Finite Group Databasebeta

← #14682921

Subgroups — #14682921

Order 2816.

1558 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×#10622834C211yesmaximal, characteristic
2#13066863C212yesmaximal, complemented
3#13066863C212yesmaximal, complemented
4#13066857C211yesmaximal, characteristic
5#13066853C212yesmaximal, complemented
6#13066853C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
8#13066842C212yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23#10622834C418yescomplemented
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—24no—
35C22×D4×C11—42no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4—41no—
49C2×C11×C22⋊C4—42no—
50C2×C11×C22⋊C4—42no—
51C2×C11×C22⋊C4—41no—
52C2×C11×C22⋊C4—42no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—42no—
56C2×C22⋊Dic11—42no—
57C2×C22⋊Dic11—42no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—41no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—41no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11C2×C418yes—
65C2×C22⋊Dic11C2×C418yes—
66C2×C4⋊Dic11—41no—
67C2×C4⋊Dic11—41no—
68C2×C4⋊Dic11C2×C414yes—
69C2×C4×Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—42no—
72C2×C4×Dic11—42no—
73C2×C4×Dic11C2×C414yes—
74C11×#95—24no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83#14503—111nomaximal, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11C22×C412yes—
101C24×C11C22×C412yes—
102C24×C11C2411yescharacteristic
103C2×D4×C11—28no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—48no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
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×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11#4114yes—
126C22×C4×C11#4114yes—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
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×Dic11C22×C414yes—
153C22×Dic11C22×C414yes—
154C22×Dic11#4114yes—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—48no—
157C11×C22⋊C4—44no—
158C22⋊Dic11—48no—
159C22⋊Dic11—48no—
160C22⋊Dic11—44no—
161C22⋊Dic11—48no—
162C22⋊Dic11—44no—
163C4⋊Dic11—44no—
164C4×Dic11—44no—
165C4×Dic11—48no—
166C2×#390—111no—
167#1440—112no—
168#1440—112no—
169#1438—111no—
170#1438D1111yescharacteristic
171#1437—112no—
172#1437—112no—
173#1436—112no—
174#1434—112no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11C23×C411yescharacteristic
218C23×C11C2×#4112yes—
219C23×C11C2×#4112yes—
220C23×C11C2×#4112yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C11H(5,𝔽2)11yescharacteristic
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226D4×C11—416no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11#11714yes—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
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—
274C23×D4C2×D1111yescharacteristic
275C22×C4⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4C2×D1111yescharacteristic
282C22×C22⋊C4C2×D1112yes—
283C22×C22⋊C4C2×D1111yescharacteristic
284C22×C42—111no—
285C22×C42—112no—
286#390—118no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95C2×D1112yes—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11C2×#11711yescharacteristic
315C22×C11C4×#4112yes—
316C22×C11#51811yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11#51812yes—
319C22×C11#53812yes—
320C22×C11#53812yes—
321C22×C11#53812yes—
322C22×C11#53812yes—
323C22×C11#54012yes—
324C22×C11#54012yes—
325C22×C11#55111yescharacteristic
326C22×C11#55111yescharacteristic
327C22×C11#55312yes—
328C22×C11#55312yes—
329C22×C11#55512yes—
330C22×C11#55912yes—
331C22×C11#55912yes—
332C22×C11#56011yescharacteristic
333C22×C11#56012yes—
334C22×C11#56011yescharacteristic
335C4×C11—24no—
336C4×C11—44no—
337C4×C11—82no—
338Dic11—44no—
339Dic11—44no—
340Dic11—44no—
341Dic11—82no—
342C25C22×D1111yescharacteristic
343C25C22×D1111yescharacteristic
344C22×D4—24no—
345C22×D4—42no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4C4×D1114yes—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—112no—
353C23×C4C22×D1112yes—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C2×C4⋊C4—114no—
357C2×C4⋊C4—441no—
358C2×C4⋊C4—441no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—442no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—441no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—441no—
378C2×C22⋊C4—442no—
379C2×C42—114no—
380C2×C42—442no—
381C2×C42—442no—
382C2×C42—442no—
383C2×C42—442no—
384#95—24no—
385#95—224no—
386#95—224no—
387#95—224no—
388#95—442no—
389#95—442no—
390#95—442no—
391#95—442no—
392#95—442no—
393C2×C11—82no—
394C2×C11—82no—
395C2×C11#231211yescharacteristic
396C2×C11#233312yes—
397C2×C11#235712yes—
398C2×C11#237211yescharacteristic
399C2×C11#238011yescharacteristic
400C2×C11#279712yes—
401C2×C11#279712yes—
402C2×C11#280312yes—
403C2×C11#280312yes—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24C2×C4×D1112yes—
421C24C2×C4×D1112yes—
422C24C23×D1111yescharacteristic
423C2×D4—28no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—48no—
427C2×D4—48no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—114no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
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×C4C2×C4×D1112yes—
473C22×C4#434114yes—
474C22×C4#434114yes—
475C4⋊C4—444no—
476C22⋊C4—44no—
477C22⋊C4—48no—
478C22⋊C4—44no—
479C22⋊C4—448no—
480C22⋊C4—448no—
481C22⋊C4—444no—
482C22⋊C4—448no—
483C22⋊C4—444no—
484C42—444no—
485C42—448no—
486C11#1450311yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23C22×C4×D1111yescharacteristic
530C23C2×#434112yes—
531C23C2×#434112yes—
532C23#6703712yes—
533C23#6703711yescharacteristic
534C23#6703712yes—
535C23#6703711yescharacteristic
536C23#41×D1112yes—
537C23#6704212yes—
538D4—416no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
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#6693014yes—
586C22—44no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—44no—
595C22—44no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22C2×#6693011yescharacteristic
605C22#1062301711yescharacteristic
606C22#1062301711yescharacteristic
607C22C4×#434112yes—
608C22#1062307612yes—
609C22#1062311811yescharacteristic
610C22#1062312412yes—
611C22#1062312412yes—
612C22#1062312412yes—
613C22#1062312611yescharacteristic
614C22#1062314512yes—
615C22#1062314612yes—
616C22#1062314712yes—
617C22#1062314912yes—
618C22#1062315012yes—
619C22#1062315112yes—
620C22#1062318812yes—
621C22#1062319011yescharacteristic
622C22#1062319711yescharacteristic
623C22#1062321212yes—
624C22#1062324412yes—
625C4—24no—
626C4—44no—
627C4—82no—
628C4—444no—
629C4—444no—
630C4—444no—
631C4—882no—
632C2—82no—
633C2—82no—
634C2#1307121211yescharacteristic
635C2#1307137712yes—
636C2#1307158812yes—
637C2#1307172511yescharacteristic
638C2#1307179111yescharacteristic
639C2#1307647512yes—
640C2#1307648012yes—
641C2#1307655112yes—
642C2#1307655512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #13066863C2semidirect
3. #13066863C2semidirect
5. #13066853C2semidirect
6. #13066853C2semidirect
7. #13066850C2semidirect
8. #13066842C2semidirect
23. #10622834C4semidirect
486. C11#14503semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
#130668632
#130668572
#130668532
#130668502
#130668422
C11×#14382
#1450311