Finite Group Databasebeta

← #14755171

Subgroups — #14755171

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623329C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4#13071208C211yesmaximal, characteristic, complemented
5#13068966C214yesmaximal, complemented
6#13068952C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—24no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)C418yescomplemented
15C22×C11×SD16C2212yes—
16C22×C11×D8C2212yes—
17C22×C11×M16C2211yescharacteristic
18C22×C22⋊Dic11—22no—
19#10623329—24no—
20#10623329—24no—
21C2×D4×Dic11—22no—
22C2×D4×Dic11C2214yes—
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10622846—24no—
28#10622843C2212yescomplemented
29C2×#66899C2212yescomplemented
30#10622834C2212yescomplemented
31#10622833—22no—
32C2×#66896—24no—
33C2×#66896C2214yes—
34C2×#66896C2212yescomplemented
35#10622825—22no—
36#10622189C2214yescomplemented
37#10622188C2214yescomplemented
38C25×C11—21no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yescomplemented
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11C2×C414yes—
52C22×D4×C11D414yes—
53C22×D4×C11D414yes—
54C22×D4×C11C2311yescharacteristic
55C22×D4×C11C2312yes—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—24no—
59C23×Dic11—21no—
60C11×AGL(1,ℤ/8)—232no—
61C2×C11×SD16—24no—
62C2×C11×SD16—24no—
63C2×C11×SD16C2×C418yescomplemented
64C2×C11×D8—24no—
65C2×C11×D8—24no—
66C2×C11×D8C2×C418yescomplemented
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2×C414yescomplemented
70C22×C8×C11C2312yes—
71C2×C22⋊Dic11—216no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11D412yes—
76D4×Dic11—216no—
77D4×Dic11—28no—
78D4×Dic11—28no—
79#66979—22no—
80#66979—22no—
81#66979—22no—
82#66979D414yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D412yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2312yes—
91C22×C11⋊C8—22no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8C2312yes—
95#66899—24no—
96#66896—28no—
97#66896—24no—
98C11⋊#95—24no—
99#20929—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—21no—
105C24×C11—82no—
106C24×C11—82no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C2×D4×C11—24no—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11C22⋊C4116yescomplemented
136C2×D4×C11C22×C412yes—
137C2×D4×C11C22×C414yes—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—216no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—42no—
156C22×Dic11—82no—
157C22×Dic11—84no—
158C22×Dic11—84no—
159C22×Dic11C2×D414yes—
160C11×SD16—216no—
161C11×D8—216no—
162C11×M16—28no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C22×C414yes—
166C22⋊Dic11—216no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—84no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—42no—
175C4⋊Dic11C2×D414yes—
176C4×Dic11—24no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—44no—
183C22×AGL(1,ℤ/8)D1111yescharacteristic
184C2×#518—111no—
185C2×#416—111no—
186C22×#102—111no—
187#2311—111no—
188#1879—114no—
189#1877—114no—
190#1736—111no—
191#1729—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—216no—
198C23×C11—22no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—88no—
206C23×C11—88no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11C4×D412yes—
210C23×C11#12012yes—
211C23×C11#12112yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—41no—
216Q8×C11—41no—
217D4×C11—22no—
218D4×C11—24no—
219D4×C11—22no—
220D4×C11—24no—
221D4×C11—24no—
222D4×C11—216no—
223D4×C11—48no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11C2×C22⋊C418yes—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—48no—
231C2×C4×C11C2×C22⋊C414yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D412yes—
234C2×C4×C11#12012yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12112yes—
237C2×C4×C11#12314yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—44no—
252C2×Dic11—816no—
253C2×Dic11—84no—
254C8×C11—24no—
255C11⋊C8—42no—
256C22×#41C2×D1111yescharacteristic
257C23×D4C2×D1111yescharacteristic
258C2×AGL(1,ℤ/8)—24no—
259C2×AGL(1,ℤ/8)—24no—
260C2×AGL(1,ℤ/8)Dic1118yescomplemented
261C22×SD16C2×D1112yes—
262C22×D8C2×D1112yes—
263C22×M16C2×D1111yescharacteristic
264C23×C8—111no—
265#518—224no—
266#518—224no—
267C2×C4×D4—114no—
268C2×C4×D4—222no—
269C2×#117—111no—
270C2×#117—111no—
271C22×C4⋊C4—111no—
272C22×C22⋊C4—222no—
273#416—224no—
274C2×#103—112no—
275C2×#102—114no—
276C2×#102—112no—
277C2×#102—224no—
278#391—112no—
279#390—112no—
280#386—222no—
281#380—222no—
282#340—114no—
283#336—114no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—28no—
289C22×C11—48no—
290C22×C11—48no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—816no—
296C22×C11—82no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11#38614yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×#12111yescharacteristic
303C22×C11#57612yes—
304C22×C11#57712yes—
305C4×C11—42no—
306C4×C11#38614yes—
307C4×C11C22×C22⋊C411yescharacteristic
308C4×C11C2×C4×D411yescharacteristic
309C4×C11C2×#12111yescharacteristic
310C4×C11C2×#12311yescharacteristic
311Dic11—44no—
312Dic11—44no—
313Dic11—82no—
314C25—21no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41C2×Dic1114yescomplemented
321C22×Q8C22×D1111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4C2×Dic1114yes—
328C22×D4C22⋊D1114yes—
329C22×D4C22⋊D1114yes—
330C22×D4C22×D1111yescharacteristic
331C22×D4C22×D1112yes—
332C23×C4—21no—
333C23×C4—224no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336AGL(1,ℤ/8)—232no—
337C2×SD16—24no—
338C2×SD16—24no—
339C2×SD16C2×Dic1118yescomplemented
340C2×D8—24no—
341C2×D8—24no—
342C2×D8C2×Dic1118yescomplemented
343C2×M16—22no—
344C2×M16—22no—
345C2×M16C2×Dic1114yescomplemented
346C22×C8—112no—
347C22×C8—222no—
348C22×C8—222no—
349C22×C8—222no—
350C22×C8C22×D1112yes—
351C4×D4—228no—
352C4×D4—2216no—
353C4×D4—228no—
354#117—114no—
355#117—222no—
356#117—222no—
357#117—222no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—2216no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—224no—
369C2×C42—112no—
370C2×C42—221no—
371#103—224no—
372#102—224no—
373#102—228no—
374#95—224no—
375C2×C11—24no—
376C2×C11—48no—
377C2×C11—82no—
378C2×C11C2×#38611yescharacteristic
379C2×C11#294612yes—
380C2×C11#301212yes—
381C2×C11#304111yescharacteristic
382C2×C11#304211yescharacteristic
383C24—22no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—21no—
388C24—82no—
389C24—82no—
390C24D4×D1111yescharacteristic
391#41—28no—
392#41—28no—
393#41—44no—
394#41—44no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8C22×Dic1112yes—
401C2×D4—24no—
402C2×D4—28no—
403C2×D4—24no—
404C2×D4—28no—
405C2×D4—24no—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C22⋊Dic11116yescomplemented
419C2×D4C22×Dic1112yes—
420C2×D4C22×Dic1114yes—
421C2×D4C2×C22⋊D1114yes—
422C2×D4C2×C22⋊D1114yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—114no—
428C22×C4—222no—
429C22×C4—2216no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4—884no—
433C22×C4—884no—
434C22×C4—882no—
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1112yes—
437C22×C4#434112yes—
438C22×C4#434112yes—
439C22×C4C22×Dic1112yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C23×D1111yescharacteristic
443SD16—216no—
444D8—216no—
445M16—28no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—444no—
452C2×C8C22×Dic1114yes—
453C4⋊C4—114no—
454C4⋊C4—224no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—442no—
459C22⋊C4—2216no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—884no—
463C42—224no—
464C42—222no—
465C42—222no—
466C11#2092911yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—216no—
473C23—22no—
474C23—44no—
475C23—44no—
476C23—42no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—84no—
481C23—84no—
482C23—88no—
483C23—88no—
484C23D4×Dic1112yes—
485C23#6699012yes—
486C23#6699212yes—
487C23C2×D4×D1111yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—41no—
491Q8—41no—
492D4—24no—
493D4—22no—
494D4—24no—
495D4—24no—
496D4—216no—
497D4—22no—
498D4—48no—
499D4—41no—
500D4—41no—
501D4C2×C22⋊Dic1118yes—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—48no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—444no—
513C2×C4—442no—
514C2×C4—8816no—
515C2×C4—884no—
516C2×C4D4×Dic1114yes—
517C2×C4D4×Dic1112yes—
518C2×C4#6698814yes—
519C2×C4#6699012yes—
520C2×C4#6699214yes—
521C2×C4#6699212yes—
522C2×C4C2×C22⋊Dic1114yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C2×C4C23×Dic1111yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—24no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—24no—
535C22—28no—
536C22—44no—
537C22—44no—
538C22—48no—
539C22—48no—
540C22—42no—
541C22—44no—
542C22—816no—
543C22—81no—
544C22—81no—
545C22—82no—
546C22#1062283314yes—
547C22#1062330512yes—
548C22#1062330612yes—
549C22C2×D4×Dic1111yescharacteristic
550C22C2×#6699011yescharacteristic
551C22C2×#6699211yescharacteristic
552C4—42no—
553C4—444no—
554C4—444no—
555C4—882no—
556C4#1062283314yes—
557C4C2×D4×Dic1111yescharacteristic
558C4C2×#6698811yescharacteristic
559C4C2×#6699211yescharacteristic
560C4C22×C22⋊Dic1111yescharacteristic
561C2—24no—
562C2—48no—
563C2—82no—
564C2C2×#1062283311yescharacteristic
565C2#1307744912yes—
566C2#1307791912yes—
567C2#1307812111yescharacteristic
568C2#1307813011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#20929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10623329C2semidirect
2. C2×#10622846C2semidirect
3. C22×#66896C2semidirect
4. #13071208C2semidirect
5. #13068966C2semidirect
6. #13068952C2semidirect
7. #13068336C2semidirect
8. #13068314C2semidirect
14. C2×C11×AGL(1,ℤ/8)C4semidirect
28. #10622843C22semidirect
29. C2×#66899C22semidirect
30. #10622834C22semidirect
34. C2×#66896C22semidirect
36. #10622189C22semidirect
37. #10622188C22semidirect
44. C2×C11×#41C2×C4semidirect
63. C2×C11×SD16C2×C4semidirect
66. C2×C11×D8C2×C4semidirect
69. C2×C11×M16C2×C4semidirect
135. C2×D4×C11C22⋊C4semidirect
260. C2×AGL(1,ℤ/8)Dic11semidirect
320. C2×#41C2×Dic11semidirect
339. C2×SD16C2×Dic11semidirect
342. C2×D8C2×Dic11semidirect
345. C2×M16C2×Dic11semidirect
418. C2×D4C22⋊Dic11semidirect
466. C11#20929semidirect

Maximal subgroups

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

subgroupindex
C2×#106233292
C2×#106228462
C22×#668962
#130712082
#130689662
#130689522
#130683362
#130683142
C22×C11×AGL(1,ℤ/8)2
#2092911