Finite Group Databasebeta

← #14680807

Subgroups — #14680807

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic, complemented
2C2×#10622564C211yesmaximal, characteristic
3#13066884C211yesmaximal, characteristic, complemented
4#13066873C212yesmaximal, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066861C212yesmaximal
7#13066861C211yesmaximal, characteristic
8#13066853C212yesmaximal
9#13066850C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#397C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C11×#397C418yescomplemented
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622598—24no—
37#10622564—24no—
38C25×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—42no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C11×C22⋊C4C2×C418yes—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—42no—
70C2×C4⋊Dic11—42no—
71C2×C4⋊Dic11—42no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11D414yes—
77C11×#95C2×C418yes—
78C11×#95C2×C414yes—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89#14324—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—22no—
99C24×C11—21no—
100C24×C11C22×C412yes—
101C24×C11C2411yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C414yes—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11#4112yes—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11C2×D412yes—
157C22×Dic11C2×D412yes—
158C22×Dic11#4114yes—
159C22×Dic11#4114yes—
160C11×C4⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—48no—
163C22⋊Dic11—44no—
164C22⋊Dic11—48no—
165C22⋊Dic11—44no—
166C4⋊Dic11—44no—
167C4⋊Dic11—48no—
168C4⋊Dic11—44no—
169C4×Dic11—44no—
170C4×Dic11—48no—
171C2×#397D1111yescharacteristic
172C2×#389—111no—
173C2×#388—111no—
174#1445—111no—
175#1442—112no—
176#1442—111no—
177#1439—111no—
178#1439—112no—
179#1437—112no—
180#1436—112no—
181C4×#95—111no—
182C23×C11—22no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11C23×C411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)11yescharacteristic
211C23×C11H(5,𝔽2)11yescharacteristic
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)11yescharacteristic
214C23×C112−1+412yes—
215C23×C112−1+411yescharacteristic
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11C4×D414yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
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#12414yes—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4C2×D1111yescharacteristic
282C22×C22⋊C4C2×D1112yes—
283C22×C42—111no—
284C22×C42—112no—
285#397Dic1118yescomplemented
286#389—224no—
287#388—224no—
288C2×#95—112no—
289C2×#95—111no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—111no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95C2×D1111yescharacteristic
299C2×#95C2×D1112yes—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11C2×C4×D411yescharacteristic
312C22×C11C4×#4112yes—
313C22×C11#51811yescharacteristic
314C22×C11#52012yes—
315C22×C11#52011yescharacteristic
316C22×C11C2×#12411yescharacteristic
317C22×C11#52912yes—
318C22×C11#53211yescharacteristic
319C22×C11#53411yescharacteristic
320C22×C11#53511yescharacteristic
321C22×C11#53611yescharacteristic
322C22×C11#53711yescharacteristic
323C22×C11#53812yes—
324C22×C11#53812yes—
325C22×C11#53912yes—
326C22×C11#53912yes—
327C22×C11#53912yes—
328C22×C11#54011yescharacteristic
329C22×C11#54012yes—
330C22×C11#54112yes—
331C22×C11#54212yes—
332C22×C11#54211yescharacteristic
333C22×C11#54212yes—
334C4×C11—24no—
335C4×C11—44no—
336C4×C11—44no—
337C4×C11—42no—
338Dic11—24no—
339Dic11—44no—
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343Dic11—82no—
344C25C22×D1111yescharacteristic
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—442no—
362C2×C4⋊C4—442no—
363C2×C4⋊C4—442no—
364C2×C4⋊C4C2×Dic1114yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4C2×Dic1114yes—
377C2×C22⋊C4C2×Dic1118yes—
378C2×C42—114no—
379C2×C42—224no—
380C2×C42—442no—
381C2×C42—442no—
382C2×C42—442no—
383#95—224no—
384#95—224no—
385#95—222no—
386#95—224no—
387#95—222no—
388#95—222no—
389#95—442no—
390#95—442no—
391#95—442no—
392#95—442no—
393#95C2×Dic1118yes—
394#95C2×Dic1114yes—
395C2×C11—82no—
396C2×C11C4×#12411yescharacteristic
397C2×C11#232211yescharacteristic
398C2×C11#232411yescharacteristic
399C2×C11#233412yes—
400C2×C11#233512yes—
401C2×C11#263911yescharacteristic
402C2×C11#264011yescharacteristic
403C2×C11#264912yes—
404C2×C11#265412yes—
405C2×C11#266111yescharacteristic
406C2×C11#266411yescharacteristic
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—22no—
415C24—21no—
416C24—22no—
417C24C22×Dic1112yes—
418C24C23×D1111yescharacteristic
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4D4×D1112yes—
472C22×C4#434112yes—
473C22×C4C22×Dic1112yes—
474C22×C4C22×Dic1114yes—
475C22×C4C22×Dic1114yes—
476C22×C4C22×Dic1112yes—
477C4⋊C4—28no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C4⋊C4—448no—
481C22⋊C4—28no—
482C22⋊C4—48no—
483C22⋊C4—444no—
484C22⋊C4—448no—
485C22⋊C4—444no—
486C42—444no—
487C42—448no—
488C11#1432411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23C2×D4×D1111yescharacteristic
513C23C2×#434111yescharacteristic
514C23#6703711yescharacteristic
515C23#6703711yescharacteristic
516C23#41×D1112yes—
517C23#41×D1112yes—
518C23#6704211yescharacteristic
519C23#6704212yes—
520C23#6704311yescharacteristic
521C23#6704312yes—
522C23C23×Dic1111yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—114no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—222no—
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—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4D4×Dic1114yes—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—82no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—82no—
592C22#1062313411yescharacteristic
593C22#1062313811yescharacteristic
594C22#1062313911yescharacteristic
595C22#1062315011yescharacteristic
596C22#1062317911yescharacteristic
597C22#1062318411yescharacteristic
598C22#1062318812yes—
599C22#1062319112yes—
600C22#1062319312yes—
601C22#1062319412yes—
602C22#1062319612yes—
603C22#1062319911yescharacteristic
604C22D11×#12411yescharacteristic
605C22#1062321112yes—
606C22#1062323212yes—
607C22#1062323512yes—
608C22#1062323812yes—
609C22#1062324112yes—
610C22C2×D4×Dic1111yescharacteristic
611C22#1062332911yescharacteristic
612C22#41×Dic1112yes—
613C22#1062335811yescharacteristic
614C22#1062335812yes—
615C4—24no—
616C4—44no—
617C4—42no—
618C4—44no—
619C4—224no—
620C4—442no—
621C4—444no—
622C4—882no—
623C4—881no—
624C4—881no—
625C2—82no—
626C2#124×Dic1111yescharacteristic
627C2#1307128811yescharacteristic
628C2#1307131111yescharacteristic
629C2#1307139512yes—
630C2#1307141012yes—
631C2#1307454311yescharacteristic
632C2#1307455111yescharacteristic
633C2#1307461612yes—
634C2#1307469112yes—
635C2#1307475011yescharacteristic
636C2#1307478411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#397C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#397D11
hypocenterC11#14324
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×#10622598C2semidirect
3. #13066884C2semidirect
4. #13066873C2semidirect
5. #13066873C2semidirect
9. #13066850C2semidirect
10. #95×Dic11C2semidirect
23. C11×#397C4semidirect
285. #397Dic11semidirect
488. C11#14324semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225642
#130668842
#130668732
#130668612
#130668532
#130668502
#95×Dic112
C2×C11×#3972
#1432411