Finite Group Databasebeta

← D53×#2083 #27413050

Subgroups — D53×#2083 #27413050

Order 13568.

1086 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D53C212yesmaximal
2#389×D53C211yesmaximal, characteristic
3#384×D53C211yesmaximal, characteristic
4#20276190C212yesmaximal, complemented
5#20276189C212yesmaximal, complemented
6#20276188C211yesmaximal, characteristic, complemented
7#20276187C211yesmaximal, characteristic, complemented
8#20276186C211yesmaximal, characteristic, complemented
9#340×D53C212yesmaximal
10#336×D53C211yesmaximal, characteristic
11C53×#2083C211yesmaximal, characteristic, complemented
12C22×C8×D53C2212yes—
13C2×C4⋊C4×D53—21no—
14C2×C4⋊C4×D53—21no—
15C2×C4⋊C4×D53—21no—
16C2×C4⋊C4×D53C2212yes—
17C2×C4⋊C4×D53C2211yescharacteristic
18C2×C4⋊C4×D53C2211yescharacteristic
19C2×C42×D53C2211yescharacteristic
20C2×#13133151C2212yes—
21C2×#13133150C2212yes—
22C2×#13133150C2212yes—
23#107×D53—28no—
24#16810522C2211yescharacteristic
25#16810521C2211yescharacteristic
26#16810520—21no—
27#16810519C2211yescharacteristic
28#16810518—21no—
29#16810493C2211yescharacteristic
30#16810492—21no—
31#16810492—21no—
32#16810492C2212yes—
33#95×D53—21no—
34#16810386C2212yes—
35#16810385C2212yes—
36#16810385C2212yes—
37#16810378C2211yescharacteristic
38#16810377C2212yes—
39C2×#107×C53C2212yes—
40C53×#389C2211yescharacteristic
41C53×#384C2211yescharacteristic
42C53×#340C2212yes—
43C53×#336C2211yescharacteristic
44C22×C4×D53—21no—
45C22×C4×D53—22no—
46C22×C4×D53—21no—
47C22×C4×D53D411yescharacteristic
48C22×C4×D53D411yescharacteristic
49C22×C4×D53C2311yescharacteristic
50C22×#88322C2312yes—
51C2×C8×D53—24no—
52C2×C8×D53—24no—
53C2×C8×D53Q818yes—
54C2×C4⋊Dic53—21no—
55C2×C4⋊Dic53—21no—
56C2×C4⋊Dic53—21no—
57C2×C4⋊Dic53C2311yescharacteristic
58C2×C4⋊Dic53C2312yes—
59C2×C4⋊Dic53C2311yescharacteristic
60C2×#11719919—21no—
61C2×#11719919—21no—
62C2×#11719919—21no—
63C2×#11719919—21no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—22no—
67C4⋊C4×D53—22no—
68C4⋊C4×D53—24no—
69C4⋊C4×D53—24no—
70C4⋊C4×D53—24no—
71C4⋊C4×D53—44no—
72C4⋊C4×D53—44no—
73C4⋊C4×D53—44no—
74C4⋊C4×D53D414yes—
75C2×C4×Dic53D411yescharacteristic
76C2×C4×Dic53D411yescharacteristic
77C2×C4×Dic53C2311yescharacteristic
78C42×D53—24no—
79#13133151—24no—
80#13133150—24no—
81#13133150—24no—
82#13133124—21no—
83#13133124—21no—
84#13133124—21no—
85C22×C8×C53C2312yes—
86C2×C4⋊C4×C53—21no—
87C2×C4⋊C4×C53—21no—
88C2×C4⋊C4×C53—21no—
89C2×C4⋊C4×C53C2311yescharacteristic
90C2×C4⋊C4×C53C2312yes—
91C2×C4⋊C4×C53C2311yescharacteristic
92C2×C42×C53C2311yescharacteristic
93#107×C53—24no—
94#95×C53—21no—
95C23×D53C2×D411yescharacteristic
96C22×C4×C53—21no—
97C22×C4×C53—21no—
98C22×C4×C53—22no—
99C22×C4×C53C2×D411yescharacteristic
100C22×C4×C53C2×D411yescharacteristic
101C22×C4×C53C2411yescharacteristic
102C22×Dic53—21no—
103C22×Dic53—21no—
104C22×Dic53—22no—
105C22×Dic53C2×D411yescharacteristic
106C22×Dic53C2×D411yescharacteristic
107C22×Dic53C2×D411yescharacteristic
108C2×C4×D53—22no—
109C2×C4×D53—22no—
110C2×C4×D53—22no—
111C2×C4×D53—22no—
112C2×C4×D53—24no—
113C2×C4×D53—42no—
114C2×C4×D53—42no—
115C2×C4×D53—44no—
116C2×C4×D53—42no—
117C2×C4×D53—44no—
118C2×C4×D53—42no—
119C2×C4×D53—44no—
120C2×C4×D53—42no—
121C2×C4×D53D814yes—
122C2×C4×D53Q1614yes—
123C2×C4×D53C2×D412yes—
124C2×C4×D53C2×Q814yes—
125C2×C4×D53#4114yes—
126C2×C4×D53#4112yes—
127C2×C8×C53—22no—
128C2×C8×C53—22no—
129C2×C8×C53C2×Q814yes—
130C4⋊C4×C53—21no—
131C4⋊C4×C53—22no—
132C4⋊C4×C53—22no—
133C4⋊C4×C53—22no—
134C4⋊C4×C53—42no—
135C4⋊C4×C53—42no—
136C4⋊C4×C53—42no—
137C4⋊C4×C53C2×D412yes—
138C42×C53—22no—
139C4⋊Dic53—21no—
140C4⋊Dic53—22no—
141C4⋊Dic53—22no—
142C4⋊Dic53—22no—
143C4⋊Dic53—42no—
144C4⋊Dic53—42no—
145C4⋊Dic53—42no—
146C4⋊Dic53C2×D412yes—
147#11719919—24no—
148#11719919—44no—
149#11719919—42no—
150#11719919—44no—
151#11719919—42no—
152#11719919—42no—
153#11719919—44no—
154C4×Dic53—22no—
155C4×Dic53—22no—
156C4×Dic53—22no—
157C2×#88322—22no—
158C2×#88322—22no—
159C2×#88322C2×Q814yes—
160C8×D53—216no—
161C23×C53C22×D411yescharacteristic
162C22×D53#12112yes—
163C22×D53#12312yes—
164C22×D53C4⋊Q812yes—
165C22×D53C2×D812yes—
166C22×D53C2×Q1612yes—
167C22×D53AGL(1,ℤ/8)12yes—
168C22×D53#13712yes—
169C2×C4×C53—21no—
170C2×C4×C53—21no—
171C2×C4×C53—21no—
172C2×C4×C53—21no—
173C2×C4×C53—22no—
174C2×C4×C53—41no—
175C2×C4×C53—41no—
176C2×C4×C53—42no—
177C2×C4×C53—41no—
178C2×C4×C53—41no—
179C2×C4×C53—42no—
180C2×C4×C53—42no—
181C2×C4×C53—41no—
182C2×C4×C53C2×D812yes—
183C2×C4×C53C2×Q1612yes—
184C2×C4×C53C22×D411yescharacteristic
185C2×C4×C53C22×Q812yes—
186C2×C4×C53C2×#4112yes—
187C2×C4×C53C2×#4111yescharacteristic
188C2×Dic53—21no—
189C2×Dic53—21no—
190C2×Dic53—21no—
191C2×Dic53—21no—
192C2×Dic53—22no—
193C2×Dic53—41no—
194C2×Dic53—41no—
195C2×Dic53—42no—
196C2×Dic53—41no—
197C2×Dic53—41no—
198C2×Dic53—42no—
199C2×Dic53—42no—
200C2×Dic53—41no—
201C2×Dic53#12112yes—
202C2×Dic53#12312yes—
203C2×Dic53C4⋊Q812yes—
204C2×Dic53C2×D812yes—
205C2×Dic53C2×Q1612yes—
206C4×D53—28no—
207C4×D53—28no—
208C4×D53—48no—
209C4×D53—88no—
210C4×D53—84no—
211C4×D53C22⋊Q818yes—
212C4×D53#12518yes—
213C8×C53—24no—
214#88322—24no—
215C2×#2083—531nomaximal, Sylow
216C22×C53C2×#12111yescharacteristic
217C22×C53C2×#12311yescharacteristic
218C22×C53C2×C4⋊Q811yescharacteristic
219C22×C53C22×D811yescharacteristic
220C22×C53C22×Q1611yescharacteristic
221C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
222C22×C53C2×#13711yescharacteristic
223C2×D53#39814yes—
224C2×D53#45914yes—
225C2×D53#46214yes—
226C2×D53#48014yes—
227C2×D53#48414yes—
228C2×D53#50014yes—
229C2×D53#50114yes—
230C4×C53—22no—
231C4×C53—22no—
232C4×C53—42no—
233C4×C53—81no—
234C4×C53—82no—
235C4×C53C2×C22⋊Q812yes—
236C4×C53C2×#12512yes—
237Dic53—22no—
238Dic53—22no—
239Dic53—42no—
240Dic53—81no—
241Dic53—82no—
242Dic53#39814yes—
243C22×#107—532no—
244C2×#389—531no—
245C2×#384—531no—
246#2083—532no—
247#2083—531no—
248#2083—531no—
249#2083—532no—
250#2083—531no—
251#2083D5311yescharacteristic, direct product factor
252C2×#340—532no—
253C2×#336—531no—
254C2×C53C2×#39811yescharacteristic
255C2×C53C2×#45911yescharacteristic
256C2×C53C2×#46211yescharacteristic
257C2×C53C2×#48011yescharacteristic
258C2×C53C2×#48411yescharacteristic
259C2×C53C2×#50011yescharacteristic
260C2×C53C2×#50111yescharacteristic
261D53#208318yesdirect product factor
262C23×C8—532no—
263C22×C4⋊C4—531no—
264C22×C4⋊C4—532no—
265C22×C4⋊C4—531no—
266C22×C4⋊C4—1061no—
267C22×C4⋊C4—1061no—
268C22×C4⋊C4—1061no—
269C22×C42—531no—
270C2×#107—532no—
271C2×#107—532no—
272C2×#107—532no—
273C2×#107—1068no—
274C2×#107C2×D5312yes—
275#389—531no—
276#389—531no—
277#389—531no—
278#389—1061no—
279#389—1061no—
280#389C2×D5311yescharacteristic
281#384—532no—
282#384—531no—
283#384—1061no—
284#384—1061no—
285#384C2×D5311yescharacteristic
286C2×#95—1061no—
287#340—532no—
288#340—532no—
289#340—532no—
290#340C2×D5312yes—
291#336—532no—
292#336—531no—
293#336C2×D5311yescharacteristic
294C53C2×#208311yescharacteristic, complemented, Sylow
295C23×C4—531no—
296C23×C4—531no—
297C23×C4—531no—
298C23×C4—1061no—
299C23×C4—1062no—
300C23×C4—1061no—
301C22×C8—532no—
302C22×C8—538no—
303C22×C8—1064no—
304C22×C8—1064no—
305C22×C8C22×D5312yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—531no—
310C2×C4⋊C4—534no—
311C2×C4⋊C4—531no—
312C2×C4⋊C4—532no—
313C2×C4⋊C4—1062no—
314C2×C4⋊C4—1064no—
315C2×C4⋊C4—1064no—
316C2×C4⋊C4—1064no—
317C2×C4⋊C4—1061no—
318C2×C4⋊C4—1062no—
319C2×C4⋊C4—1061no—
320C2×C4⋊C4—1062no—
321C2×C4⋊C4—1062no—
322C2×C4⋊C4—1061no—
323C2×C4⋊C4—1061no—
324C2×C4⋊C4—1061no—
325C2×C4⋊C4—1061no—
326C2×C4⋊C4—1061no—
327C2×C4⋊C4—2124no—
328C2×C4⋊C4—2124no—
329C2×C4⋊C4—2124no—
330C2×C4⋊C4C22×D5311yescharacteristic
331C2×C4⋊C4C22×D5312yes—
332C2×C4⋊C4C22×D5311yescharacteristic
333C2×C42—531no—
334C2×C42—531no—
335C2×C42—531no—
336C2×C42—1064no—
337C2×C42C22×D5311yescharacteristic
338#107—24no—
339#107—1064no—
340#107—1064no—
341#107—1064no—
342#95—21no—
343#95—1061no—
344#95—1061no—
345#95—1061no—
346C24—531no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—531no—
351C22×C4—532no—
352C22×C4—534no—
353C22×C4—534no—
354C22×C4—532no—
355C22×C4—531no—
356C22×C4—531no—
357C22×C4—534no—
358C22×C4—534no—
359C22×C4—1062no—
360C22×C4—1062no—
361C22×C4—1062no—
362C22×C4—1062no—
363C22×C4—1064no—
364C22×C4—1061no—
365C22×C4—1061no—
366C22×C4—1062no—
367C22×C4—2124no—
368C22×C4—2122no—
369C22×C4—2124no—
370C22×C4—2122no—
371C22×C4—2124no—
372C22×C4—2122no—
373C22×C4—2122no—
374C22×C4—2122no—
375C22×C4D4×D5311yescharacteristic
376C22×C4D4×D5311yescharacteristic
377C22×C4C23×D5311yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—534no—
381C2×C8—10616no—
382C2×C8—1062no—
383C2×C8—1062no—
384C2×C8Q8×D5314yes—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—532no—
393C4⋊C4—1064no—
394C4⋊C4—1061no—
395C4⋊C4—1062no—
396C4⋊C4—1062no—
397C4⋊C4—1062no—
398C4⋊C4—2122no—
399C4⋊C4—2124no—
400C4⋊C4—2122no—
401C4⋊C4—2124no—
402C4⋊C4—2122no—
403C4⋊C4—2122no—
404C4⋊C4—2124no—
405C4⋊C4—2122no—
406C4⋊C4—2122no—
407C4⋊C4D4×D5312yes—
408C42—22no—
409C42—1062no—
410C42—1062no—
411C42—1062no—
412C23—532no—
413C23—532no—
414C23—532no—
415C23—532no—
416C23—532no—
417C23—532no—
418C23—532no—
419C23C2×D4×D5311yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—532no—
434C2×C4—532no—
435C2×C4—532no—
436C2×C4—538no—
437C2×C4—538no—
438C2×C4—532no—
439C2×C4—532no—
440C2×C4—1068no—
441C2×C4—1068no—
442C2×C4—1061no—
443C2×C4—1061no—
444C2×C4—1061no—
445C2×C4—1061no—
446C2×C4—1062no—
447C2×C4—4244no—
448C2×C4—4248no—
449C2×C4—2128no—
450C2×C4—2122no—
451C2×C4—2121no—
452C2×C4—2121no—
453C2×C4—2122no—
454C2×C4—2122no—
455C2×C4—2121no—
456C2×C4—2121no—
457C2×C4—2121no—
458C2×C4D8×D5312yes—
459C2×C4Q16×D5312yes—
460C2×C4C2×D4×D5311yescharacteristic
461C2×C4C2×Q8×D5312yes—
462C2×C4#41×D5312yes—
463C2×C4#41×D5311yescharacteristic
464C8—24no—
465C8—1064no—
466C22—534no—
467C22—534no—
468C22—534no—
469C22—534no—
470C22—534no—
471C22—534no—
472C22—534no—
473C22#121×D5311yescharacteristic
474C22#123×D5311yescharacteristic
475C22C4⋊Q8×D5311yescharacteristic
476C22C2×D8×D5311yescharacteristic
477C22C2×Q16×D5311yescharacteristic
478C22AGL(1,ℤ/8)×D5311yescharacteristic
479C22#137×D5311yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—534no—
486C4—1062no—
487C4—1062no—
488C4—4241no—
489C4—4242no—
490C4—2122no—
491C4C22⋊Q8×D5312yes—
492C4#125×D5312yes—
493C2—538no—
494C2#398×D5311yescharacteristic
495C2#459×D5311yescharacteristic
496C2#462×D5311yescharacteristic
497C2#480×D5311yescharacteristic
498C2#484×D5311yescharacteristic
499C2#500×D5311yescharacteristic
500C2#501×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2083C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenter#2083D53
hypocenterC53C2×#2083
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
4. #20276190C2semidirect
5. #20276189C2semidirect
6. #20276188C2semidirect
7. #20276187C2semidirect
8. #20276186C2semidirect
11. C53×#2083C2semidirect
251. #2083D53direct (N × H)
261. D53#2083direct (N × H)
294. C53C2×#2083semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D532
#389×D532
#384×D532
#202761902
#202761892
#202761882
#202761872
#202761862
#340×D532
#336×D532
C53×#20832
C2×#208353