Finite Group Databasebeta

← D53×#1952 #27387634

Subgroups — D53×#1952 #27387634

Order 13568.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D53C211yesmaximal, characteristic
2#428×D53C212yesmaximal
3C2×#107×D53C211yesmaximal, characteristic
4#405×D53C211yesmaximal, characteristic
5#20275501C211yesmaximal, characteristic, complemented
6#20275500C211yesmaximal, characteristic, complemented
7#20275499C212yesmaximal, complemented
8#20275498C211yesmaximal, characteristic, complemented
9#20275497C212yesmaximal, complemented
10#343×D53C212yesmaximal
11C53×#1952C211yesmaximal, characteristic, complemented
12C2×M16×D53C2212yes—
13C2×M16×D53C2211yescharacteristic
14C22×C8×D53C2211yescharacteristic
15#117×D53C2211yescharacteristic
16C2×C4⋊C4×D53C2212yes—
17C2×#13133153C2211yescharacteristic
18C2×#13133152C2212yes—
19#108×D53C418yescomplemented
20#16810666C2212yes—
21#16810665C2212yes—
22#16810664—22no—
23#16810663C2212yes—
24#16810662—22no—
25C2×#13133151C2211yescharacteristic
26C2×#13133150C2212yes—
27#107×D53—21no—
28#107×D53—21no—
29#107×D53—21no—
30#107×D53—21no—
31#107×D53—22no—
32#106×D53—22no—
33#16810581C2211yescharacteristic
34#16810580—21no—
35#16810579C2211yescharacteristic
36#16810578C2211yescharacteristic
37#16810577—21no—
38#97×D53—21no—
39C4×C8×D53—21no—
40#16810392C2212yes—
41#16810391C2212yes—
42#16810391C2212yes—
43C2×#108×C53C2211yescharacteristic
44C53×#428C2212yes—
45C2×#107×C53C2211yescharacteristic
46C53×#405C2211yescharacteristic
47C53×#343C2212yes—
48C22×C4×D53—22no—
49C22×C4×D53C2311yescharacteristic
50C2×#11719917C2312yes—
51C2×#11719917C2311yescharacteristic
52C2×#11719912—21no—
53C2×#11719912—22no—
54M16×D53—24no—
55M16×D53—22no—
56M16×D53C2×C418yes—
57M16×D53Q814yes—
58C22×#88322C2311yescharacteristic
59C2×C8×D53—21no—
60C2×C8×D53—22no—
61C2×C8×D53C2×C414yes—
62C2×C8×D53D411yescharacteristic
63C2×C8×D53D411yescharacteristic
64C2×C8×D53D411yescharacteristic
65C2×C8×D53D411yescharacteristic
66C2×C8×D53Q814yes—
67#13133176C2311yescharacteristic
68#13133175D411yescharacteristic
69#13133175D411yescharacteristic
70#13133174—21no—
71#13133173—21no—
72C2×C4⋊Dic53C2312yes—
73C2×#11719919—22no—
74C4⋊C4×D53—22no—
75C4⋊C4×D53—22no—
76C4⋊C4×D53—22no—
77C4⋊C4×D53—22no—
78C4⋊C4×D53D411yescharacteristic
79C4⋊C4×D53D411yescharacteristic
80C22⋊C4×D53—21no—
81C42×D53—21no—
82#13133153C2×C414yescomplemented
83#13133152C2×C418yescomplemented
84#13133151—21no—
85#13133151—21no—
86#13133151—22no—
87#13133150—22no—
88#13133150—22no—
89#13133150—22no—
90#13133150—22no—
91#13133149—22no—
92#13133148—22no—
93#13133148—22no—
94#13133128—21no—
95#13133127—21no—
96#13133127—21no—
97C4×#88322—21no—
98C8×Dic53—21no—
99C8×Dic53—21no—
100C2×M16×C53C2312yes—
101C2×M16×C53C2311yescharacteristic
102C22×C8×C53C2311yescharacteristic
103#117×C53C2311yescharacteristic
104C2×C4⋊C4×C53C2312yes—
105#108×C53C2×C414yescomplemented
106#107×C53—21no—
107#107×C53—21no—
108#107×C53—22no—
109#106×C53—22no—
110#97×C53—21no—
111C4×C8×C53—21no—
112C23×D53#4111yescharacteristic
113C22×C4×C53—22no—
114C22×C4×C53C2411yescharacteristic
115C22×Dic53—22no—
116C22×Dic53#4111yescharacteristic
117C2×C4×D53—21no—
118C2×C4×D53—21no—
119C2×C4×D53—42no—
120C2×C4×D53—42no—
121C2×C4×D53—84no—
122C2×C4×D53C22×C412yes—
123C2×C4×D53C2×D411yescharacteristic
124C2×C4×D53C2×D411yescharacteristic
125C2×C4×D53C2×D411yescharacteristic
126C2×C4×D53C2×D411yescharacteristic
127C2×C4×D53C2×Q812yes—
128C2×C4×D53C2×Q812yes—
129C2×C4×D53#4112yes—
130M16×C53—22no—
131M16×C53—21no—
132M16×C53C22×C414yes—
133M16×C53C2×Q812yes—
134C2×C8×C53—21no—
135C2×C8×C53—22no—
136C2×C8×C53C22×C412yes—
137C2×C8×C53C2×D411yescharacteristic
138C2×C8×C53C2×D411yescharacteristic
139C2×C8×C53C2×Q812yes—
140C4⋊C4×C53—22no—
141C4⋊C4×C53—22no—
142C4⋊C4×C53C2×D411yescharacteristic
143C4⋊C4×C53C2×D411yescharacteristic
144C22⋊C4×C53—21no—
145C42×C53—21no—
146C22⋊Dic53—21no—
147#11719921—21no—
148#11719921—21no—
149C4⋊Dic53—22no—
150C4⋊Dic53—22no—
151C4⋊Dic53C2×D411yescharacteristic
152C4⋊Dic53C2×D411yescharacteristic
153#11719919—21no—
154#11719919—21no—
155#11719919—42no—
156#11719919—42no—
157C4×Dic53—21no—
158C4×Dic53—21no—
159C4×Dic53—21no—
160#11719917—22no—
161#11719917—21no—
162#11719917C22×C414yes—
163#11719917C2×Q812yes—
164C2×#88322—21no—
165C2×#88322—22no—
166C2×#88322C22×C412yes—
167C2×#88322C2×D411yescharacteristic
168C2×#88322C2×D411yescharacteristic
169C2×#88322C2×Q812yes—
170#11719912—28no—
171#11719912—24no—
172C8×D53—28no—
173C8×D53—24no—
174C8×D53C4⋊C414yes—
175C8×D53C4⋊C414yes—
176C8×D53C4⋊C414yes—
177C8×D53C4⋊C414yes—
178C23×C53C2×#4111yescharacteristic
179C22×D53—22no—
180C22×D53—22no—
181C22×D53C4×Q812yes—
182C22×D53#12111yescharacteristic
183C22×D53#12111yescharacteristic
184C22×D53#12512yes—
185C2×C4×C53—21no—
186C2×C4×C53—21no—
187C2×C4×C53—42no—
188C2×C4×C53—82no—
189C2×C4×C53C23×C411yescharacteristic
190C2×C4×C53C22×D411yescharacteristic
191C2×C4×C53C22×D411yescharacteristic
192C2×C4×C53C22×Q811yescharacteristic
193C2×C4×C53C22×Q811yescharacteristic
194C2×C4×C53C2×#4111yescharacteristic
195C2×Dic53—21no—
196C2×Dic53—21no—
197C2×Dic53—42no—
198C2×Dic53—82no—
199C2×Dic53C4×Q812yes—
200C2×Dic53#12111yescharacteristic
201C2×Dic53#12111yescharacteristic
202C2×Dic53#12512yes—
203C4×D53—42no—
204C4×D53—42no—
205C4×D53—84no—
206C4×D53—84no—
207C4×D53C2×C4⋊C412yes—
208C4×D53C2×C4⋊C412yes—
209C4×D53C4×D412yes—
210C4×D53C4×D412yes—
211C4×D53C22⋊Q812yes—
212C4×D53C22⋊Q812yes—
213C4×D53C4⋊Q812yes—
214C4×D53C4⋊Q812yes—
215C8×C53—24no—
216C8×C53—22no—
217C8×C53C2×C4⋊C412yes—
218C8×C53C2×C4⋊C412yes—
219#88322—24no—
220#88322—22no—
221#88322C2×C4⋊C412yes—
222#88322C2×C4⋊C412yes—
223C2×#1952—531nomaximal, Sylow
224C22×C53—21no—
225C22×C53—21no—
226C22×C53C2×C4×Q811yescharacteristic
227C22×C53C2×#12111yescharacteristic
228C22×C53C2×#12511yescharacteristic
229C2×D53—21no—
230C2×D53—21no—
231C2×D53—24no—
232C2×D53—24no—
233C2×D53#38912yes—
234C2×D53#38912yes—
235C2×D53#47212yes—
236C2×D53#47312yes—
237C4×C53—41no—
238C4×C53—41no—
239C4×C53—82no—
240C4×C53C22×C4⋊C411yescharacteristic
241C4×C53C2×C4×D411yescharacteristic
242C4×C53C2×C22⋊Q811yescharacteristic
243C4×C53C2×C4⋊Q811yescharacteristic
244Dic53—41no—
245Dic53—41no—
246Dic53—82no—
247Dic53#38912yes—
248Dic53#38912yes—
249C22×#108—531no—
250C2×#428—532no—
251C22×#107—531no—
252C2×#405—531no—
253#1952—531no—
254#1952—532no—
255#1952—531no—
256#1952—531no—
257#1952—532no—
258#1952D5311yescharacteristic, direct product factor
259C2×#343—532no—
260C2×C53—21no—
261C2×C53—21no—
262C2×C53C2×#38911yescharacteristic
263C2×C53C2×#47211yescharacteristic
264C2×C53C2×#47311yescharacteristic
265D53—22no—
266D53#195214yesdirect product factor
267C22×M16—531no—
268C22×M16—532no—
269C23×C8—531no—
270C2×#117—531no—
271C22×C4⋊C4—532no—
272C2×#108—532no—
273C2×#108—531no—
274C2×#108—538no—
275C2×#108C2×D5311yescharacteristic
276#428—532no—
277#428—532no—
278#428—532no—
279#428—1062no—
280#428—1062no—
281#428C2×D5312yes—
282C2×#107—531no—
283C2×#107—532no—
284C2×#107—1062no—
285C2×#107—1061no—
286C2×#107—1061no—
287C2×#107—1061no—
288C2×#107—1061no—
289C2×#107C2×D5311yescharacteristic
290C2×#106—1062no—
291#405—531no—
292#405—531no—
293#405—531no—
294#405—1061no—
295#405—1061no—
296#405C2×D5311yescharacteristic
297C2×#97—1061no—
298C2×C4×C8—1061no—
299#343—532no—
300#343—532no—
301#343—532no—
302#343C2×D5312yes—
303C53C2×#195211yescharacteristic, complemented, Sylow
304C23×C4—531no—
305C23×C4—1062no—
306C2×M16—531no—
307C2×M16—532no—
308C2×M16—538no—
309C2×M16—534no—
310C2×M16—1061no—
311C2×M16—1062no—
312C2×M16—1062no—
313C2×M16—1064no—
314C2×M16C22×D5312yes—
315C2×M16C22×D5311yescharacteristic
316C22×C8—531no—
317C22×C8—534no—
318C22×C8—531no—
319C22×C8—531no—
320C22×C8—531no—
321C22×C8—531no—
322C22×C8—534no—
323C22×C8—1061no—
324C22×C8—1062no—
325C22×C8C22×D5311yescharacteristic
326#117—531no—
327#117—531no—
328#117—531no—
329#117—1061no—
330#117—1061no—
331#117C22×D5311yescharacteristic
332C2×C4⋊C4—531no—
333C2×C4⋊C4—531no—
334C2×C4⋊C4—532no—
335C2×C4⋊C4—1062no—
336C2×C4⋊C4—1062no—
337C2×C4⋊C4—1062no—
338C2×C4⋊C4—1062no—
339C2×C4⋊C4—1062no—
340C2×C4⋊C4C22×D5312yes—
341C2×C22⋊C4—1061no—
342C2×C42—1061no—
343#108—538no—
344#108—534no—
345#108C4×D5314yescomplemented
346#107—21no—
347#107—21no—
348#107—22no—
349#107—1062no—
350#107—1062no—
351#107—1062no—
352#107—1062no—
353#107—1061no—
354#107—1061no—
355#107—1062no—
356#106—22no—
357#106—1062no—
358#106—1062no—
359#106—1062no—
360#97—21no—
361#97—1061no—
362#97—1061no—
363#97—1061no—
364C4×C8—21no—
365C4×C8—1061no—
366C4×C8—1061no—
367C4×C8—1061no—
368C24—531no—
369C22×C4—22no—
370C22×C4—531no—
371C22×C4—532no—
372C22×C4—531no—
373C22×C4—531no—
374C22×C4—531no—
375C22×C4—531no—
376C22×C4—532no—
377C22×C4—532no—
378C22×C4—532no—
379C22×C4—1061no—
380C22×C4—1061no—
381C22×C4—1062no—
382C22×C4—4244no—
383C22×C4—2122no—
384C22×C4—2122no—
385C22×C4C23×D5311yescharacteristic
386M16—22no—
387M16—21no—
388M16—534no—
389M16—532no—
390M16—1068no—
391M16—1064no—
392M16—1062no—
393M16—1061no—
394M16C2×C4×D5314yes—
395M16Q8×D5312yes—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—532no—
399C2×C8—531no—
400C2×C8—531no—
401C2×C8—532no—
402C2×C8—534no—
403C2×C8—534no—
404C2×C8—534no—
405C2×C8—534no—
406C2×C8—1068no—
407C2×C8—1064no—
408C2×C8—1061no—
409C2×C8—1062no—
410C2×C8C2×C4×D5312yes—
411C2×C8D4×D5311yescharacteristic
412C2×C8D4×D5311yescharacteristic
413C2×C8Q8×D5312yes—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—531no—
417C4⋊C4—531no—
418C4⋊C4—1061no—
419C4⋊C4—1061no—
420C4⋊C4—1062no—
421C4⋊C4—1062no—
422C4⋊C4—2122no—
423C4⋊C4—2122no—
424C4⋊C4D4×D5311yescharacteristic
425C4⋊C4D4×D5311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—1061no—
428C22⋊C4—1061no—
429C22⋊C4—1061no—
430C42—21no—
431C42—1061no—
432C42—1061no—
433C42—1061no—
434C23—531no—
435C23—532no—
436C23—531no—
437C23—532no—
438C23—1062no—
439C23—1062no—
440C23#41×D5311yescharacteristic
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—532no—
446C2×C4—531no—
447C2×C4—531no—
448C2×C4—532no—
449C2×C4—532no—
450C2×C4—532no—
451C2×C4—532no—
452C2×C4—532no—
453C2×C4—532no—
454C2×C4—532no—
455C2×C4—532no—
456C2×C4—532no—
457C2×C4—1061no—
458C2×C4—1061no—
459C2×C4—4244no—
460C2×C4—4244no—
461C2×C4—4242no—
462C2×C4—2122no—
463C2×C4—2122no—
464C2×C4—2122no—
465C2×C4C22×C4×D5311yescharacteristic
466C2×C4C2×D4×D5311yescharacteristic
467C2×C4C2×D4×D5311yescharacteristic
468C2×C4C2×Q8×D5311yescharacteristic
469C2×C4C2×Q8×D5311yescharacteristic
470C2×C4#41×D5311yescharacteristic
471C8—24no—
472C8—22no—
473C8—532no—
474C8—532no—
475C8—1064no—
476C8—1062no—
477C8C4⋊C4×D5312yes—
478C8C4⋊C4×D5312yes—
479C22—21no—
480C22—21no—
481C22—532no—
482C22—532no—
483C22—532no—
484C22—532no—
485C22—1064no—
486C22—1064no—
487C22—1061no—
488C22—1061no—
489C22C4×Q8×D5311yescharacteristic
490C22#121×D5311yescharacteristic
491C22#125×D5311yescharacteristic
492C4—41no—
493C4—41no—
494C4—82no—
495C4—532no—
496C4—532no—
497C4—4242no—
498C4—2121no—
499C4—2121no—
500C4C2×C4⋊C4×D5311yescharacteristic
501C4C4×D4×D5311yescharacteristic
502C4C22⋊Q8×D5311yescharacteristic
503C4C4⋊Q8×D5311yescharacteristic
504C2—21no—
505C2—21no—
506C2—534no—
507C2—1062no—
508C2#389×D5311yescharacteristic
509C2#472×D5311yescharacteristic
510C2#473×D5311yescharacteristic
subgroupG/H
centerC22#121×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1952C2
socleC22×C53C2×#121
prime radicalC23×D53#41
cosocleC22×C4×C53C24
hypercenter#1952D53
hypocenterC53C2×#1952
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
5. #20275501C2semidirect
6. #20275500C2semidirect
7. #20275499C2semidirect
8. #20275498C2semidirect
9. #20275497C2semidirect
11. C53×#1952C2semidirect
19. #108×D53C4semidirect
82. #13133153C2×C4semidirect
83. #13133152C2×C4semidirect
105. #108×C53C2×C4semidirect
258. #1952D53direct (N × H)
266. D53#1952direct (N × H)
303. C53C2×#1952semidirect
345. #108C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D532
#428×D532
C2×#107×D532
#405×D532
#202755012
#202755002
#202754992
#202754982
#202754972
#343×D532
C53×#19522
C2×#195253