Finite Group Databasebeta

← #14727744

Subgroups — #14727744

Order 2816.

1312 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C212yesmaximal, complemented
2#13074366C211yesmaximal, characteristic, complemented
3#13067551C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#3449C211yesmaximal, characteristic, complemented
8C22×C11×#41—21no—
9C11×#537—21no—
10C11×#537C2212yes—
11C11×#536—22no—
12C11×#535—22no—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C11×#532C2212yes—
17C11×#525—24no—
18C2×C11×#117C2211yescharacteristic
19C2×#66983—21no—
20C2×#66927C2211yescharacteristic, complemented
21#10622701—22no—
22#10622686—22no—
23#10622649C2218yescomplemented
24#10622628—24no—
25#10622604—21no—
26#10622604C2212yescomplemented
27#10622573—21no—
28#10622573C2212yes—
29#10622552—21no—
30#10622549C2211yescharacteristic, complemented
31#10622538C2212yescomplemented
32#10622175C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yes—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—44no—
40C2×C11×#41—44no—
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11D411yescharacteristic
46C22×C22⋊D11—22no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8D412yescomplemented
52C11×#127—21no—
53C11×#127D412yescomplemented
54C11×#124—22no—
55C11×#124—22no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×#121—24no—
61C11×#121—24no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121C2314yes—
66C11×#120—24no—
67C11×#120—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11D414yescomplemented
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4C2311yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×#4323—28no—
81#66983—44no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11—21no—
86#66927—22no—
87#66927—22no—
88C11⋊#95—21no—
89C11⋊#95C2312yes—
90C22⋊(C11⋊C8)C2314yes—
91#66873—28no—
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#18300—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C23×D11—22no—
98C11×#41—44no—
99C11×#41—48no—
100C11×#41—48no—
101C11×#41—44no—
102C11×#41—44no—
103C11×#41—44no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—44no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11C2×D414yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—48no—
125C22×C4×C11D814yescomplemented
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—44no—
133C2×C22⋊D11—82no—
134C2×C22⋊D11—82no—
135C22×Dic11—22no—
136C2×D44—24no—
137C2×D44—42no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—82no—
143C2×D44—82no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C2×D414yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—24no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160#4323—88no—
161(C2×D11)⋊C4—44no—
162(C2×D11)⋊C4—82no—
163(C2×D11)⋊C4—82no—
164C4⋊Dic11—42no—
165C2×C11⋊C8—24no—
166#3449D1111yescharacteristic, complemented
167#3205—112no—
168#2619—111no—
169#1598—114no—
170#1595—114no—
171#1517—112no—
172#1458—111no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—24no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—44no—
179C23×C11—82no—
180C23×C11—82no—
181C23×C11C2×D812yes—
182C23×C11C22×D411yescharacteristic
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190Q8×C11—44no—
191Q8×C11—44no—
192D4×C11—44no—
193D4×C11—44no—
194D4×C11—48no—
195D4×C11—44no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—48no—
211C2×C4×C11—44no—
212C2×C4×C11—48no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11C2×D812yes—
219C2×C4×C11C2×D812yes—
220C2×C4×C11AGL(1,ℤ/8)12yes—
221C2×C4×C11C22×D412yes—
222C22⋊D11—88no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226D44—48no—
227D44—84no—
228D44—82no—
229D44—82no—
230C11⋊C8—44no—
231C22×#41—21no—
232#537—21no—
233#537C2×D1112yes—
234#536—22no—
235#535—22no—
236#534—21no—
237#534C2×D1112yes—
238#532—21no—
239#532C2×D1112yes—
240C2×#127—111no—
241#525—24no—
242C2×#121—221no—
243C2×#117C2×D1111yescharacteristic
244#493—222no—
245#486—222no—
246#459—224no—
247#447—118no—
248#431—112no—
249#394—112no—
250#394—221no—
251#392—112no—
252#392—221no—
253#390—221no—
254#382—111no—
255#327—118no—
256#324—112no—
257#323—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—81no—
268C22×C11—88no—
269C22×C11C2×#12011yescharacteristic
270C22×C11C22×D811yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—44no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11#44712yes—
286C4×C11#44712yes—
287Dic11—82no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—44no—
293C2×#41—44no—
294C22×Q8—21no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—112no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—221no—
301C23×C4—22no—
302C23×C4C22⋊D1111yescharacteristic
303C2×D8—228no—
304C4⋊Q8—21no—
305C4⋊Q8C22⋊D1112yescomplemented
306#127—21no—
307#127—222no—
308#127—222no—
309#127C22⋊D1112yescomplemented
310#124—22no—
311#124—22no—
312#123—24no—
313#123—24no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316#121—24no—
317#121—24no—
318#121—22no—
319#121—22no—
320#121—22no—
321#121—444no—
322#121C22×D1114yes—
323#120—24no—
324#120—24no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4C22⋊D1114yescomplemented
329#117—22no—
330#117—22no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22×D1111yescharacteristic
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4C22⋊D1111yescharacteristic
338C2×C22⋊C4C22×D1111yescharacteristic
339C2×C42C22⋊D1111yescharacteristic
340C2×C42C22×D1111yescharacteristic
341C4⋊C8—222no—
342#102—228no—
343C22⋊C8—114no—
344C4×C8—222no—
345#95—112no—
346#95—221no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—42no—
350C2×C11—84no—
351C2×C11C2×#44711yescharacteristic
352C2×C11#302111yescharacteristic
353C2×C11#302711yescharacteristic
354D11—162no—
355C24—22no—
356C24—222no—
357C24C2×C22⋊D1111yescharacteristic
358#41—44no—
359#41—48no—
360#41—48no—
361#41—44no—
362#41—44no—
363#41—44no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—44no—
367C2×D4—24no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—224no—
378C2×D4—444no—
379C2×D4—442no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—882no—
385C2×D4—882no—
386C2×D4—882no—
387C2×D4—882no—
388C2×D4C2×C22⋊D1114yes—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—48no—
396C22×C4—222no—
397C22×C4#432314yescomplemented
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C23×D1111yescharacteristic
404D8—888no—
405C2×C8—224no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—442no—
412C4⋊C4C2×C22⋊D1114yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—24no—
419C22⋊C4—444no—
420C22⋊C4—882no—
421C22⋊C4—882no—
422C42—21no—
423C42—21no—
424C42C2×C22⋊D1112yes—
425C42C2×C22⋊D1112yes—
426C11#1830011yescharacteristic, complemented, Sylow
427C23—21no—
428C23—21no—
429C23—24no—
430C23—41no—
431C23—41no—
432C23—44no—
433C23—82no—
434C23—82no—
435C23—442no—
436C23—442no—
437C23—442no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23C2×#432312yes—
443C23C22×C22⋊D1111yescharacteristic
444Q8—44no—
445Q8—44no—
446D4—44no—
447D4—44no—
448D4—48no—
449D4—44no—
450D4—44no—
451D4—44no—
452D4—82no—
453D4—82no—
454D4—82no—
455D4—448no—
456D4—884no—
457D4—888no—
458D4—882no—
459D4—882no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—44no—
471C2×C4—48no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4C2×#432312yes—
478C2×C4C2×#432312yes—
479C2×C4#6698512yes—
480C2×C4#6700612yes—
481C2×C4#6700611yescharacteristic
482C2×C4#6700611yescharacteristic
483C2×C4C22×C22⋊D1112yes—
484C8—444no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—81no—
495C22—88no—
496C22—882no—
497C22—882no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22C22×#432311yescharacteristic
504C22C2×#6698511yescharacteristic
505C22C2×#6700611yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—41no—
510C4—44no—
511C4—41no—
512C4—882no—
513C4#1062283012yes—
514C4#1062283012yes—
515C2—21no—
516C2—21no—
517C2—42no—
518C2—84no—
519C2—1762no—
520C2C2×#1062283011yescharacteristic
521C2#1307798811yescharacteristic
522C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18300
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. #13074366C2semidirect
3. #13067551C2semidirect
4. #13067534C2semidirect
5. #13067176C2semidirect
6. #13066930C2semidirect
7. C11×#3449C2semidirect
20. C2×#66927C22semidirect
23. #10622649C22semidirect
26. #10622604C22semidirect
30. #10622549C22semidirect
31. #10622538C22semidirect
32. #10622175C22semidirect
33. #10622166C22semidirect
51. C11×C4⋊Q8D4semidirect
53. C11×#127D4semidirect
71. C4×D4×C11D4semidirect
125. C22×C4×C11D8semidirect
166. #3449D11semidirect
305. C4⋊Q8C22⋊D11semidirect
309. #127C22⋊D11semidirect
328. C4×D4C22⋊D11semidirect
397. C22×C4#4323semidirect
426. C11#18300semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130743662
#130675512
#130675342
#130671762
#130669302
C11×#34492
#1830011