Finite Group Databasebeta

← #14764941

Subgroups — #14764941

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622831C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic, complemented
3#13069469C212yesmaximal, complemented
4#13069302C212yesmaximal, complemented
5#13069240C212yesmaximal, complemented
6#13068974C212yesmaximal, complemented
7#13068923C211yesmaximal, characteristic, complemented
8#13068809C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4—21no—
15C22×C11×C22⋊C4—21no—
16C22×C42×C11C2211yescharacteristic
17C22×#4324C2212yes—
18C2×#66977C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic, complemented
20C11×#390—21no—
21C11×#390—21no—
22C11×#390C2212yes—
23C11×#390C2212yes—
24#10622831C418yescomplemented
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28#10622825C2211yescharacteristic
29#10622823—21no—
30C4×C22⋊Dic11—21no—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66874C2212yescomplemented
34C2×#66872C2212yescomplemented
35C4×C4⋊Dic11C2211yescharacteristic, complemented
36#10622546—21no—
37C4×Dic11⋊C4—21no—
38#10622542C2211yescharacteristic, complemented
39#10622541C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2212yescomplemented
41#10622167C2212yescomplemented
42#10622167C2212yescomplemented
43#10622162C2212yescomplemented
44C25×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—42no—
48C22×D4×C11—42no—
49C22×D4×C11C2×C414yes—
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×Dic22C2311yescharacteristic
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—44no—
64C2×C11×C22⋊C4—44no—
65C2×C42×C11—42no—
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×#4324—42no—
73C2×#4324—42no—
74C2×#4324C2×C418yescomplemented
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78#66977—22no—
79#66977C2×C414yes—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87C4×Dic22—42no—
88#66896—42no—
89#66896—42no—
90#66896C2×C418yescomplemented
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)C2×C414yes—
98#66874—42no—
99#66872—42no—
100C4×C11⋊C8—42no—
101#22043—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11C2×D411yescharacteristic
111C2×D4×C11—24no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—48no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—48no—
121C2×D4×C11C22×C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11SD1614yescomplemented
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22C22×C412yes—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—41no—
160C42×C11—41no—
161C22⋊Dic11—24no—
162C22⋊Dic11—42no—
163#4324—48no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—42no—
170Dic11⋊C4—42no—
171C4×Dic11—42no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C22×C414yes—
179C2×#450—111no—
180C4×C22⋊Q8—111no—
181C2×#390D1111yescharacteristic
182#1968—112no—
183#1934—112no—
184#1926—112no—
185#1880—112no—
186#1872—111no—
187#1853—111no—
188#1786—111no—
189C4×C22⋊C8—111no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—48no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11C4×D412yes—
209C23×C11C2×SD1612yes—
210C23×C11#13512yes—
211C23×C11C22×D411yescharacteristic
212D4×C11—24no—
213D4×C11—24no—
214D4×C11—48no—
215D4×C11—42no—
216D4×C11—42no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11C4×D412yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11C2×SD1612yes—
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)12yes—
243C2×C4×C11H(5,𝔽2)12yes—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256Dic22—24no—
257Dic22—42no—
258C11⋊C8—24no—
259C11⋊C8—42no—
260C23×D4C2×D1111yescharacteristic
261C22×SD16—112no—
262C2×C22⋊Q8—111no—
263C2×C4×Q8—111no—
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C42C2×D1111yescharacteristic
268#450—118no—
269C2×#106—112no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8—111no—
275C2×C22⋊C8—111no—
276C2×C4×C8—112no—
277#391—111no—
278#390—21no—
279#390—21no—
280#390C2×D1112yes—
281#390C2×D1112yes—
282#389—111no—
283#387—221no—
284#385—221no—
285#380—111no—
286C4×C4⋊C4—111no—
287C4×C4⋊C4—221no—
288C4×C22⋊C4—221no—
289#340—112no—
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—816no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11C4×SD1614yes—
307C22×C11C2×C4×D411yescharacteristic
308C22×C11#53411yescharacteristic
309C22×C11#53511yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11#57511yescharacteristic
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—41no—
319C4×C11—82no—
320C4×C11#51812yes—
321C4×C11#53812yes—
322Dic11—42no—
323Dic11—42no—
324Dic11—81no—
325Dic11—81no—
326C25—21no—
327C22×Q8—111no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4C4×D1114yes—
333C22×D4C22×D1112yes—
334C23×C4—21no—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×SD16—118no—
339C2×SD16—442no—
340C2×SD16—442no—
341C22×C8—112no—
342C22×C8—112no—
343C22⋊Q8—114no—
344C22⋊Q8—222no—
345C4×Q8—442no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363C2×C42—42no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42C22⋊D1111yescharacteristic
367C2×C42C22⋊D1111yescharacteristic
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370#106—442no—
371#103—442no—
372#102—118no—
373#102—442no—
374#102—442no—
375C22⋊C8—114no—
376C22⋊C8—222no—
377C4×C8—442no—
378#95—221no—
379#95—221no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—24no—
384C2×C11—84no—
385C2×C11#232111yescharacteristic
386C2×C11C2×C4×SD1611yescharacteristic
387C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
388C2×C11#318711yescharacteristic
389C2×C11#318811yescharacteristic
390C2×C11#320811yescharacteristic
391C2×C11#321111yescharacteristic
392C24—24no—
393C24—22no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24C2×C22⋊D1111yescharacteristic
401C2×Q8—112no—
402C2×Q8—221no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—48no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—48no—
415C2×D4C2×C4×D1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4#432414yescomplemented
432C22×C4C2×C4×D1112yes—
433C22×C4#433912yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—448no—
441C2×C8—114no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8—222no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—112no—
451C4⋊C4—224no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—442no—
456C4⋊C4—442no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—44no—
461C22⋊C4—224no—
462C22⋊C4—442no—
463C42—22no—
464C42—22no—
465C42—41no—
466C42—41no—
467C42—442no—
468C42—442no—
469C11#2204311yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—24no—
475C23—48no—
476C23—48no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—48no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23—84no—
488C23C4×C22⋊D1112yes—
489C23C2×#432412yes—
490C23#6700312yes—
491C23C22×C22⋊D1111yescharacteristic
492Q8—224no—
493Q8—442no—
494D4—24no—
495D4—24no—
496D4—48no—
497D4—42no—
498D4—42no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C4×C22⋊D1112yes—
531C2×C4#6698512yes—
532C2×C4C2×#432412yes—
533C2×C4C2×#432412yes—
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×#433911yescharacteristic
536C2×C4#6703712yes—
537C2×C4#6703712yes—
538C8—224no—
539C8—442no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—816no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22C4×#432414yes—
555C22C2×C4×C22⋊D1111yescharacteristic
556C22C2×#6698511yescharacteristic
557C22C22×#432411yescharacteristic
558C22#1062333511yescharacteristic
559C22#1062333611yescharacteristic
560C22C2×#6700311yescharacteristic
561C22#1062335311yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—82no—
568C4—442no—
569C4—442no—
570C4—881no—
571C4—881no—
572C4#1062301712yes—
573C4#1062302512yes—
574C2—24no—
575C2—84no—
576C2#1307127411yescharacteristic
577C2C2×C4×#432411yescharacteristic
578C2C4×#6698511yescharacteristic
579C2#1307937311yescharacteristic
580C2#1307938111yescharacteristic
581C2#1307955711yescharacteristic
582C2#1307958111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#390C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#390D11
hypocenterC11#22043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C4×#66977C2semidirect
3. #13069469C2semidirect
4. #13069302C2semidirect
5. #13069240C2semidirect
6. #13068974C2semidirect
7. #13068923C2semidirect
8. #13068809C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
19. C2×C4×Dic22C22semidirect
24. #10622831C4semidirect
33. C2×#66874C22semidirect
34. C2×#66872C22semidirect
35. C4×C4⋊Dic11C22semidirect
38. #10622542C22semidirect
39. #10622541C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622167C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
74. C2×#4324C2×C4semidirect
90. #66896C2×C4semidirect
133. C22×C4×C11SD16semidirect
431. C22×C4#4324semidirect
469. C11#22043semidirect

Maximal subgroups

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

subgroupindex
C2×#106228312
C4×#669772
#130694692
#130693022
#130692402
#130689742
#130689232
#130688092
#130685472
C4×C22⋊(C11⋊C8)2
C2×C11×#3902
#2204311