Finite Group Databasebeta

← #14763703

Subgroups — #14763703

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic, complemented
3#13071011C211yesmaximal, characteristic, complemented
4#13069566C212yesmaximal, complemented
5#13069541C212yesmaximal, complemented
6#13069055C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069052C211yesmaximal, characteristic, complemented
9#13068625C212yesmaximal, complemented
10#13068624C212yesmaximal, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C22×C11×M16C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C2×#66993C2211yescharacteristic
16C2×#66992—21no—
17C2×D4×Dic11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21#10623127—24no—
22#10623127C418yescomplemented
23C2×#66946C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66938—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×C11×#102C2212yes—
28C11×#380C2211yescharacteristic
29C2×#66896C2212yes—
30#10622825C2211yescharacteristic
31#10622731—24no—
32C2×#66885C2212yes—
33C2×Dic11⋊C8C2212yes—
34C2×Dic11⋊C8C2212yes—
35#10622590C2212yes—
36C4⋊C4×Dic11C2212yes—
37C2×#66873C2212yes—
38#10622556—21no—
39C22⋊C4×Dic11—21no—
40#10622264—21no—
41#10622261—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C23×Dic11D411yescharacteristic
55C2×#4341—28no—
56C2×#4341—48no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×Dic22—21no—
60C2×C11×M16—22no—
61C2×C11×M16—42no—
62C22×C8×C11C2312yes—
63C11×#121—22no—
64C11×#121C2×C414yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66993—22no—
72#66993C2×C414yes—
73#66992—28no—
74D4×Dic11—22no—
75D4×Dic11C2×C414yes—
76#66983—22no—
77#66983C2×C414yes—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11C2×C414yes—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D414yes—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×#4318—22no—
91C2×#4318—42no—
92C22×C11⋊C8C2312yes—
93#66946—22no—
94#66946C2×C414yes—
95#66941—22no—
96#66941C2×C414yes—
97#66938—28no—
98(C22⋊D11)⋊C4—28no—
99C11×#102—42no—
100C11×#95—21no—
101#66896—42no—
102C11⋊#95—21no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106#66885—42no—
107Dic11⋊C8—24no—
108Dic11⋊C8—24no—
109#66873—42no—
110#21891—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—44no—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—42no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—44no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—44no—
142C22×Dic11C22⋊C414yes—
143C22×Dic11C22⋊C414yes—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148#4341—432no—
149C2×D44—21no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44C22×C412yes—
153C2×C4×D11—24no—
154C2×C4×D11—44no—
155C2×Dic22—24no—
156C2×Dic22—44no—
157C11×M16—44no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C22×C412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—42no—
167C22⋊Dic11—24no—
168C22⋊Dic11—42no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11C22×C412yes—
175Dic11⋊C4—24no—
176C4×Dic11—44no—
177C4×Dic11C22⋊C414yes—
178C4×Dic11C22⋊C414yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C4×Dic11C2×D412yes—
183#4318—44no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#532—111no—
188C2×#423—111no—
189#2283—111no—
190#1988—112no—
191#1982—112no—
192#1895—111no—
193#1895—111no—
194#1895—111no—
195#1895D1111yescharacteristic, complemented
196#1804—112no—
197#1804—112no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—22no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C2×C22⋊C412yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—41no—
213C22×D11—41no—
214D4×C11—24no—
215D4×C11—48no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11H(5,𝔽2)12yes—
231C2×C4×C112−1+412yes—
232C22⋊D11—48no—
233C22⋊D11—48no—
234C22⋊D11—48no—
235C2×Dic11—22no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—28no—
241C2×Dic11—22no—
242C2×Dic11—44no—
243C2×Dic11—48no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11C2×C22⋊C412yes—
249C2×Dic11C2×C22⋊C412yes—
250C2×Dic11C2×C22⋊C412yes—
251C2×Dic11C2×C22⋊C412yes—
252C2×Dic11AGL(1,ℤ/8)14yes—
253D44—24no—
254D44—41no—
255D44—41no—
256C4×D11—48no—
257Dic22—48no—
258C8×C11—42no—
259C11⋊C8—42no—
260C22×#41—221no—
261C22×M16—111no—
262C22×M16C2×D1111yescharacteristic
263#532—118no—
264#532—224no—
265C2×C4⋊Q8—111no—
266C2×#127—111no—
267C2×#124—221no—
268C2×#121—111no—
269C2×#121—221no—
270C2×#121C2×D1111yescharacteristic
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4—221no—
274C22×C42—111no—
275#423—224no—
276C2×C4⋊C8—112no—
277C2×C4⋊C8—112no—
278C2×#102—112no—
279C2×#102—112no—
280C2×#102—112no—
281C2×#102C2×D1112yes—
282#383—221no—
283#382—112no—
284#381—221no—
285#380—111no—
286#380C2×D1111yescharacteristic
287C4×C4⋊C4—112no—
288C4×C22⋊C4—221no—
289#376—221no—
290#340—112no—
291#340—112no—
292#340—112no—
293#340C2×D1112yes—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11#53712yes—
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11#57511yescharacteristic
308C22×C11#57511yescharacteristic
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—82no—
313C2×D11—82no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11#52012yes—
318C4×C11#53511yescharacteristic
319C4×C11#53611yescharacteristic
320Dic11—22no—
321Dic11—22no—
322Dic11—22no—
323Dic11—42no—
324Dic11—82no—
325Dic11#41814yes—
326C2×#41—228no—
327C2×#41—448no—
328C22×Q8—221no—
329C22×D4—21no—
330C22×D4—111no—
331C22×D4—221no—
332C22×D4—221no—
333C22×D4—221no—
334C22×D4C22×D1111yescharacteristic
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—221no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340C2×M16—22no—
341C2×M16—42no—
342C2×M16—222no—
343C2×M16—442no—
344C22×C8—112no—
345C22×C8C22×D1112yes—
346C4⋊Q8—114no—
347C4⋊Q8—222no—
348#127—114no—
349#127—222no—
350#124—228no—
351#121—22no—
352#121—114no—
353#121—228no—
354#121—222no—
355#121C4×D1114yes—
356C4×D4—114no—
357C4×D4—114no—
358C4×D4—228no—
359C4×D4—222no—
360C4×D4—222no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C42—114no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—114no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—222no—
379C4⋊C8—224no—
380C4⋊C8—224no—
381#102—42no—
382#102—442no—
383#102—442no—
384#102—442no—
385#95—21no—
386#95—222no—
387#95—222no—
388#95—222no—
389#95—221no—
390C2×C11—42no—
391C2×C11—82no—
392C2×C11#231111yescharacteristic
393C2×C11C2×#41811yescharacteristic
394C2×C11#289611yescharacteristic
395C2×C11#325112yes—
396C2×C11#325112yes—
397D11—82no—
398C24—21no—
399C24—221no—
400C24D4×D1111yescharacteristic
401#41—4432no—
402C2×Q8—224no—
403C2×Q8—444no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—44no—
409C2×D4—112no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4—224no—
413C2×D4—221no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—444no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4—444no—
420C2×D4C2×C4×D1112yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—111no—
426C22×C4—114no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—114no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—444no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4—444no—
440C22×C4C2×C4×D1112yes—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1112yes—
443C22×C4C23×D1111yescharacteristic
444M16—44no—
445M16—444no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—222no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4C2×C4×D1112yes—
461C22⋊C4—24no—
462C22⋊C4—42no—
463C22⋊C4—224no—
464C22⋊C4—224no—
465C22⋊C4—224no—
466C22⋊C4—442no—
467C42—114no—
468C42—114no—
469C42—112no—
470C42—112no—
471C42—112no—
472C42—112no—
473C42—444no—
474C11#2189111yescharacteristic, complemented, Sylow
475C23—22no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—22no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—222no—
485C23—442no—
486C23—441no—
487C23—441no—
488C23—442no—
489C23C22⋊C4×D1112yes—
490C23C2×D4×D1111yescharacteristic
491Q8—448no—
492D4—24no—
493D4—48no—
494D4—41no—
495D4—41no—
496D4—224no—
497D4—448no—
498D4—448no—
499D4—448no—
500D4—441no—
501D4—441no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—112no—
512C2×C4—114no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—228no—
517C2×C4—222no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—448no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4C22⋊C4×D1112yes—
531C2×C4C22×C4×D1111yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4#6703712yes—
534C2×C4#6704312yes—
535C8—42no—
536C8—442no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—82no—
546C22—82no—
547C22—442no—
548C22—442no—
549C22—442no—
550C22—882no—
551C22—882no—
552C22C2×C22⋊C4×D1111yescharacteristic
553C22#1062312812yes—
554C22D11×AGL(1,ℤ/8)12yes—
555C22#1062330411yescharacteristic
556C22#1062330811yescharacteristic
557C4—22no—
558C4—42no—
559C4—82no—
560C4—114no—
561C4—222no—
562C4—222no—
563C4—222no—
564C4—442no—
565C4—882no—
566C4#1062307712yes—
567C4#1062312311yescharacteristic
568C4#1062317911yescharacteristic
569C2—42no—
570C2—82no—
571C2—882no—
572C2#1307120311yescharacteristic
573C2D11×#41811yescharacteristic
574C2#1307713211yescharacteristic
575C2#1307997112yes—
576C2#1307997312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#21891
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
3. #13071011C2semidirect
4. #13069566C2semidirect
5. #13069541C2semidirect
6. #13069055C2semidirect
7. #13069054C2semidirect
8. #13069052C2semidirect
9. #13068625C2semidirect
10. #13068624C2semidirect
11. C11×#1895C2semidirect
22. #10623127C4semidirect
195. #1895D11semidirect
474. C11#21891semidirect

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106227312
#130710112
#130695662
#130695412
#130690552
#130690542
#130690522
#130686252
#130686242
C11×#18952
#2189111