Finite Group Databasebeta

← #14755162

Subgroups — #14755162

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic, complemented
5#13068973C214yesmaximal, complemented
6#13068966C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—24no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)C418yescomplemented
15C22×C11×SD16C2212yes—
16C22×C11×D8C2212yes—
17C22×C11×M16C2211yescharacteristic
18C22×C22⋊Dic11—22no—
19#41×Dic11—24no—
20#41×Dic11—24no—
21C2×Q8×Dic11C2212yescomplemented
22C2×D4×Dic11—22no—
23C2×D4×Dic11C2212yescomplemented
24C2×#66979—21no—
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11—21no—
28C22×C4×Dic11C2211yescharacteristic
29C22×#4318C2211yescharacteristic
30#10622845—24no—
31C2×#66899C2212yescomplemented
32#10622834—21no—
33#10622834—21no—
34#10622834C2214yes—
35#10622828—24no—
36C2×#66896C2214yes—
37C2×#66896C2212yescomplemented
38#10622189C2214yescomplemented
39#10622188C2214yescomplemented
40C25×C11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2×C414yescomplemented
56C22×D4×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—22no—
61C23×Dic11—21no—
62C23×Dic11D412yes—
63C11×AGL(1,ℤ/8)—232no—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×SD16C2×C418yescomplemented
67C2×C11×D8—24no—
68C2×C11×D8—24no—
69C2×C11×D8C2×C418yescomplemented
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16C2×C414yescomplemented
73C22×C8×C11C2312yes—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—48no—
79Q8×Dic11—24no—
80Q8×Dic11—24no—
81D4×Dic11—216no—
82D4×Dic11—24no—
83D4×Dic11—24no—
84#66979—28no—
85#66979—22no—
86#66979D414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4×Dic11—28no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2312yes—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—22no—
104C22×C11⋊C8C2312yes—
105#66899—24no—
106#66896—24no—
107#66896—28no—
108#20928—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—44no—
113C24×C11—44no—
114C24×C11—42no—
115C24×C11—42no—
116C24×C11C2×D411yescharacteristic
117C11×#41—28no—
118C11×#41—28no—
119C11×#41—28no—
120C11×#41C22⋊C4116yescomplemented
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11C22×C412yes—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—42no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11—44no—
145C2×D4×C11C22×C414yes—
146C2×D4×C11C22×C412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—42no—
167C22×Dic11—44no—
168C22×Dic11—44no—
169C22×Dic11—44no—
170C22×Dic11—42no—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C11×SD16—216no—
174C11×D8—216no—
175C11×M16—28no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11C22×C414yes—
179C22⋊Dic11—28no—
180C22⋊Dic11—24no—
181C22⋊Dic11—48no—
182C22⋊Dic11—48no—
183C4⋊Dic11—28no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—42no—
188C4⋊Dic11C2×D414yes—
189C4×Dic11—28no—
190C4×Dic11—22no—
191C4×Dic11—24no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195#4318—44no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C22×AGL(1,ℤ/8)D1111yescharacteristic
200C2×C4×#41—111no—
201C2×#417—111no—
202C2×#418—111no—
203C2×#390—111no—
204#1880—114no—
205#1879—114no—
206#1736—111no—
207#1728—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—416no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—88no—
223C23×C11—84no—
224C23×C11—84no—
225C23×C11C4×D412yes—
226C23×C11#12012yes—
227C23×C11#12112yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11C2×C22⋊C414yescomplemented
233D4×C11—216no—
234D4×C11—24no—
235D4×C11—22no—
236D4×C11—24no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—48no—
242D4×C11C2×C22⋊C414yescomplemented
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—216no—
247C2×C4×C11C2×C22⋊C414yes—
248C2×C4×C11C4×D414yes—
249C2×C4×C11C4×D412yes—
250C2×C4×C11#12012yes—
251C2×C4×C11#12114yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#12314yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—48no—
267C2×Dic11—416no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—84no—
273C2×Dic11AGL(1,ℤ/8)14yescomplemented
274C8×C11—24no—
275C11⋊C8—42no—
276C22×#41C2×D1111yescharacteristic
277C23×D4C2×D1111yescharacteristic
278C2×AGL(1,ℤ/8)—24no—
279C2×AGL(1,ℤ/8)—24no—
280C2×AGL(1,ℤ/8)Dic1118yescomplemented
281C22×SD16C2×D1112yes—
282C22×D8C2×D1112yes—
283C22×M16—111no—
284C22×M16C2×D1111yescharacteristic
285C4×#41—224no—
286C4×#41—224no—
287C2×C4×Q8—112no—
288C2×C4×D4—112no—
289C2×C4×D4—222no—
290C2×#117—111no—
291C2×#117—221no—
292C22×C4⋊C4—111no—
293C22×C22⋊C4—222no—
294C22×C42—111no—
295C22×C42—221no—
296#418—224no—
297#417—224no—
298C2×#103—112no—
299C2×#102—114no—
300C2×#102—112no—
301#390—114no—
302#390—221no—
303#390—221no—
304#340—114no—
305#336—114no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—24no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—48no—
316C22×C11—44no—
317C22×C11—816no—
318C22×C11—84no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11#38614yes—
322C22×C11C2×C4×D411yescharacteristic
323C22×C11C2×#12011yescharacteristic
324C22×C11C2×#12111yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)12yes—
326C22×C11#57512yes—
327C4×C11—24no—
328C4×C11#38614yes—
329C4×C11C22×C22⋊C411yescharacteristic
330C4×C11C2×C4×D411yescharacteristic
331C4×C11C2×#12111yescharacteristic
332C4×C11C2×#12311yescharacteristic
333Dic11—24no—
334Dic11—42no—
335Dic11—44no—
336Dic11—82no—
337C25—21no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C2×Dic1114yes—
342C2×#41C22⋊D1114yes—
343C2×#41C22⋊D1114yes—
344C22×Q8C22×D1111yescharacteristic
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4C2×Dic1114yescomplemented
353C22×D4C22×D1112yes—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—112no—
357C23×C4—222no—
358C23×C4—221no—
359C23×C4C22×D1111yescharacteristic
360AGL(1,ℤ/8)—232no—
361C2×SD16—24no—
362C2×SD16—24no—
363C2×SD16C2×Dic1118yescomplemented
364C2×D8—24no—
365C2×D8—24no—
366C2×D8C2×Dic1118yescomplemented
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—222no—
370C2×M16—222no—
371C2×M16—222no—
372C2×M16C2×Dic1114yescomplemented
373C22×C8—112no—
374C22×C8C22×D1112yes—
375C4×Q8—224no—
376C4×Q8—224no—
377C4×D4—224no—
378C4×D4—2216no—
379C4×D4—224no—
380#117—114no—
381#117—228no—
382#117—222no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—448no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—112no—
397C2×C42—222no—
398C2×C42—228no—
399C2×C42—221no—
400C2×C42—222no—
401C2×C42—222no—
402#103—224no—
403#102—228no—
404#102—224no—
405C2×C11—24no—
406C2×C11—44no—
407C2×C11—84no—
408C2×C11C2×#38611yescharacteristic
409C2×C11C4×AGL(1,ℤ/8)12yes—
410C2×C11#300612yes—
411C2×C11#303811yescharacteristic
412C2×C11#304011yescharacteristic
413C24—21no—
414C24—24no—
415C24—22no—
416C24—44no—
417C24—44no—
418C24—42no—
419C24—42no—
420C24D4×D1111yescharacteristic
421#41—28no—
422#41—28no—
423#41—28no—
424#41C22⋊Dic11116yescomplemented
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C22×Dic1112yes—
429C2×Q8C2×C22⋊D1112yes—
430C2×Q8C2×C22⋊D1112yes—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—28no—
435C2×D4—24no—
436C2×D4—28no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—44no—
448C2×D4—42no—
449C2×D4C22×Dic1114yes—
450C2×D4C22×Dic1112yes—
451C2×D4C2×C22⋊D1112yes—
452C2×D4C2×C22⋊D1112yes—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—444no—
465C22×C4—442no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4—442no—
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1112yes—
471C22×C4#434112yes—
472C22×C4#434112yes—
473C22×C4C22×Dic1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1112yes—
476C22×C4C23×D1111yescharacteristic
477SD16—216no—
478D8—216no—
479M16—28no—
480M16—444no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8C22×Dic1114yes—
487C4⋊C4—114no—
488C4⋊C4—228no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—442no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C42—228no—
498C42—222no—
499C42—222no—
500C42—224no—
501C42—222no—
502C42—222no—
503C11#2092811yescharacteristic, complemented, Sylow
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—416no—
511C23—42no—
512C23—42no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—42no—
517C23—48no—
518C23—84no—
519C23—84no—
520C23—88no—
521C23D4×Dic1112yes—
522C23#6699012yes—
523C23#6699212yes—
524C23C2×D4×D1111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8C2×C22⋊Dic1114yescomplemented
529D4—216no—
530D4—22no—
531D4—24no—
532D4—22no—
533D4—22no—
534D4—24no—
535D4—42no—
536D4—42no—
537D4—48no—
538D4C2×C22⋊Dic1114yescomplemented
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—216no—
543C2×C4—114no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—448no—
551C2×C4—4416no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4—884no—
557C2×C4D4×Dic1114yes—
558C2×C4D4×Dic1112yes—
559C2×C4#6698814yes—
560C2×C4#6699012yes—
561C2×C4#6699214yes—
562C2×C4#6699212yes—
563C2×C4C2×C22⋊Dic1114yes—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4C23×Dic1111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—24no—
571C8—442no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—44no—
580C22—44no—
581C22—48no—
582C22—44no—
583C22—816no—
584C22—82no—
585C22—82no—
586C22—84no—
587C22#1062283314yes—
588C22D11×AGL(1,ℤ/8)12yes—
589C22#1062330412yes—
590C22C2×D4×Dic1111yescharacteristic
591C22C2×#6699011yescharacteristic
592C22C2×#6699211yescharacteristic
593C4—24no—
594C4—224no—
595C4—442no—
596C4—444no—
597C4—882no—
598C4#1062283314yes—
599C4C2×D4×Dic1111yescharacteristic
600C4C2×#6698811yescharacteristic
601C4C2×#6699211yescharacteristic
602C4C22×C22⋊Dic1111yescharacteristic
603C2—24no—
604C2—44no—
605C2—84no—
606C2C2×#1062283311yescharacteristic
607C2AGL(1,ℤ/8)×Dic1112yes—
608C2#1307786412yes—
609C2#1307809411yescharacteristic
610C2#1307810811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#20928
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic11C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622834C2semidirect
5. #13068973C2semidirect
6. #13068966C2semidirect
7. #13068336C2semidirect
8. #13068309C2semidirect
14. C2×C11×AGL(1,ℤ/8)C4semidirect
21. C2×Q8×Dic11C22semidirect
23. C2×D4×Dic11C22semidirect
31. C2×#66899C22semidirect
37. C2×#66896C22semidirect
38. #10622189C22semidirect
39. #10622188C22semidirect
55. C22×D4×C11C2×C4semidirect
66. C2×C11×SD16C2×C4semidirect
69. C2×C11×D8C2×C4semidirect
72. C2×C11×M16C2×C4semidirect
120. C11×#41C22⋊C4semidirect
232. Q8×C11C2×C22⋊C4semidirect
242. D4×C11C2×C22⋊C4semidirect
273. C2×Dic11AGL(1,ℤ/8)semidirect
280. C2×AGL(1,ℤ/8)Dic11semidirect
352. C22×D4C2×Dic11semidirect
363. C2×SD16C2×Dic11semidirect
366. C2×D8C2×Dic11semidirect
372. C2×M16C2×Dic11semidirect
424. #41C22⋊Dic11semidirect
503. C11#20928semidirect
528. Q8C2×C22⋊Dic11semidirect
538. D4C2×C22⋊Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
C2×#106228452
C2×#106228282
C2×#106228342
#130689732
#130689662
#130683362
#130683092
C22×C11×AGL(1,ℤ/8)2
#2092811