Finite Group Databasebeta

← #14727908

Subgroups — #14727908

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079418C211yesmaximal, characteristic, complemented
2#13079413C211yesmaximal, characteristic
3#13074096C211yesmaximal, characteristic, complemented
4#13067647C214yesmaximal, complemented
5#13067545C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067132C211yesmaximal, characteristic, complemented
8#13066946C211yesmaximal, characteristic, complemented
9C2×C11×#539C211yesmaximal, characteristic, complemented
10C11×#539—22no—
11C11×#539—22no—
12C11×#539—22no—
13C11×#539C2214yes—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24#10622840—21no—
25#10622830—21no—
26#10622826—21no—
27#10622826—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622662—22no—
32#10622659C2212yescomplemented
33#10622657C2212yescomplemented
34#10622652—22no—
35#10622649C2212yes—
36#10622647C2212yes—
37#10622604C2212yescomplemented
38#10622603—22no—
39#10622599C2212yescomplemented
40#10622581—21no—
41#10622580—21no—
42#10622176C2214yescomplemented
43#10622175C2214yes—
44#10622166C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C22×D44C2311yescharacteristic
54C11×#126—24no—
55C11×#126—24no—
56C11×#125—24no—
57C11×#125—24no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×#123—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8D412yes—
67C11×C22⋊Q8C2312yes—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121D412yes—
71C11×#121C2312yes—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4325—22no—
94C2×#4323—22no—
95#66983—21no—
96#66983—21no—
97#66983—21no—
98#66983—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4×Dic11—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106#66899—22no—
107#66896—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95C2312yes—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2312yes—
114C22⋊(C11⋊C8)C2312yes—
115#66873—22no—
116#66873—22no—
117#66872—22no—
118#66871—22no—
119#18320—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C23×D11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—81no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—44no—
130C2×D4×C11—81no—
131C2×D4×C11C2×D412yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—21no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11—82no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—44no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11—41no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—81no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C42×C11—24no—
181C22⋊Dic11—42no—
182#4325—82no—
183#4323—82no—
184(C2×D11)⋊C4—44no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—82no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4×Dic11—81no—
191#4318—81no—
192#4318—81no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×#539D1111yescharacteristic, complemented
196#3193—111no—
197#3192—111no—
198#2591—111no—
199#1615—114no—
200#1597—114no—
201#1508—111no—
202#1507—111no—
203#1463—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11#12011yescharacteristic
212C23×C11#12011yescharacteristic
213C23×C11C22×D411yescharacteristic
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—41no—
217C22×D11—42no—
218Q8×C11—42no—
219Q8×C11—81no—
220D4×C11—42no—
221D4×C11—44no—
222D4×C11—44no—
223D4×C11—81no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—81no—
245C2×C4×C11—84no—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—82no—
251C22⋊D11—82no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257D44—42no—
258D44—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261#539—22no—
262#539—22no—
263#539—22no—
264#539C2×D1114yes—
265C2×#126—21no—
266C2×#125—21no—
267C2×#123—21no—
268C2×#123—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8C2×D1111yescharacteristic
271C2×#121—111no—
272C2×#121C2×D1111yescharacteristic
273C2×C4×D4—21no—
274C22×C4⋊C4C2×D1111yescharacteristic
275#484—112no—
276#481—112no—
277#481—221no—
278#480—221no—
279#469—222no—
280#468—222no—
281#450—112no—
282#448—221no—
283#447—112no—
284#447—221no—
285#407—111no—
286#407—111no—
287#400—112no—
288#394—112no—
289#388—222no—
290#386—221no—
291#386—221no—
292C4×C22⋊C4—111no—
293#328—114no—
294#327—114no—
295#324—114no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—84no—
308C22×C11#45412yes—
309C22×C11C2×#12011yescharacteristic
310C22×C11#57512yes—
311C2×D11—84no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—42no—
324Dic11—82no—
325Dic11—81no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×D4—21no—
328C22×D4—111no—
329C22×D4—221no—
330C22×D4C22⋊D1111yescharacteristic
331C23×C4—21no—
332C23×C4C22⋊D1111yescharacteristic
333C23×C4C22⋊D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C2×SD16—222no—
336C2×D8—222no—
337C2×M16—221no—
338C2×M16—221no—
339#126—24no—
340#126—24no—
341#125—24no—
342#125—24no—
343#123—24no—
344#123—24no—
345#123—24no—
346#123—24no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8C22⋊D1112yes—
352C22⋊Q8C22×D1112yes—
353#121—21no—
354#121—21no—
355#121—221no—
356#121—221no—
357#121—221no—
358#121—221no—
359#121C22⋊D1112yes—
360#121C22×D1112yes—
361C4×D4—24no—
362C4×D4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4C22⋊D1112yes—
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22⋊D1111yescharacteristic
375C2×C4⋊C4C22×D1112yes—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—221no—
387#107—222no—
388#106—222no—
389#103—222no—
390#102—222no—
391#102—222no—
392#102—222no—
393C22⋊C8—112no—
394C22⋊C8—112no—
395C22⋊C8—221no—
396C22⋊C8—221no—
397#95—112no—
398#95—222no—
399#95—222no—
400C2×C11—22no—
401C2×C11—22no—
402C2×C11—41no—
403C2×C11—82no—
404C2×C11#300511yescharacteristic
405C2×C11C2×#45411yescharacteristic
406C2×C11#302611yescharacteristic
407D11—161no—
408C24—21no—
409C24—221no—
410C24C2×C22⋊D1111yescharacteristic
411C2×Q8—21no—
412C2×Q8—81no—
413C2×Q8C2×C22⋊D1112yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—44no—
418C2×D4—81no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—444no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—881no—
425C2×D4C2×C22⋊D1112yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—82no—
438C22×C4—222no—
439C22×C4—221no—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C23×D1111yescharacteristic
448SD16—882no—
449D8—882no—
450M16—881no—
451M16—881no—
452C2×C8—222no—
453C2×C8—222no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4C2×C22⋊D1112yes—
468C4⋊C4C2×C22⋊D1112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—444no—
477C22⋊C4—442no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C22⋊C4—882no—
481C42—24no—
482C42—881no—
483C11#1832011yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—22no—
487C23—41no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—441no—
495C23#6700611yescharacteristic
496C23#6700611yescharacteristic
497C23C22×C22⋊D1111yescharacteristic
498Q8—42no—
499Q8—81no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—81no—
504D4—442no—
505D4—442no—
506D4—882no—
507D4—882no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—84no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—441no—
535C2×C4#6700611yescharacteristic
536C2×C4#6700611yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—442no—
540C8—442no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—84no—
553C22—884no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062285812yes—
558C22#1062335312yes—
559C22C2×#6700611yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—882no—
570C4—881no—
571C2—22no—
572C2—22no—
573C2—41no—
574C2—82no—
575C2—1761no—
576C2#1307785811yescharacteristic
577C2C2×#1062285811yescharacteristic
578C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC22×C11C2×#120
prime radical#13079413C2
hypercenterC2×#539D11
hypocenterC11#18320
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #13079418C2semidirect
3. #13074096C2semidirect
4. #13067647C2semidirect
5. #13067545C2semidirect
6. #13067136C2semidirect
7. #13067132C2semidirect
8. #13066946C2semidirect
9. C2×C11×#539C2semidirect
32. #10622659C22semidirect
33. #10622657C22semidirect
37. #10622604C22semidirect
39. #10622599C22semidirect
42. #10622176C22semidirect
44. #10622166C22semidirect
195. C2×#539D11semidirect
483. C11#18320semidirect

Maximal subgroups

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

subgroupindex
#130794182
#130794132
#130740962
#130676472
#130675452
#130671362
#130671322
#130669462
C2×C11×#5392
#1832011