Finite Group Databasebeta

← #14685000

Subgroups — #14685000

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic
2C2×#10622268C212yesmaximal, complemented
3C2×#10622563C211yesmaximal, characteristic
4C2×#10622559C211yesmaximal, characteristic
5#13066850C212yesmaximal, complemented
6#13066847C212yesmaximal, complemented
7#13066842C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11—24no—
23C22×C4×Dic11—28no—
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37#10622563—24no—
38#10622559C418yescomplemented
39#10622268—28no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11Q814yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11C2×C414yes—
59C23×Dic11D414yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11C2×C414yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4C2×C418yescomplemented
85C2×C4×Dic11—232no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11D418yes—
92C11×#95—24no—
93C11×#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95C2×C418yescomplemented
103#14695—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11C22×C412yes—
109C24×C11C2×D412yes—
110C24×C11C2×Q812yes—
111C24×C11#4112yes—
112C24×C11#4112yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11C2411yescharacteristic
116C22×C4×C11—28no—
117C22×C4×C11—216no—
118C22×C4×C11—28no—
119C22×C4×C11—28no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—216no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×Q814yes—
144C22×C4×C11#4114yes—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—216no—
148C22×Dic11—216no—
149C22×Dic11—216no—
150C22×Dic11—216no—
151C22×Dic11—28no—
152C22×Dic11—28no—
153C22×Dic11—28no—
154C22×Dic11—28no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11C22×C414yes—
182C22×Dic11C22×C414yes—
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D412yes—
187C22×Dic11#4114yes—
188C22×Dic11#4114yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—44no—
191C22⋊Dic11—28no—
192C22⋊Dic11—44no—
193C4⋊Dic11—44no—
194C4⋊Dic11—44no—
195Dic11⋊C4—216no—
196C4×Dic11—216no—
197C4×Dic11—216no—
198C23×C42—111no—
199C2×#387—112no—
200C2×#385—111no—
201C2×#385—111no—
202#1436—112no—
203#1436—112no—
204#1434—112no—
205C22⋊#95—111no—
206C22⋊#95—111no—
207C22⋊#95—111no—
208C22⋊#95D1111yescharacteristic
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11#11714yes—
226C23×C11C4×D414yes—
227C23×C11C4×Q814yes—
228C23×C11C22⋊Q814yes—
229C23×C11#12314yes—
230C23×C11#12514yes—
231C23×C11#12614yes—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D412yes—
235C23×C11C22×Q811yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4112yes—
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4112yes—
242C23×C11C2×#4112yes—
243C2×C4×C11—232no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11C22⋊Q818yes—
268C2×Dic11—232no—
269C2×Dic11—232no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—42no—
296C2×Dic11—41no—
297C2×Dic11—42no—
298C2×Dic11—41no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11C4×D418yes—
302C2×Dic11#12014yes—
303C2×Dic11#12314yes—
304C24×C4—111no—
305C24×C4—111no—
306C24×C4C2×D1111yescharacteristic
307C22×C4⋊C4—112no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—111no—
310C22×C22⋊C4—111no—
311C22×C22⋊C4—111no—
312C22×C22⋊C4C2×D1111yescharacteristic
313C22×C22⋊C4C2×D1111yescharacteristic
314C22×C42—112no—
315C22×C42—112no—
316C22×C42—228no—
317C22×C42—224no—
318#387—228no—
319#385—118no—
320#385—224no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—111no—
329C2×#95—111no—
330C2×#95C2×D1112yes—
331C2×#95C2×D1112yes—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—28no—
335C22×C11—28no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—28no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—28no—
342C22×C11#38718yescomplemented
343C22×C11C2×#11711yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11C2×C4×D412yes—
346C22×C11C2×C4×Q811yescharacteristic
347C22×C11C4×#4112yes—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×C22⋊Q812yes—
350C22×C11C2×C22⋊Q811yescharacteristic
351C22×C11C2×#12311yescharacteristic
352C22×C11C2×#12311yescharacteristic
353C22×C11#52512yes—
354C22×C11#52512yes—
355C22×C11#52511yescharacteristic
356C22×C11#52512yes—
357C22×C11#52512yes—
358C22×C11#52511yescharacteristic
359C22×C11C2×#12511yescharacteristic
360C22×C11C2×#12611yescharacteristic
361C22×C11#52912yes—
362C22×C11#52912yes—
363C22×C11#52912yes—
364C22×C11#52912yes—
365C22×C11#53312yes—
366C4×C11—28no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—82no—
370Dic11—24no—
371Dic11—24no—
372Dic11—28no—
373Dic11—44no—
374Dic11—81no—
375Dic11—81no—
376C25C22×D1111yescharacteristic
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—112no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—114no—
385C23×C4—114no—
386C23×C4—112no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—224no—
390C23×C4—224no—
391C23×C4—224no—
392C23×C4—224no—
393C23×C4—222no—
394C23×C4—222no—
395C23×C4—222no—
396C23×C4—222no—
397C23×C4Dic2214yes—
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1112yes—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C22⋊C4C4×D1114yes—
421C2×C42—118no—
422C2×C42—224no—
423C2×C42—224no—
424C2×C42—224no—
425C2×C42—224no—
426C2×C42—2232no—
427C2×C42—224no—
428#95—24no—
429#95—24no—
430#95—118no—
431#95—224no—
432#95—224no—
433#95—222no—
434#95—222no—
435#95—224no—
436#95—224no—
437#95—224no—
438#95—224no—
439C2×C11—28no—
440C2×C11C2×#38711yescharacteristic
441C2×C11#229012yes—
442C2×C11C4×#12011yescharacteristic
443C2×C11C4×#12311yescharacteristic
444C2×C11C4×C22⋊Q812yes—
445C2×C11#284811yescharacteristic
446C2×C11#284911yescharacteristic
447C2×C11#285112yes—
448C2×C11#285212yes—
449C2×C11#285311yescharacteristic
450C2×C11#285511yescharacteristic
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24C2×Dic2212yes—
456C24C2×C4×D1112yes—
457C24#433912yes—
458C24D4×D1112yes—
459C24#434112yes—
460C24#434112yes—
461C24#434312yes—
462C24C23×D1111yescharacteristic
463C22×C4—28no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—216no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—114no—
488C22×C4—114no—
489C22×C4—114no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—114no—
495C22×C4—228no—
496C22×C4—2216no—
497C22×C4—228no—
498C22×C4—228no—
499C22×C4—2216no—
500C22×C4—2216no—
501C22×C4—2216no—
502C22×C4—228no—
503C22×C4—228no—
504C22×C4—228no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—222no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4C2×Dic2214yes—
532C22×C4C2×C4×D1112yes—
533C22×C4C2×C4×D1112yes—
534C22×C4D4×D1114yes—
535C22×C4#434114yes—
536C4⋊C4—2216no—
537C4⋊C4—444no—
538C4⋊C4—444no—
539C22⋊C4—28no—
540C22⋊C4—44no—
541C22⋊C4—228no—
542C22⋊C4—444no—
543C42—2216no—
544C42—2216no—
545C11#1469511yescharacteristic, complemented, Sylow
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—24no—
554C23—22no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—22no—
561C23—22no—
562C23C4×Dic2214yes—
563C23#6693114yes—
564C23#6693214yes—
565C23(C22⋊D11)⋊C414yes—
566C23#6694314yes—
567C23#6694514yes—
568C23#6694714yes—
569C23C22×Dic2211yescharacteristic
570C23C22×C4×D1111yescharacteristic
571C23C2×#433911yescharacteristic
572C23C2×D4×D1111yescharacteristic
573C23C2×D4×D1112yes—
574C23C2×#434111yescharacteristic
575C23C2×#434112yes—
576C23C2×#434111yescharacteristic
577C23C2×#434311yescharacteristic
578C23#41×D1112yes—
579C23#41×D1112yes—
580C2×C4—232no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—118no—
605C2×C4—114no—
606C2×C4—114no—
607C2×C4—2232no—
608C2×C4—2232no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—222no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4#6693118yes—
641C22—24no—
642C22—24no—
643C22—28no—
644C22—24no—
645C22—24no—
646C22—28no—
647C22—28no—
648C22—28no—
649C22—24no—
650C22—24no—
651C22#1062226818yescomplemented
652C22C2×C4×Dic2211yescharacteristic
653C22C2×#6693112yes—
654C22C2×#6693111yescharacteristic
655C22C2×#6693211yescharacteristic
656C22C2×(C22⋊D11)⋊C411yescharacteristic
657C22C2×#6694311yescharacteristic
658C22C2×#6694511yescharacteristic
659C22C2×#6694711yescharacteristic
660C22#1062304812yes—
661C22C4×#434112yes—
662C22#1062306912yes—
663C22C4×D4×D1112yes—
664C22#1062307812yes—
665C22#1062311711yescharacteristic
666C22#1062311712yes—
667C22D11×#12011yescharacteristic
668C22#1062313112yes—
669C22#1062313712yes—
670C22#1062315512yes—
671C22#1062315812yes—
672C22#1062318012yes—
673C22D11×#12311yescharacteristic
674C22#1062318711yescharacteristic
675C4—28no—
676C4—42no—
677C4—42no—
678C4—82no—
679C4—228no—
680C4—224no—
681C4—224no—
682C4—444no—
683C4—881no—
684C4—881no—
685C2—28no—
686C2C2×#1062226811yescharacteristic
687C2#1307105212yes—
688C2#1307112111yescharacteristic
689C2#1307114111yescharacteristic
690C2C4×#6693112yes—
691C2#1307690111yescharacteristic
692C2#1307691111yescharacteristic
693C2#1307692412yes—
694C2#1307692912yes—
695C2#1307694111yescharacteristic
696C2#1307695311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14695
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622268C2semidirect
5. #13066850C2semidirect
6. #13066847C2semidirect
7. #13066842C2semidirect
38. #10622559C4semidirect
84. C2×Dic11⋊C4C2×C4semidirect
102. C11⋊#95C2×C4semidirect
342. C22×C11#387semidirect
545. C11#14695semidirect
651. C22#10622268semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106222682
C2×#106225632
C2×#106225592
#130668502
#130668472
#130668422
#130668392
#130668382
C11×C22⋊#952
#1469511