Finite Group Databasebeta

← #14759433

Subgroups — #14759433

Order 2816.

1520 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622840C211yesmaximal, characteristic
3C2×#10622430C212yesmaximal, complemented
4#13071122C211yesmaximal, characteristic
5#13068969C212yesmaximal, complemented
6#13068931C211yesmaximal, characteristic
7#13068868C212yesmaximal, complemented
8#13068803C211yesmaximal, characteristic, complemented
9#13068448C212yesmaximal, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11—28no—
14C2×Q8×Dic11—21no—
15C2×Q8×Dic11—21no—
16C2×Q8×Dic11C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4325C2212yes—
19C2×#66983C2211yescharacteristic
20C22×C4⋊Dic11—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11—21no—
23C22×C4×Dic11C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×(C22⋊D11)⋊C4—21no—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30#10622840C418yescomplemented
31C2×#66899C2212yes—
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2212yes—
34C2×#66879C2212yes—
35#10622601C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66871C2212yes—
39#10622571—21no—
40#10622430—28no—
41#10622282—21no—
42#10622279—21no—
43#10622189C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yescomplemented
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C8×C11C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64Q8×Dic11—28no—
65Q8×Dic11—28no—
66Q8×Dic11—24no—
67Q8×Dic11—24no—
68Q8×Dic11—24no—
69Q8×Dic11D418yescomplemented
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325C2×C418yescomplemented
73#66983—22no—
74#66983C2×C414yes—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—28no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—28no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2312yes—
97#66946—24no—
98(C22⋊D11)⋊C4—44no—
99C11×#103—24no—
100C11×#103—24no—
101C11×C22⋊C8—22no—
102C11×#95—21no—
103#66899C2×C418yescomplemented
104C11⋊#95—21no—
105C11⋊#95—21no—
106C22⋊(C11⋊C8)C2×C414yescomplemented
107#66885—24no—
108#66879—24no—
109#66871—24no—
110#21454—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C23×D11—21no—
113C2×Q8×C11—24no—
114C2×Q8×C11—216no—
115C2×Q8×C11—24no—
116C2×Q8×C11—216no—
117C2×Q8×C11—24no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C22×C414yes—
122C2×Q8×C11C2×D414yes—
123C2×Q8×C11#4114yes—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—42no—
138C2×C22⋊D11—42no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—41no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44C22×C412yes—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C22⋊C4—42no—
167#4325—216no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—28no—
173C4⋊Dic11—24no—
174C4⋊Dic11—28no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11C22×C412yes—
178C4⋊Dic11C2×D414yes—
179Dic11⋊C4—42no—
180C4×Dic11—28no—
181C4×Dic11—28no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—42no—
186C4×Dic11C2×D414yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C414yes—
190C22×C4×Q8—111no—
191C2×#448—111no—
192C2×#440—112no—
193C4×#121—111no—
194#1880—112no—
195#1874—111no—
196#1863—112no—
197#1852—111no—
198#1787D1111yescharacteristic, complemented
199#1763—112no—
200#1749—111no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11C4×D412yes—
206C23×C11AGL(1,ℤ/8)12yes—
207C23×C11#13712yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216Q8×C11—216no—
217Q8×C11—24no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11C4×D418yescomplemented
221C2×C4×C11—216no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11C4×D412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—48no—
241C2×Dic11—28no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—21no—
250C2×Dic11—24no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—44no—
254C2×Dic11—48no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11#12012yes—
260C2×Dic11#12012yes—
261C2×Dic11#13712yes—
262D44—24no—
263D44—42no—
264C4×D11—84no—
265C8×C11—42no—
266C11⋊C8—24no—
267C23×Q8C2×D1111yescharacteristic
268C22×SD16—112no—
269C2×#121—111no—
270C2×C4×Q8—112no—
271C2×C4×Q8—112no—
272C2×C4×Q8—221no—
273C2×C4×Q8—221no—
274C2×C4×Q8—228no—
275C2×C4×D4—111no—
276C2×C4×D4—221no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—221no—
279C22×C42—111no—
280C22×C42—221no—
281#448—118no—
282#440—228no—
283C2×#107—112no—
284C2×#103—112no—
285C2×#103C2×D1112yes—
286C2×#103C2×D1112yes—
287C2×#102—112no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97—112no—
291#390—111no—
292#389—111no—
293#388—221no—
294#386—221no—
295#380C2×D1111yescharacteristic
296C4×C4⋊C4—111no—
297C4×C22⋊C4—221no—
298#340—112no—
299#340—112no—
300#336—112no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11#44014yescomplemented
308C22×C11C2×C4×D411yescharacteristic
309C22×C11C2×#12011yescharacteristic
310C22×C11#52511yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11C2×#13711yescharacteristic
313C22×C11C2×#13711yescharacteristic
314C22×C11#57511yescharacteristic
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C4×C11—28no—
323C4×C11—22no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11C2×C4×D412yes—
327C4×C11#52512yes—
328Dic11—22no—
329Dic11—22no—
330Dic11—22no—
331Dic11—42no—
332Dic11—41no—
333Dic11—44no—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8C4×D1114yescomplemented
339C22×Q8C22×D1112yes—
340C22×D4—111no—
341C22×D4—221no—
342C23×C4—21no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×SD16—118no—
349C2×SD16—224no—
350C2×SD16—224no—
351C22×C8—112no—
352C22×C8C22×D1112yes—
353#121—114no—
354#121—222no—
355C4×Q8—118no—
356C4×Q8—224no—
357C4×Q8—224no—
358C4×Q8—228no—
359C4×Q8—228no—
360C4×Q8—224no—
361C4×D4—224no—
362C4×D4—444no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—228no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—224no—
383C2×C42—222no—
384C2×C42—222no—
385C2×C42—228no—
386C2×C42—221no—
387#107—224no—
388#103—24no—
389#103—24no—
390#103—118no—
391#102—224no—
392C22⋊C8—22no—
393C22⋊C8—114no—
394#97—224no—
395#95—21no—
396#95—221no—
397#95—221no—
398C2×C11—24no—
399C2×C11C4×#12011yescharacteristic
400C2×C11C2×#44011yescharacteristic
401C2×C11C4×#13711yescharacteristic
402C2×C11#300411yescharacteristic
403C2×C11#300611yescharacteristic
404C2×C11#311211yescharacteristic
405C2×C11#311711yescharacteristic
406D11—82no—
407C24—221no—
408C24D4×D1111yescharacteristic
409C2×Q8—24no—
410C2×Q8—216no—
411C2×Q8—24no—
412C2×Q8—216no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8C2×C4×D1114yes—
418C2×Q8D4×D1114yes—
419C2×Q8#434114yes—
420C2×D4—112no—
421C2×D4—224no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—221no—
425C2×D4—442no—
426C2×D4—442no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—222no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—441no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4C2×C4×D1112yes—
454C22×C4D4×D1111yescharacteristic
455C22×C4#434112yes—
456C22×C4C23×D1111yescharacteristic
457SD16—2216no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—114no—
462C2×C8—222no—
463C2×C8—222no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—112no—
467C4⋊C4—114no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4—222no—
472C4⋊C4—221no—
473C4⋊C4—442no—
474C22⋊C4—42no—
475C22⋊C4—224no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C42—114no—
480C42—222no—
481C42—222no—
482C42—228no—
483C42—228no—
484C42—222no—
485C42—442no—
486C11#2145411yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—222no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23(C22⋊D11)⋊C412yes—
499C23#6696712yes—
500C23#6697112yes—
501C23C2×D4×D1111yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8(C22⋊D11)⋊C418yescomplemented
507D4—224no—
508D4—448no—
509D4—442no—
510C2×C4—216no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—228no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—222no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—224no—
538C2×C4—221no—
539C2×C4—444no—
540C2×C4—448no—
541C2×C4—441no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—442no—
545C2×C4—884no—
546C2×C4(C22⋊D11)⋊C412yes—
547C2×C4C22×C4×D1111yescharacteristic
548C2×C4C2×D4×D1112yes—
549C2×C4C2×#434112yes—
550C2×C4C2×#434111yescharacteristic
551C8—42no—
552C8—224no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—442no—
560C22—442no—
561C22—442no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22#1062243014yescomplemented
567C22C2×(C22⋊D11)⋊C411yescharacteristic
568C22#1062311711yescharacteristic
569C22D11×#12011yescharacteristic
570C22C2×#6696711yescharacteristic
571C22C2×#6697111yescharacteristic
572C22D11×#13711yescharacteristic
573C22#1062330811yescharacteristic
574C4—28no—
575C4—22no—
576C4—81no—
577C4—81no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—441no—
582C4—444no—
583C4—442no—
584C4C2×(C22⋊D11)⋊C412yes—
585C4#1062311712yes—
586C2—24no—
587C2—882no—
588C2#1307111511yescharacteristic
589C2C2×#1062243011yescharacteristic
590C2#1307743111yescharacteristic
591C2#1307785111yescharacteristic
592C2#1307786711yescharacteristic
593C2#1307873311yescharacteristic
594C2#1307878811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#21454
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
3. C2×#10622430C2semidirect
5. #13068969C2semidirect
7. #13068868C2semidirect
8. #13068803C2semidirect
9. #13068448C2semidirect
10. #13068380C2semidirect
11. C11×#1787C2semidirect
30. #10622840C4semidirect
50. C22×Q8×C11C2×C4semidirect
69. Q8×Dic11D4semidirect
72. C2×#4325C2×C4semidirect
103. #66899C2×C4semidirect
106. C22⋊(C11⋊C8)C2×C4semidirect
198. #1787D11semidirect
220. Q8×C11C4×D4semidirect
307. C22×C11#440semidirect
338. C22×Q8C4×D11semidirect
486. C11#21454semidirect
506. Q8(C22⋊D11)⋊C4semidirect
566. C22#10622430semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228402
C2×#106224302
#130711222
#130689692
#130689312
#130688682
#130688032
#130684482
#130683802
C11×#17872
#2145411