Finite Group Databasebeta

← #14721627

Subgroups — #14721627

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082470C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic, complemented
3#13071527C211yesmaximal, characteristic, complemented
4#13067180C211yesmaximal, characteristic, complemented
5#13067177C211yesmaximal, characteristic, complemented
6#13067158C214yesmaximal, complemented
7#13067119C214yesmaximal, complemented
8#13067110C211yesmaximal, characteristic, complemented
9C11×#1503C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623265C412yescomplemented
12#10623257C412yescomplemented
13#10623226—22no—
14#10623175—22no—
15#10623158C2214yes—
16#10623116—22no—
17#10623115C412yescomplemented
18#10623108C412yescomplemented
19#10623056—21no—
20#10623054—21no—
21#10623008C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622602—22no—
27#10622549C2211yescharacteristic
28#10622541—21no—
29#10622538C2211yescharacteristic
30#10622451—22no—
31#10622339C2214yes—
32#10622301—22no—
33#10622280C2212yes—
34D11×#95C2212yes—
35C11×#328C2212yes—
36C11×#328C2212yes—
37#10622176C2214yes—
38#10622108C2214yes—
39#10622089C2212yes—
40#10622089C2212yes—
41C2×#4343C2×C414yescomplemented
42C2×#4339—21no—
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2312yes—
46C11×C4⋊Q8C2×C411yescharacteristic, complemented
47C11×C4⋊Q8C2×C411yescharacteristic, complemented
48C11×#125—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8C2312yes—
51C4×Q8×C11—21no—
52C4×Q8×C11C2×C412yescomplemented
53C11×#117—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#67000—24no—
58#66999C2×C414yescomplemented
59#66983—21no—
60#66983C2312yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D412yes—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×#4313—24no—
67#66951—24no—
68#66948—22no—
69#66948—22no—
70#66948—24no—
71#66948C2×C414yescomplemented
72#66947—24no—
73#66947—24no—
74#66946—24no—
75#66945—22no—
76#66945C2×C414yescomplemented
77C4⋊C4×D11—22no—
78#66935—24no—
79(C22⋊D11)⋊C4—24no—
80#66928—22no—
81#66928—21no—
82#66927—22no—
83#66927C2×C411yescharacteristic, complemented
84C4×D44—21no—
85C4×D44—22no—
86C4×D44—44no—
87C4×D44C2×C412yes—
88C4×D44C2×C412yes—
89C4×D44C2×C412yescomplemented
90C4×D44D412yes—
91C4×D44D412yes—
92#66922C2×C411yescharacteristic, complemented
93C4×Dic22—22no—
94C11×C4⋊C8—21no—
95C11×C22⋊C8C2312yes—
96C4×C8×C11—21no—
97C11×#95C2311yescharacteristic
98C11×#95C2311yescharacteristic
99C11⋊#95—21no—
100C11⋊#95—22no—
101C11⋊#95C2312yes—
102C22⋊(C11⋊C8)C2312yes—
103(C2×D11)⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4×C11⋊C8—21no—
106#17630—111nomaximal, Sylow
107C23×D11C2×D412yes—
108C2×Q8×C11—21no—
109C2×Q8×C11C22×C412yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—22no—
116C22×Dic11—22no—
117C22×Dic11C2×D412yes—
118#4343—84no—
119#4339—42no—
120#4339—42no—
121C2×D44—24no—
122C2×D44—24no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44C22⋊C412yes—
128C2×D44C22⋊C412yes—
129C2×D44C22×C412yes—
130C2×C4×D11—24no—
131C2×C4×D11—22no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11—82no—
135C2×C4×D11—82no—
136C2×C4×D11C22×C414yes—
137C2×C4×D11C2×D414yes—
138C2×Dic22—21no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4C22×C412yes—
147C11×C22⋊C4—22no—
148C42×C11—22no—
149C42×C11—42no—
150C42×C11C22×C411yescharacteristic
151C42×C11C22×C411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—22no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4C22⋊C414yes—
161(C2×D11)⋊C4C22⋊C414yes—
162C4⋊Dic11—21no—
163C4⋊Dic11—42no—
164C4⋊Dic11C22⋊C412yes—
165C4⋊Dic11C22⋊C412yes—
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—24no—
168Dic11⋊C4—82no—
169C4×Dic11—24no—
170C2×C11⋊C8—22no—
171#4313—84no—
172#3506—111no—
173#2975—111no—
174#2349—111no—
175#1518—111no—
176#1517—111no—
177#1513—114no—
178#1504—114no—
179#1503D1111yescharacteristic, complemented
180#1502—111no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11C2×C22⋊C414yes—
188Q8×C11—42no—
189Q8×C11—81no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C2×C4×C11C2×C22⋊C411yescharacteristic
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—42no—
209C22⋊D11—42no—
210C2×Dic11—22no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C2×C22⋊C414yes—
216D44—24no—
217D44—24no—
218D44—42no—
219D44—42no—
220D44—81no—
221D44—84no—
222D44—84no—
223C4×D11—44no—
224C4×D11—44no—
225C4×D11—44no—
226C4×D11—84no—
227C4×D11—88no—
228Dic22—42no—
229C8×C11—42no—
230C11⋊C8—42no—
231#559—222no—
232#556—112no—
233#555—112no—
234#553—222no—
235#550—112no—
236#547—112no—
237#538—222no—
238#535—221no—
239#533C2×D1111yescharacteristic
240#532—111no—
241#525—114no—
242#520—221no—
243C2×C4×D4—111no—
244C2×C4×D4—221no—
245#436—222no—
246#436—222no—
247#431—111no—
248#431C2×D1111yescharacteristic
249#407—114no—
250#389—221no—
251#385—222no—
252#382—111no—
253#380—112no—
254C4×C4⋊C4C2×D1111yescharacteristic
255C2×#95—112no—
256#328—114no—
257#328C2×D1112yes—
258#328C2×D1112yes—
259#327—114no—
260#327—112no—
261#327—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C22×C22⋊C411yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C2×D11—24no—
268C2×D11—24no—
269C2×D11—24no—
270C2×D11—44no—
271C2×D11—44no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11#41712yes—
284C4×C11#41712yes—
285Dic11—24no—
286Dic11—42no—
287Dic11—82no—
288C2×#41—114no—
289C2×#41—221no—
290C22×D4—111no—
291C23×C4—112no—
292C23×C4—222no—
293C2×M16—224no—
294C4⋊Q8—111no—
295C4⋊Q8C4×D1111yescharacteristic, complemented
296C4⋊Q8C4×D1111yescharacteristic, complemented
297#127—111no—
298#127—222no—
299#126—224no—
300#125—21no—
301#124—222no—
302#124—224no—
303#124—221no—
304#123—224no—
305#123—224no—
306C22⋊Q8—21no—
307C22⋊Q8—114no—
308C22⋊Q8C22×D1112yes—
309#121—112no—
310#121—114no—
311#121—224no—
312#121—222no—
313#121—222no—
314#121—221no—
315#120—224no—
316C4×Q8—21no—
317C4×Q8—222no—
318C4×Q8C4×D1112yescomplemented
319C4×D4—112no—
320C4×D4—112no—
321C4×D4—112no—
322C4×D4—112no—
323C4×D4—112no—
324C4×D4—222no—
325C4×D4—224no—
326C4×D4—224no—
327C4×D4—221no—
328C4×D4—444no—
329#117—21no—
330#117—114no—
331#117—222no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—222no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—222no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—221no—
343C22⋊C8—112no—
344C22⋊C8—224no—
345C22⋊C8C22×D1112yes—
346C4×C8—21no—
347C4×C8—221no—
348#95—112no—
349#95—222no—
350#95—221no—
351#95C22×D1111yescharacteristic
352#95C22×D1111yescharacteristic
353C2×C11—21no—
354C2×C11—21no—
355C2×C11#288311yescharacteristic
356C2×C11C2×#41711yescharacteristic
357C2×C11#290111yescharacteristic
358D11—44no—
359D11—82no—
360C24—112no—
361#41—442no—
362#41—442no—
363#41—884no—
364C2×Q8—21no—
365C2×Q8—221no—
366C2×Q8C2×C4×D1112yes—
367C2×D4—112no—
368C2×D4—112no—
369C2×D4—112no—
370C2×D4—224no—
371C2×D4—224no—
372C2×D4—222no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—222no—
376C2×D4—222no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—112no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—224no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—444no—
386C22×C4—444no—
387C22×C4—882no—
388C22×C4—882no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—884no—
393C2×C8—22no—
394C2×C8—222no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—42no—
401C4⋊C4—112no—
402C4⋊C4—112no—
403C4⋊C4—112no—
404C4⋊C4—224no—
405C4⋊C4—221no—
406C4⋊C4—442no—
407C4⋊C4—882no—
408C4⋊C4C2×C4×D1112yes—
409C22⋊C4—22no—
410C22⋊C4—114no—
411C22⋊C4—114no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C22⋊C4—444no—
418C42—22no—
419C42—42no—
420C42—224no—
421C42C2×C4×D1111yescharacteristic
422C42C2×C4×D1111yescharacteristic
423C42D4×D1111yescharacteristic
424C42D4×D1111yescharacteristic
425C11#1763011yescharacteristic, complemented, Sylow
426C23—114no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23—442no—
431C23—442no—
432C23C2×D4×D1111yescharacteristic
433Q8—42no—
434Q8—81no—
435Q8—442no—
436D4—224no—
437D4—224no—
438D4—442no—
439D4—442no—
440D4—442no—
441D4—442no—
442D4—881no—
443D4—884no—
444D4—884no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—114no—
456C2×C4—222no—
457C2×C4—444no—
458C2×C4—444no—
459C2×C4—442no—
460C2×C4—444no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—884no—
465C2×C4—888no—
466C2×C4C22⋊C4×D1111yescharacteristic
467C2×C4C22⋊C4×D1111yescharacteristic
468C2×C4C22⋊C4×D1111yescharacteristic
469C2×C4C22⋊C4×D1111yescharacteristic
470C2×C4#6696712yes—
471C2×C4#6697112yes—
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C8—42no—
475C8—442no—
476C22—21no—
477C22—21no—
478C22—224no—
479C22—224no—
480C22—224no—
481C22—444no—
482C22—444no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22C2×C22⋊C4×D1111yescharacteristic
487C22C2×#6696711yescharacteristic
488C22C2×#6697111yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—81no—
497C4—224no—
498C4—442no—
499C4—882no—
500C4#1062241612yes—
501C4#1062241612yes—
502C2—21no—
503C2—21no—
504C2—444no—
505C2—882no—
506C2#1307707511yescharacteristic
507C2C2×#1062241611yescharacteristic
508C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1503C2
socleC22×C11C22×C22⋊C4
prime radical#13082470C2
cosocleC22×C4×C11C24
hypercenter#1503D11
hypocenterC11#17630
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13071527C2semidirect
4. #13067180C2semidirect
5. #13067177C2semidirect
6. #13067158C2semidirect
7. #13067119C2semidirect
8. #13067110C2semidirect
9. C11×#1503C2semidirect
11. #10623265C4semidirect
12. #10623257C4semidirect
17. #10623115C4semidirect
18. #10623108C4semidirect
41. C2×#4343C2×C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
47. C11×C4⋊Q8C2×C4semidirect
52. C4×Q8×C11C2×C4semidirect
58. #66999C2×C4semidirect
71. #66948C2×C4semidirect
76. #66945C2×C4semidirect
83. #66927C2×C4semidirect
89. C4×D44C2×C4semidirect
92. #66922C2×C4semidirect
179. #1503D11semidirect
295. C4⋊Q8C4×D11semidirect
296. C4⋊Q8C4×D11semidirect
318. C4×Q8C4×D11semidirect
425. C11#17630semidirect

Maximal subgroups

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

subgroupindex
#130824702
#130776562
#130715272
#130671802
#130671772
#130671582
#130671192
#130671102
C11×#15032
#1763011