Finite Group Databasebeta

← #14769488

Subgroups — #14769488

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4324C211yesmaximal, characteristic
2C2×#10622631C212yesmaximal, complemented
3C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069496C212yesmaximal, complemented
5#13068974C212yesmaximal, complemented
6#13068950C212yesmaximal, complemented
7#13068643C211yesmaximal, characteristic, complemented
8#13068550C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic
10#13068394C211yesmaximal, characteristic, complemented
11D4×C11×C22⋊C4C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C22×C11×C22⋊C4—21no—
16C22×#4324—28no—
17C22×#4324C418yescomplemented
18C22×#4324C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C4×Dic22C2212yescomplemented
24C11×#390C2212yes—
25C11×#386—22no—
26C11×#380C2211yescharacteristic
27C11×#379—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622631—28no—
34C2×#66874C2212yescomplemented
35C2×#66874C2212yescomplemented
36C2×#66871C2212yescomplemented
37#10622555—21no—
38C22⋊C4×Dic11—21no—
39#10622542C2212yescomplemented
40C2×#66867C2212yescomplemented
41#10622259—22no—
42#10622167C2212yescomplemented
43#10622162C2212yescomplemented
44C25×C11—21no—
45C22×D4×C11—24no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11C2×C414yes—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—22no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C22×Dic22—24no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22—42no—
59C22×Dic22C2×C414yescomplemented
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C4×D4×C11—24no—
63C4×D4×C11—42no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—44no—
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2312yes—
73C2×C22⋊Dic11—21no—
74C2×#4324—24no—
75C2×#4324—24no—
76C2×#4324—232no—
77C2×#4324—24no—
78C2×#4324C2×C414yes—
79C2×#4324C2×C414yes—
80C2×#4324C2×C414yescomplemented
81C2×#4324C2×C414yescomplemented
82C2×#4324D418yes—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—22no—
86C22×C11⋊C8—24no—
87C22×C11⋊C8C2×C414yescomplemented
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C4×Dic22—24no—
92C4×Dic22—42no—
93C11×#95—21no—
94C11×#95D412yes—
95#66896—24no—
96#66896—42no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C22⋊(C11⋊C8)—22no—
101#66874—24no—
102#66874—42no—
103#66871—24no—
104#66867—24no—
105#22437—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—24no—
109C24×C11—44no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—82no—
113C24×C11C2×D411yescharacteristic
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—44no—
122C2×D4×C11—48no—
123C2×D4×C11—44no—
124C2×D4×C11C22×C412yes—
125C2×D4×C11C22×C412yes—
126C2×D4×C11C2×D414yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11—82no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—24no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—44no—
144C2×Dic22—28no—
145C2×Dic22—24no—
146C2×Dic22—22no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—44no—
152C2×Dic22—48no—
153C2×Dic22—44no—
154C2×Dic22C22×C412yes—
155C2×Dic22C22×C412yes—
156C2×Dic22C2×D414yes—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—82no—
165C42×C11—22no—
166C42×C11—22no—
167C22⋊Dic11—42no—
168#4324—28no—
169#4324—28no—
170#4324—28no—
171#4324C22⋊C4116yescomplemented
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174Dic11⋊C4—44no—
175C4×Dic11—44no—
176C2×C11⋊C8—28no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8C22×C412yes—
182C2×C11⋊C8C22×C412yes—
183C2×C11⋊C8C2×D414yes—
184C23×SD16—111no—
185C2×#440—112no—
186Q8×C22⋊C4—111no—
187D4×C22⋊C4D1111yescharacteristic
188#1973—112no—
189#1880—112no—
190#1877—112no—
191#1808—111no—
192#1787—111no—
193#1786—111no—
194#1752—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—48no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—48no—
209C23×C11—84no—
210C23×C11—88no—
211C23×C11—88no—
212C23×C11C4×D412yes—
213C23×C11AGL(1,ℤ/8)12yes—
214C23×C11#13712yes—
215C23×C11C22×D411yescharacteristic
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11—42no—
222D4×C11C2×C22⋊C414yes—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—88no—
237C2×C4×C11C4×D412yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)12yes—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—48no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250Dic22—22no—
251Dic22—24no—
252Dic22—22no—
253Dic22—22no—
254Dic22—48no—
255Dic22—42no—
256Dic22C2×C22⋊C414yescomplemented
257C11⋊C8—22no—
258C11⋊C8—42no—
259C11⋊C8C2×C22⋊C414yescomplemented
260C23×Q8—111no—
261C23×D4C2×D1111yescharacteristic
262C22×SD16—111no—
263C22×SD16—111no—
264C22×SD16—111no—
265C22×SD16—111no—
266C22×SD16—118no—
267C22×SD16—228no—
268C23×C8—111no—
269C2×C4×Q8—112no—
270C2×C4×D4C2×D1112yes—
271C22×C22⋊C4—21no—
272#440—228no—
273C2×#107—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×C22⋊C8—111no—
279C2×#97—112no—
280#391—112no—
281#391—222no—
282#390C2×D1112yes—
283#386—22no—
284#380—111no—
285#380—221no—
286#380C2×D1111yescharacteristic
287#379—21no—
288C4×C22⋊C4—221no—
289C4×C22⋊C4C2×D1111yescharacteristic
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—816no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11#44014yescomplemented
308C22×C11C2×C4×D411yescharacteristic
309C22×C11D4212yes—
310C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C11C2×#13711yescharacteristic
312C22×C11#57712yes—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11C22×C22⋊C411yescharacteristic
318C4×C11#51811yescharacteristic
319C4×C11#54612yes—
320Dic11—24no—
321Dic11—42no—
322Dic11—82no—
323C25—21no—
324C22×Q8—114no—
325C22×Q8—111no—
326C22×Q8—111no—
327C22×Q8—224no—
328C22×Q8—222no—
329C22×Q8—221no—
330C22×Q8—442no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—42no—
335C22×D4C4×D1114yes—
336C22×D4C22×D1111yescharacteristic
337C22×D4C22×D1111yescharacteristic
338C23×C4—22no—
339C23×C4—221no—
340C23×C4C22×D1111yescharacteristic
341C2×SD16—114no—
342C2×SD16—118no—
343C2×SD16—114no—
344C2×SD16—114no—
345C2×SD16—114no—
346C2×SD16—224no—
347C2×SD16—2232no—
348C2×SD16—224no—
349C2×SD16—224no—
350C22×C8—111no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—112no—
354C22×C8—224no—
355C4×Q8—224no—
356C4×Q8—442no—
357C4×D4—24no—
358C4×D4—42no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4C22⋊D1111yescharacteristic
369C2×C22⋊C4C22⋊D1111yescharacteristic
370C2×C42—222no—
371C2×C42C22×D1112yes—
372#107—224no—
373#103—224no—
374#103—442no—
375#102—224no—
376#102—442no—
377C22⋊C8—222no—
378#97—224no—
379#95—21no—
380#95—222no—
381#95—221no—
382#95—222no—
383#95C22⋊D1112yes—
384C2×C11—24no—
385C2×C11—44no—
386C2×C11—82no—
387C2×C11D4×C22⋊C411yescharacteristic
388C2×C11C2×#44011yescharacteristic
389C2×C11#294911yescharacteristic
390C2×C11#326512yes—
391C2×C11#326612yes—
392C24—21no—
393C24—21no—
394C24—24no—
395C24—44no—
396C24—42no—
397C24—42no—
398C24—82no—
399C24C2×C22⋊D1111yescharacteristic
400C2×Q8—112no—
401C2×Q8—112no—
402C2×Q8—114no—
403C2×Q8—228no—
404C2×Q8—224no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—444no—
411C2×Q8—444no—
412C2×Q8—448no—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4C2×C4×D1112yes—
424C2×D4C2×C4×D1112yes—
425C2×D4D4×D1114yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—82no—
432C22×C4—221no—
433C22×C4—224no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—444no—
437C22×C4C2×C4×D1112yes—
438C22×C4#433912yes—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—1116no—
444SD16—228no—
445SD16—228no—
446SD16—228no—
447C2×C8—112no—
448C2×C8—114no—
449C2×C8—112no—
450C2×C8—228no—
451C2×C8—222no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8—222no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—444no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—42no—
465C22⋊C4—82no—
466C22⋊C4—442no—
467C42—22no—
468C42—22no—
469C42—444no—
470C11#2243711yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—22no—
476C23—48no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—48no—
485C23—84no—
486C23—88no—
487C23—88no—
488C23C4×C22⋊D1112yes—
489C23#6698512yes—
490C23#6700412yes—
491C23C22×C22⋊D1111yescharacteristic
492Q8—114no—
493Q8—222no—
494Q8—224no—
495Q8—222no—
496Q8—222no—
497Q8—448no—
498Q8—442no—
499D4—22no—
500D4—22no—
501D4—22no—
502D4—24no—
503D4—48no—
504D4—42no—
505D4C22⋊C4×D1114yes—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—88no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—448no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4C4×C22⋊D1112yes—
529C2×C4C22×C4×D1111yescharacteristic
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×D4×D1112yes—
532C2×C4#6703712yes—
533C8—114no—
534C8—222no—
535C8—442no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—22no—
540C22—24no—
541C22—44no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—816no—
549C22—82no—
550C22—82no—
551C22#1062263114yescomplemented
552C22C2×C4×C22⋊D1111yescharacteristic
553C22C2×#6698511yescharacteristic
554C22D4×C22⋊D1112yes—
555C22C2×#6700411yescharacteristic
556C22#1062336712yes—
557C4—22no—
558C4—42no—
559C4—42no—
560C4—82no—
561C4—224no—
562C4—442no—
563C4—882no—
564C4C2×C22⋊C4×D1111yescharacteristic
565C4#1062301711yescharacteristic
566C4#1062302112yes—
567C2—24no—
568C2—44no—
569C2—82no—
570C2C22⋊C4×C22⋊D1111yescharacteristic
571C2C2×#1062263111yescharacteristic
572C2#1307747311yescharacteristic
573C2#1308010712yes—
574C2#1308012212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22437
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. C22⋊C4×Dic22C2semidirect
4. #13069496C2semidirect
5. #13068974C2semidirect
6. #13068950C2semidirect
7. #13068643C2semidirect
8. #13068550C2semidirect
10. #13068394C2semidirect
17. C22×#4324C4semidirect
23. C2×C4×Dic22C22semidirect
34. C2×#66874C22semidirect
35. C2×#66874C22semidirect
36. C2×#66871C22semidirect
39. #10622542C22semidirect
40. C2×#66867C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
59. C22×Dic22C2×C4semidirect
80. C2×#4324C2×C4semidirect
81. C2×#4324C2×C4semidirect
87. C22×C11⋊C8C2×C4semidirect
171. #4324C22⋊C4semidirect
256. Dic22C2×C22⋊C4semidirect
259. C11⋊C8C2×C22⋊C4semidirect
307. C22×C11#440semidirect
470. C11#22437semidirect
551. C22#10622631semidirect

Maximal subgroups

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

subgroupindex
C23×#43242
C2×#106226312
C22⋊C4×Dic222
#130694962
#130689742
#130689502
#130686432
#130685502
#130685472
#130683942
D4×C11×C22⋊C42
#2243711