Finite Group Databasebeta

← #14727607

Subgroups — #14727607

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079364C212yesmaximal, complemented
2#13074350C211yesmaximal, characteristic, complemented
3#13067602C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067184C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C2×C11×#534C211yesmaximal, characteristic, complemented
8C23×D4×C11—21no—
9C11×#534—24no—
10C11×#534—22no—
11C11×#534C2214yes—
12C2×C11×#123—22no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C11×#120—22no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#67006—21no—
18C2×#66983C2211yescharacteristic, complemented
19#10622830—22no—
20#10622826—21no—
21#10622825C2211yescharacteristic, complemented
22C2×C22⋊(C11⋊C8)C2212yescomplemented
23#10622651—24no—
24#10622649C2214yescomplemented
25#10622646C2214yescomplemented
26#10622580—22no—
27#10622574—22no—
28#10622573C2212yescomplemented
29#10622566C2212yescomplemented
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C25×C11—21no—
33C25×C11D411yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11—24no—
38C22×D4×C11—21no—
39C22×D4×C11—44no—
40C22×D4×C11—44no—
41C22×D4×C11D412yescomplemented
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×C22⋊D11—22no—
47C22×D44C2311yescharacteristic, complemented
48C11×#123—28no—
49C11×#123—28no—
50C11×#121—24no—
51C11×#121—24no—
52C11×#121—22no—
53C11×#121—22no—
54C11×#121D414yescomplemented
55C11×#121C2314yes—
56C11×#120—28no—
57C11×#120—28no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D412yescomplemented
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yes—
65C2×C11×C22⋊C4C2312yes—
66#67006—44no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—21no—
69C2×#4323—24no—
70#66983—22no—
71#66983—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic, complemented
76C22×C11⋊C8—22no—
77#66896—24no—
78C11⋊#95—22no—
79C11⋊#95C2312yescomplemented
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—24no—
89C24×C11—22no—
90C24×C11—44no—
91C24×C11—81no—
92C24×C11—81no—
93C24×C11—82no—
94C24×C11—82no—
95C24×C11D814yescomplemented
96C24×C11C2×D412yes—
97C24×C11C2×D411yescharacteristic
98C23×D11—21no—
99C2×D4×C11—28no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—48no—
105C2×D4×C11—416no—
106C2×D4×C11—48no—
107C2×D4×C11—48no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11—82no—
111C2×D4×C11—82no—
112C2×D4×C11C2×D414yes—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—44no—
118C22×C4×C11—81no—
119C22×C4×C11—81no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—44no—
128C2×C22⋊D11—42no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—82no—
131C2×C22⋊D11—82no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C2×D44—22no—
135C2×D44—81no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D414yes—
139C11×C22⋊C4—28no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C22⋊Dic11—44no—
145C22⋊Dic11—42no—
146#4323—84no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—82no—
149C4⋊Dic11—22no—
150C4⋊Dic11—81no—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—82no—
153C2×#534D1111yescharacteristic, complemented
154#3186—112no—
155#2617—111no—
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—24no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—48no—
172C23×C11—44no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11—84no—
178C23×C11—84no—
179C23×C11—84no—
180C23×C11—84no—
181C23×C11—816no—
182C23×C11#12011yescharacteristic
183C23×C11#12011yescharacteristic
184C23×C11C2×D814yes—
185C23×C11C2×D812yes—
186C23×C11AGL(1,ℤ/8)12yes—
187C23×C11C22×D411yescharacteristic
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193D4×C11—44no—
194D4×C11—416no—
195D4×C11—44no—
196D4×C11—44no—
197D4×C11—48no—
198D4×C11—82no—
199D4×C11—84no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—81no—
211C2×C4×C11#12012yes—
212C2×C4×C11C22×D412yes—
213C22⋊D11—88no—
214C22⋊D11—82no—
215C22⋊D11—82no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222D44—44no—
223C11⋊C8—44no—
224C23×D4—21no—
225#534—24no—
226#534—22no—
227#534C2×D1114yes—
228C2×#123—22no—
229C2×#121—21no—
230C2×#121—111no—
231C2×#121C2×D1112yes—
232C2×#120—22no—
233C2×#120—221no—
234C22×C22⋊C4C2×D1111yescharacteristic
235#480—114no—
236#480—222no—
237#466—224no—
238#447—114no—
239#447—222no—
240C2×C22⋊C8—112no—
241#397—112no—
242#394—222no—
243#392—112no—
244#386—221no—
245#380—111no—
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—44no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—82no—
265C22×C11—84no—
266C22×C11—88no—
267C22×C11—816no—
268C22×C11#44712yes—
269C22×C11#44712yes—
270C22×C11C2×#12011yescharacteristic
271C22×C11C22×D811yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—44no—
281C4×C11—42no—
282Dic11—82no—
283Dic11—81no—
284C25—21no—
285C25C22⋊D1111yescharacteristic
286C22×D4—22no—
287C22×D4—24no—
288C22×D4—22no—
289C22×D4—24no—
290C22×D4—21no—
291C22×D4—44no—
292C22×D4—44no—
293C22×D4—111no—
294C22×D4—221no—
295C22×D4—222no—
296C22×D4C22⋊D1112yescomplemented
297C23×C4—21no—
298C23×C4C22⋊D1111yescharacteristic
299C23×C4C22×D1111yescharacteristic
300C2×D8—224no—
301C22×C8—222no—
302#123—28no—
303#123—28no—
304#121—24no—
305#121—24no—
306#121—22no—
307#121—22no—
308#121—222no—
309#121—222no—
310#121C22⋊D1114yescomplemented
311#121C22×D1114yes—
312#120—28no—
313#120—28no—
314#120—444no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22⋊D1112yescomplemented
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
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—112no—
335#95—222no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—22no—
339C2×C11—22no—
340C2×C11—44no—
341C2×C11—84no—
342C2×C11C2×#44711yescharacteristic
343C2×C11#301911yescharacteristic
344C2×C11#302611yescharacteristic
345D11—161no—
346C24—21no—
347C24—22no—
348C24—21no—
349C24—24no—
350C24—22no—
351C24—44no—
352C24—81no—
353C24—81no—
354C24—82no—
355C24—82no—
356C24—221no—
357C24#432314yescomplemented
358C24C2×C22⋊D1112yes—
359C24C2×C22⋊D1111yescharacteristic
360C2×D4—28no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—48no—
366C2×D4—416no—
367C2×D4—48no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—82no—
372C2×D4—82no—
373C2×D4—222no—
374C2×D4—444no—
375C2×D4—442no—
376C2×D4—442no—
377C2×D4—441no—
378C2×D4—441no—
379C2×D4—881no—
380C2×D4—882no—
381C2×D4—882no—
382C2×D4C2×C22⋊D1114yes—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—44no—
388C22×C4—81no—
389C22×C4—81no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4C2×C22⋊D1112yes—
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1112yes—
396C22×C4C23×D1111yescharacteristic
397D8—884no—
398C2×C8—224no—
399C2×C8—882no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—222no—
403C4⋊C4—881no—
404C4⋊C4C2×C22⋊D1114yes—
405C22⋊C4—28no—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—444no—
411C22⋊C4—442no—
412C22⋊C4—442no—
413C22⋊C4—882no—
414C11#1828411yescharacteristic, complemented, Sylow
415C23—24no—
416C23—22no—
417C23—22no—
418C23—24no—
419C23—24no—
420C23—41no—
421C23—41no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—48no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—81no—
431C23—81no—
432C23—84no—
433C23—84no—
434C23—84no—
435C23—84no—
436C23—816no—
437C23—442no—
438C23—442no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23C2×#432314yes—
443C23C2×#432312yes—
444C23#6698512yes—
445C23#6700611yescharacteristic
446C23#6700611yescharacteristic
447C23C22×C22⋊D1111yescharacteristic
448D4—44no—
449D4—416no—
450D4—44no—
451D4—44no—
452D4—48no—
453D4—82no—
454D4—84no—
455D4—444no—
456D4—888no—
457D4—882no—
458D4—882no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—48no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—81no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4#6700612yes—
477C2×C4C22×C22⋊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—44no—
493C22—44no—
494C22—44no—
495C22—82no—
496C22—84no—
497C22—88no—
498C22—816no—
499C22—882no—
500C22—882no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062283012yes—
505C22#1062283012yes—
506C22C22×#432311yescharacteristic
507C22C2×#6698511yescharacteristic
508C22C2×#6700611yescharacteristic
509C4—22no—
510C4—22no—
511C4—44no—
512C4—42no—
513C4—882no—
514C4—881no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—44no—
520C2—84no—
521C2—1761no—
522C2C2×#1062283011yescharacteristic
523C2#1307797311yescharacteristic
524C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#534C2
socleC22×C11C2×#120
hypercenterC2×#534D11
hypocenterC11#18284
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. #13079364C2semidirect
2. #13074350C2semidirect
3. #13067602C2semidirect
4. #13067534C2semidirect
5. #13067184C2semidirect
6. C2×#10622163C2semidirect
7. C2×C11×#534C2semidirect
18. C2×#66983C22semidirect
21. #10622825C22semidirect
22. C2×C22⋊(C11⋊C8)C22semidirect
24. #10622649C22semidirect
25. #10622646C22semidirect
28. #10622573C22semidirect
29. #10622566C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
41. C22×D4×C11D4semidirect
47. C22×D44C23semidirect
54. C11×#121D4semidirect
59. C2×C11×C4⋊C4D4semidirect
75. C2×C4⋊Dic11C23semidirect
79. C11⋊#95C23semidirect
81. C22⋊(C11⋊C8)C23semidirect
95. C24×C11D8semidirect
153. C2×#534D11semidirect
296. C22×D4C22⋊D11semidirect
310. #121C22⋊D11semidirect
318. C2×C4⋊C4C22⋊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
#130793642
#130743502
#130676022
#130675342
#130671842
C2×#106221632
C2×C11×#5342
#1828411