Finite Group Databasebeta

← #14788811

Subgroups — #14788811

Order 2816.

1514 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×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×#10622783C212yesmaximal
4C4×#66991C211yesmaximal, characteristic
5#13069860C212yesmaximal, complemented
6#13069697C212yesmaximal, complemented
7#13069540C211yesmaximal, characteristic, complemented
8#13069538C211yesmaximal, characteristic, complemented
9#13068593C211yesmaximal, characteristic, complemented
10#13068549C212yesmaximal, complemented
11C2×C11×#461C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66997C2212yes—
17C2×#66991C2211yescharacteristic
18C22×#4324C2212yes—
19C2×C4×C22⋊D11—21no—
20D11×C4⋊Q8—24no—
21D11×C4⋊Q8—24no—
22C2×C4⋊C4×D11—21no—
23C2×C4⋊C4×D11—21no—
24C2×#66941—21no—
25C2×#66941—21no—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#461—24no—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×#66899C2212yes—
32C2×#66899C2212yes—
33#10622834C2211yescharacteristic
34C4×C22⋊Dic11—21no—
35#10622783—28no—
36C2×(C2×D11)⋊C8C2212yes—
37C2×#66880C2212yes—
38C2×#66880C2212yes—
39#10622632—24no—
40#10622600C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66874C2212yes—
43#10622569—21no—
44#10622557—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622188C2212yes—
48C22×Q8×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C22×C22⋊D11—21no—
52C2×Q8×D11—24no—
53C2×Q8×D11—24no—
54C2×Q8×D11—24no—
55C2×Q8×D11—24no—
56C2×Q8×D11—42no—
57C2×Q8×D11—42no—
58C22×C4×D11—22no—
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22—22no—
63C22×Dic22C2312yes—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×SD16—42no—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8D414yescomplemented
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66997—24no—
81#66997—24no—
82#66991—22no—
83#66991D414yes—
84C2×#4324—24no—
85C2×#4324—24no—
86C2×#4324—42no—
87C4×C22⋊D11—44no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2312yes—
101C4⋊C4×D11—28no—
102C4⋊C4×D11—28no—
103#66941—28no—
104#66941—28no—
105C42×D11—22no—
106C42×D11—22no—
107#66922—22no—
108#66922D414yescomplemented
109C11×C4⋊C8—22no—
110C11×#103—24no—
111#66899—24no—
112#66899—42no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116(C2×D11)⋊C8—24no—
117#66880—24no—
118#66880—42no—
119#66874—24no—
120C4⋊(C11⋊C8)—22no—
121#24209—111nomaximal, Sylow
122C24×C11—21no—
123C23×D11C2×D411yescharacteristic
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11C2×D414yes—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153Q8×D11—48no—
154Q8×D11—48no—
155Q8×D11—48no—
156Q8×D11—48no—
157C2×C4×D11—22no—
158C2×C4×D11—28no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11SD1614yescomplemented
170C2×C4×D11C2×D412yes—
171C2×C4×D11#4112yes—
172C2×Dic22—28no—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—44no—
179C2×Dic22—44no—
180C2×Dic22C2×D414yes—
181C11×SD16—48no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C22⋊C4—42no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192C22⋊Dic11—24no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195#4324—48no—
196(C2×D11)⋊C4—42no—
197C4⋊Dic11—24no—
198C4⋊Dic11—24no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—28no—
204Dic11⋊C4—28no—
205Dic11⋊C4—42no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C22×C4⋊Q8—111no—
215C2×#461—111no—
216C2×#461D1111yescharacteristic, complemented
217C2×#448—112no—
218C4×#121—111no—
219#2043—112no—
220#2013—112no—
221#1981—111no—
222#1981—111no—
223#1797—111no—
224#1787—112no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11#12112yes—
238C22×D11C2×SD1612yes—
239C22×D11#13712yes—
240Q8×C11—24no—
241Q8×C11—24no—
242Q8×C11—42no—
243Q8×C11—42no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—24no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—84no—
257C2×C4×C11#12012yes—
258C2×C4×C11#12012yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11#13712yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—48no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11#12112yes—
284C2×Dic11C2×SD1612yes—
285C2×Dic11#13712yes—
286C4×D11—28no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—28no—
292C4×D11—416no—
293Dic22—24no—
294Dic22—24no—
295Dic22—416no—
296Dic22—42no—
297Dic22—42no—
298C8×C11—42no—
299C11⋊C8—42no—
300C23×Q8—112no—
301C22×SD16—112no—
302C22×SD16C2×D1112yes—
303C2×C4⋊Q8—112no—
304C2×C4⋊Q8—111no—
305C2×C4⋊Q8—221no—
306C2×C4⋊Q8—221no—
307C2×C4⋊Q8—224no—
308C2×C4⋊Q8—224no—
309C2×C4⋊Q8C2×D1111yescharacteristic
310C2×#121—111no—
311C2×C4×D4—221no—
312C2×C4×D4C2×D1111yescharacteristic
313C22×C4⋊C4—221no—
314C22×C4⋊C4—221no—
315C22×C42—111no—
316#461—24no—
317#461—224no—
318#448—228no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—112no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103—112no—
326C2×#103C2×D1112yes—
327C2×C22⋊C8—112no—
328#390—111no—
329#389—111no—
330#388—221no—
331#386—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—221no—
335#336—112no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×#12111yescharacteristic
345C22×C11#53511yescharacteristic
346C22×C11C22×SD1611yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11#46114yescomplemented
357C4×C11—22no—
358C4×C11—44no—
359C4×C11—81no—
360C4×C11#44814yescomplemented
361C4×C11D4211yescharacteristic
362C4×C11D4211yescharacteristic
363C4×C11#54611yescharacteristic
364C4×C11#54611yescharacteristic
365Dic11—22no—
366Dic11—22no—
367Dic11—22no—
368Dic11—44no—
369Dic11—42no—
370Dic11—81no—
371C22×Q8—112no—
372C22×Q8—222no—
373C22×Q8—224no—
374C22×Q8—224no—
375C22×Q8—224no—
376C22×Q8—224no—
377C22×Q8—442no—
378C22×Q8—442no—
379C22×Q8C22×D1112yes—
380C22×D4—221no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—21no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—222no—
387C2×SD16—24no—
388C2×SD16—24no—
389C2×SD16—42no—
390C2×SD16—224no—
391C2×SD16—224no—
392C2×SD16—442no—
393C22×C8—112no—
394C22×C8C22×D1112yes—
395C4⋊Q8—22no—
396C4⋊Q8—114no—
397C4⋊Q8—228no—
398C4⋊Q8—228no—
399C4⋊Q8—224no—
400C4⋊Q8—224no—
401C4⋊Q8—222no—
402C4⋊Q8C22⋊D1114yescomplemented
403#121—114no—
404#121—222no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—444no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—228no—
413C2×C4⋊C4—228no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—222no—
429C2×C42—222no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432C4⋊C8—22no—
433C4⋊C8—222no—
434#103—24no—
435#103—224no—
436#103—224no—
437#103—224no—
438#103—442no—
439#103—442no—
440C22⋊C8—224no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—82no—
445C2×C11#240811yescharacteristic
446C2×C11C2×#44811yescharacteristic
447C2×C11#300411yescharacteristic
448C2×C11C2×#46111yescharacteristic
449C2×C11#303911yescharacteristic
450C2×C11#320611yescharacteristic
451C2×C11#321811yescharacteristic
452D11—24no—
453C24—21no—
454C24—111no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—114no—
461C2×Q8—228no—
462C2×Q8—222no—
463C2×Q8—222no—
464C2×Q8—222no—
465C2×Q8—222no—
466C2×Q8—222no—
467C2×Q8—444no—
468C2×Q8—444no—
469C2×Q8—448no—
470C2×Q8—448no—
471C2×Q8—448no—
472C2×Q8—448no—
473C2×Q8C2×C22⋊D1114yes—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—224no—
480C2×D4—442no—
481C2×D4—442no—
482C2×D4D4×D1112yes—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—228no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—222no—
506C22×C4—221no—
507C22×C4—444no—
508C22×C4—444no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512SD16—48no—
513SD16—448no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—222no—
518C2×C8—222no—
519C2×C8—222no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—112no—
525C4⋊C4—228no—
526C4⋊C4—228no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—442no—
533C22⋊C4—42no—
534C22⋊C4—224no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C42—222no—
539C42—222no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42D4×D1112yes—
544C42C2×C22⋊D1112yes—
545C11#2420911yescharacteristic, complemented, Sylow
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—112no—
554C23—112no—
555C23—112no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23C2×D4×D1111yescharacteristic
561Q8—24no—
562Q8—24no—
563Q8—42no—
564Q8—42no—
565Q8—224no—
566Q8—224no—
567Q8—4416no—
568Q8—442no—
569Q8—442no—
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4—448no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—24no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—228no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—228no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—4416no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4SD16×D1112yes—
610C2×C4#6696812yes—
611C2×C4#6699012yes—
612C2×C4#6699012yes—
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4#6703711yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#6704211yescharacteristic
618C2×C4C22×C22⋊D1111yescharacteristic
619C8—42no—
620C8—442no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—114no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—222no—
634C22—222no—
635C22D11×#12111yescharacteristic
636C22#1062313811yescharacteristic
637C22C2×SD16×D1111yescharacteristic
638C22C2×#6696811yescharacteristic
639C22D11×#13711yescharacteristic
640C22D11×#13711yescharacteristic
641C22C2×#6699011yescharacteristic
642C4—22no—
643C4—44no—
644C4—81no—
645C4—222no—
646C4—222no—
647C4—222no—
648C4—442no—
649C4—444no—
650C4—881no—
651C4#1062278314yescomplemented
652C4#1062314011yescharacteristic
653C4#1062314311yescharacteristic
654C4D4×C22⋊D1111yescharacteristic
655C4#1062336011yescharacteristic
656C2—82no—
657C2—224no—
658C2#1307196811yescharacteristic
659C2C2×#1062278311yescharacteristic
660C2#1307784811yescharacteristic
661C2D11×#46111yescharacteristic
662C2#1307809811yescharacteristic
663C2#1307954011yescharacteristic
664C2#1307964211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#461D11
hypocenterC11#24209
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622632C2semidirect
5. #13069860C2semidirect
6. #13069697C2semidirect
7. #13069540C2semidirect
8. #13069538C2semidirect
9. #13068593C2semidirect
10. #13068549C2semidirect
11. C2×C11×#461C2semidirect
69. C11×C4⋊Q8D4semidirect
108. #66922D4semidirect
169. C2×C4×D11SD16semidirect
216. C2×#461D11semidirect
356. C2×D11#461semidirect
360. C4×C11#448semidirect
402. C4⋊Q8C22⋊D11semidirect
545. C11#24209semidirect
651. C4#10622783semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106226322
C2×#106227832
C4×#669912
#130698602
#130696972
#130695402
#130695382
#130685932
#130685492
C2×C11×#4612
#2420911