Finite Group Databasebeta

← #14788875

Subgroups — #14788875

Order 2816.

1642 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic, complemented
2C2×#10622629C212yesmaximal, complemented
3C2×#10622653C211yesmaximal, characteristic, complemented
4C2×#10622649C211yesmaximal, characteristic
5#13069857C212yesmaximal, complemented
6#13069692C212yesmaximal, complemented
7#13069548C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9#13068550C211yesmaximal, characteristic, complemented
10#13068546C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2211yescharacteristic, complemented
17C22×C42×C11C2211yescharacteristic
18C22×#4324C2212yescomplemented
19C22×#4323C2212yes—
20C22×(C2×D11)⋊C4—21no—
21C22×(C2×D11)⋊C4—21no—
22C2×#66928—21no—
23C2×#66928—21no—
24C2×#66928—28no—
25C2×#66928C2212yes—
26C2×#66928C2212yes—
27C11×#390C2211yescharacteristic, complemented
28C11×#389C2211yescharacteristic, complemented
29C11×#388—21no—
30C11×#386—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic, complemented
33C4×C11×C22⋊C4—21no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622653—24no—
37#10622649—24no—
38#10622629—28no—
39C2×#66874C2212yescomplemented
40C2×#66874C2212yescomplemented
41C2×#66874C2212yescomplemented
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66873C2212yes—
45C2×C4⋊(C11⋊C8)C2212yescomplemented
46#10622162C2212yescomplemented
47C24×D11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C22×D44—21no—
56C22×D44—24no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—42no—
60C22×D44C2312yes—
61C22×Dic22—21no—
62C22×Dic22—24no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—42no—
66C22×Dic22C2312yes—
67C11×#121—22no—
68C11×#121D414yes—
69C4×D4×C11—24no—
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—24no—
81C2×C42×C11—21no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324—24no—
87C2×#4324—24no—
88C2×#4324—42no—
89C2×#4323—24no—
90C2×#4323—24no—
91C2×#4323—42no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C22×C11⋊C8C2312yes—
99C22×C11⋊C8C2312yes—
100#66928—28no—
101#66928—28no—
102#66928—24no—
103#66928—24no—
104#66928—24no—
105#66928D418yescomplemented
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—22no—
111#66874—24no—
112#66874—24no—
113#66874—42no—
114#66873—24no—
115#66873—24no—
116#66873—42no—
117C4⋊(C11⋊C8)—24no—
118#24215—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—42no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11—42no—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
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×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C2×D44—24no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—48no—
169C2×D44—48no—
170C2×D44—42no—
171C2×D44—42no—
172C2×D44C2×D414yes—
173C2×Dic22—24no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—48no—
180C2×Dic22—48no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22C2×D414yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—42no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—22no—
197C42×C11—42no—
198C42×C11C2×D414yes—
199#4324—48no—
200#4323—48no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C22×#124—111no—
212C2×#463—112no—
213C2×#448—111no—
214C2×#447—111no—
215C4×#121D1111yescharacteristic, complemented
216#2042—112no—
217#2012—112no—
218#1983—112no—
219#1797—111no—
220#1787—111no—
221#1786—111no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11#12112yes—
234C23×C11#13512yes—
235C23×C11AGL(1,ℤ/8)12yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—24no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—84no—
248C22×D11—84no—
249C22×D11—84no—
250C22×D11—84no—
251D4×C11—24no—
252D4×C11—48no—
253D4×C11—42no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—44no—
270C2×C4×C11—44no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—84no—
280C2×C4×C11#12012yes—
281C2×C4×C11#12012yes—
282C2×C4×C11#12112yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D412yes—
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)12yes—
287C2×Dic11—24no—
288C2×Dic11—48no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291D44—24no—
292D44—24no—
293D44—48no—
294D44—42no—
295D44—42no—
296Dic22—24no—
297Dic22—24no—
298Dic22—48no—
299Dic22—42no—
300Dic22—42no—
301C11⋊C8—42no—
302C11⋊C8—42no—
303C23×Q8—111no—
304C23×D4—111no—
305C22×SD16—112no—
306C22×D8—112no—
307C2×#124—112no—
308C2×#124—112no—
309C2×#124—228no—
310C2×#124—221no—
311C2×#124—221no—
312C2×#121C2×D1111yescharacteristic
313C2×C4×D4—21no—
314C2×C4×D4C2×D1111yescharacteristic, complemented
315C22×C22⋊C4—221no—
316C22×C22⋊C4—221no—
317C22×C42C2×D1111yescharacteristic
318#463—228no—
319#448—224no—
320#447—224no—
321C2×C4⋊C8—112no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#102—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—111no—
330#390C2×D1111yescharacteristic, complemented
331#389C2×D1111yescharacteristic, complemented
332#388—21no—
333#386—21no—
334#380C2×D1111yescharacteristic
335C4×C4⋊C4C2×D1111yescharacteristic, complemented
336C4×C22⋊C4—21no—
337#336—112no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11#46314yescomplemented
352C22×C11C2×#12011yescharacteristic
353C22×C11C2×#12111yescharacteristic
354C22×C11#53511yescharacteristic
355C22×C11C2×#13511yescharacteristic
356C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—816no—
363C2×D11—82no—
364C2×D11—82no—
365C2×D11—82no—
366C2×D11—82no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11D4212yes—
376C4×C11#54612yes—
377Dic11—44no—
378C25—221no—
379C22×Q8—112no—
380C22×Q8—224no—
381C22×Q8—221no—
382C22×Q8—222no—
383C22×Q8—222no—
384C22×Q8—442no—
385C22×D4—21no—
386C22×D4—112no—
387C22×D4—224no—
388C22×D4—222no—
389C22×D4—222no—
390C22×D4—221no—
391C22×D4—442no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—221no—
395C23×C4C22⋊D1111yescharacteristic
396C23×C4C22⋊D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C2×SD16—224no—
399C2×SD16—224no—
400C2×SD16—442no—
401C2×D8—224no—
402C2×D8—224no—
403C2×D8—442no—
404C22×C8—112no—
405C22×C8—112no—
406#124—118no—
407#124—224no—
408#124—224no—
409#124—228no—
410#124—228no—
411#124—224no—
412#121—22no—
413#121D4414yes—
414C4×D4—24no—
415C4×D4—44no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—228no—
426C2×C22⋊C4—228no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C22⋊C4—222no—
431C2×C42—24no—
432C2×C42—21no—
433C2×C42C22⋊D1111yescharacteristic
434C2×C42C22⋊D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—224no—
438#103—224no—
439#103—224no—
440#103—442no—
441#102—224no—
442#102—224no—
443#102—442no—
444C22⋊C8—222no—
445C22⋊C8—222no—
446#95—21no—
447#95—21no—
448#95—21no—
449C2×C11—24no—
450C2×C11—82no—
451C2×C11#240811yescharacteristic
452C2×C11#300211yescharacteristic
453C2×C11#300611yescharacteristic
454C2×C11C2×#46311yescharacteristic
455C2×C11#304011yescharacteristic
456C2×C11#321111yescharacteristic
457C2×C11#321311yescharacteristic
458D11—84no—
459C24—21no—
460C24—224no—
461C24—222no—
462C24—442no—
463C24—442no—
464C24—442no—
465C24—442no—
466C24—442no—
467C24—442no—
468C24C2×C22⋊D1111yescharacteristic
469C2×Q8—114no—
470C2×Q8—224no—
471C2×Q8—222no—
472C2×Q8—222no—
473C2×Q8—222no—
474C2×Q8—222no—
475C2×Q8—222no—
476C2×Q8—448no—
477C2×Q8—448no—
478C2×Q8—442no—
479C2×Q8—442no—
480C2×D4—24no—
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—114no—
487C2×D4—224no—
488C2×D4—222no—
489C2×D4—222no—
490C2×D4—222no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—448no—
494C2×D4—448no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4C2×D4412yes—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4C2×D4412yes—
517C22×C4#433912yes—
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524SD16—448no—
525D8—448no—
526C2×C8—222no—
527C2×C8—222no—
528C2×C8—222no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—42no—
536C4⋊C4C2×D4412yes—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—228no—
543C22⋊C4—228no—
544C22⋊C4—228no—
545C22⋊C4—228no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—42no—
550C42D4×D1114yes—
551C11#2421511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—224no—
564C23—448no—
565C23—448no—
566C23—448no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23—442no—
571C23—442no—
572C23—442no—
573C23—884no—
574C23—884no—
575C23—884no—
576C23—884no—
577C23#6698312yes—
578C23#6698512yes—
579C23#6700312yes—
580C23C22×C22⋊D1111yescharacteristic
581Q8—224no—
582Q8—224no—
583Q8—448no—
584Q8—442no—
585Q8—442no—
586D4—24no—
587D4—48no—
588D4—42no—
589D4—224no—
590D4—224no—
591D4—448no—
592D4—442no—
593D4—442no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4—224no—
621C2×C4—448no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4#6698312yes—
625C2×C4#6699012yes—
626C2×C4#6699012yes—
627C2×C4C22×D4411yescharacteristic
628C2×C4C2×#433911yescharacteristic
629C2×C4C2×D4×D1112yes—
630C2×C4#6704212yes—
631C8—442no—
632C8—442no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—444no—
647C22—444no—
648C22—444no—
649C22—8816no—
650C22—882no—
651C22—882no—
652C22—882no—
653C22—882no—
654C22#1062262914yescomplemented
655C22C2×#6698311yescharacteristic
656C22C2×#6698511yescharacteristic
657C22C2×#6699011yescharacteristic
658C22C2×#6700311yescharacteristic
659C22#1062335311yescharacteristic
660C22#1062335311yescharacteristic
661C22#1062336111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—444no—
671C4D4×D4412yes—
672C4#1062308112yes—
673C2—24no—
674C2—82no—
675C2—884no—
676C2#1307197211yescharacteristic
677C2#1307783211yescharacteristic
678C2#1307786611yescharacteristic
679C2C2×#1062262911yescharacteristic
680C2#1307811011yescharacteristic
681C2#1307957711yescharacteristic
682C2#1307959911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenterC4×#121D11
hypocenterC11#24215
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. C22×#66928C2semidirect
2. C2×#10622629C2semidirect
3. C2×#10622653C2semidirect
5. #13069857C2semidirect
6. #13069692C2semidirect
7. #13069548C2semidirect
8. #13068596C2semidirect
9. #13068550C2semidirect
10. #13068546C2semidirect
11. C4×C11×#121C2semidirect
16. C2×C4×D4×C11C22semidirect
18. C22×#4324C22semidirect
27. C11×#390C22semidirect
28. C11×#389C22semidirect
32. C4×C11×C4⋊C4C22semidirect
39. C2×#66874C22semidirect
40. C2×#66874C22semidirect
41. C2×#66874C22semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. #10622162C22semidirect
105. #66928D4semidirect
215. C4×#121D11semidirect
314. C2×C4×D4C2×D11semidirect
330. #390C2×D11semidirect
331. #389C2×D11semidirect
335. C4×C4⋊C4C2×D11semidirect
351. C22×C11#463semidirect
551. C11#24215semidirect
654. C22#10622629semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C2×#106226292
C2×#106226532
C2×#106226492
#130698572
#130696922
#130695482
#130685962
#130685502
#130685462
C4×C11×#1212
#2421511