Finite Group Databasebeta

← #14677431

Subgroups — #14677431

Order 2816.

2222 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
1C2×#10622591C212yesmaximal, complemented
2C2×#10622823C211yesmaximal, characteristic
3C2×C4×C22⋊Dic11C211yesmaximal, characteristic
4#13066875C212yesmaximal, complemented
5#13066866C212yesmaximal, complemented
6#13066848C212yesmaximal, complemented
7#13066839C211yesmaximal, characteristic
8#13066839C211yesmaximal, characteristic
9#13066839C211yesmaximal, characteristic
10#13066839C211yesmaximal, characteristic
11C23×C11×C4⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×C4⋊C4—24no—
16C22×C11×C4⋊C4—28no—
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26#10622823C418yescomplemented
27C4×C22⋊Dic11—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622591—28no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—42no—
53C23×C4×C11—42no—
54C23×C4×C11C2×C414yes—
55C23×C4×C11D414yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C4⋊C4—232no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4D418yes—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11C2×C414yes—
83C2×C22⋊Dic11C2×C414yes—
84C2×C22⋊Dic11Q814yes—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4C2×C418yescomplemented
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—42no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95C2×C418yescomplemented
103#14039—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—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—216no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—44no—
142C22×C4×C11—48no—
143C22×C4×C11—48no—
144C22×C4×C11—48no—
145C22×C4×C11—48no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4114yes—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C414yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C2×Q812yes—
188C22×Dic11C2×Q812yes—
189C11×C4⋊C4—216no—
190C11×C4⋊C4—216no—
191C22⋊Dic11—28no—
192C22⋊Dic11—28no—
193C22⋊Dic11—28no—
194C22⋊Dic11—44no—
195Dic11⋊C4—216no—
196C4×Dic11—44no—
197C4×Dic11—44no—
198C23×C4⋊C4D1111yescharacteristic
199C2×#387—112no—
200C2×#385—111no—
201C2×C4×C22⋊C4—111no—
202#1442—112no—
203#1441—112no—
204#1436—112no—
205C22⋊#95—111no—
206C22⋊#95—111no—
207C22⋊#95—111no—
208C22⋊#95—111no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
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×#4112yes—
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11H(5,𝔽2)12yes—
242C23×C112−1+412yes—
243C2×C4×C11—232no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—416no—
261C2×C4×C11—416no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11C4×D418yes—
269C2×C4×C11#12014yes—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C24×C4C2×D1111yescharacteristic
305C24×C4C2×D1111yescharacteristic
306C24×C4C2×D1111yescharacteristic
307C22×C4⋊C4—24no—
308C22×C4⋊C4—28no—
309C22×C4⋊C4—112no—
310C22×C4⋊C4C2×D1112yes—
311C22×C4⋊C4C2×D1112yes—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—111no—
314C22×C22⋊C4—111no—
315C22×C22⋊C4—111no—
316C22×C42—111no—
317C22×C42—111no—
318#387—228no—
319#385—118no—
320C4×C22⋊C4—224no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—111no—
328C2×#95—111no—
329C2×#95—112no—
330C2×#95—112no—
331C2×#95—112no—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—28no—
335C22×C11—28no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—28no—
339C22×C11—28no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11#38718yescomplemented
343C22×C11C2×#11711yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11C2×C4×D412yes—
346C22×C11C2×C4×Q811yescharacteristic
347C22×C11#52012yes—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×C22⋊Q811yescharacteristic
350C22×C11C2×#12311yescharacteristic
351C22×C11#52511yescharacteristic
352C22×C11#52512yes—
353C22×C11C2×#12511yescharacteristic
354C22×C11C2×#12611yescharacteristic
355C22×C11#53411yescharacteristic
356C22×C11#53611yescharacteristic
357C22×C11#53912yes—
358C22×C11#54612yes—
359C22×C11#54612yes—
360C22×C11#54812yes—
361C22×C11D4×Q812yes—
362C22×C11#55212yes—
363C22×C11#55212yes—
364C22×C11#55312yes—
365C22×C11#55412yes—
366C4×C11—24no—
367C4×C11—28no—
368C4×C11—42no—
369C4×C11—44no—
370Dic11—42no—
371Dic11—42no—
372Dic11—44no—
373Dic11—42no—
374Dic11—42no—
375Dic11—82no—
376C25C22×D1111yescharacteristic
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—111no—
391C23×C4—112no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—112no—
396C23×C4C4×D1114yes—
397C23×C4C22⋊D1114yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1112yes—
400C23×C4C22×D1112yes—
401C23×C4C22×D1111yescharacteristic
402C2×C4⋊C4—232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—224no—
411C2×C4⋊C4C22⋊D1118yes—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
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⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—222no—
424C2×C42—222no—
425C2×C42—222no—
426C2×C42—224no—
427C2×C42—442no—
428#95—118no—
429#95—224no—
430#95—222no—
431#95—222no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—442no—
437#95—442no—
438#95—442no—
439C2×C11—28no—
440C2×C11C2×#38711yescharacteristic
441C2×C11C4×#12011yescharacteristic
442C2×C11#232211yescharacteristic
443C2×C11#235212yes—
444C2×C11#236012yes—
445C2×C11#240511yescharacteristic
446C2×C11#240911yescharacteristic
447C2×C11#247312yes—
448C2×C11#248112yes—
449C2×C11#248411yescharacteristic
450C2×C11#257911yescharacteristic
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24C2×C4×D1112yes—
456C24#433912yes—
457C24#434112yes—
458C24#434112yes—
459C24Q8×D1112yes—
460C24#434312yes—
461C24C2×C22⋊D1112yes—
462C24C23×D1111yescharacteristic
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—216no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—216no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—21no—
478C22×C4—21no—
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—28no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—222no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4C2×C4×D1114yes—
530C22×C4#433914yes—
531C22×C4C2×C22⋊D1112yes—
532C22×C4C2×C22⋊D1114yes—
533C22×C4C2×C22⋊D1114yes—
534C22×C4C2×C22⋊D1114yes—
535C22×C4C2×C22⋊D1112yes—
536C4⋊C4—216no—
537C4⋊C4—216no—
538C4⋊C4—2216no—
539C22⋊C4—228no—
540C22⋊C4—228no—
541C22⋊C4—228no—
542C22⋊C4—444no—
543C42—444no—
544C42—444no—
545C11#1403911yescharacteristic, complemented, Sylow
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—22no—
555C23—22no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—22no—
560C23—24no—
561C23—22no—
562C23#6694014yes—
563C23#6694214yes—
564C23#6694514yes—
565C23#6695114yes—
566C23C4×C22⋊D1114yes—
567C23#6698814yes—
568C23#6699914yes—
569C23C22×C4×D1111yescharacteristic
570C23C2×#433911yescharacteristic
571C23C2×#433912yes—
572C23C2×#434111yescharacteristic
573C23C2×#434111yescharacteristic
574C23#6703712yes—
575C23C2×Q8×D1111yescharacteristic
576C23C2×#434311yescharacteristic
577C23#6704012yes—
578C23C22×C22⋊D1111yescharacteristic
579C23C22×C22⋊D1112yes—
580C2×C4—232no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—416no—
598C2×C4—416no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—441no—
621C2×C4—442no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—442no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4C4×C22⋊D1118yes—
640C2×C4#6700614yes—
641C22—28no—
642C22—24no—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—28no—
648C22—24no—
649C22—28no—
650C22—28no—
651C22#1062259118yescomplemented
652C22C2×#6694011yescharacteristic
653C22C2×#6694211yescharacteristic
654C22C2×#6694511yescharacteristic
655C22#1062303512yes—
656C22#1062304212yes—
657C22C2×#6695111yescharacteristic
658C22#1062304412yes—
659C22#1062304412yes—
660C22#1062304512yes—
661C22#1062304612yes—
662C22C2×C4×C22⋊D1112yes—
663C22C2×C4×C22⋊D1111yescharacteristic
664C22#1062332211yescharacteristic
665C22#1062332212yes—
666C22C2×#6698811yescharacteristic
667C22#1062333511yescharacteristic
668C22#1062333712yes—
669C22#1062333712yes—
670C22C2×#6699911yescharacteristic
671C22Q8×C22⋊D1112yes—
672C22#1062334711yescharacteristic
673C22#1062334812yes—
674C22C2×#6700611yescharacteristic
675C4—28no—
676C4—24no—
677C4—42no—
678C4—44no—
679C4—442no—
680C4—442no—
681C4—442no—
682C4—442no—
683C4—444no—
684C4—882no—
685C2—28no—
686C2C2×#1062259111yescharacteristic
687C2C4×#6700611yescharacteristic
688C2#1307128511yescharacteristic
689C2#1307154112yes—
690C2#1307162112yes—
691C2#1307193911yescharacteristic
692C2#1307197511yescharacteristic
693C2#1307275112yes—
694C2#1307287112yes—
695C2#1307290311yescharacteristic
696C2#1307396311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11#14039
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622591C2semidirect
4. #13066875C2semidirect
5. #13066866C2semidirect
6. #13066848C2semidirect
26. #10622823C4semidirect
87. C2×Dic11⋊C4C2×C4semidirect
102. C11⋊#95C2×C4semidirect
342. C22×C11#387semidirect
545. C11#14039semidirect
651. C22#10622591semidirect

Maximal subgroups

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

subgroupindex
C2×#106225912
C2×#106228232
C2×C4×C22⋊Dic112
#130668752
#130668662
#130668482
#130668392
C23×C11×C4⋊C42
#1403911