Finite Group Databasebeta

← #14718914

Subgroups — #14718914

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#13066877C212yesmaximal, complemented
2#13066870C212yesmaximal, complemented
3#13066861C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066857C211yesmaximal, characteristic
8#13066857C211yesmaximal, characteristic
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yes—
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C25×C11C2311yescharacteristic
32C25×C11C2311yescharacteristic
33C22×D4×C11—42no—
34C22×D4×C11—42no—
35C22×D4×C11—41no—
36C22×D4×C11—41no—
37C22×D4×C11Q814yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—42no—
48C2×C11×C22⋊C4—42no—
49C2×C11×C22⋊C4—42no—
50C2×C11×C22⋊C4—42no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—41no—
54C2×C22⋊Dic11—42no—
55C2×C22⋊Dic11—42no—
56C2×C22⋊Dic11—42no—
57C2×C22⋊Dic11—41no—
58C2×C22⋊Dic11—41no—
59C2×C22⋊Dic11—42no—
60C2×C22⋊Dic11—41no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C4⋊Dic11—42no—
66C2×C4⋊Dic11—42no—
67C2×C4⋊Dic11—42no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—42no—
70C2×Dic11⋊C4—42no—
71C11×#95—41no—
72C11×#95—41no—
73C11⋊#95—24no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81#17272—111nomaximal, Sylow
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—21no—
92C24×C11—21no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C2×Q812yes—
99C24×C11C2×Q812yes—
100C24×C11C2411yescharacteristic
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—48no—
105C2×D4×C11—48no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
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×C11C2×Q812yes—
124C22×C4×C11#4114yes—
125C22×Dic11—22no—
126C22×Dic11—22no—
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×Dic11#4114yes—
153C11×C22⋊C4—48no—
154C11×C22⋊C4—48no—
155C22⋊Dic11—44no—
156C22⋊Dic11—48no—
157C22⋊Dic11—44no—
158C22⋊Dic11—48no—
159C22⋊Dic11—44no—
160C22⋊Dic11—44no—
161C4⋊Dic11—48no—
162Dic11⋊C4—48no—
163#1443—112no—
164#1441—112no—
165#1439—112no—
166#1439—112no—
167#1439—112no—
168#1439—112no—
169#1438—111no—
170#1438—111no—
171#1438D1111yescharacteristic
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
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—41no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×Q811yescharacteristic
215C23×C11C2×#4112yes—
216C23×C11C2×#4112yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)11yescharacteristic
219C23×C11H(5,𝔽2)12yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C11H(5,𝔽2)12yes—
223D4×C11—416no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
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×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
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—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C23×D4C2×D1111yescharacteristic
272C22×C4⋊C4—112no—
273C22×C4⋊C4—112no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—111no—
280C22×C22⋊C4C2×D1112yes—
281C22×C22⋊C4C2×D1112yes—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95C2×D1111yescharacteristic
291C2×#95C2×D1111yescharacteristic
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11#53812yes—
311C22×C11#53812yes—
312C22×C11#53812yes—
313C22×C11#53812yes—
314C22×C11#54012yes—
315C22×C11#54012yes—
316C22×C11#54311yescharacteristic
317C22×C11#54311yescharacteristic
318C22×C11#54311yescharacteristic
319C22×C11#55111yescharacteristic
320C22×C11#55312yes—
321C22×C11#55412yes—
322C22×C11#55412yes—
323C22×C11#55512yes—
324C22×C11#55911yescharacteristic
325C22×C11#56011yescharacteristic
326C22×C11#56012yes—
327C22×C11#56012yes—
328C22×C11#56012yes—
329C22×C11#56012yes—
330C22×C11H(3,𝔽4)11yescharacteristic
331C4×C11—44no—
332C4×C11—42no—
333C4×C11—82no—
334Dic11—44no—
335Dic11—82no—
336Dic11—82no—
337Dic11—82no—
338C25C22×D1111yescharacteristic
339C25C22×D1111yescharacteristic
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4Dic2214yes—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4C22×D1112yes—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C2×C4⋊C4—224no—
353C2×C4⋊C4—442no—
354C2×C4⋊C4—442no—
355C2×C4⋊C4—442no—
356C2×C4⋊C4—442no—
357C2×C4⋊C4—442no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—441no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—441no—
371C2×C22⋊C4—441no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—441no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378#95—41no—
379#95—41no—
380#95—224no—
381#95—442no—
382#95—442no—
383#95—442no—
384#95—442no—
385#95—442no—
386#95—442no—
387#95—442no—
388C2×C11—82no—
389C2×C11—82no—
390C2×C11#274811yescharacteristic
391C2×C11#275612yes—
392C2×C11#278012yes—
393C2×C11#278412yes—
394C2×C11#280312yes—
395C2×C11#280411yescharacteristic
396C2×C11#282512yes—
397C2×C11#282812yes—
398C2×C11#284211yescharacteristic
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24C2×Dic2212yes—
416C24C2×Dic2212yes—
417C24C23×D1111yescharacteristic
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—48no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
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—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—114no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
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×C4C2×Dic2212yes—
469C22×C4#434114yes—
470C4⋊C4—448no—
471C4⋊C4—448no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C22⋊C4—444no—
475C22⋊C4—448no—
476C22⋊C4—444no—
477C22⋊C4—448no—
478C22⋊C4—444no—
479C22⋊C4—444no—
480C11#1727211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×Dic2211yescharacteristic
524C23C2×#434112yes—
525C23#6703711yescharacteristic
526C23#6703711yescharacteristic
527C23#6703712yes—
528C23#6703712yes—
529C23#6703712yes—
530C23#41×D1112yes—
531C23#6704212yes—
532D4—416no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
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—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—442no—
556C2×C4—442no—
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—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—
580C22—44no—
581C22—44no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—44no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22#1062301411yescharacteristic
599C22#1062301411yescharacteristic
600C22#1062301411yescharacteristic
601C22#1062307012yes—
602C22#1062307412yes—
603C22#1062312412yes—
604C22#1062312412yes—
605C22#1062312612yes—
606C22#1062312612yes—
607C22#1062314512yes—
608C22#1062314612yes—
609C22#1062314712yes—
610C22#1062314812yes—
611C22#1062315112yes—
612C22#1062315112yes—
613C22#1062318812yes—
614C22#1062319412yes—
615C22#1062321011yescharacteristic
616C22#1062321411yescharacteristic
617C22#1062324411yescharacteristic
618C22#1062325111yescharacteristic
619C4—42no—
620C4—44no—
621C4—82no—
622C4—444no—
623C4—882no—
624C4—882no—
625C4—882no—
626C2—82no—
627C2—82no—
628C2#1307582911yescharacteristic
629C2#1307593712yes—
630C2#1307626812yes—
631C2#1307631412yes—
632C2#1307655512yes—
633C2#1307656211yescharacteristic
634C2#1307670412yes—
635C2#1307673212yes—
636C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#17272
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13066877C2semidirect
2. #13066870C2semidirect
3. #13066861C2semidirect
4. #13066861C2semidirect
5. #13066859C2semidirect
6. #13066859C2semidirect
480. C11#17272semidirect

Maximal subgroups

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

subgroupindex
#130668772
#130668702
#130668612
#130668592
#130668572
C11×#14382
#1727211