Finite Group Databasebeta

← #14727606

Subgroups — #14727606

Order 2816.

1486 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 187 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#13079364C212yesmaximal, complemented
3#13067601C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C11×#2617C211yesmaximal, characteristic, complemented
8C23×C22⋊D11—21no—
9C2×C11×#121C2211yescharacteristic, complemented
10C2×C11×#120—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C2×#66983—21no—
13C2×#66983C2212yes—
14#10623024—22no—
15#10623024—24no—
16#10623024C2214yes—
17C2×#66939—22no—
18C2×#66935—22no—
19C11×#397C2212yescomplemented
20C11×#394—22no—
21C11×#392C2212yescomplemented
22C11×#386—21no—
23C11×#380C2211yescharacteristic, complemented
24#10622830C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yescomplemented
26#10622651—24no—
27#10622649—22no—
28#10622646—22no—
29#10622580C2214yescomplemented
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—44no—
44C22×C22⋊D11—44no—
45C23×Dic11—21no—
46C22×D44—21no—
47C22×D44D412yescomplemented
48C11×#121—22no—
49C11×#121—22no—
50C11×#120—44no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic, complemented
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4D412yes—
60C2×C11×C22⋊C4C2312yes—
61C2×#4323—24no—
62#66983—24no—
63#66983—22no—
64#66983—22no—
65#66983—24no—
66#66983D414yescomplemented
67#66983C2314yes—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D412yescomplemented
72C22×C11⋊C8—22no—
73#66939—28no—
74#66939—28no—
75#66935—28no—
76#66935—28no—
77C11×#95—22no—
78C11×#95C2312yescomplemented
79#66896—24no—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yescomplemented
82#66873—24no—
83#66871—24no—
84#18284—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—22no—
88C24×C11—21no—
89C24×C11—81no—
90C24×C11—81no—
91C24×C11D814yescomplemented
92C24×C11C2×D412yes—
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C23×D11—24no—
96C23×D11—44no—
97C23×D11—82no—
98C23×D11—82no—
99C2×D4×C11—22no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—44no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—81no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—81no—
113C22×C4×C11—81no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C2×C22⋊D11—48no—
123C2×C22⋊D11—416no—
124C2×C22⋊D11—48no—
125C2×C22⋊D11—48no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—44no—
131C2×D44—24no—
132C2×D44—22no—
133C2×D44—82no—
134C2×D44—82no—
135C2×D44C2×D414yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—81no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—82no—
144#4323—84no—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—24no—
148C4⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11C2×D414yes—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—82no—
153C2×#534—111no—
154#3186—112no—
155#2617D1111yescharacteristic, complemented
156#1607—114no—
157#1595—114no—
158#1519—112no—
159C2×#323—111no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11—84no—
178C23×C11—84no—
179C23×C11#12011yescharacteristic
180C23×C11#12011yescharacteristic
181C23×C11C2×D814yes—
182C23×C11C2×D812yes—
183C23×C11AGL(1,ℤ/8)12yes—
184C23×C11C22×D411yescharacteristic
185C22×D11—24no—
186C22×D11—44no—
187C22×D11—44no—
188C22×D11—48no—
189C22×D11—44no—
190C22×D11—84no—
191C22×D11—84no—
192C22×D11—816no—
193D4×C11—44no—
194D4×C11—88no—
195D4×C11—82no—
196D4×C11—82no—
197C2×C4×C11—22no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—81no—
211C2×C4×C11#12012yes—
212C2×C4×C11C22×D412yes—
213C22⋊D11—416no—
214C22⋊D11—44no—
215C22⋊D11—44no—
216C22⋊D11—48no—
217C2×Dic11—24no—
218C2×Dic11—48no—
219C2×Dic11—44no—
220D44—44no—
221D44—82no—
222D44—84no—
223C11⋊C8—44no—
224C23×D4—221no—
225#534—114no—
226#534—224no—
227#534—222no—
228C2×#123—222no—
229C2×#121—112no—
230C2×#121—221no—
231C2×#121C2×D1111yescharacteristic, complemented
232C2×#120—21no—
233C2×#120—222no—
234C22×C22⋊C4C2×D1111yescharacteristic
235#480—114no—
236#480—222no—
237#466—224no—
238#447—114no—
239#447—222no—
240C2×C22⋊C8—112no—
241#397C2×D1112yescomplemented
242#394—22no—
243#392C2×D1112yescomplemented
244#386—21no—
245#380C2×D1111yescharacteristic, complemented
246#327—118no—
247#323—114no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—24no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—44no—
258C22×C11—48no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—82no—
262C22×C11—84no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11#44712yes—
269C22×C11#44712yes—
270C22×C11C2×#12011yescharacteristic
271C22×C11C22×D811yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—88no—
277C2×D11—816no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11—81no—
283Dic11—44no—
284C25—221no—
285C25C22⋊D1111yescharacteristic
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—112no—
289C22×D4—221no—
290C22×D4—222no—
291C22×D4—224no—
292C22×D4—222no—
293C22×D4—224no—
294C22×D4—444no—
295C22×D4—444no—
296C22×D4C22×D1111yescharacteristic, complemented
297C23×C4—221no—
298C23×C4C22⋊D1111yescharacteristic
299C23×C4C22×D1111yescharacteristic
300C2×D8—224no—
301C22×C8—222no—
302#123—228no—
303#123—228no—
304#121—22no—
305#121—22no—
306#121—114no—
307#121—114no—
308#121—224no—
309#121—222no—
310#121—222no—
311#121—224no—
312#120—44no—
313#120—228no—
314#120—228no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22×D1111yescharacteristic, complemented
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4C22⋊D1112yes—
328C2×C22⋊C4C22×D1112yes—
329#107—224no—
330#102—224no—
331#102—224no—
332C22⋊C8—114no—
333C22⋊C8—222no—
334#95—22no—
335#95C22×D1112yescomplemented
336C2×C11—21no—
337C2×C11—22no—
338C2×C11—21no—
339C2×C11—22no—
340C2×C11—44no—
341C2×C11—161no—
342C2×C11C2×#44711yescharacteristic
343C2×C11#301911yescharacteristic
344C2×C11#302611yescharacteristic
345D11—84no—
346C24—21no—
347C24—21no—
348C24—22no—
349C24—21no—
350C24—81no—
351C24—81no—
352C24—224no—
353C24—222no—
354C24—444no—
355C24—882no—
356C24—882no—
357C24#432314yescomplemented
358C24C2×C22⋊D1112yes—
359C24C2×C22⋊D1111yescharacteristic
360C2×D4—22no—
361C2×D4—44no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—42no—
366C2×D4—81no—
367C2×D4—82no—
368C2×D4—82no—
369C2×D4—114no—
370C2×D4—224no—
371C2×D4—228no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—222no—
375C2×D4—448no—
376C2×D4—4416no—
377C2×D4—448no—
378C2×D4—448no—
379C2×D4—444no—
380C2×D4—444no—
381C2×D4—882no—
382C2×D4—882no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—224no—
390C22×C4—222no—
391C22×C4—444no—
392C22×C4D4×D1112yes—
393C22×C4D4×D1112yes—
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397D8—884no—
398C2×C8—224no—
399C2×C8—882no—
400C4⋊C4—22no—
401C4⋊C4—81no—
402C4⋊C4—114no—
403C4⋊C4—224no—
404C4⋊C4—222no—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—44no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—82no—
411C22⋊C4—228no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C11#1828411yescharacteristic, complemented, Sylow
415C23—22no—
416C23—24no—
417C23—22no—
418C23—24no—
419C23—41no—
420C23—41no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—81no—
431C23—81no—
432C23—84no—
433C23—84no—
434C23—224no—
435C23—448no—
436C23—444no—
437C23—444no—
438C23—444no—
439C23—884no—
440C23—884no—
441C23—8816no—
442C23C2×#432314yes—
443C23C2×#432312yes—
444C23#6699011yescharacteristic
445C23#6699011yescharacteristic
446C23#6700212yes—
447C23C22×C22⋊D1111yescharacteristic
448D4—44no—
449D4—88no—
450D4—82no—
451D4—82no—
452D4—444no—
453D4—4416no—
454D4—444no—
455D4—444no—
456D4—448no—
457D4—882no—
458D4—884no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—81no—
473C2×C4—224no—
474C2×C4—448no—
475C2×C4—444no—
476C2×C4#6699012yes—
477C2×C4C2×D4×D1112yes—
478C8—444no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—24no—
486C22—42no—
487C22—42no—
488C22—44no—
489C22—48no—
490C22—42no—
491C22—42no—
492C22—82no—
493C22—84no—
494C22—82no—
495C22—82no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—444no—
500C22—444no—
501C22—444no—
502C22—888no—
503C22—8816no—
504C22#1062264912yes—
505C22#1062264912yes—
506C22C22×#432311yescharacteristic
507C22C2×#6699011yescharacteristic
508C22C2×#6700211yescharacteristic
509C4—22no—
510C4—22no—
511C4—42no—
512C4—82no—
513C4—81no—
514C4—444no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—44no—
520C2—161no—
521C2—884no—
522C2C2×#1062264911yescharacteristic
523C2#1307797211yescharacteristic
524C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2617C2
socleC22×C11C2×#120
hypercenter#2617D11
hypocenterC11#18284
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. #13079364C2semidirect
3. #13067601C2semidirect
4. #13067533C2semidirect
5. #13067183C2semidirect
6. C2×#10622163C2semidirect
7. C11×#2617C2semidirect
9. C2×C11×#121C22semidirect
19. C11×#397C22semidirect
21. C11×#392C22semidirect
23. C11×#380C22semidirect
24. #10622830C22semidirect
25. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622580C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
36. C22×D4×C11C23semidirect
47. C22×D44D4semidirect
52. C2×C11×C4⋊C4C23semidirect
66. #66983D4semidirect
71. C2×C4⋊Dic11D4semidirect
78. C11×#95C23semidirect
81. C22⋊(C11⋊C8)C23semidirect
91. C24×C11D8semidirect
155. #2617D11semidirect
231. C2×#121C2×D11semidirect
241. #397C2×D11semidirect
243. #392C2×D11semidirect
245. #380C2×D11semidirect
296. C22×D4C22×D11semidirect
318. C2×C4⋊C4C22×D11semidirect
335. #95C22×D11semidirect
357. C24#4323semidirect
414. C11#18284semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
#130793642
#130676012
#130675332
#130671832
C2×#106221632
C11×#26172
#1828411