Finite Group Databasebeta

← #14756709

Subgroups — #14756709

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C211yesmaximal, characteristic
2#13071091C211yesmaximal, characteristic, complemented
3C4×D4×Dic11C211yesmaximal, characteristic
4#13069260C211yesmaximal, characteristic, complemented
5#13069254C211yesmaximal, characteristic, complemented
6#13069195C211yesmaximal, characteristic, complemented
7#13069193C211yesmaximal, characteristic, complemented
8#13068952C211yesmaximal, characteristic
9#13068863C211yesmaximal, characteristic
10#13068861C211yesmaximal, characteristic
11#13068508C211yesmaximal, characteristic, complemented
12#103×Dic11C211yesmaximal, characteristic, complemented
13#102×Dic11C211yesmaximal, characteristic
14#13068360C211yesmaximal, characteristic, complemented
15C11×#1877C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×C4×Dic11—21no—
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#391C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C4×C22⋊Dic11—21no—
31SD16×Dic11C418yescomplemented
32C2×#66881C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C22⋊C4×Dic11—21no—
42C22⋊C4×Dic11—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C42×Dic11C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622267—21no—
47#10622266—21no—
48#10622262—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78Q8×Dic11—22no—
79Q8×Dic11C2×C414yescomplemented
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11C2×C414yes—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—44no—
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#103—22no—
106C11×#102—22no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899C2×C414yescomplemented
111#66896—22no—
112#66896C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66881C2×C414yescomplemented
122C8×Dic11—22no—
123C8×Dic11C2×C414yescomplemented
124#66871—22no—
125#66871—22no—
126#21114—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C22×C412yes—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C22×C412yes—
138C2×D4×C11#4112yes—
139C2×D4×C11#4112yes—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C11×SD16—28no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C412yes—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—24no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—24no—
178C22⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190C4×Dic11—24no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C4×Dic11C22×C412yes—
202C4×Dic11#4112yes—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C412yes—
209C2×C4×SD16—111no—
210#2295—111no—
211C42×D4—111no—
212#1928—111no—
213#1928—111no—
214#1919—111no—
215#1919—111no—
216#1877—111no—
217#1877D1111yescharacteristic
218#1862—111no—
219#1862—111no—
220C4×#107—111no—
221C4×#103—111no—
222C4×#102—111no—
223#1744—111no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11#11714yes—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—48no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11#13512yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—48no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—48no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C4×D412yes—
284C2×Dic11C4×D412yes—
285C2×Dic11#13512yes—
286C2×Dic11AGL(1,ℤ/8)12yes—
287C2×Dic11#13712yes—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—22no—
291C11⋊C8—41no—
292C22×SD16C2×D1111yescharacteristic
293C2×C4×Q8—111no—
294C2×C4×D4—111no—
295C2×C4×D4—111no—
296C2×C4×D4C2×D1111yescharacteristic
297C22×C42—221no—
298C4×SD16—118no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102—111no—
307C2×#102C2×D1111yescharacteristic
308C2×C4×C8—111no—
309C2×C4×C8—111no—
310#391—111no—
311#391C2×D1111yescharacteristic
312#389—111no—
313#389—111no—
314#387—221no—
315#387—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—221no—
321C4×C22⋊C4—221no—
322C4×C22⋊C4—221no—
323C4×C22⋊C4—221no—
324#376—221no—
325C43—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332#336—111no—
333#336—111no—
334#336—111no—
335#336C2×D1111yescharacteristic
336C22×C11—24no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#52511yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C4×C11—22no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11C2×#11711yescharacteristic
356C4×C11C4×#4111yescharacteristic
357C4×C11#52911yescharacteristic
358C4×C11#52911yescharacteristic
359Dic11—22no—
360Dic11—22no—
361Dic11—42no—
362Dic11—41no—
363Dic11—42no—
364Dic11—42no—
365Dic11—81no—
366Dic11#44014yes—
367C22×Q8C22×D1111yescharacteristic
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C23×C4—221no—
371C23×C4—221no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16C4×D1114yes—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379C4×Q8—114no—
380C4×Q8—222no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—114no—
384C4×D4—222no—
385C4×D4—222no—
386C4×D4—222no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42—444no—
411C2×C42C22×D1111yescharacteristic
412#107—222no—
413#107—222no—
414#106—114no—
415#103—22no—
416#103—114no—
417#103—222no—
418#102—22no—
419#102—114no—
420#102—222no—
421C4×C8—114no—
422C4×C8—222no—
423#95—21no—
424#95—21no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11—44no—
434C2×C11#229011yescharacteristic
435C2×C11C4×#13511yescharacteristic
436C2×C11C2×#44011yescharacteristic
437C2×C11#310511yescharacteristic
438C2×C11#310511yescharacteristic
439C2×C11#310711yescharacteristic
440C2×C11#310711yescharacteristic
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×C4×D1112yes—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4C2×C4×D1112yes—
452C2×D4#434112yes—
453C2×D4#434112yes—
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—28no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—112no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8C2×C4×D1112yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—112no—
494C4⋊C4—112no—
495C4⋊C4—112no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4#434112yes—
505C22⋊C4—24no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C42—21no—
509C42—21no—
510C42—112no—
511C42—112no—
512C42—222no—
513C42—222no—
514C42—222no—
515C42—224no—
516C42—222no—
517C42—221no—
518C42—221no—
519C42—442no—
520C42—442no—
521C42—442no—
522C42—442no—
523C11#2111411yescharacteristic, complemented, Sylow
524C23—22no—
525C23—22no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23C2×D4×D1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536D4—22no—
537D4—22no—
538D4—22no—
539D4#6693014yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—48no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—112no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—448no—
571C2×C4—448no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4#6696912yes—
582C2×C4C22×C4×D1111yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C8—22no—
589C8—41no—
590C8—222no—
591C8—441no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22C4×D4×D1111yescharacteristic
600C22#1062311711yescharacteristic
601C22#1062313711yescharacteristic
602C22C2×#6696911yescharacteristic
603C22D11×#13511yescharacteristic
604C22D11×AGL(1,ℤ/8)11yescharacteristic
605C22D11×#13711yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—42no—
610C4—81no—
611C4—114no—
612C4—222no—
613C4—222no—
614C4—442no—
615C4—442no—
616C4—442no—
617C4—441no—
618C4—881no—
619C4C2×#6693011yescharacteristic
620C4C4×#434111yescharacteristic
621C4#1062313111yescharacteristic
622C4#1062318011yescharacteristic
623C2—44no—
624C2#1307105611yescharacteristic
625C2C4×#6696911yescharacteristic
626C2D11×#44011yescharacteristic
627C2#1307866211yescharacteristic
628C2#1307866411yescharacteristic
629C2#1307868011yescharacteristic
630C2#1307868411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1877D11
hypocenterC11#21114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
2. #13071091C2semidirect
4. #13069260C2semidirect
5. #13069254C2semidirect
6. #13069195C2semidirect
7. #13069193C2semidirect
11. #13068508C2semidirect
12. #103×Dic11C2semidirect
14. #13068360C2semidirect
31. SD16×Dic11C4semidirect
79. Q8×Dic11C2×C4semidirect
110. #66899C2×C4semidirect
121. #66881C2×C4semidirect
123. C8×Dic11C2×C4semidirect
523. C11#21114semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
#130710912
C4×D4×Dic112
#130692602
#130692542
#130691952
#130691932
#130689522
#130688632
#130688612
#130685082
#103×Dic112
#102×Dic112
#130683602
C11×#18772
#2111411