Finite Group Databasebeta

← #14676669

Subgroups — #14676669

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622541C211yesmaximal, characteristic, complemented
4C2×#10622590C211yesmaximal, characteristic, complemented
5#13066859C214yesmaximal, complemented
6#13066845C211yesmaximal, characteristic, complemented
7#13066839C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2212yes—
12C2×C4×D4×C11—24no—
13C2×C4×D4×C11—24no—
14C2×C4×D4×C11—24no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2214yes—
19C22×C22⋊Dic11C2214yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25#10622834—24no—
26#10622834C418yescomplemented
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32#10622590—24no—
33#10622541—24no—
34C25×C11C2312yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D414yes—
41C22×D4×C11Q814yes—
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—28no—
46C23×C4×C11—44no—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C4×D4×C11—232no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—24no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D414yes—
65C2×C22⋊Dic11—28no—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—44no—
68C2×C22⋊Dic11—44no—
69C2×C22⋊Dic11—44no—
70C2×C22⋊Dic11C2×C4116yescomplemented
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2×C414yescomplemented
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—44no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11C2×C414yescomplemented
85C11⋊#95—24no—
86C11⋊#95—28no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—44no—
90#13979—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—24no—
99C24×C11C22×C414yes—
100C24×C11C2×D414yes—
101C24×C11C2×Q814yes—
102C24×C11C2411yescharacteristic
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—28no—
107C2×D4×C11—28no—
108C2×D4×C11—28no—
109C2×D4×C11C4⋊C4116yescomplemented
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—216no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—416no—
123C22×C4×C11—416no—
124C22×C4×C11—48no—
125C22×C4×C11—48no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11C22×C414yes—
159C22×Dic11C22×C414yes—
160C22×Dic11#4114yes—
161C11×C4⋊C4—28no—
162C11×C22⋊C4—216no—
163C42×C11—28no—
164C22⋊Dic11—416no—
165C22⋊Dic11—416no—
166C4⋊Dic11—28no—
167C4⋊Dic11—44no—
168Dic11⋊C4—48no—
169C4×Dic11—28no—
170C4×Dic11—44no—
171C22×C4×D4D1111yescharacteristic
172C2×#390—111no—
173C2×#390—111no—
174C2×#389—111no—
175C2×#382—111no—
176#1439—114no—
177C4⋊#95—111no—
178C22⋊#95—114no—
179C4×#95—111no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—28no—
183C23×C11—28no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—42no—
193C23×C11—44no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11C2×C4⋊C418yes—
203C23×C11C23×C411yescharacteristic
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C22×Q811yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)12yes—
214D4×C11—232no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—28no—
224C2×C4×C11—432no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11C2×C4⋊C414yes—
231C2×C4×C11C4×D414yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11#12014yes—
234C2×C4×C11C22⋊Q814yes—
235C2×C4×C11C22⋊Q814yes—
236C2×C4×C11#12314yes—
237C2×C4×C11#12414yes—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—28no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—44no—
261C2×Dic11—44no—
262C23×D4C2×D1111yescharacteristic
263C24×C4C2×D1112yes—
264C2×C4×D4—24no—
265C2×C4×D4—24no—
266C2×C4×D4—24no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—114no—
272C22×C22⋊C4—114no—
273C22×C22⋊C4C2×D1112yes—
274C22×C42—111no—
275C22×C42—111no—
276C22×C42C2×D1111yescharacteristic
277#390—118no—
278#390—224no—
279#389—224no—
280#382—224no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—114no—
285C2×#95—114no—
286C22×C11—216no—
287C22×C11—28no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—48no—
292C22×C11—48no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—48no—
296C22×C11—44no—
297C22×C11C22×C4⋊C411yescharacteristic
298C22×C11C2×C4×D411yescharacteristic
299C22×C11C2×C4×D411yescharacteristic
300C22×C11C4×#4112yes—
301C22×C11#51812yes—
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×C22⋊Q811yescharacteristic
304C22×C11C2×C22⋊Q811yescharacteristic
305C22×C11C2×#12311yescharacteristic
306C22×C11C2×#12411yescharacteristic
307C22×C11#52912yes—
308C22×C11#53211yescharacteristic
309C22×C11#53511yescharacteristic
310C22×C11#53511yescharacteristic
311C22×C11#54012yes—
312C22×C11#54612yes—
313C22×C11#54612yes—
314C22×C11#54612yes—
315C22×C11#55012yes—
316C22×C11#55312yes—
317C22×C11#55412yes—
318C22×C11#55412yes—
319C22×C11#55512yes—
320C4×C11—24no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11#38518yes—
324Dic11—44no—
325Dic11—44no—
326Dic11—44no—
327Dic11—82no—
328C25C22×D1112yes—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4Dic2214yes—
334C22×D4C4×D1114yes—
335C22×D4C22⋊D1114yes—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—28no—
340C23×C4—44no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4—112no—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C4×D4—232no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—444no—
360C2×C4⋊C4C22⋊D1114yes—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—1116no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—444no—
368C2×C22⋊C4—444no—
369C2×C22⋊C4—444no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—114no—
373C2×C42—222no—
374C2×C42—222no—
375C2×C42—222no—
376C2×C42—222no—
377C2×C42—222no—
378C2×C42C22⋊D1114yes—
379#95—224no—
380#95—224no—
381#95—228no—
382#95—224no—
383#95—444no—
384C2×C11—48no—
385C2×C11C2×#38511yescharacteristic
386C2×C11C4×#12411yescharacteristic
387C2×C11#232811yescharacteristic
388C2×C11#234912yes—
389C2×C11#236312yes—
390C2×C11#242012yes—
391C2×C11#243111yescharacteristic
392C2×C11#243511yescharacteristic
393C2×C11#245412yes—
394C2×C11#256311yescharacteristic
395C2×C11#256611yescharacteristic
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24C2×Dic2214yes—
405C24C2×C4×D1114yes—
406C24C2×C22⋊D1114yes—
407C24C23×D1111yescharacteristic
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4Dic11⋊C4116yescomplemented
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—216no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—416no—
428C22×C4—416no—
429C22×C4—48no—
430C22×C4—48no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4C2×Dic2212yes—
456C22×C4C2×C4×D1112yes—
457C22×C4#433912yes—
458C22×C4#433912yes—
459C22×C4#434114yes—
460C22×C4C2×C22⋊D1114yes—
461C22×C4C2×C22⋊D1112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C2×C22⋊D1112yes—
466C4⋊C4—28no—
467C4⋊C4—228no—
468C4⋊C4—448no—
469C4⋊C4—444no—
470C22⋊C4—216no—
471C22⋊C4—4416no—
472C22⋊C4—4416no—
473C42—28no—
474C42—228no—
475C42—444no—
476C11#1397911yescharacteristic, complemented, Sylow
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—28no—
483C23—28no—
484C23—28no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—24no—
489C23—42no—
490C23—42no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23C2×Dic11⋊C418yes—
500C23C22×Dic2211yescharacteristic
501C23C22×C4×D1111yescharacteristic
502C23C2×#433911yescharacteristic
503C23C2×#433911yescharacteristic
504C23C2×#434112yes—
505C23#6703712yes—
506C23#41×D1112yes—
507C23#6704212yes—
508C23C22×C22⋊D1111yescharacteristic
509C23C22×C22⋊D1111yescharacteristic
510C23C22×C22⋊D1111yescharacteristic
511D4—232no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—28no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—432no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—228no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—444no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—444no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—444no—
550C2×C4—442no—
551C2×C4C2×Dic11⋊C414yes—
552C2×C4#6697714yes—
553C2×C4#6697714yes—
554C2×C4C4×C22⋊D1114yes—
555C2×C4C4×C22⋊D1114yes—
556C2×C4#6698214yes—
557C2×C4#6698914yes—
558C2×C4#6700614yes—
559C22—216no—
560C22—28no—
561C22—48no—
562C22—44no—
563C22—48no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—48no—
569C22—44no—
570C22C4×#434112yes—
571C22#1062307012yes—
572C22#1062307412yes—
573C22#1062307612yes—
574C22#1062308812yes—
575C22#1062308912yes—
576C22#1062309312yes—
577C22#1062309412yes—
578C22C22×Dic11⋊C411yescharacteristic
579C22C2×#6697711yescharacteristic
580C22C2×#6697711yescharacteristic
581C22C2×C4×C22⋊D1111yescharacteristic
582C22C2×C4×C22⋊D1111yescharacteristic
583C22C2×#6698211yescharacteristic
584C22C2×#6698911yescharacteristic
585C22#1062333611yescharacteristic
586C22#1062333712yes—
587C22#1062333712yes—
588C22#1062336012yes—
589C22#1062336111yescharacteristic
590C22#1062336311yescharacteristic
591C22#1062336512yes—
592C22C2×#6700611yescharacteristic
593C4—24no—
594C4—42no—
595C4—44no—
596C4—444no—
597C4—444no—
598C4—444no—
599C4—882no—
600C4#1062282318yes—
601C2—48no—
602C2C2×#1062282311yescharacteristic
603C2C4×#6698911yescharacteristic
604C2#1307133811yescharacteristic
605C2#1307152112yes—
606C2#1307165012yes—
607C2#1307210212yes—
608C2#1307223111yescharacteristic
609C2#1307226311yescharacteristic
610C2#1307248212yes—
611C2#1307378911yescharacteristic
612C2#1307381211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13979
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#10622541C2semidirect
4. C2×#10622590C2semidirect
5. #13066859C2semidirect
6. #13066845C2semidirect
7. #13066839C2semidirect
8. C4×C11⋊#95C2semidirect
26. #10622834C4semidirect
70. C2×C22⋊Dic11C2×C4semidirect
76. C2×C4⋊Dic11C2×C4semidirect
84. C2×C4×Dic11C2×C4semidirect
109. C2×D4×C11C4⋊C4semidirect
414. C2×D4Dic11⋊C4semidirect
476. C11#13979semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225412
C2×#106225902
#130668592
#130668452
#130668392
C4×C11⋊#952
C22×C4×D4×C112
#1397911