Finite Group Databasebeta

← #14754753

Subgroups — #14754753

Order 2816.

1550 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2C2×#10622734C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic
4C2×#10622746C211yesmaximal, characteristic
5C2×#10622541C211yesmaximal, characteristic, complemented
6#13068887C212yesmaximal, complemented
7#13068880C212yesmaximal, complemented
8#13068873C212yesmaximal, complemented
9#13068866C212yesmaximal, complemented
10#13068336C211yesmaximal, characteristic, complemented
11C11×#1728C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×C4×C22⋊D11—21no—
17C2×C4×C22⋊D11—21no—
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4—21no—
22C4×#4339—24no—
23C4×#4339—24no—
24C2×C4×D44C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66925—21no—
27C2×C42×D11—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11⋊#95—21no—
31#10622746—24no—
32#10622746C418yescomplemented
33#10622734—24no—
34C2×#66885C2212yes—
35C2×#66885C2212yes—
36C2×#66882C2212yes—
37C2×#66881C2212yes—
38C2×#66880C2212yes—
39C2×#66880C2212yes—
40#10622541—21no—
41#10622541—21no—
42#10622541C2212yes—
43#10622541C2212yes—
44C11×#336C2212yes—
45C11×#336C2212yes—
46#10622189C2212yes—
47#10622189C2212yes—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11—21no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339C2×C414yes—
58C2×#4339D414yes—
59C2×#4339Q814yes—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×Dic22C2311yescharacteristic
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16C2×C414yescomplemented
71C22×C8×C11C2312yes—
72C22×C8×C11C2312yes—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C4×C22⋊D11—28no—
81C4×C22⋊D11—28no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—22no—
85#66979D414yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2×C414yescomplemented
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—44no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—22no—
108#66925—28no—
109C42×D11—28no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C4×Dic22—22no—
113C4×Dic22—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116#66885—24no—
117#66885C2×C418yescomplemented
118#66882—24no—
119#66881—24no—
120#66880—24no—
121#66880C2×C418yescomplemented
122#20875—111nomaximal, Sylow
123C24×C11C2×D411yescharacteristic
124C23×D11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×Q812yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—24no—
144C2×C22⋊D11—24no—
145C2×C22⋊D11—24no—
146C22×Dic11—24no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157#4339—28no—
158#4339—28no—
159#4339—28no—
160#4339C4⋊C4116yescomplemented
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22×C412yes—
165C2×D44C2×D412yes—
166C2×D44C2×Q812yes—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C2×Dic22C2×D412yes—
181C2×Dic22C2×Q812yes—
182C11×M16—28no—
183C11×M16—44no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11C22×C414yes—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—42no—
206C4⋊Dic11C22×C414yes—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11C2×D412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—44no—
212Dic11⋊C4—44no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C2×C4×#41—111no—
217C2×#428—111no—
218C2×#417—111no—
219C2×#417—111no—
220C2×#389—111no—
221#1865—112no—
222#1864—112no—
223#1863—112no—
224#1862—112no—
225#1736—111no—
226#1728D1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×D412yes—
232C23×C11#12012yes—
233C23×C11C22⋊Q812yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11C2×C4⋊C414yes—
255C2×C4×C11C4×D412yes—
256C2×C4×C11C4×D414yes—
257C2×C4×C11#12012yes—
258C2×C4×C11C22⋊Q814yes—
259C2×C4×C11C22⋊Q812yes—
260C2×C4×C11#12314yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11#13712yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C22⋊D11—216no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—48no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—84no—
287D44—22no—
288D44—22no—
289D44—22no—
290D44C2×C4⋊C414yescomplemented
291C4×D11—216no—
292C4×D11—48no—
293C4×D11—48no—
294Dic22—22no—
295Dic22—22no—
296Dic22—22no—
297Dic22C2×C4⋊C414yescomplemented
298C8×C11—24no—
299C8×C11—42no—
300C22×#41—111no—
301C22×M16C2×D1111yescharacteristic
302C22×M16C2×D1111yescharacteristic
303C4×#41—224no—
304C4×#41—224no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4—221no—
310C2×C4×D4—221no—
311C2×#117—111no—
312C2×#117—221no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—221no—
316C22×C42—221no—
317C22×C42C2×D1111yescharacteristic
318#428—224no—
319C2×#107—112no—
320C2×#106—112no—
321#417—118no—
322#417—224no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#102—112no—
326C2×#102—112no—
327#389—112no—
328#389—112no—
329#389—221no—
330#389—221no—
331C2×#95—221no—
332#340—112no—
333#340—112no—
334#336C2×D1112yes—
335#336C2×D1112yes—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11#38514yes—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×#12011yescharacteristic
345C22×C11C2×C22⋊Q811yescharacteristic
346C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57511yescharacteristic
350C2×D11—24no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11#38514yes—
362C4×C11C22×C4⋊C411yescharacteristic
363C4×C11C2×C4×D411yescharacteristic
364C4×C11C2×C22⋊Q811yescharacteristic
365C4×C11C2×#12311yescharacteristic
366Dic11—24no—
367Dic11—44no—
368Dic11—42no—
369Dic11—42no—
370Dic11—82no—
371C2×#41—114no—
372C2×#41—114no—
373C2×#41—114no—
374C2×#41—222no—
375C2×#41—222no—
376C2×#41—222no—
377C22×Q8—111no—
378C22×D4—111no—
379C22×D4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4—221no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4D4411yescharacteristic
386C23×C4D4411yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16C4×D1114yescomplemented
394C22×C8C22×D1112yes—
395C22×C8C22×D1112yes—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—222no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—228no—
405C4×D4—228no—
406#117—114no—
407#117—228no—
408#117—222no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—444no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—228no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42D4411yescharacteristic
434C2×C42D4411yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#107—224no—
438#106—224no—
439#103—118no—
440#103—224no—
441#102—118no—
442#102—224no—
443#95—222no—
444#95—222no—
445C2×C11—24no—
446C2×C11C2×#38511yescharacteristic
447C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C11C4×#13711yescharacteristic
449C2×C11#300611yescharacteristic
450C2×C11#300711yescharacteristic
451C2×C11#307911yescharacteristic
452C2×C11#308011yescharacteristic
453D11—44no—
454C24—221no—
455C24C2×D4411yescharacteristic
456#41—1116no—
457#41—228no—
458#41—228no—
459#41—228no—
460C2×Q8—112no—
461C2×Q8—112no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×D4—112no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—224no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—221no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4C2×C4×D1112yes—
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4#433912yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1112yes—
510C22×C4#434112yes—
511C22×C4Q8×D1112yes—
512C22×C4C23×D1111yescharacteristic
513M16—28no—
514M16—44no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8C2×C4×D1114yes—
521C4⋊C4—114no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4—222no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—444no—
533C4⋊C4—442no—
534C4⋊C4—444no—
535C22⋊C4—224no—
536C22⋊C4—224no—
537C22⋊C4—224no—
538C42—22no—
539C42—22no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—224no—
545C42—224no—
546C42—224no—
547C11#2087511yescharacteristic, complemented, Sylow
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—222no—
553C23—222no—
554C23—222no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C4×D4412yes—
560C23#6693512yes—
561C23#6695012yes—
562C23C22×D4411yescharacteristic
563Q8—114no—
564Q8—222no—
565Q8—222no—
566Q8—222no—
567D4—114no—
568D4—2216no—
569D4—222no—
570D4—222no—
571D4—222no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—2216no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—448no—
592C2×C4—448no—
593C2×C4—448no—
594C2×C4—442no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—884no—
604C2×C4C4×D4412yes—
605C2×C4(C22⋊D11)⋊C414yes—
606C2×C4#6693512yes—
607C2×C4#6693614yes—
608C2×C4C4⋊C4×D1114yes—
609C2×C4#6694914yes—
610C2×C4#6695012yes—
611C2×C4#6696112yes—
612C2×C4#6696212yes—
613C2×C4C22×C4×D1111yescharacteristic
614C2×C4C2×#433911yescharacteristic
615C2×C4C2×D4×D1111yescharacteristic
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×#434111yescharacteristic
618C2×C4C2×Q8×D1111yescharacteristic
619C8—24no—
620C8—42no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—224no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22#1062228114yes—
635C22C2×C4×D4411yescharacteristic
636C22C2×#6693511yescharacteristic
637C22C2×#6695011yescharacteristic
638C22C2×#6696111yescharacteristic
639C22C2×#6696211yescharacteristic
640C22#1062327911yescharacteristic
641C22#1062327911yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—224no—
647C4—442no—
648C4—442no—
649C4—444no—
650C4—882no—
651C4#1062228114yes—
652C4C2×(C22⋊D11)⋊C411yescharacteristic
653C4C2×#6693611yescharacteristic
654C4C2×C4⋊C4×D1111yescharacteristic
655C4C2×#6694911yescharacteristic
656C2—24no—
657C2—444no—
658C2C2×#1062228111yescharacteristic
659C2C4×#6696111yescharacteristic
660C2C4×#6696211yescharacteristic
661C2#1307787011yescharacteristic
662C2#1307787811yescharacteristic
663C2#1307843211yescharacteristic
664C2#1307843911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1728C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1728D11
hypocenterC11#20875
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. C2×#10622734C2semidirect
5. C2×#10622541C2semidirect
6. #13068887C2semidirect
7. #13068880C2semidirect
8. #13068873C2semidirect
9. #13068866C2semidirect
10. #13068336C2semidirect
11. C11×#1728C2semidirect
32. #10622746C4semidirect
70. C2×C11×M16C2×C4semidirect
91. C2×C4⋊Dic11C2×C4semidirect
117. #66885C2×C4semidirect
121. #66880C2×C4semidirect
160. #4339C4⋊C4semidirect
226. #1728D11semidirect
290. D44C2×C4⋊C4semidirect
297. Dic22C2×C4⋊C4semidirect
393. C2×M16C4×D11semidirect
547. C11#20875semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
C2×#106227342
C2×#106227462
C2×#106225412
#130688872
#130688802
#130688732
#130688662
#130683362
C11×#17282
#2087511