Finite Group Databasebeta

← #14727917

Subgroups — #14727917

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079437C211yesmaximal, characteristic, complemented
2#13079422C211yesmaximal, characteristic
3#13073996C211yesmaximal, characteristic, complemented
4#13067613C214yesmaximal, complemented
5#13067579C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067132C211yesmaximal, characteristic
8#13066946C211yesmaximal, characteristic, complemented
9C2×C11×#539C211yesmaximal, characteristic
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×#66977C2211yescharacteristic
24#10622841—21no—
25#10622831—21no—
26#10622823—21no—
27#10622823—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622665—22no—
32#10622663C2212yescomplemented
33#10622656C2212yescomplemented
34#10622655—22no—
35#10622653C2212yes—
36#10622646C2212yes—
37#10622596C2212yescomplemented
38#10622592C2212yescomplemented
39#10622585—22no—
40#10622584—21no—
41#10622583—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×Dic22C2311yescharacteristic
53C11×#126—24no—
54C11×#126—24no—
55C11×#125—24no—
56C11×#125—24no—
57C11×#123—24no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8D412yes—
66C11×C22⋊Q8C2312yes—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121D412yes—
70C11×#121C2312yes—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C2×C11×C4⋊C4—21no—
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⋊C4D412yes—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4326—22no—
94C2×#4324—22no—
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—21no—
97#66977—21no—
98#66977—21no—
99#66977—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
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#66874—22no—
116#66874—22no—
117#66872—22no—
118#66871—22no—
119#18321—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—81no—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—44no—
129C2×D4×C11—81no—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—81no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C22⋊Dic11—24no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181#4326—82no—
182#4324—82no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185Dic11⋊C4—44no—
186Dic11⋊C4—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4—82no—
189C4×Dic11—81no—
190#4318—81no—
191#4318—81no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×#539D1111yescharacteristic
195#3195—111no—
196#3193—111no—
197#2583—111no—
198#1609—114no—
199#1603—114no—
200#1508—111no—
201#1507—111no—
202#1463—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11#12011yescharacteristic
211C23×C11#12011yescharacteristic
212C23×C11C22×D411yescharacteristic
213Q8×C11—42no—
214Q8×C11—81no—
215D4×C11—42no—
216D4×C11—44no—
217D4×C11—44no—
218D4×C11—81no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—81no—
240C2×C4×C11—84no—
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252Dic22—42no—
253Dic22—42no—
254C11⋊C8—42no—
255C11⋊C8—42no—
256#539—22no—
257#539—22no—
258#539—22no—
259#539C2×D1114yes—
260C2×#126—21no—
261C2×#125—21no—
262C2×#123—21no—
263C2×#123—21no—
264C2×C22⋊Q8—21no—
265C2×C22⋊Q8—111no—
266C2×C22⋊Q8C2×D1111yescharacteristic
267C2×#121C2×D1111yescharacteristic
268C2×C4×D4—21no—
269C22×C4⋊C4C2×D1111yescharacteristic
270#484—221no—
271#483—112no—
272#483—221no—
273#480—112no—
274#470—222no—
275#468—222no—
276#451—112no—
277#451—221no—
278#450—221no—
279#448—112no—
280#407—111no—
281#407—111no—
282#398—112no—
283#395—112no—
284#389—222no—
285#385—221no—
286#385—221no—
287C4×C22⋊C4—111no—
288#328—114no—
289#327—114no—
290#324—114no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—44no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—84no—
303C22×C11#45612yes—
304C22×C11C2×#12011yescharacteristic
305C22×C11#57512yes—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315Dic11—44no—
316Dic11—81no—
317Dic11—81no—
318C22×Q8—111no—
319C22×Q8C22⋊D1111yescharacteristic
320C22×D4—21no—
321C22×D4C22⋊D1111yescharacteristic
322C23×C4—21no—
323C23×C4C22⋊D1111yescharacteristic
324C23×C4C22⋊D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C2×Q16—222no—
327C2×SD16—222no—
328C2×M16—221no—
329C2×M16—221no—
330#126—24no—
331#126—24no—
332#125—24no—
333#125—24no—
334#123—24no—
335#123—24no—
336#123—24no—
337#123—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—221no—
343C22⋊Q8—221no—
344C22⋊Q8—221no—
345C22⋊Q8—221no—
346C22⋊Q8C22⋊D1112yes—
347C22⋊Q8C22×D1112yes—
348#121—21no—
349#121—21no—
350#121C22⋊D1112yes—
351#121C22×D1112yes—
352C4×D4—24no—
353C4×D4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4C22⋊D1112yes—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22⋊D1111yescharacteristic
369C2×C4⋊C4C22×D1112yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—221no—
379#107—222no—
380#106—222no—
381#103—222no—
382#103—222no—
383#103—222no—
384#102—222no—
385C22⋊C8—112no—
386C22⋊C8—112no—
387C22⋊C8—221no—
388C22⋊C8—221no—
389#95—112no—
390#95—222no—
391#95—222no—
392C2×C11—22no—
393C2×C11—22no—
394C2×C11—41no—
395C2×C11—82no—
396C2×C11#300511yescharacteristic
397C2×C11C2×#45611yescharacteristic
398C2×C11#302611yescharacteristic
399C24—21no—
400C24C2×C22⋊D1111yescharacteristic
401C2×Q8—21no—
402C2×Q8—81no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—881no—
406C2×Q8C2×C22⋊D1112yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—44no—
411C2×D4—81no—
412C2×D4C2×C22⋊D1112yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—82no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436Q16—882no—
437SD16—882no—
438M16—881no—
439M16—881no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—444no—
456C4⋊C4—441no—
457C4⋊C4—441no—
458C4⋊C4—882no—
459C4⋊C4C2×C22⋊D1112yes—
460C4⋊C4C2×C22⋊D1112yes—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—224no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C42—24no—
472C42—881no—
473C11#1832111yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23#6700611yescharacteristic
482C23#6700611yescharacteristic
483C23C22×C22⋊D1111yescharacteristic
484Q8—42no—
485Q8—81no—
486Q8—442no—
487Q8—442no—
488D4—42no—
489D4—44no—
490D4—44no—
491D4—81no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—81no—
513C2×C4—84no—
514C2×C4—224no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4#6700611yescharacteristic
522C2×C4#6700611yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—442no—
526C8—442no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—44no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22#1062285912yes—
540C22#1062335312yes—
541C22C2×#6700611yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—444no—
552C4—881no—
553C4—881no—
554C2—22no—
555C2—22no—
556C2—41no—
557C2—82no—
558C2#1307785811yescharacteristic
559C2C2×#1062285911yescharacteristic
560C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC22×C11C2×#120
prime radicalC2×C11×#121C22
hypercenterC2×#539D11
hypocenterC11#18321
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. #13079437C2semidirect
3. #13073996C2semidirect
4. #13067613C2semidirect
5. #13067579C2semidirect
6. #13067136C2semidirect
8. #13066946C2semidirect
32. #10622663C22semidirect
33. #10622656C22semidirect
37. #10622596C22semidirect
38. #10622592C22semidirect
42. #10622176C22semidirect
44. #10622166C22semidirect
473. C11#18321semidirect

Maximal subgroups

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

subgroupindex
#130794372
#130794222
#130739962
#130676132
#130675792
#130671362
#130671322
#130669462
C2×C11×#5392
#1832111