Finite Group Databasebeta

← #14681815

Subgroups — #14681815

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622557C212yesmaximal, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622555C212yesmaximal, complemented
4#13066874C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066857C211yesmaximal, characteristic
7#13066853C212yesmaximal, complemented
8#13066851C212yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24#10622833C418yescomplemented
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622557—28no—
33#10622555—28no—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—24no—
37C22×D4×C11—42no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×Dic11—24no—
45C23×Dic11—24no—
46C23×Dic11—41no—
47C23×Dic11—41no—
48C23×Dic11C2×C414yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—41no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—41no—
69C2×C22⋊Dic11C2×C418yes—
70C2×C22⋊Dic11C2×C414yes—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—42no—
76C2×Dic11⋊C4—42no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—42no—
80C11×#95—41no—
81C11×#95—41no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C418yes—
88C11⋊#95D418yescomplemented
89#14410—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C22×C412yes—
107C24×C11#4114yes—
108C24×C11C2411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C2×D4×C11—48no—
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×C11—21no—
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×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D414yes—
133C22×Dic11—216no—
134C22×Dic11—22no—
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×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—44no—
158C22×Dic11—44no—
159C22×Dic11—48no—
160C22×Dic11—44no—
161C22×Dic11C22×C414yes—
162C22×Dic11C22×C414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11#4114yes—
166C11×C22⋊C4—48no—
167C11×C22⋊C4—48no—
168C22⋊Dic11—216no—
169C22⋊Dic11—44no—
170C22⋊Dic11—48no—
171C22⋊Dic11—44no—
172C22⋊Dic11—44no—
173Dic11⋊C4—48no—
174Dic11⋊C4—48no—
175C4×Dic11—48no—
176C2×#388—112no—
177C2×#386—111no—
178C2×#380—112no—
179#1442—112no—
180#1439—112no—
181#1438—111no—
182#1438D1111yescharacteristic
183#1437—112no—
184#1436—112no—
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11#11714yes—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C2×#4112yes—
230C23×C11C2×#4112yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236D4×C11—416no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
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—42no—
255C2×C4×C11—42no—
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—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—416no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11C4×D418yes—
285C23×D4C2×D1111yescharacteristic
286C24×C4—111no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4C2×D1112yes—
295C22×C22⋊C4C2×D1112yes—
296C22×C42—112no—
297#388—228no—
298#386—118no—
299#380—228no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95C2×D1111yescharacteristic
308C2×#95C2×D1111yescharacteristic
309C22×C11—24no—
310C22×C11—28no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11C2×#11711yescharacteristic
328C22×C11C2×C4×D412yes—
329C22×C11#51811yescharacteristic
330C22×C11#51811yescharacteristic
331C22×C11#52012yes—
332C22×C11#53512yes—
333C22×C11#53712yes—
334C22×C11#53812yes—
335C22×C11#53812yes—
336C22×C11#54012yes—
337C22×C11#54212yes—
338C22×C11D4211yescharacteristic
339C22×C11#54612yes—
340C22×C11#54612yes—
341C22×C11#54812yes—
342C22×C11#55111yescharacteristic
343C22×C11#55212yes—
344C22×C11#55312yes—
345C22×C11#56011yescharacteristic
346C22×C11#56212yes—
347C22×C11#56311yescharacteristic
348C4×C11—42no—
349C4×C11—44no—
350C4×C11—82no—
351Dic11—28no—
352Dic11—44no—
353Dic11—44no—
354Dic11—82no—
355C25C22×D1111yescharacteristic
356C25C22×D1111yescharacteristic
357C22×D4—24no—
358C22×D4—41no—
359C22×D4—41no—
360C22×D4—42no—
361C22×D4C4×D1114yes—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—114no—
366C23×C4—112no—
367C23×C4—224no—
368C23×C4—224no—
369C23×C4—441no—
370C23×C4—441no—
371C23×C4C22×D1112yes—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1112yes—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—442no—
379C2×C4⋊C4—442no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—441no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—441no—
398C2×C42—224no—
399C2×C42—442no—
400C2×C42—442no—
401#95—41no—
402#95—41no—
403#95—118no—
404#95—118no—
405#95—224no—
406#95—224no—
407#95—442no—
408#95—442no—
409#95—442no—
410C2×C11—44no—
411C2×C11—82no—
412C2×C11#231211yescharacteristic
413C2×C11#232412yes—
414C2×C11#235212yes—
415C2×C11#235811yescharacteristic
416C2×C11#237611yescharacteristic
417C2×C11#267612yes—
418C2×C11#270212yes—
419C2×C11#270312yes—
420C2×C11#274112yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24C2×C4×D1112yes—
437C24C2×C4×D1112yes—
438C24#434114yes—
439C24C23×D1111yescharacteristic
440C2×D4—28no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—48no—
444C2×D4—48no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—2216no—
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×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—444no—
492C22×C4—444no—
493C22×C4—448no—
494C22×C4—444no—
495C22×C4C2×C4×D1112yes—
496C22×C4D4×D1114yes—
497C4⋊C4—448no—
498C4⋊C4—448no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C22⋊C4—2216no—
502C22⋊C4—444no—
503C22⋊C4—444no—
504C22⋊C4—448no—
505C22⋊C4—444no—
506C42—448no—
507C11#1441011yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—24no—
522C23—24no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23#6693014yes—
550C23C22×C4×D1111yescharacteristic
551C23C2×D4×D1112yes—
552C23C2×#434112yes—
553C23#6703711yescharacteristic
554C23#6703711yescharacteristic
555C23#6703712yes—
556C23#6703712yes—
557C23#41×D1112yes—
558C23#6704312yes—
559D4—416no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—118no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—4416no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C22—24no—
609C22—28no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—42no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×#6693011yescharacteristic
627C22#1062301711yescharacteristic
628C22#1062301711yescharacteristic
629C22C4×D4×D1112yes—
630C22#1062307712yes—
631C22#1062312212yes—
632C22#1062312312yes—
633C22#1062312412yes—
634C22#1062312412yes—
635C22#1062312912yes—
636C22#1062313212yes—
637C22#1062313912yes—
638C22#1062314112yes—
639C22#1062314612yes—
640C22#1062315212yes—
641C22#1062318112yes—
642C22#1062319312yes—
643C22#1062320311yescharacteristic
644C22#1062321011yescharacteristic
645C22#1062324811yescharacteristic
646C22#1062325111yescharacteristic
647C4—44no—
648C4—42no—
649C4—82no—
650C4—228no—
651C4—444no—
652C4—444no—
653C4—882no—
654C2—44no—
655C2—82no—
656C2#1307121211yescharacteristic
657C2#1307130612yes—
658C2#1307154312yes—
659C2#1307159711yescharacteristic
660C2#1307176611yescharacteristic
661C2#1307492212yes—
662C2#1307524912yes—
663C2#1307526412yes—
664C2#1307572412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C2×#10622557C2semidirect
3. C2×#10622555C2semidirect
4. #13066874C2semidirect
5. #13066859C2semidirect
7. #13066853C2semidirect
8. #13066851C2semidirect
24. #10622833C4semidirect
88. C11⋊#95D4semidirect
507. C11#14410semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106228332
C2×#106225552
#130668742
#130668592
#130668572
#130668532
#130668512
C11×#14382
#1441011