Finite Group Databasebeta

← #14786708

Subgroups — #14786708

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic, complemented
3#13072924C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069795C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068863C212yesmaximal, complemented
9#13068547C211yesmaximal, characteristic, complemented
10#13068547C212yesmaximal, complemented
11C2×D42×C11C211yesmaximal, characteristic
12C23×D4×C11—21no—
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15D42×C11—24no—
16D42×C11—24no—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#120—21no—
22C2×C11×#120—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×#66988—21no—
26C22×C4⋊Dic11C2211yescharacteristic, complemented
27C23×C11⋊C8C2211yescharacteristic, complemented
28C2×#66896—24no—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2212yescomplemented
32C2×#66896C2212yescomplemented
33C2×#66896C2212yescomplemented
34C2×#66896C2212yescomplemented
35#10622825C2212yescomplemented
36#10622825C2211yescharacteristic, complemented
37C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
38C2×C22⋊(C11⋊C8)C2212yescomplemented
39#10622646—24no—
40#10622596—21no—
41C2×#66871C2212yescomplemented
42#10622566—21no—
43#10622556—21no—
44#10622541C2212yescomplemented
45#10622167C2212yescomplemented
46#10622162C2212yescomplemented
47C25×C11—21no—
48C25×C11—21no—
49C22×D4×C11—24no—
50C22×D4×C11—28no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—24no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—22no—
60C22×D4×C11—21no—
61C22×D4×C11—42no—
62C22×D4×C11—42no—
63C22×D4×C11—44no—
64C22×D4×C11—44no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11D414yes—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×Dic11—21no—
74C11×#127—22no—
75C11×#127—22no—
76C11×#121—28no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121D414yes—
81C11×#120—28no—
82C11×#120—28no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
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×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—22no—
97#66988—44no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×Dic11⋊C4—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—42no—
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2312yes—
108#66896—24no—
109#66896—24no—
110#66896—24no—
111#66896—24no—
112#66896—42no—
113#66896—42no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—42no—
119#66871—24no—
120#24032—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—24no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—24no—
126C24×C11—44no—
127C24×C11—44no—
128C24×C11—42no—
129C24×C11—42no—
130C24×C11—42no—
131C24×C11—42no—
132C24×C11—82no—
133C24×C11—82no—
134C24×C11C2×D411yescharacteristic
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—44no—
154C2×D4×C11—48no—
155C2×D4×C11—44no—
156C2×D4×C11—44no—
157C2×D4×C11—42no—
158C2×D4×C11—48no—
159C2×D4×C11—432no—
160C2×D4×C11—44no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—44no—
166C2×D4×C11—42no—
167C2×D4×C11—82no—
168C2×D4×C11D814yes—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D412yes—
171C2×D4×C11C2×D412yes—
172C2×D4×C11#4114yes—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—24no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2×D412yes—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—22no—
203C42×C11—21no—
204C42×C11—21no—
205C22⋊Dic11—44no—
206C22⋊Dic11—42no—
207C4⋊Dic11—22no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11—42no—
212Dic11⋊C4—44no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—44no—
220C2×D42D1111yescharacteristic
221C2×#480—111no—
222C22×#102—111no—
223#2486—111no—
224#2041—112no—
225#2033—112no—
226#1893—111no—
227#1869—111no—
228#1862—112no—
229#1786—112no—
230#1786—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—48no—
242C23×C11—48no—
243C23×C11—48no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—48no—
256C23×C11—84no—
257C23×C11—88no—
258C23×C11—88no—
259C23×C11—88no—
260C23×C11—84no—
261C23×C11—88no—
262C23×C11#12012yes—
263C23×C11C2×D812yes—
264C23×C11C2×D812yes—
265C23×C11AGL(1,ℤ/8)12yes—
266C23×C11C22×D411yescharacteristic
267D4×C11—28no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—22no—
271D4×C11—24no—
272D4×C11—24no—
273D4×C11—48no—
274D4×C11—48no—
275D4×C11—48no—
276D4×C11—48no—
277D4×C11—48no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—42no—
281D4×C11—84no—
282D4×C11#12314yescomplemented
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—48no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—42no—
300C2×C4×C11#12012yes—
301C2×C4×C11C2×D812yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2×#4112yes—
305C2×C4×C11H(5,𝔽2)12yes—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—84no—
313C11⋊C8—42no—
314C11⋊C8—42no—
315C23×D4—21no—
316C23×D4C2×D1111yescharacteristic
317C23×D4C2×D1111yescharacteristic
318C23×C8—111no—
319D42—24no—
320D42—24no—
321C2×#127C2×D1111yescharacteristic
322C2×#123—221no—
323C2×#121—21no—
324C2×#121C2×D1111yescharacteristic
325C2×#121C2×D1111yescharacteristic
326C2×#120—21no—
327C2×#120—21no—
328C2×C4×D4C2×D1111yescharacteristic
329C2×C4×D4C2×D1111yescharacteristic
330C22×C4⋊C4—111no—
331#480—224no—
332C2×#107—112no—
333C2×#102—112no—
334C2×#102—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×#102—112no—
338C2×#102—112no—
339C2×#102—224no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—112no—
342#398—221no—
343#397—221no—
344#389—112no—
345#381—221no—
346#380—111no—
347#380—112no—
348#340—112no—
349#336—112no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—24no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11—22no—
356C22×C11—24no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—44no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—816no—
371C22×C11—816no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11#44714yes—
377C22×C11C2×#12011yescharacteristic
378C22×C11#54612yes—
379C22×C11C22×D811yescharacteristic
380C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C11#57712yes—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11C2×#12311yescharacteristic
388C4×C11#53411yescharacteristic
389C4×C11#54612yes—
390Dic11—82no—
391Dic11—82no—
392C25—21no—
393C25—21no—
394C22×D4—24no—
395C22×D4—28no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—24no—
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—22no—
405C22×D4—21no—
406C22×D4—42no—
407C22×D4—42no—
408C22×D4—44no—
409C22×D4—44no—
410C22×D4C22⋊D1111yescharacteristic
411C22×D4C22⋊D1114yes—
412C22×D4C22×D1111yescharacteristic
413C22×D4C22×D1111yescharacteristic
414C22×D4C22×D1111yescharacteristic
415C23×C4—21no—
416C23×C4—221no—
417C23×C4C22×D1111yescharacteristic
418C23×C4C22×D1111yescharacteristic
419C22×C8—112no—
420C22×C8—112no—
421C22×C8—222no—
422C22×C8—442no—
423#127—22no—
424#127—22no—
425#123—444no—
426#121—28no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121C22⋊D1114yes—
431#120—28no—
432#120—28no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4C22⋊D1111yescharacteristic
444C2×C4⋊C4C22×D1111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4C22⋊D1111yescharacteristic
451C2×C22⋊C4C22⋊D1111yescharacteristic
452C2×C42C22×D1111yescharacteristic
453#107—224no—
454#102—224no—
455#102—224no—
456#102—224no—
457#102—224no—
458#102—442no—
459#102—442no—
460C22⋊C8—222no—
461C22⋊C8—442no—
462#95—222no—
463#95—221no—
464#95—222no—
465C2×C11—24no—
466C2×C11—42no—
467C2×C11—44no—
468C2×C11—82no—
469C2×C11—82no—
470C2×C11#240511yescharacteristic
471C2×C11C2×#44711yescharacteristic
472C2×C11#300911yescharacteristic
473C2×C11#329412yes—
474C2×C11#331012yes—
475C24—21no—
476C24—24no—
477C24—21no—
478C24—21no—
479C24—24no—
480C24—44no—
481C24—44no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—82no—
487C24—82no—
488C24C2×C22⋊D1111yescharacteristic
489C24C2×C22⋊D1111yescharacteristic
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—28no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—44no—
508C2×D4—48no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—42no—
512C2×D4—48no—
513C2×D4—432no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—44no—
520C2×D4—42no—
521C2×D4—82no—
522C2×D4#432314yes—
523C2×D4#434114yes—
524C2×D4C2×C22⋊D1112yes—
525C2×D4C2×C22⋊D1112yes—
526C2×D4C2×C22⋊D1112yes—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1112yes—
547C22×C4C2×C22⋊D1112yes—
548C22×C4C23×D1111yescharacteristic
549C2×C8—222no—
550C2×C8—222no—
551C2×C8—222no—
552C2×C8—222no—
553C2×C8—222no—
554C2×C8—222no—
555C2×C8—444no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—222no—
559C4⋊C4—222no—
560C4⋊C4—222no—
561C4⋊C4—222no—
562C4⋊C4—444no—
563C4⋊C4—442no—
564C4⋊C4C2×C22⋊D1112yes—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—22no—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—442no—
571C22⋊C4—444no—
572C42—21no—
573C42—21no—
574C11#2403211yescharacteristic, complemented, Sylow
575C23—22no—
576C23—22no—
577C23—21no—
578C23—22no—
579C23—24no—
580C23—22no—
581C23—21no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—48no—
586C23—48no—
587C23—48no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—48no—
598C23—42no—
599C23—42no—
600C23—84no—
601C23—88no—
602C23—88no—
603C23—88no—
604C23—84no—
605C23—88no—
606C23C2×#432312yes—
607C23C2×#432312yes—
608C23#6698512yes—
609C23#6700612yes—
610C23C22×C22⋊D1111yescharacteristic
611D4—28no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—24no—
616D4—24no—
617D4—48no—
618D4—48no—
619D4—48no—
620D4—48no—
621D4—48no—
622D4—41no—
623D4—41no—
624D4—42no—
625D4—84no—
626D4#6698814yescomplemented
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—48no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—442no—
650C2×C4—884no—
651C2×C4C2×#432312yes—
652C2×C4#6700612yes—
653C2×C4C2×#434112yes—
654C2×C4#6703712yes—
655C2×C4C22×C22⋊D1111yescharacteristic
656C2×C4C22×C22⋊D1111yescharacteristic
657C8—442no—
658C8—442no—
659C22—24no—
660C22—22no—
661C22—24no—
662C22—22no—
663C22—22no—
664C22—24no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—44no—
669C22—41no—
670C22—44no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—816no—
680C22—816no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22#1062283014yes—
686C22C22×#432311yescharacteristic
687C22C2×#6698511yescharacteristic
688C22#1062333712yes—
689C22#1062336712yes—
690C22C2×#6700611yescharacteristic
691C4—22no—
692C4—22no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—882no—
697C4—882no—
698C4C2×#6698811yescharacteristic
699C4#1062333511yescharacteristic
700C4#1062333712yes—
701C2—24no—
702C2—42no—
703C2—44no—
704C2—82no—
705C2—82no—
706C2#1307193911yescharacteristic
707C2C2×#1062283011yescharacteristic
708C2#1307789311yescharacteristic
709C2#1308042912yes—
710C2#1308063712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11#24032
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10622646C2semidirect
2. C22×#66896C2semidirect
3. #13072924C2semidirect
4. #13069847C2semidirect
5. #13069795C2semidirect
6. #13069045C2semidirect
7. #13068909C2semidirect
8. #13068863C2semidirect
9. #13068547C2semidirect
10. #13068547C2semidirect
26. C22×C4⋊Dic11C22semidirect
27. C23×C11⋊C8C22semidirect
31. C2×#66896C22semidirect
32. C2×#66896C22semidirect
33. C2×#66896C22semidirect
34. C2×#66896C22semidirect
35. #10622825C22semidirect
36. #10622825C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
41. C2×#66871C22semidirect
44. #10622541C22semidirect
45. #10622167C22semidirect
46. #10622162C22semidirect
282. D4×C11#123semidirect
574. C11#24032semidirect
626. D4#66988semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
C22×#668962
#130729242
#130698472
#130697952
#130690452
#130689092
#130688632
#130685472
C2×D42×C112
#2403211