Finite Group Databasebeta

← #14684378

Subgroups — #14684378

Order 2816.

1550 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2#13066864C212yesmaximal, complemented
3#13066856C212yesmaximal
4#13066852C212yesmaximal, complemented
5#13066852C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066848C211yesmaximal, characteristic, complemented
8#13066840C212yesmaximal, complemented
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×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×D44—42no—
42C22×D44—42no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
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)⋊C4C2×C418yes—
66C2×(C2×D11)⋊C4C2×C418yes—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—42no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—41no—
72C11×#95—42no—
73C11×#95—41no—
74C11×#95—42no—
75C11×#95—41no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—41no—
82C11⋊#95C2×C414yes—
83#14617—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×D11C22×C414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
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—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
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×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
148C22×Dic11#4114yes—
149C22×Dic11#4114yes—
150C2×D44—44no—
151C2×D44—48no—
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—48no—
163C4×Dic11—44no—
164C2×#394—111no—
165#1445D1111yescharacteristic, complemented
166#1440—112no—
167#1438—112no—
168#1437—112no—
169#1437—112no—
170#1437—112no—
171#1436—111no—
172#1434—112no—
173C23×C11C23×C411yescharacteristic
174C23×C11C2×#4112yes—
175C23×C11C2×#4112yes—
176C23×C11C2×#4112yes—
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)12yes—
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)12yes—
181C23×C11H(5,𝔽2)12yes—
182C22×D11—24no—
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—42no—
190C22×D11—42no—
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—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
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×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—
267D44—416no—
268C23×D4—111no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C22⋊C4—112no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C42—112no—
277C22×C42—111no—
278#394—118no—
279C2×#95—111no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—111no—
286C2×#95C2×D1112yes—
287C2×#95C2×D1112yes—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1111yescharacteristic
290C22×C11C4×#4111yescharacteristic
291C22×C11C4×#4112yes—
292C22×C11#51811yescharacteristic
293C22×C11#51811yescharacteristic
294C22×C11#51812yes—
295C22×C11#53812yes—
296C22×C11#53812yes—
297C22×C11#53812yes—
298C22×C11#54012yes—
299C22×C11#54012yes—
300C22×C11#54012yes—
301C22×C11#55112yes—
302C22×C11#55112yes—
303C22×C11#55312yes—
304C22×C11#55312yes—
305C22×C11#55511yescharacteristic
306C22×C11#55511yescharacteristic
307C22×C11#55912yes—
308C22×C11#56011yescharacteristic
309C22×C11#56012yes—
310C22×C11H(3,𝔽4)11yescharacteristic
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—44no—
330C4×C11—82no—
331Dic11—44no—
332Dic11—44no—
333Dic11—44no—
334C25—112no—
335C22×D4—114no—
336C22×D4—442no—
337C22×D4—441no—
338C22×D4—441no—
339C22×D4—442no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1112yes—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4C4×D1114yes—
351C2×C22⋊C4—118no—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—224no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—224no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—442no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4—442no—
362C2×C22⋊C4—442no—
363C2×C22⋊C4—442no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C42—224no—
370C2×C42—442no—
371C2×C42—442no—
372C2×C42—441no—
373C2×C42—442no—
374#95—42no—
375#95—41no—
376#95—42no—
377#95—41no—
378#95—114no—
379#95—224no—
380#95—224no—
381#95—441no—
382#95—442no—
383#95—442no—
384#95—442no—
385C2×C11#233311yescharacteristic
386C2×C11#233312yes—
387C2×C11#237211yescharacteristic
388C2×C11#237412yes—
389C2×C11#237511yescharacteristic
390C2×C11#275212yes—
391C2×C11#275312yes—
392C2×C11#275612yes—
393C2×C11#280312yes—
394D11—84no—
395C24—114no—
396C24—222no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24—222no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24C23×D1111yescharacteristic
411C2×D4—444no—
412C2×D4—448no—
413C2×D4—444no—
414C2×D4—448no—
415C2×D4—444no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
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—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—114no—
442C22×C4—114no—
443C22×C4—114no—
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×C4C2×C4×D1112yes—
463C22×C4C2×C4×D1112yes—
464C22×C4C2×C4×D1112yes—
465C22×C4#434314yes—
466C4⋊C4—44no—
467C22⋊C4—448no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C42—448no—
474C42—444no—
475C11#1461711yescharacteristic, complemented, Sylow
476C23—224no—
477C23—224no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—224no—
482C23—224no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—442no—
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—
511C23C22×C4×D1111yescharacteristic
512C23#6703711yescharacteristic
513C23#6703712yes—
514C23#6703711yescharacteristic
515C23C2×#434312yes—
516C23#41×D1112yes—
517C23#41×D1112yes—
518C23#6704212yes—
519C23#6704212yes—
520D4—4416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
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—
571C22—444no—
572C22—444no—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—444no—
578C22—882no—
579C22—882no—
580C22—882no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22—882no—
585C22—882no—
586C22#1062301711yescharacteristic
587C22#1062305211yescharacteristic
588C22#1062305311yescharacteristic
589C22#1062307612yes—
590C22C4×#434312yes—
591C22#1062315112yes—
592C22#1062316812yes—
593C22#1062316812yes—
594C22#1062317512yes—
595C22#1062318812yes—
596C22#1062319412yes—
597C22#1062319412yes—
598C22#1062319512yes—
599C22#1062320111yescharacteristic
600C22#1062321411yescharacteristic
601C22#1062322612yes—
602C22#1062322912yes—
603C22#1062323512yes—
604C22#1062324012yes—
605C22#1062325111yescharacteristic
606C22#1062326511yescharacteristic
607C4—42no—
608C4—42no—
609C4—42no—
610C4—44no—
611C4—82no—
612C4—444no—
613C4—444no—
614C4—444no—
615C2—884no—
616C2#1307137811yescharacteristic
617C2#1307138012yes—
618C2#1307172711yescharacteristic
619C2#1307174812yes—
620C2#1307175311yescharacteristic
621C2#1307588512yes—
622C2#1307589912yes—
623C2#1307594412yes—
624C2#1307655412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#14617
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. #13066864C2semidirect
4. #13066852C2semidirect
5. #13066852C2semidirect
6. #13066852C2semidirect
7. #13066848C2semidirect
8. #13066840C2semidirect
9. C11×#1445C2semidirect
31. #10622604C4semidirect
165. #1445D11semidirect
475. C11#14617semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
#130668642
#130668562
#130668522
#130668482
#130668402
C11×#14452
#1461711