Finite Group Databasebeta

← #14788824

Subgroups — #14788824

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic, complemented
4C2×#10622650C212yesmaximal, complemented
5#13069857C212yesmaximal, complemented
6#13069692C212yesmaximal, complemented
7#13069543C211yesmaximal, characteristic, complemented
8#13069539C211yesmaximal, characteristic, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068554C212yesmaximal, complemented
11C4×C11×#121C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×#4324C2212yes—
18C22×#4323C2212yes—
19C2×#66983—21no—
20C2×#66983—21no—
21#10623008—24no—
22#10623008—24no—
23C2×#66928C2212yes—
24C2×#66927C2211yescharacteristic
25C2×C4×D44—21no—
26C2×C4×D44—21no—
27C2×#66922C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#388—21no—
31C11×#386—21no—
32C11×#380C2211yescharacteristic
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C22⋊C4—21no—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622650—28no—
37#10622632—24no—
38#10622628—24no—
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66874C2212yes—
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66873C2212yes—
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622162C2212yes—
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—22no—
55C2×#4339—24no—
56C2×#4339—24no—
57C2×#4339—24no—
58C2×#4339—24no—
59C2×#4339—42no—
60C2×#4339—42no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44C2312yes—
64C22×C4×D11—22no—
65C22×Dic22C2312yes—
66C11×#121—22no—
67C11×#121D414yescomplemented
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—44no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11—21no—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—24no—
88C2×#4324—24no—
89C2×#4324—42no—
90C2×#4323—24no—
91C2×#4323—24no—
92C2×#4323—42no—
93#66983—28no—
94#66983—28no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66928—24no—
102#66928—24no—
103#66927—22no—
104#66927D414yescomplemented
105C4×D44—28no—
106C4×D44—28no—
107#66922—22no—
108#66922D414yescomplemented
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C22⋊(C11⋊C8)—24no—
113#66874—24no—
114#66874—24no—
115#66874—42no—
116#66873—24no—
117#66873—24no—
118#66873—42no—
119C4⋊(C11⋊C8)—22no—
120C4⋊(C11⋊C8)—22no—
121#24210—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C23×D11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C22×Dic11—22no—
162#4339—48no—
163#4339—48no—
164#4339—48no—
165#4339—48no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—42no—
174C2×D44—42no—
175C2×D44—42no—
176C2×D44—42no—
177C2×D44C2×D414yes—
178C2×C4×D11—28no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×Dic22—22no—
182C2×Dic22—22no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22C2×D414yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—42no—
196C11×C22⋊C4—42no—
197C11×C22⋊C4—42no—
198C11×C22⋊C4—42no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—42no—
204C42×C11C2×D412yes—
205C42×C11C2×D412yes—
206#4324—48no—
207#4323—48no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210C4⋊Dic11—24no—
211C4⋊Dic11—24no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×#532—111no—
219C2×#461—111no—
220C2×#459—111no—
221C2×#449—112no—
222C4×#121D1111yescharacteristic, complemented
223#2042—112no—
224#2012—112no—
225#1982—111no—
226#1981—111no—
227#1797—111no—
228#1788—112no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11#12112yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—24no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—48no—
254D4×C11—41no—
255D4×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—44no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—44no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—84no—
282C2×C4×C11#12012yes—
283C2×C4×C11#12012yes—
284C2×C4×C11#12112yes—
285C2×C4×C11#13512yes—
286C2×C4×C11AGL(1,ℤ/8)12yes—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C22⋊D11—416no—
294C2×Dic11—24no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297D44—24no—
298D44—24no—
299D44—48no—
300D44—42no—
301D44—42no—
302D44—48no—
303C4×D11—416no—
304Dic22—24no—
305Dic22—24no—
306Dic22—42no—
307Dic22—42no—
308C11⋊C8—42no—
309C11⋊C8—42no—
310C22×#41—112no—
311C22×SD16—112no—
312C22×D8—112no—
313#532—224no—
314#532—224no—
315C2×C4⋊Q8—111no—
316C2×#127—111no—
317C2×#124—112no—
318C2×#121—221no—
319C2×#121—221no—
320C2×#121C2×D1111yescharacteristic
321C2×C4×D4—21no—
322C2×C4×D4—221no—
323C2×C4×D4—221no—
324C2×C4×D4C2×D1111yescharacteristic
325C22×C42C2×D1111yescharacteristic
326#461—224no—
327#459—224no—
328#449—228no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8—111no—
331C2×#103—112no—
332C2×#103—112no—
333C2×#103—112no—
334C2×#102—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×C22⋊C8—112no—
338#390C2×D1111yescharacteristic
339#389C2×D1111yescharacteristic
340#388—21no—
341#386—21no—
342#380C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—21no—
345#336—112no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11#53511yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57511yescharacteristic
367C2×D11—44no—
368C2×D11—44no—
369C2×D11—44no—
370C2×D11—82no—
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#44914yescomplemented
382C4×C11D4211yescharacteristic
383C4×C11D4211yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#54611yescharacteristic
386Dic11—44no—
387C2×#41—224no—
388C2×#41—224no—
389C2×#41—224no—
390C2×#41—224no—
391C2×#41—442no—
392C2×#41—442no—
393C22×Q8—112no—
394C22×D4—21no—
395C22×D4—112no—
396C22×D4—222no—
397C22×D4—221no—
398C22×D4—221no—
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
401C23×C4—222no—
402C23×C4C22⋊D1111yescharacteristic
403C23×C4C22⋊D1111yescharacteristic
404C23×C4C22×D1111yescharacteristic
405C2×SD16—224no—
406C2×SD16—224no—
407C2×SD16—442no—
408C2×D8—224no—
409C2×D8—224no—
410C2×D8—442no—
411C22×C8—112no—
412C22×C8—112no—
413C4⋊Q8—114no—
414C4⋊Q8—222no—
415#127—114no—
416#127—222no—
417#124—224no—
418#124—224no—
419#121—22no—
420#121—228no—
421#121—228no—
422#121D4414yescomplemented
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—44no—
426C4×D4—228no—
427C4×D4—228no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—21no—
444C2×C42C22⋊D1111yescharacteristic
445C2×C42C22⋊D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—222no—
449C4⋊C8—222no—
450#103—224no—
451#103—224no—
452#103—442no—
453#102—224no—
454#102—224no—
455#102—442no—
456C22⋊C8—224no—
457#95—21no—
458#95—21no—
459#95—21no—
460C2×C11—42no—
461C2×C11—82no—
462C2×C11#240811yescharacteristic
463C2×C11C2×#44911yescharacteristic
464C2×C11#300511yescharacteristic
465C2×C11#303511yescharacteristic
466C2×C11#303611yescharacteristic
467C2×C11#321211yescharacteristic
468C2×C11#321411yescharacteristic
469D11—84no—
470C24—21no—
471C24—222no—
472C24C2×C22⋊D1111yescharacteristic
473#41—448no—
474#41—448no—
475#41—448no—
476#41—448no—
477C2×Q8—114no—
478C2×Q8—222no—
479C2×Q8—222no—
480C2×Q8—222no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—114no—
492C2×D4—228no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—222no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4—222no—
499C2×D4—222no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—444no—
503C2×D4—444no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4C2×D4412yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—228no—
524C22×C4—222no—
525C22×C4—444no—
526C22×C4—444no—
527C22×C4C2×D4412yes—
528C22×C4#433912yes—
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1111yescharacteristic
532C22×C4C2×C22⋊D1111yescharacteristic
533C22×C4C2×C22⋊D1111yescharacteristic
534C22×C4C23×D1111yescharacteristic
535SD16—448no—
536D8—448no—
537C2×C8—222no—
538C2×C8—222no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—222no—
542C2×C8—222no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4C2×D4412yes—
552C22⋊C4—24no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C42—22no—
560C42—22no—
561C42—21no—
562C42—21no—
563C42—42no—
564C42D4×D1112yes—
565C42D4×D1112yes—
566C11#2421011yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—224no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23—442no—
585C23—442no—
586C23—442no—
587C23#6698312yes—
588C23C22×C22⋊D1111yescharacteristic
589Q8—224no—
590Q8—224no—
591Q8—442no—
592Q8—442no—
593D4—22no—
594D4—22no—
595D4—48no—
596D4—41no—
597D4—41no—
598D4—224no—
599D4—224no—
600D4—448no—
601D4—4416no—
602D4—442no—
603D4—442no—
604D4—448no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—44no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—44no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—84no—
631C2×C4—224no—
632C2×C4—4416no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4#6698312yes—
636C2×C4#6698512yes—
637C2×C4#6699012yes—
638C2×C4#6699012yes—
639C2×C4#6700312yes—
640C2×C4C22×D4411yescharacteristic
641C2×C4C2×#433911yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C2×C4C2×D4×D1111yescharacteristic
644C2×C4#6704211yescharacteristic
645C2×C4#6704211yescharacteristic
646C8—442no—
647C8—442no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—444no—
663C22—444no—
664C22—444no—
665C22—882no—
666C22—882no—
667C22—882no—
668C22—882no—
669C22C2×#6698311yescharacteristic
670C22C2×#6698511yescharacteristic
671C22C2×#6699011yescharacteristic
672C22C2×#6700311yescharacteristic
673C22#1062335311yescharacteristic
674C22#1062335311yescharacteristic
675C22#1062336111yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—42no—
680C4—41no—
681C4—81no—
682C4—81no—
683C4—444no—
684C4#1062265014yescomplemented
685C4D4×D4411yescharacteristic
686C4D4×D4411yescharacteristic
687C4#1062308111yescharacteristic
688C4#1062308111yescharacteristic
689C2—42no—
690C2—82no—
691C2—884no—
692C2#1307197211yescharacteristic
693C2C2×#1062265011yescharacteristic
694C2#1307785611yescharacteristic
695C2#1307807111yescharacteristic
696C2#1307808011yescharacteristic
697C2#1307958811yescharacteristic
698C2#1307960711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
hypercenterC4×#121D11
hypocenterC11#24210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10622632C2semidirect
3. C2×#10622628C2semidirect
4. C2×#10622650C2semidirect
5. #13069857C2semidirect
6. #13069692C2semidirect
7. #13069543C2semidirect
8. #13069539C2semidirect
9. #13068596C2semidirect
10. #13068554C2semidirect
11. C4×C11×#121C2semidirect
67. C11×#121D4semidirect
104. #66927D4semidirect
108. #66922D4semidirect
222. C4×#121D11semidirect
381. C4×C11#449semidirect
422. #121D44semidirect
566. C11#24210semidirect
684. C4#10622650semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106226322
C2×#106226282
C2×#106226502
#130698572
#130696922
#130695432
#130695392
#130685962
#130685542
C4×C11×#1212
#2421011