Finite Group Databasebeta

← #14786719

Subgroups — #14786719

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic, complemented
3#13072933C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069802C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068877C212yesmaximal, 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
25C22×C4⋊Dic11C2211yescharacteristic, complemented
26C23×C11⋊C8C2211yescharacteristic, complemented
27#10622833—21no—
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#10622647—24no—
40#10622599—21no—
41C2×#66872C2212yescomplemented
42#10622562—21no—
43#10622559—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—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×Dic11⋊C4—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—42no—
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2312yes—
107#66896—24no—
108#66896—24no—
109#66896—24no—
110#66896—24no—
111#66896—42no—
112#66896—42no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—21no—
116C22⋊(C11⋊C8)—22no—
117C22⋊(C11⋊C8)—42no—
118#66872—24no—
119#24033—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11—24no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—24no—
125C24×C11—44no—
126C24×C11—44no—
127C24×C11—42no—
128C24×C11—42no—
129C24×C11—42no—
130C24×C11—42no—
131C24×C11—82no—
132C24×C11—82no—
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—28no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—44no—
153C2×D4×C11—48no—
154C2×D4×C11—44no—
155C2×D4×C11—44no—
156C2×D4×C11—42no—
157C2×D4×C11—48no—
158C2×D4×C11—432no—
159C2×D4×C11—44no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—44no—
165C2×D4×C11—42no—
166C2×D4×C11—82no—
167C2×D4×C11SD1614yes—
168C2×D4×C11C2×D412yes—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D412yes—
171C2×D4×C11#4114yes—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—24no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—42no—
192C22×Dic11—82no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C42×C11—21no—
202C42×C11—21no—
203C22⋊Dic11—42no—
204C22⋊Dic11—82no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—22no—
209C4⋊Dic11—42no—
210Dic11⋊C4—82no—
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×D42D1111yescharacteristic
219C2×#481—111no—
220C22×#102—111no—
221#2487—111no—
222#2041—112no—
223#2034—112no—
224#1893—111no—
225#1869—111no—
226#1864—112no—
227#1786—112no—
228#1786—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—21no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11—48no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—48no—
254C23×C11—84no—
255C23×C11—88no—
256C23×C11—88no—
257C23×C11—88no—
258C23×C11—84no—
259C23×C11—88no—
260C23×C11#12012yes—
261C23×C11C2×SD1612yes—
262C23×C11C2×SD1612yes—
263C23×C11AGL(1,ℤ/8)12yes—
264C23×C11C22×D411yescharacteristic
265D4×C11—28no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—24no—
270D4×C11—24no—
271D4×C11—48no—
272D4×C11—48no—
273D4×C11—48no—
274D4×C11—48no—
275D4×C11—48no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—42no—
279D4×C11—84no—
280D4×C11#12314yes—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—48no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11#12012yes—
299C2×C4×C11C2×SD1612yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4112yes—
303C2×C4×C11H(5,𝔽2)12yes—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—84no—
311C11⋊C8—42no—
312C11⋊C8—42no—
313C23×D4—21no—
314C23×D4C2×D1111yescharacteristic
315C23×D4C2×D1111yescharacteristic
316C23×C8—111no—
317D42—24no—
318D42—24no—
319C2×#127C2×D1111yescharacteristic
320C2×#121—21no—
321C2×#121C2×D1111yescharacteristic
322C2×#121C2×D1111yescharacteristic
323C2×#120—21no—
324C2×#120—21no—
325C2×C4×D4C2×D1111yescharacteristic
326C2×C4×D4C2×D1111yescharacteristic
327C22×C4⋊C4—111no—
328#481—224no—
329C2×#106—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102—112no—
333C2×#102—112no—
334C2×#102—112no—
335C2×#102—112no—
336C2×#102—224no—
337C2×C22⋊C8—111no—
338C2×C22⋊C8—112no—
339#400—221no—
340#399—221no—
341#389—112no—
342#386—221no—
343#385—221no—
344#380—111no—
345#380—112no—
346#340—112no—
347#336—112no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—24no—
351C22×C11—24no—
352C22×C11—24no—
353C22×C11—22no—
354C22×C11—24no—
355C22×C11—41no—
356C22×C11—42no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—44no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—816no—
369C22×C11—816no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11#45014yes—
375C22×C11C2×#12011yescharacteristic
376C22×C11#54612yes—
377C22×C11C22×SD1611yescharacteristic
378C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C11#57612yes—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11C2×#12311yescharacteristic
386C4×C11#53411yescharacteristic
387C4×C11#54612yes—
388Dic11—82no—
389Dic11—82no—
390C25—21no—
391C25—21no—
392C22×D4—24no—
393C22×D4—28no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—24no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—22no—
403C22×D4—21no—
404C22×D4—42no—
405C22×D4—42no—
406C22×D4—44no—
407C22×D4—44no—
408C22×D4C22⋊D1111yescharacteristic
409C22×D4C22⋊D1114yes—
410C22×D4C22×D1111yescharacteristic
411C22×D4C22×D1111yescharacteristic
412C22×D4C22×D1111yescharacteristic
413C23×C4—21no—
414C23×C4—221no—
415C23×C4C22×D1111yescharacteristic
416C23×C4C22×D1111yescharacteristic
417C22×C8—112no—
418C22×C8—112no—
419C22×C8—222no—
420C22×C8—442no—
421#127—22no—
422#127—22no—
423#121—28no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121C22⋊D1114yes—
428#120—28no—
429#120—28no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4C22⋊D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4C22⋊D1111yescharacteristic
448C2×C22⋊C4C22⋊D1111yescharacteristic
449C2×C42C22×D1111yescharacteristic
450#106—224no—
451#102—224no—
452#102—224no—
453#102—224no—
454#102—224no—
455#102—442no—
456#102—442no—
457C22⋊C8—222no—
458C22⋊C8—442no—
459#95—222no—
460#95—221no—
461#95—222no—
462C2×C11—24no—
463C2×C11—42no—
464C2×C11—44no—
465C2×C11—82no—
466C2×C11—82no—
467C2×C11#240511yescharacteristic
468C2×C11C2×#45011yescharacteristic
469C2×C11#300811yescharacteristic
470C2×C11#329512yes—
471C2×C11#331812yes—
472C24—21no—
473C24—24no—
474C24—21no—
475C24—21no—
476C24—24no—
477C24—44no—
478C24—44no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—82no—
484C24—82no—
485C24C2×C22⋊D1111yescharacteristic
486C24C2×C22⋊D1111yescharacteristic
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—44no—
505C2×D4—48no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—48no—
510C2×D4—432no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—44no—
517C2×D4—42no—
518C2×D4—82no—
519C2×D4#432414yes—
520C2×D4#434114yes—
521C2×D4C2×C22⋊D1112yes—
522C2×D4C2×C22⋊D1112yes—
523C2×D4C2×C22⋊D1112yes—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—442no—
537C22×C4—882no—
538C22×C4C2×C22⋊D1111yescharacteristic
539C22×C4C2×C22⋊D1111yescharacteristic
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C2×C22⋊D1111yescharacteristic
542C22×C4C2×C22⋊D1112yes—
543C22×C4C2×C22⋊D1112yes—
544C22×C4C23×D1111yescharacteristic
545C2×C8—222no—
546C2×C8—222no—
547C2×C8—222no—
548C2×C8—222no—
549C2×C8—222no—
550C2×C8—222no—
551C2×C8—444no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—222no—
555C4⋊C4—222no—
556C4⋊C4—222no—
557C4⋊C4—222no—
558C4⋊C4—442no—
559C4⋊C4—882no—
560C4⋊C4C2×C22⋊D1112yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—22no—
564C22⋊C4—24no—
565C22⋊C4—22no—
566C22⋊C4—442no—
567C22⋊C4—882no—
568C42—21no—
569C42—21no—
570C11#2403311yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—21no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—21no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—48no—
582C23—48no—
583C23—48no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—42no—
592C23—42no—
593C23—48no—
594C23—42no—
595C23—42no—
596C23—84no—
597C23—88no—
598C23—88no—
599C23—88no—
600C23—84no—
601C23—88no—
602C23#6698512yes—
603C23C2×#432412yes—
604C23C2×#432412yes—
605C23#6700612yes—
606C23C22×C22⋊D1111yescharacteristic
607D4—28no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—24no—
612D4—24no—
613D4—48no—
614D4—48no—
615D4—48no—
616D4—48no—
617D4—48no—
618D4—41no—
619D4—41no—
620D4—42no—
621D4—84no—
622D4#6698814yes—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—442no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—884no—
647C2×C4C2×#432412yes—
648C2×C4#6700612yes—
649C2×C4C2×#434112yes—
650C2×C4#6703712yes—
651C2×C4C22×C22⋊D1111yescharacteristic
652C2×C4C22×C22⋊D1111yescharacteristic
653C8—442no—
654C8—442no—
655C22—22no—
656C22—24no—
657C22—22no—
658C22—24no—
659C22—22no—
660C22—24no—
661C22—24no—
662C22—42no—
663C22—41no—
664C22—44no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—44no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—816no—
676C22—816no—
677C22—82no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22#1062283114yes—
682C22C2×#6698511yescharacteristic
683C22C22×#432411yescharacteristic
684C22#1062333712yes—
685C22#1062336612yes—
686C22C2×#6700611yescharacteristic
687C4—22no—
688C4—22no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—882no—
693C4—882no—
694C4C2×#6698811yescharacteristic
695C4#1062333511yescharacteristic
696C4#1062333712yes—
697C2—24no—
698C2—42no—
699C2—44no—
700C2—82no—
701C2—82no—
702C2#1307193911yescharacteristic
703C2C2×#1062283111yescharacteristic
704C2#1307788411yescharacteristic
705C2#1308044012yes—
706C2#1308075712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11#24033
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×#10622647C2semidirect
2. C22×#66896C2semidirect
3. #13072933C2semidirect
4. #13069847C2semidirect
5. #13069802C2semidirect
6. #13069045C2semidirect
7. #13068909C2semidirect
8. #13068877C2semidirect
9. #13068547C2semidirect
10. #13068547C2semidirect
25. C22×C4⋊Dic11C22semidirect
26. 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×#66872C22semidirect
44. #10622541C22semidirect
45. #10622167C22semidirect
46. #10622162C22semidirect
570. C11#24033semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
C22×#668962
#130729332
#130698472
#130698022
#130690452
#130689092
#130688772
#130685472
C2×D42×C112
#2403311