261C22×D11—44no—
262C22×D11—44no—
263C22×D11—44no—
264C22×D11—44no—
265C22×D11—44no—
266C22×D11—44no—
267D4×C11—416no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—28no—
272C2×C4×C11—24no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—44no—
279C2×C4×C11—42no—
280C2×C4×C11#12014yes—
281C2×C4×C11#12114yes—
282C2×C4×C11#12114yes—
283C2×C4×C11#12114yes—
284C2×C4×C11#12314yes—
285C2×C4×C11#12314yes—
286C2×C4×C11#12414yes—
287C22⋊D11—432no—
288C22⋊D11—432no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—44no—
308C2×Dic11—44no—
309C2×Dic11#12414yes—
310C2×Dic11#12714yes—
311D44—416no—
312C23×D4—112no—
313C23×D4—112no—
314C23×D4—111no—
315C23×D4C2×D1111yescharacteristic
316C2×#127—224no—
317C2×#127—224no—
318C2×#127—224no—
319C22×C4⋊C4—112no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4C2×D1111yescharacteristic
322C22×C22⋊C4—114no—
323C22×C22⋊C4—114no—
324C22×C22⋊C4—114no—
325C22×C22⋊C4C2×D1114yes—
326C22×C42—111no—
327C22×C42—111no—
328C22×C42C2×D1111yescharacteristic
329#394—2216no—
330#390—24no—
331#390—224no—
332#390—224no—
333#390—224no—
334#389—224no—
335C2×#95—112no—
336C2×#95—112no—
337C2×#95—112no—
338C22×C11—44no—
339C22×C11—48no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—48no—
343C22×C11—82no—
344C22×C11—82no—
345C22×C11—84no—
346C22×C11—84no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11C2×#12011yescharacteristic
350C22×C11C2×#12111yescharacteristic
351C22×C11C2×#12111yescharacteristic
352C22×C11C2×#12111yescharacteristic
353C22×C11C2×#12311yescharacteristic
354C22×C11C2×#12311yescharacteristic
355C22×C11C2×#12411yescharacteristic
356C22×C11C2×#12411yescharacteristic
357C22×C11C2×#12711yescharacteristic
358C22×C11#53212yes—
359C22×C11#53212yes—
360C22×C11#53511yescharacteristic
361C22×C11#53511yescharacteristic
362C22×C11#54012yes—
363C22×C11#54012yes—
364C22×C11D4212yes—
365C22×C11D4212yes—
366C22×C11D4212yes—
367C22×C11#54612yes—
368C22×C11#54612yes—
369C22×C11#55012yes—
370C22×C11#55012yes—
371C22×C11#55912yes—
372C2×D11—44no—
373C2×D11—48no—
374C2×D11—44no—
375C2×D11—44no—
376C2×D11—48no—
377C2×D11—82no—
378C2×D11—82no—
379C2×D11—84no—
380C2×D11—84no—
381C2×D11—82no—
382C2×D11—82no—
383C4×C11—44no—
384C4×C11—44no—
385C4×C11#39418yescomplemented
386Dic11—24no—
387Dic11—24no—
388Dic11—44no—
389Dic11—82no—
390C25—112no—
391C25C22×D1112yes—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—114no—
399C22×D4—224no—
400C22×D4—224no—
401C22×D4—228no—
402C22×D4—228no—
403C22×D4—224no—
404C22×D4—224no—
405C22×D4—224no—
406C22×D4—224no—
407C22×D4—222no—
408C22×D4—222no—
409C22×D4—222no—
410C22×D4—222no—
411C22×D4—222no—
412C22×D4—222no—
413C22×D4—444no—
414C22×D4—444no—
415C22×D4D4414yes—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4—112no—
419C23×C4—112no—
420C23×C4C22×D1112yes—
421C23×C4C22×D1112yes—
422C23×C4C22×D1111yescharacteristic
423#127—2232no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—224no—
427C2×C4⋊C4—228no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4C22⋊D1114yescomplemented
432C2×C22⋊C4—28no—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—228no—
436C2×C22⋊C4—228no—
437C2×C22⋊C4—228no—
438C2×C22⋊C4—228no—
439C2×C22⋊C4—228no—
440C2×C22⋊C4—228no—
441C2×C22⋊C4—444no—
442C2×C22⋊C4—444no—
443C2×C22⋊C4—444no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—114no—
448C2×C42—222no—
449C2×C42—222no—
450C2×C42—222no—
451C2×C42—222no—
452C2×C42—222no—
453#95—118no—
454#95—224no—
455#95—224no—
456C2×C11—84no—
457C2×C11C2×#39411yescharacteristic
458C2×C11#242812yes—
459C2×C11#242812yes—
460C2×C11#243311yescharacteristic
461C2×C11#243511yescharacteristic
462C2×C11#244512yes—
463C2×C11#244512yes—
464C2×C11#254111yescharacteristic
465C2×C11#254811yescharacteristic
466C2×C11#264111yescharacteristic
467C2×C11#285811yescharacteristic
468D11—84no—
469C24—22no—
470C24—24no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24—22no—
479C24—114no—
480C24—222no—
481C24—222no—
482C24—224no—
483C24—222no—
484C24—222no—
485C24—222no—
486C24—224no—
487C24—224no—
488C24—224no—
489C24—222no—
490C24C2×D4414yes—
491C24C23×D1111yescharacteristic
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—2216no—
500C2×D4—2216no—
501C2×D4—228no—
502C2×D4—228no—
503C2×D4—228no—
504C2×D4—448no—
505C2×D4—448no—
506C2×D4—4416no—
507C2×D4—4416no—
508C2×D4—4416no—
509C2×D4—4416no—
510C2×D4—448no—
511C2×D4—448no—
512C2×D4—444no—
513C2×D4—444no—
514C2×D4—444no—
515C2×D4—444no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—114no—
527C22×C4—112no—
528C22×C4—112no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—224no—
546C22×C4—222no—
547C22×C4—224no—
548C22×C4C2×D4412yes—
549C22×C4#433912yes—
550C22×C4D4×D1114yes—
551C22×C4D4×D1112yes—
552C22×C4D4×D1112yes—
553C22×C4#434112yes—
554C22×C4#434112yes—
555C22×C4C2×C22⋊D1114yes—
556C22×C4C2×C22⋊D1112yes—
557C4⋊C4—28no—
558C4⋊C4—448no—
559C4⋊C4—444no—
560C22⋊C4—416no—
561C22⋊C4—4416no—
562C22⋊C4—4416no—
563C22⋊C4—4416no—
564C42—44no—
565C42—228no—
566C42—444no—
567C11#1514011yescharacteristic, complemented, Sylow
568C23—24no—
569C23—24no—
570C23—24no—
571C23—28no—
572C23—28no—
573C23—42no—
574C23—42no—
575C23—44no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—44no—
580C23—42no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—42no—
589C23—42no—
590C23—44no—
591C23—224no—
592C23—224no—
593C23—224no—
594C23—228no—
595C23—228no—
596C23—442no—
597C23—442no—
598C23—444no—
599C23—442no—
600C23—442no—
601C23—442no—
602C23—444no—
603C23—442no—
604C23—444no—
605C23—444no—
606C23—444no—
607C23—444no—
608C23—444no—
609C23—444no—
610C23—444no—
611C23—442no—
612C23—442no—
613C23—444no—
614C23C22×D4411yescharacteristic
615C23C2×#433911yescharacteristic
616C23C2×D4×D1111yescharacteristic
617C23C2×D4×D1112yes—
618C23C2×D4×D1111yescharacteristic
619C23C2×#434111yescharacteristic
620C23C2×#434111yescharacteristic
621C23#6703712yes—
622C23#41×D1112yes—
623C23#6704212yes—
624C23C22×C22⋊D1111yescharacteristic
625D4—416no—
626D4—4432no—
627D4—4432no—
628D4—4416no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—222no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—224no—
649C2×C4—224no—
650C2×C4—222no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—442no—
655C2×C4—442no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—444no—
661C2×C4—444no—
662C2×C4—442no—
663C2×C4#6693514yes—
664C2×C4#6693614yes—
665C2×C4#6693814yes—
666C2×C4#6693914yes—
667C2×C4#6698314yes—
668C2×C4#6699114yes—
669C2×C4#6699214yes—
670C22—48no—
671C22—44no—
672C22—44no—
673C22—44no—
674C22—48no—
675C22—84no—
676C22—82no—
677C22—82no—
678C22—82no—
679C22—82no—
680C22—84no—
681C22—448no—
682C22—444no—
683C22—444no—
684C22—444no—
685C22—448no—
686C22—884no—
687C22—882no—
688C22—882no—
689C22—882no—
690C22—882no—
691C22—884no—
692C22C2×#6693511yescharacteristic
693C22C2×#6693611yescharacteristic
694C22C2×#6693811yescharacteristic
695C22C2×#6693911yescharacteristic
696C22#1062307912yes—
697C22D4×D4412yes—
698C22#1062308512yes—
699C22#1062309312yes—
700C22#1062312712yes—
701C22#1062314012yes—
702C22#1062314312yes—
703C22#1062315012yes—
704C22D11×#12411yescharacteristic
705C22#1062320511yescharacteristic
706C22#1062321212yes—
707C22D11×#12711yescharacteristic
708C22#1062324611yescharacteristic
709C22#1062324912yes—
710C22C2×#6698311yescharacteristic
711C22C2×#6699111yescharacteristic
712C22D4×C22⋊D1112yes—
713C22C2×#6699211yescharacteristic
714C22#1062336512yes—
715C4—44no—
716C4—44no—
717C4—224no—
718C4—224no—
719C4—444no—
720C4—882no—
721C4#1062257418yescomplemented
722C2—84no—
723C2—884no—
724C2C2×#1062257411yescharacteristic
725C2#1307219812yes—
726C2#1307220012yes—
727C2#1307225211yescharacteristic
728C2#1307226611yescharacteristic
729C2#1307237912yes—
730C2#1307238212yes—
731C2#1307356011yescharacteristic
732C2#1307361611yescharacteristic
733C2#1307456011yescharacteristic
734C2#1307697011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#390C2
prime radicalC22×#66993C2
hypercenterC2×#390D11
hypocenterC11#15140
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622574C2semidirect
3. C2×#10622834C2semidirect
4. C2×#10622552C2semidirect
5. C2×#10622601C2semidirect
6. C2×#10622598C2semidirect
7. #13066855C2semidirect
8. C4×C11⋊#95C2semidirect
9. C2×C11×#390C2semidirect
71. C2×C11×C4⋊C4D4semidirect
101. C11⋊#95D4semidirect
206. C2×#390D11semidirect
385. C4×C11#394semidirect
431. C2×C4⋊C4C22⋊D11semidirect
567. C11#15140semidirect
721. C4#10622574semidirect

Maximal subgroups

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

subgroupindex
C22×#669932
C2×#106225742
C2×#106228342
C2×#106225522
C2×#106226012
C2×#106225982
#130668552
C4×C11⋊#952
C2×C11×#3902
#1514011