Finite Group Databasebeta

← #14789007

Subgroups — #14789007

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078076C212yesmaximal, complemented
2C2×#10622858C212yesmaximal, complemented
3#13071323C211yesmaximal, characteristic, complemented
4#13069837C212yesmaximal, complemented
5#13069658C212yesmaximal, complemented
6#13069449C212yesmaximal, complemented
7#13068612C211yesmaximal, characteristic, complemented
8#13068575C212yesmaximal, complemented
9C11×#3497C211yesmaximal, characteristic, complemented
10C2×C11×2−1+4C2212yes—
11C11×#550—22no—
12D4×Q8×C11—22no—
13C11×#548—24no—
14C11×#537—22no—
15C11×#537C2212yes—
16C11×#532—22no—
17C11×#532C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67002C2214yes—
20C2×#67000C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22#10622858—28no—
23C2×#66901C2214yes—
24C2×#66901C2214yes—
25#10622845C2214yes—
26#10622843C2211yescharacteristic
27C2×#66900C2212yes—
28#10622696—22no—
29#10622685—22no—
30#10622670—24no—
31#10622602—22no—
32#10622601C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622553—22no—
35#10622545C2211yescharacteristic
36#10622537C2212yes—
37#10622168C2212yes—
38C11×2−1+4—24no—
39C11×2−1+4—24no—
40C11×2−1+4—44no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41C2314yes—
44C22×Q8×C11—24no—
45C22×Q8×C11C2311yescharacteristic
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D412yes—
50C11×#127—22no—
51C11×#127D412yes—
52C11×#124—24no—
53C11×#124D414yes—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—24no—
56C11×#121—28no—
57C11×#121—24no—
58C11×#121—22no—
59C11×#121—24no—
60C11×#121—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11D412yes—
70C2×C42×C11C2311yescharacteristic
71#67002—28no—
72#67002—44no—
73#67000—22no—
74#67000D414yescomplemented
75C2×#4325—24no—
76C2×#4323—24no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2314yes—
85C4×D44—22no—
86C4×D44—22no—
87#66901—28no—
88#66901—44no—
89#66900—24no—
90#66899—24no—
91#66896—24no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24227—111nomaximal, Sylow
98C23×D11—21no—
99C11×#41—24no—
100C11×#41—24no—
101C11×#41—24no—
102C11×#41—24no—
103C11×#41—48no—
104C11×#41—48no—
105C11×#41—48no—
106C11×#41—48no—
107C2×Q8×C11—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—48no—
111C2×Q8×C11—48no—
112C2×Q8×C11C2×D414yes—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11#4112yes—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C2×D414yes—
121C22×C4×C11—28no—
122C22×C4×C11—24no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×D44—22no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44C2×D412yes—
135C2×C4×D11—42no—
136C2×C4×D11—82no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149#4325—48no—
150#4323—48no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—82no—
155C4⋊Dic11—22no—
156Dic11⋊C4—82no—
157C4×Dic11—21no—
158C4×Dic11—22no—
159C4×Dic11C2×D412yes—
160#4318—24no—
161#4318—24no—
162C2×C11⋊C8—24no—
163#3497D1111yescharacteristic, complemented
164#3036—112no—
165C2×#454—112no—
166#2326—111no—
167#2039—112no—
168#2006—112no—
169#1963—112no—
170#1801—111no—
171#1793—112no—
172C23×C11—24no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—41no—
178C22×D11—41no—
179Q8×C11—24no—
180Q8×C11—24no—
181Q8×C11—24no—
182Q8×C11—24no—
183Q8×C11—48no—
184D4×C11—24no—
185D4×C11—24no—
186D4×C11—44no—
187D4×C11—48no—
188D4×C11—44no—
189D4×C11—44no—
190D4×C11—82no—
191D4×C11—84no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—416no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12012yes—
205C2×C4×C11#12114yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D412yes—
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)12yes—
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218D44—24no—
219D44—42no—
220C4×D11—84no—
221C11⋊C8—44no—
222C2×2−1+4C2×D1112yes—
223C2×AGL(1,ℤ/8)—114no—
224#550—22no—
225D4×Q8—22no—
226#548—24no—
227#537—22no—
228#537C2×D1112yes—
229#532—22no—
230#532C2×D1112yes—
231C2×#124—111no—
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4—111no—
234#463—224no—
235#461—222no—
236#459—222no—
237#454—228no—
238#423—112no—
239C2×#104—114no—
240C2×#104—114no—
241#417—114no—
242C2×#101—112no—
243#391—111no—
244#390—111no—
245#388—222no—
246#385—222no—
247#384—111no—
248#376—111no—
249#343—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11C2×#12011yescharacteristic
256C22×C11C2×#12111yescharacteristic
257C22×C11#53511yescharacteristic
258C2×D11—44no—
259C2×D11—42no—
260C2×D11—82no—
261C2×D11—81no—
262C2×D11—81no—
263C4×C11—24no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—22no—
267C4×C11—44no—
268C4×C11—42no—
269C4×C11D4212yes—
270C4×C11#54612yes—
271Dic11—42no—
272Dic11—81no—
273Dic11—81no—
2742−1+4—24no—
2752−1+4—24no—
2762−1+4—44no—
277C2×#41—24no—
278C2×#41—24no—
279C2×#41C22×D1114yes—
280C22×Q8—24no—
281C22×Q8C22×D1111yescharacteristic
282C22×D4—111no—
283C23×C4—221no—
284AGL(1,ℤ/8)—228no—
285AGL(1,ℤ/8)—444no—
286C2×SD16—224no—
287C2×D8—224no—
288C2×M16—114no—
289C4⋊Q8—22no—
290C4⋊Q8C22⋊D1112yes—
291#127—22no—
292#127C22⋊D1112yes—
293#124—24no—
294#124—114no—
295#124—222no—
296#124C22⋊D1114yes—
297C22⋊Q8—28no—
298C22⋊Q8—24no—
299#121—28no—
300#121—24no—
301#121—22no—
302#121—24no—
303#121—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×D4—24no—
307C4×D4—24no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—222no—
311C4×D4—222no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22⋊D1112yes—
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C22⋊C4—222no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42C22⋊D1112yes—
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—222no—
324C4⋊C8—222no—
325#104—228no—
326#104—444no—
327#103—224no—
328#102—224no—
329#101—224no—
330#95—221no—
331#95—221no—
332#95—222no—
333C2×C11—21no—
334C2×C11—21no—
335C2×C11—84no—
336C2×C11#240811yescharacteristic
337C2×C11#302011yescharacteristic
338C2×C11#302111yescharacteristic
339D11—82no—
340C24—221no—
341#41—24no—
342#41—24no—
343#41—24no—
344#41—24no—
345#41—48no—
346#41—48no—
347#41—48no—
348#41—48no—
349C2×Q8—24no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—48no—
353C2×Q8—48no—
354C2×Q8D4×D1112yes—
355C2×Q8#434112yes—
356C2×Q8C2×C22⋊D1114yes—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—112no—
363C2×D4—221no—
364C2×D4—222no—
365C2×D4—222no—
366C2×D4C2×C22⋊D1114yes—
367C22×C4—28no—
368C22×C4—24no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—442no—
373C22×C4—882no—
374C22×C4C2×C22⋊D1112yes—
375C22×C4C2×C22⋊D1112yes—
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C23×D1111yescharacteristic
379SD16—448no—
380D8—448no—
381M16—224no—
382M16—224no—
383C2×C8—224no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—222no—
390C4⋊C4—882no—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—24no—
394C22⋊C4—228no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—882no—
398C42—22no—
399C42—22no—
400C42—112no—
401C42—221no—
402C42—222no—
403C42C2×C22⋊D1112yes—
404C42C2×C22⋊D1112yes—
405C11#2422711yescharacteristic, complemented, Sylow
406C23—24no—
407C23—222no—
408C23—442no—
409C23—442no—
410C23—441no—
411C23—441no—
412C23C22×C22⋊D1111yescharacteristic
413Q8—24no—
414Q8—24no—
415Q8—24no—
416Q8—24no—
417Q8—48no—
418D4—24no—
419D4—24no—
420D4—44no—
421D4—48no—
422D4—44no—
423D4—44no—
424D4—82no—
425D4—84no—
426D4—224no—
427D4—442no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—416no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—222no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—884no—
447C2×C4#6699114yes—
448C2×C4#6700611yescharacteristic
449C2×C4#6700611yescharacteristic
450C2×C4#6700612yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4#6703712yes—
454C2×C4C22×C22⋊D1112yes—
455C8—444no—
456C22—21no—
457C22—21no—
458C22—44no—
459C22—44no—
460C22—44no—
461C22—444no—
462C22—442no—
463C22—882no—
464C22—881no—
465C22—881no—
466C22C2×#6699111yescharacteristic
467C22#1062333611yescharacteristic
468C22C2×#6700611yescharacteristic
469C4—24no—
470C4—21no—
471C4—21no—
472C4—22no—
473C4—44no—
474C4—42no—
475C4—442no—
476C4—881no—
477C4—881no—
478C4D4×C22⋊D1112yes—
479C4#1062333712yes—
480C2—21no—
481C2—21no—
482C2—84no—
483C2—882no—
484C2#1307196611yescharacteristic
485C2#1307798011yescharacteristic
486C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#24227
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13078076C2semidirect
2. C2×#10622858C2semidirect
3. #13071323C2semidirect
4. #13069837C2semidirect
5. #13069658C2semidirect
6. #13069449C2semidirect
7. #13068612C2semidirect
8. #13068575C2semidirect
9. C11×#3497C2semidirect
74. #67000D4semidirect
163. #3497D11semidirect
405. C11#24227semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106228582
#130713232
#130698372
#130696582
#130694492
#130686122
#130685752
C11×#34972
#2422711