Finite Group Databasebeta

← #14785920

Subgroups — #14785920

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 686 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#13069749C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068964C212yesmaximal, complemented
8#13068933C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068702C211yesmaximal, characteristic, complemented
11C2×C11×#547C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C23×D44C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic, complemented
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
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—
48C2×C11×#41—28no—
49C2×C11×#41—44no—
50C2×C11×#41—44no—
51C22×Q8×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—22no—
62C22×D44—22no—
63C22×D44—24no—
64C22×D44—22no—
65C22×D44—21no—
66C22×D44—42no—
67C22×D44C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×#123—28no—
71C11×#123—28no—
72C11×C22⋊Q8—28no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121D414yescomplemented
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D414yescomplemented
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99#66990—44no—
100C2×#4323—24no—
101C2×#4323—24no—
102C2×#4323—42no—
103#66983—24no—
104#66983—42no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×C4⋊Dic11C2312yes—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—42no—
111C22×C11⋊C8C2312yes—
112C22×C11⋊C8C2312yes—
113#66896—42no—
114C11⋊#95—21no—
115C22⋊(C11⋊C8)—22no—
116C22⋊(C11⋊C8)—42no—
117#66873—24no—
118#66873—24no—
119#66873—24no—
120#23960—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C24×C11C2×D411yescharacteristic
124C23×D11—22no—
125C23×D11—44no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11—42no—
129C23×D11—82no—
130C11×#41—432no—
131C2×Q8×C11—24no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11D814yescomplemented
146C2×D4×C11C2×D412yes—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—44no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—82no—
175C22×Dic11—22no—
176C2×D44—28no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—44no—
183C2×D44—48no—
184C2×D44—44no—
185C2×D44—42no—
186C2×D44#4114yescomplemented
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×D412yes—
196C11×C4⋊C4C2×D412yes—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—22no—
202C42×C11—21no—
203C42×C11—21no—
204C22⋊Dic11—42no—
205#4323—48no—
206(C2×D11)⋊C4—44no—
207(C2×D11)⋊C4—44no—
208(C2×D11)⋊C4—82no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—44no—
218C2×#547D1111yescharacteristic, complemented
219C2×#447—111no—
220C22×#102—111no—
221#2408—111no—
222#2023—112no—
223#1999—112no—
224#1893—111no—
225#1879—112no—
226#1874—112no—
227#1869—111no—
228#1823—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11#12012yes—
241C23×C11C2×D812yes—
242C23×C11C2×D812yes—
243C23×C11AGL(1,ℤ/8)12yes—
244C23×C11C22×D411yescharacteristic
245C22×D11—24no—
246C22×D11—48no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—88no—
254C22×D11—88no—
255C22×D11—84no—
256C22×D11—84no—
257Q8×C11—48no—
258D4×C11—28no—
259D4×C11—24no—
260D4×C11—48no—
261D4×C11—48no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—48no—
278C2×C4×C11—48no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—48no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11#12012yes—
290C2×C4×C11C2×D812yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4112yes—
294C2×C4×C11H(5,𝔽2)12yes—
295C22⋊D11—88no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299D44—24no—
300D44—24no—
301D44—48no—
302D44—42no—
303D44—42no—
304C11⋊C8—42no—
305C11⋊C8—42no—
306C22×#41—21no—
307C23×D4—111no—
308C22×D8—112no—
309C23×C8—111no—
310#547—24no—
311#547—24no—
312C2×C4⋊Q8C2×D1111yescharacteristic, complemented
313C2×#123—21no—
314C2×#123—21no—
315C2×C22⋊Q8—21no—
316C2×#121—112no—
317C2×#121C2×D1111yescharacteristic
318C2×#121C2×D1111yescharacteristic, complemented
319C2×#120—221no—
320C2×C4×D4C2×D1111yescharacteristic
321C2×C4×D4C2×D1111yescharacteristic, complemented
322C22×C4⋊C4C2×D1111yescharacteristic
323C22×C4⋊C4C2×D1111yescharacteristic, complemented
324#447—224no—
325C2×#102—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×#102—224no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—112no—
332#394—221no—
333#392—221no—
334#390—112no—
335#380—111no—
336#379—221no—
337#340—112no—
338#340—112no—
339#340—112no—
340#336—112no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—22no—
346C22×C11—24no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—82no—
354C22×C11—82no—
355C22×C11#44714yes—
356C22×C11C2×#12011yescharacteristic
357C22×C11#54612yes—
358C22×C11C22×D811yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57712yes—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—816no—
365C2×D11—82no—
366C2×D11—82no—
367C2×D11—82no—
368C2×D11—82no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11#52511yescharacteristic
377C4×C11#53511yescharacteristic
378C4×C11#54612yes—
379Dic11—82no—
380C25—221no—
381C2×#41—28no—
382C2×#41—44no—
383C2×#41—44no—
384C22×Q8—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—112no—
388C22×D4—224no—
389C22×D4—222no—
390C22×D4—222no—
391C22×D4—222no—
392C22×D4—221no—
393C22×D4—442no—
394C22×D4C22⋊D1111yescharacteristic
395C22×D4C22×D1111yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C2×D8—224no—
402C2×D8—224no—
403C2×D8—442no—
404C22×C8—112no—
405C22×C8—112no—
406C22×C8—222no—
407C22×C8—442no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410#123—28no—
411#123—28no—
412C22⋊Q8—28no—
413#121—22no—
414#121—22no—
415#121—22no—
416#121—224no—
417#121—442no—
418#121C22⋊D1114yescomplemented
419#120—444no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4C22⋊D1111yescharacteristic
432C2×C4⋊C4C22⋊D1114yescomplemented
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—222no—
442C2×C22⋊C4—222no—
443C2×C22⋊C4C22⋊D1111yescharacteristic
444C2×C22⋊C4C22⋊D1111yescharacteristic
445C2×C42C22×D1111yescharacteristic
446#102—224no—
447#102—224no—
448#102—224no—
449#102—442no—
450C22⋊C8—222no—
451C22⋊C8—442no—
452#95—221no—
453C2×C11—24no—
454C2×C11—42no—
455C2×C11—82no—
456C2×C11#240411yescharacteristic
457C2×C11C2×#44711yescharacteristic
458C2×C11#301011yescharacteristic
459C2×C11#329412yes—
460C2×C11#330612yes—
461D11—84no—
462C24—21no—
463C24—222no—
464C24—444no—
465C24—442no—
466C24—442no—
467C24—442no—
468C24—882no—
469C24C2×C22⋊D1111yescharacteristic
470C24C2×C22⋊D1111yescharacteristic
471#41—432no—
472C2×Q8—24no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—114no—
487C2×D4—228no—
488C2×D4—222no—
489C2×D4—222no—
490C2×D4—222no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—448no—
494C2×D4—444no—
495C2×D4—444no—
496C2×D4—444no—
497C2×D4—444no—
498C2×D4—442no—
499C2×D4—882no—
500C2×D4#432314yescomplemented
501C2×D4C2×C22⋊D1112yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—222no—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1112yes—
526C22×C4C2×C22⋊D1112yes—
527C22×C4C23×D1111yescharacteristic
528D8—448no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—222no—
533C2×C8—222no—
534C2×C8—222no—
535C2×C8—444no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4C2×C22⋊D1112yes—
546C4⋊C4C2×C22⋊D1112yes—
547C4⋊C4C2×C22⋊D1112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—22no—
553C22⋊C4—444no—
554C22⋊C4—442no—
555C22⋊C4—444no—
556C22⋊C4—882no—
557C42—21no—
558C42—21no—
559C11#2396011yescharacteristic, complemented, Sylow
560C23—22no—
561C23—22no—
562C23—21no—
563C23—22no—
564C23—22no—
565C23—21no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—224no—
572C23—448no—
573C23—442no—
574C23—442no—
575C23—442no—
576C23—442no—
577C23—442no—
578C23—442no—
579C23—888no—
580C23—888no—
581C23—884no—
582C23—884no—
583C23C2×#432312yes—
584C23C2×#432312yes—
585C23#6698512yes—
586C23#6700612yes—
587C23C22×C22⋊D1111yescharacteristic
588Q8—48no—
589D4—28no—
590D4—24no—
591D4—48no—
592D4—48no—
593D4—41no—
594D4—41no—
595D4—224no—
596D4—224no—
597D4—448no—
598D4—442no—
599D4—442no—
600D4—888no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—48no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—48no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4C2×#432312yes—
630C2×C4#6700612yes—
631C2×C4#41×D1112yes—
632C2×C4#6704212yes—
633C2×C4C22×C22⋊D1111yescharacteristic
634C2×C4C22×C22⋊D1111yescharacteristic
635C8—442no—
636C8—442no—
637C22—22no—
638C22—24no—
639C22—22no—
640C22—24no—
641C22—22no—
642C22—24no—
643C22—41no—
644C22—41no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—82no—
650C22—82no—
651C22—444no—
652C22—444no—
653C22—444no—
654C22—8816no—
655C22—882no—
656C22—882no—
657C22—882no—
658C22—882no—
659C22#1062283014yes—
660C22C22×#432311yescharacteristic
661C22C2×#6698511yescharacteristic
662C22#1062336012yes—
663C22#1062336812yes—
664C22C2×#6700611yescharacteristic
665C4—22no—
666C4—22no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—41no—
672C4—882no—
673C4#1062335911yescharacteristic
674C4#1062336012yes—
675C4#1062336111yescharacteristic
676C2—24no—
677C2—42no—
678C2—82no—
679C2—884no—
680C2#1307193111yescharacteristic
681C2C2×#1062283011yescharacteristic
682C2#1307790211yescharacteristic
683C2#1308042312yes—
684C2#1308057112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11#23960
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. C22×#66873C2semidirect
3. #13071972C2semidirect
4. #13069749C2semidirect
5. #13069612C2semidirect
6. #13069045C2semidirect
7. #13068964C2semidirect
8. #13068933C2semidirect
9. #13068909C2semidirect
10. #13068702C2semidirect
11. C2×C11×#547C2semidirect
16. C2×C11×C4⋊Q8C22semidirect
21. C2×C11×#121C22semidirect
23. C2×C4×D4×C11C22semidirect
25. C22×C11×C4⋊C4C22semidirect
30. C2×#66896C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
46. #10622162C22semidirect
76. C11×#121D4semidirect
88. C2×C11×C4⋊C4D4semidirect
145. C2×D4×C11D8semidirect
186. C2×D44#41semidirect
218. C2×#547D11semidirect
312. C2×C4⋊Q8C2×D11semidirect
318. C2×#121C2×D11semidirect
321. C2×C4×D4C2×D11semidirect
323. C22×C4⋊C4C2×D11semidirect
418. #121C22⋊D11semidirect
432. C2×C4⋊C4C22⋊D11semidirect
500. C2×D4#4323semidirect
559. C11#23960semidirect

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
#130697492
#130696122
#130690452
#130689642
#130689332
#130689092
#130687022
C2×C11×#5472
#2396011