Finite Group Databasebeta

← #14785957

Subgroups — #14785957

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C211yesmaximal, characteristic, complemented
2C22×#66873C211yesmaximal, characteristic, complemented
3#13071972C211yesmaximal, characteristic, complemented
4#13069759C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068964C212yesmaximal, complemented
8#13068938C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068706C211yesmaximal, characteristic, complemented
11C2×C11×#553C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C11×#553—24no—
14C11×#553—24no—
15C2×C11×#126—21no—
16C2×C11×#125C2211yescharacteristic, complemented
17C2×C11×#123—21no—
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic, complemented
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic, complemented
24C2×C11×#117C2211yescharacteristic, complemented
25C22×C11×C4⋊C4C2211yescharacteristic
26C2×#66990—21no—
27C22×#4323C2212yes—
28C2×#66983C2212yes—
29C23×C11⋊C8C2211yescharacteristic
30C2×#66896C2212yescomplemented
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yescomplemented
34#10622649—24no—
35#10622604—21no—
36C2×#66873—24no—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66873C2212yes—
40#10622573—21no—
41#10622568—21no—
42#10622552C2212yes—
43#10622167C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46#10622162C2212yescomplemented
47C24×D11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—22no—
57C22×D44—22no—
58C22×D44—24no—
59C22×D44—22no—
60C22×D44—21no—
61C22×D44—42no—
62C22×D44C2312yes—
63C11×#126—28no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#123—28no—
67C11×#121—28no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121D414yescomplemented
72C4×D4×C11—28no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D414yescomplemented
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97#66990—44no—
98C2×#4323—24no—
99C2×#4323—24no—
100C2×#4323—42no—
101#66983—24no—
102#66983—42no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×C4⋊Dic11C2312yes—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—42no—
109C22×C11⋊C8C2312yes—
110C22×C11⋊C8C2312yes—
111#66896—42no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)—42no—
115#66873—24no—
116#66873—24no—
117#66873—24no—
118#23963—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C23×D11—22no—
123C23×D11—44no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C23×D11—82no—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—82no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—82no—
152C22×C4×C11—82no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—44no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11—82no—
163C22×Dic11—22no—
164C2×D44—28no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—44no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—42no—
174C2×D44#4114yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D412yes—
184C11×C4⋊C4C2×D412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C42×C11—24no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—42no—
195#4323—48no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4—82no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—44no—
208C2×#553D1111yescharacteristic, complemented
209C2×#447—111no—
210C22×#102—111no—
211#2408—111no—
212#2025—112no—
213#1999—112no—
214#1893—111no—
215#1879—112no—
216#1875—112no—
217#1869—111no—
218#1824—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11#12012yes—
232C23×C11#13512yes—
233C23×C11AGL(1,ℤ/8)12yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—24no—
236C22×D11—48no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—88no—
244C22×D11—88no—
245C22×D11—84no—
246C22×D11—84no—
247D4×C11—24no—
248D4×C11—44no—
249D4×C11—48no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—84no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—84no—
275C2×C4×C11—84no—
276C2×C4×C11#12012yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4112yes—
280C2×C4×C11H(5,𝔽2)12yes—
281C22⋊D11—88no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285D44—24no—
286D44—24no—
287D44—48no—
288D44—42no—
289D44—42no—
290C11⋊C8—42no—
291C11⋊C8—42no—
292C23×D4—111no—
293C22×D8—112no—
294C23×C8—111no—
295#553—24no—
296#553—24no—
297C2×#126—21no—
298C2×#125C2×D1111yescharacteristic, complemented
299C2×#123—21no—
300C2×#121—21no—
301C2×#121—112no—
302C2×#121C2×D1111yescharacteristic
303C2×#121C2×D1111yescharacteristic, complemented
304C2×#120—221no—
305C2×C4×D4—21no—
306C2×C4×D4C2×D1111yescharacteristic
307C2×C4×D4C2×D1111yescharacteristic, complemented
308C2×#117C2×D1111yescharacteristic, complemented
309C22×C4⋊C4C2×D1111yescharacteristic
310#447—224no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×#102—224no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—112no—
318#394—221no—
319#392—221no—
320#390—112no—
321#380—111no—
322#379—221no—
323#340—112no—
324#340—112no—
325#340—112no—
326#336—112no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11#44914yes—
342C22×C11C2×#12011yescharacteristic
343C22×C11#54612yes—
344C22×C11C2×#13511yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11#57612yes—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—816no—
351C2×D11—82no—
352C2×D11—82no—
353C2×D11—82no—
354C2×D11—82no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11#52511yescharacteristic
363C4×C11#53511yescharacteristic
364C4×C11#54612yes—
365Dic11—82no—
366C25—221no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—112no—
370C22×D4—224no—
371C22×D4—222no—
372C22×D4—222no—
373C22×D4—222no—
374C22×D4—221no—
375C22×D4—442no—
376C22×D4C22⋊D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C2×D8—224no—
383C2×D8—224no—
384C2×D8—442no—
385C22×C8—112no—
386C22×C8—112no—
387C22×C8—222no—
388C22×C8—442no—
389#126—28no—
390#125—22no—
391#125—22no—
392#123—28no—
393#121—28no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—224no—
398#121—442no—
399#121C22⋊D1114yescomplemented
400#120—444no—
401C4×D4—28no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406#117—22no—
407#117—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4C22⋊D1111yescharacteristic
414C2×C4⋊C4C22⋊D1114yescomplemented
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4C22⋊D1111yescharacteristic
427C2×C22⋊C4C22⋊D1111yescharacteristic
428C2×C42—21no—
429C2×C42C22×D1111yescharacteristic
430#102—224no—
431#102—224no—
432#102—224no—
433#102—442no—
434C22⋊C8—222no—
435C22⋊C8—442no—
436#95—221no—
437C2×C11—24no—
438C2×C11—81no—
439C2×C11—82no—
440C2×C11#240411yescharacteristic
441C2×C11C2×#44911yescharacteristic
442C2×C11#300811yescharacteristic
443C2×C11#329712yes—
444C2×C11#331812yes—
445D11—84no—
446C24—21no—
447C24—222no—
448C24—444no—
449C24—442no—
450C24—442no—
451C24—442no—
452C24—882no—
453C24C2×C22⋊D1111yescharacteristic
454C24C2×C22⋊D1111yescharacteristic
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—82no—
466C2×D4—114no—
467C2×D4—228no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—448no—
474C2×D4—444no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—444no—
478C2×D4—442no—
479C2×D4—882no—
480C2×D4C2×C22⋊D1112yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—82no—
493C22×C4—82no—
494C22×C4—222no—
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1112yes—
500C22×C4C2×C22⋊D1112yes—
501C22×C4C23×D1111yescharacteristic
502D8—448no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—444no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4C2×C22⋊D1112yes—
520C4⋊C4C2×C22⋊D1112yes—
521C4⋊C4C2×C22⋊D1112yes—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—24no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—444no—
529C22⋊C4—444no—
530C22⋊C4—442no—
531C22⋊C4—882no—
532C42—24no—
533C42—21no—
534C42—21no—
535C11#2396311yescharacteristic, complemented, Sylow
536C23—22no—
537C23—22no—
538C23—21no—
539C23—21no—
540C23—22no—
541C23—22no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—224no—
549C23—448no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—888no—
557C23—888no—
558C23—884no—
559C23—884no—
560C23#6700212yes—
561C23#6700312yes—
562C23#6700612yes—
563C23C22×C22⋊D1111yescharacteristic
564D4—24no—
565D4—44no—
566D4—48no—
567D4—41no—
568D4—41no—
569D4—84no—
570D4—224no—
571D4—224no—
572D4—448no—
573D4—442no—
574D4—442no—
575D4—888no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4#6700612yes—
603C2×C4#41×D1112yes—
604C2×C4#6704212yes—
605C2×C4C22×C22⋊D1111yescharacteristic
606C2×C4C22×C22⋊D1111yescharacteristic
607C8—442no—
608C8—442no—
609C22—22no—
610C22—22no—
611C22—24no—
612C22—24no—
613C22—41no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—42no—
620C22—42no—
621C22—82no—
622C22—82no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—8816no—
627C22—882no—
628C22—882no—
629C22—882no—
630C22—882no—
631C22#1062285114yes—
632C22C2×#6700211yescharacteristic
633C22C2×#6700311yescharacteristic
634C22#1062336012yes—
635C22#1062336612yes—
636C22C2×#6700611yescharacteristic
637C4—22no—
638C4—41no—
639C4—42no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—882no—
645C4#1062335911yescharacteristic
646C4#1062336012yes—
647C4#1062336111yescharacteristic
648C2—24no—
649C2—81no—
650C2—82no—
651C2—884no—
652C2#1307193111yescharacteristic
653C2C2×#1062285111yescharacteristic
654C2#1307788411yescharacteristic
655C2#1308046012yes—
656C2#1308075112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11#23963
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. C22×#66873C2semidirect
3. #13071972C2semidirect
4. #13069759C2semidirect
5. #13069612C2semidirect
6. #13069045C2semidirect
7. #13068964C2semidirect
8. #13068938C2semidirect
9. #13068909C2semidirect
10. #13068706C2semidirect
11. C2×C11×#553C2semidirect
16. C2×C11×#125C22semidirect
20. C2×C11×#121C22semidirect
23. C2×C4×D4×C11C22semidirect
24. C2×C11×#117C22semidirect
30. C2×#66896C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
46. #10622162C22semidirect
71. C11×#121D4semidirect
84. C2×C11×C4⋊C4D4semidirect
208. C2×#553D11semidirect
298. C2×#125C2×D11semidirect
303. C2×#121C2×D11semidirect
307. C2×C4×D4C2×D11semidirect
308. C2×#117C2×D11semidirect
399. #121C22⋊D11semidirect
414. C2×C4⋊C4C22⋊D11semidirect
535. C11#23963semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C22×#668732
#130719722
#130697592
#130696122
#130690452
#130689642
#130689382
#130689092
#130687062
C2×C11×#5532
#2396311