Finite Group Databasebeta

← #14718922

Subgroups — #14718922

Order 2816.

1426 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
1#13066885C211yesmaximal, characteristic, complemented
2#13066882C212yesmaximal, complemented
3#13066862C212yesmaximal, complemented
4#13066860C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066858C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic
8#13066856C212yesmaximal
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C24×D11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C22×D44—41no—
41C22×D44—42no—
42C22×D44—41no—
43C22×D44—42no—
44C22×D44Q814yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×(C2×D11)⋊C4—24no—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—42no—
53C2×(C2×D11)⋊C4—42no—
54C2×(C2×D11)⋊C4—42no—
55C2×(C2×D11)⋊C4—42no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
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×C4⋊Dic11—22no—
67C2×C4⋊Dic11—41no—
68C2×C4⋊Dic11—41no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—42no—
71C2×Dic11⋊C4—42no—
72C11×#95—41no—
73C11×#95—42no—
74C11×#95—41no—
75C11×#95—42no—
76C11⋊#95—41no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95—41no—
83#17273—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—22no—
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×D11C2×Q814yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
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×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
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#4114yes—
150C2×D44—48no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—48no—
154C2×D44—44no—
155C11×C4⋊C4—44no—
156(C2×D11)⋊C4—48no—
157(C2×D11)⋊C4—48no—
158(C2×D11)⋊C4—48no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4—48no—
162C4⋊Dic11—44no—
163Dic11⋊C4—48no—
164#1445—112no—
165#1445—111no—
166#1445D1111yescharacteristic, complemented
167#1439—112no—
168#1439—112no—
169#1439—112no—
170#1439—112no—
171#1438—111no—
172#1438—112no—
173C23×C11C22×Q811yescharacteristic
174C23×C11C2×#4111yescharacteristic
175C23×C11C2×#4111yescharacteristic
176C23×C11C2×#4112yes—
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)12yes—
180C23×C11H(5,𝔽2)11yescharacteristic
181C23×C11H(5,𝔽2)12yes—
182C23×C11H(5,𝔽2)11yescharacteristic
183C23×C11H(5,𝔽2)12yes—
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
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—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
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—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
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—
269D44—416no—
270C23×D4—111no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C2×#95—111no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—111no—
287C2×#95C2×D1112yes—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1111yescharacteristic
290C2×#95C2×D1112yes—
291C22×C11#53812yes—
292C22×C11#53811yescharacteristic
293C22×C11#53811yescharacteristic
294C22×C11#54012yes—
295C22×C11#54012yes—
296C22×C11#54012yes—
297C22×C11#54012yes—
298C22×C11#54312yes—
299C22×C11#54311yescharacteristic
300C22×C11#55112yes—
301C22×C11#55112yes—
302C22×C11#55411yescharacteristic
303C22×C11#55411yescharacteristic
304C22×C11#55412yes—
305C22×C11#55911yescharacteristic
306C22×C11#55911yescharacteristic
307C22×C11#56012yes—
308C22×C11#56011yescharacteristic
309C22×C11#56012yes—
310C22×C11#56012yes—
311C22×C11#56011yescharacteristic
312C22×C11H(3,𝔽4)11yescharacteristic
313C22×C11H(3,𝔽4)11yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C2×D11—82no—
328C2×D11—82no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—82no—
333C4×C11—82no—
334Dic11—44no—
335Dic11—82no—
336Dic11—82no—
337C25—112no—
338C22×D4—114no—
339C22×D4—441no—
340C22×D4—442no—
341C22×D4—441no—
342C22×D4—442no—
343C23×C4—112no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4C22×D1112yes—
347C23×C4C22×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C2×C4⋊C4—22no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—442no—
357C2×C4⋊C4—442no—
358C2×C4⋊C4—441no—
359C2×C4⋊C4—441no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—442no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378#95—42no—
379#95—41no—
380#95—41no—
381#95—42no—
382#95—442no—
383#95—441no—
384#95—441no—
385#95—442no—
386#95—442no—
387#95—442no—
388#95—442no—
389C2×C11#274812yes—
390C2×C11#274812yes—
391C2×C11#275212yes—
392C2×C11#275211yescharacteristic
393C2×C11#275211yescharacteristic
394C2×C11#280411yescharacteristic
395C2×C11#280411yescharacteristic
396C2×C11#282812yes—
397C2×C11#282811yescharacteristic
398C2×C11#282811yescharacteristic
399C2×C11#284211yescharacteristic
400D11—84no—
401C24—114no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24—222no—
411C24—222no—
412C24—222no—
413C24—222no—
414C24—222no—
415C24—222no—
416C24C23×D1111yescharacteristic
417C2×D4—444no—
418C2×D4—448no—
419C2×D4—444no—
420C2×D4—448no—
421C2×D4—444no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
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—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—114no—
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#433912yes—
470C22×C4Q8×D1112yes—
471C22×C4#434312yes—
472C4⋊C4—44no—
473C4⋊C4—444no—
474C4⋊C4—448no—
475C22⋊C4—448no—
476C22⋊C4—448no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C22⋊C4—448no—
480C22⋊C4—448no—
481C11#1727311yescharacteristic, complemented, Sylow
482C23—224no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
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—
517C23C2×#433911yescharacteristic
518C23#6703711yescharacteristic
519C23#6703712yes—
520C23#6703711yescharacteristic
521C23C2×Q8×D1111yescharacteristic
522C23C2×#434311yescharacteristic
523C23#41×D1112yes—
524C23#6704211yescharacteristic
525C23#6704212yes—
526C23#6704211yescharacteristic
527C23#6704212yes—
528D4—4416no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
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—42no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
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—
579C22—444no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22—444no—
584C22—444no—
585C22—444no—
586C22—882no—
587C22—882no—
588C22—882no—
589C22—882no—
590C22—882no—
591C22—882no—
592C22—882no—
593C22—882no—
594C22#1062302511yescharacteristic
595C22#1062305812yes—
596C22#1062309312yes—
597C22#1062311011yescharacteristic
598C22#1062311611yescharacteristic
599C22#1062315112yes—
600C22#1062316511yescharacteristic
601C22#1062316512yes—
602C22#1062316812yes—
603C22#1062317511yescharacteristic
604C22#1062319412yes—
605C22#1062319412yes—
606C22#1062319511yescharacteristic
607C22#1062319712yes—
608C22#1062319711yescharacteristic
609C22#1062321411yescharacteristic
610C22#1062321411yescharacteristic
611C22#1062322112yes—
612C22#1062322912yes—
613C22#1062323512yes—
614C22#1062324212yes—
615C22#1062325111yescharacteristic
616C22#1062326111yescharacteristic
617C4—42no—
618C4—42no—
619C4—42no—
620C4—82no—
621C4—82no—
622C4—444no—
623C4—882no—
624C4—882no—
625C2—884no—
626C2#1307582412yes—
627C2#1307582812yes—
628C2#1307587912yes—
629C2#1307588011yescharacteristic
630C2#1307588511yescharacteristic
631C2#1307656011yescharacteristic
632C2#1307656111yescharacteristic
633C2#1307673511yescharacteristic
634C2#1307673712yes—
635C2#1307674011yescharacteristic
636C2#1307688111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1445C2
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#17273
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. #13066885C2semidirect
2. #13066882C2semidirect
3. #13066862C2semidirect
4. #13066860C2semidirect
5. #13066860C2semidirect
6. #13066858C2semidirect
9. C11×#1445C2semidirect
166. #1445D11semidirect
481. C11#17273semidirect

Maximal subgroups

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

subgroupindex
#130668852
#130668822
#130668622
#130668602
#130668582
#130668562
C11×#14452
#1727311