Finite Group Databasebeta

← #14727878

Subgroups — #14727878

Order 2816.

1516 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2#13079413C212yesmaximal, complemented
3#13067635C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067131C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C11×#2539C211yesmaximal, characteristic, complemented
8C23×C22⋊D11—21no—
9C2×C11×#123—21no—
10C2×C11×#121C2211yescharacteristic, complemented
11C2×C11×#120—21no—
12C22×C11×C22⋊C4C2211yescharacteristic
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623024—22no—
16#10623024—24no—
17#10623024C2214yes—
18C2×#66939—22no—
19C2×#66935—22no—
20C11×#399C2212yescomplemented
21C11×#392C2212yescomplemented
22C11×#390—22no—
23C4×C11×C22⋊C4C2211yescharacteristic, complemented
24#10622830C2214yescomplemented
25#10622820C2212yescomplemented
26#10622652—24no—
27#10622649—22no—
28#10622647—22no—
29#10622581C2214yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C25×C11D411yescharacteristic
33C24×D11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—22no—
36C22×D4×C11C2311yescharacteristic, complemented
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C22×C22⋊D11—24no—
41C22×C22⋊D11—24no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—48no—
44C23×Dic11—21no—
45C22×D44—21no—
46C22×D44D412yescomplemented
47C11×#123—44no—
48C11×#121—22no—
49C11×#121—22no—
50C11×#120—44no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2311yescharacteristic, complemented
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4D412yes—
60C2×C11×C22⋊C4C2312yes—
61C2×C42×C11—21no—
62C2×#4323—24no—
63#66983—24no—
64#66983—22no—
65#66983—22no—
66#66983—24no—
67#66983D414yescomplemented
68#66983C2314yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D412yescomplemented
73C2×#4318—22no—
74#66939—28no—
75#66939—28no—
76#66935—28no—
77#66935—28no—
78C11×#95C2312yescomplemented
79#66896—24no—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yescomplemented
82#66873—24no—
83#66872—24no—
84#18316—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—24no—
88C24×C11—21no—
89C24×C11—42no—
90C24×C11—81no—
91C24×C11C2×D411yescharacteristic
92C24×C11C2×D412yes—
93C23×D11—22no—
94C23×D11—24no—
95C23×D11—44no—
96C23×D11—82no—
97C23×D11—82no—
98C2×D4×C11—22no—
99C2×D4×C11—44no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—44no—
105C2×D4×C11—81no—
106C2×D4×C11—82no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—42no—
112C22×C4×C11—81no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—28no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—48no—
122C2×C22⋊D11—416no—
123C2×C22⋊D11—48no—
124C2×C22⋊D11—48no—
125C2×C22⋊D11—48no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C2×D44—24no—
130C2×D44—22no—
131C2×D44—82no—
132C2×D44—82no—
133C2×D44C2×D414yes—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—44no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—42no—
142C42×C11—81no—
143#4323—84no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—22no—
149C4⋊Dic11C2×D414yes—
150#4318—82no—
151C2×C11⋊C8—24no—
152C2×#534—111no—
153#3192—112no—
154#2539D1111yescharacteristic, complemented
155#1613—114no—
156#1595—114no—
157#1507—112no—
158#1462—111no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11—88no—
178C23×C11#12011yescharacteristic
179C23×C11#12011yescharacteristic
180C23×C11AGL(1,ℤ/8)14yes—
181C23×C11C22×D411yescharacteristic
182C22×D11—24no—
183C22×D11—44no—
184C22×D11—44no—
185C22×D11—48no—
186C22×D11—44no—
187C22×D11—84no—
188C22×D11—84no—
189C22×D11—816no—
190D4×C11—44no—
191D4×C11—88no—
192D4×C11—82no—
193D4×C11—82no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—81no—
208C2×C4×C11#12012yes—
209C2×C4×C11C22×D412yes—
210C22⋊D11—416no—
211C22⋊D11—48no—
212C22⋊D11—48no—
213C2×Dic11—24no—
214C2×Dic11—44no—
215C2×Dic11—48no—
216D44—44no—
217D44—82no—
218D44—84no—
219C11⋊C8—44no—
220C23×D4—221no—
221#534—114no—
222#534—224no—
223#534—222no—
224C2×#123—21no—
225C2×#123—222no—
226C2×#121—112no—
227C2×#121—221no—
228C2×#121C2×D1111yescharacteristic, complemented
229C2×#120—21no—
230C2×#120—222no—
231C22×C22⋊C4C2×D1111yescharacteristic
232#481—114no—
233#481—222no—
234#469—224no—
235#447—114no—
236#447—222no—
237#407—112no—
238#399C2×D1112yescomplemented
239#392C2×D1112yescomplemented
240#390—22no—
241C4×C22⋊C4C2×D1111yescharacteristic, complemented
242#327—118no—
243#323—114no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—48no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—84no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#45312yes—
265C22×C11C2×#12011yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)12yes—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—88no—
271C2×D11—816no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—42no—
276C4×C11—81no—
277Dic11—44no—
278C25—221no—
279C25C22⋊D1111yescharacteristic
280C22×D4—21no—
281C22×D4—22no—
282C22×D4—112no—
283C22×D4—221no—
284C22×D4—222no—
285C22×D4—224no—
286C22×D4—222no—
287C22×D4—224no—
288C22×D4—448no—
289C22×D4C22×D1111yescharacteristic, complemented
290C23×C4—221no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C2×D8—224no—
294C2×M16—222no—
295#123—44no—
296#123—228no—
297#123—228no—
298#121—22no—
299#121—22no—
300#121—114no—
301#121—114no—
302#121—224no—
303#121—222no—
304#121—222no—
305#121—224no—
306#120—44no—
307#120—228no—
308#120—228no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1111yescharacteristic, complemented
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4C22⋊D1112yes—
322C2×C22⋊C4C22×D1112yes—
323C2×C42—21no—
324#106—224no—
325#102—224no—
326#102—224no—
327C22⋊C8—114no—
328C22⋊C8—222no—
329#95C22×D1112yescomplemented
330C2×C11—22no—
331C2×C11—22no—
332C2×C11—44no—
333C2×C11—41no—
334C2×C11—161no—
335C2×C11#300311yescharacteristic
336C2×C11C2×#45311yescharacteristic
337C2×C11#302611yescharacteristic
338D11—84no—
339C24—21no—
340C24—21no—
341C24—24no—
342C24—21no—
343C24—42no—
344C24—81no—
345C24—224no—
346C24—222no—
347C24—444no—
348C24—882no—
349C24—882no—
350C24C2×C22⋊D1111yescharacteristic
351C24C2×C22⋊D1112yes—
352C2×D4—22no—
353C2×D4—44no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—44no—
359C2×D4—81no—
360C2×D4—82no—
361C2×D4—114no—
362C2×D4—224no—
363C2×D4—228no—
364C2×D4—224no—
365C2×D4—224no—
366C2×D4—222no—
367C2×D4—448no—
368C2×D4—4416no—
369C2×D4—448no—
370C2×D4—448no—
371C2×D4—448no—
372C2×D4—882no—
373C2×D4—882no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—81no—
380C22×C4—224no—
381C22×C4—222no—
382C22×C4—444no—
383C22×C4D4×D1112yes—
384C22×C4D4×D1112yes—
385C22×C4C2×C22⋊D1112yes—
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388D8—884no—
389M16—882no—
390C2×C8—224no—
391C4⋊C4—22no—
392C4⋊C4—44no—
393C4⋊C4—114no—
394C4⋊C4—224no—
395C4⋊C4—222no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—44no—
400C22⋊C4—44no—
401C22⋊C4—42no—
402C22⋊C4—228no—
403C22⋊C4—224no—
404C22⋊C4—224no—
405C42—81no—
406C11#1831611yescharacteristic, complemented, Sylow
407C23—24no—
408C23—24no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—41no—
418C23—41no—
419C23—42no—
420C23—42no—
421C23—41no—
422C23—42no—
423C23—81no—
424C23—81no—
425C23—88no—
426C23—224no—
427C23—444no—
428C23—448no—
429C23—444no—
430C23—444no—
431C23—884no—
432C23—884no—
433C23—8816no—
434C23#6699011yescharacteristic
435C23#6699011yescharacteristic
436C23#6700214yes—
437C23C22×C22⋊D1111yescharacteristic
438D4—44no—
439D4—88no—
440D4—82no—
441D4—82no—
442D4—444no—
443D4—4416no—
444D4—448no—
445D4—448no—
446D4—882no—
447D4—884no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—81no—
462C2×C4—224no—
463C2×C4—444no—
464C2×C4—448no—
465C2×C4#6699012yes—
466C2×C4C2×D4×D1112yes—
467C8—444no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—24no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—48no—
479C22—42no—
480C22—42no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—84no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—444no—
489C22—444no—
490C22—444no—
491C22—888no—
492C22—8816no—
493C22#1062269012yes—
494C22C2×#6699011yescharacteristic
495C22C2×#6700212yes—
496C4—22no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—81no—
501C4—444no—
502C2—22no—
503C2—22no—
504C2—41no—
505C2—44no—
506C2—161no—
507C2—884no—
508C2#1307784211yescharacteristic
509C2C2×#1062269011yescharacteristic
510C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2539C2
socleC22×C11C2×#120
hypercenter#2539D11
hypocenterC11#18316
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. #13079413C2semidirect
3. #13067635C2semidirect
4. #13067533C2semidirect
5. #13067131C2semidirect
6. #13066943C2semidirect
7. C11×#2539C2semidirect
10. C2×C11×#121C22semidirect
20. C11×#399C22semidirect
21. C11×#392C22semidirect
23. C4×C11×C22⋊C4C22semidirect
24. #10622830C22semidirect
25. #10622820C22semidirect
29. #10622581C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
36. C22×D4×C11C23semidirect
46. C22×D44D4semidirect
52. C2×C11×C4⋊C4C23semidirect
67. #66983D4semidirect
72. C2×C4⋊Dic11D4semidirect
78. C11×#95C23semidirect
81. C22⋊(C11⋊C8)C23semidirect
154. #2539D11semidirect
228. C2×#121C2×D11semidirect
238. #399C2×D11semidirect
239. #392C2×D11semidirect
241. C4×C22⋊C4C2×D11semidirect
289. C22×D4C22×D11semidirect
312. C2×C4⋊C4C22×D11semidirect
329. #95C22×D11semidirect
406. C11#18316semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
#130794132
#130676352
#130675332
#130671312
#130669432
C11×#25392
#1831611