Finite Group Databasebeta

← D53×#1347 #27294309

Subgroups — D53×#1347 #27294309

Order 13568.

558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D53C211yesmaximal, characteristic
2C22⋊C16×D53C211yesmaximal, characteristic, complemented
3#340×D53C211yesmaximal, characteristic, complemented
4#20272725C211yesmaximal, characteristic, complemented
5#20272724C211yesmaximal, characteristic, complemented
6#20272723C211yesmaximal, characteristic, complemented
7C53×#1347C211yesmaximal, characteristic, complemented
8C2×D8×D53C411yescharacteristic, complemented
9C22×C8×D53C2211yescharacteristic
10#121×D53—21no—
11C2×C4⋊C4×D53—21no—
12C2×C16×D53—21no—
13#16810860C411yescharacteristic, complemented
14#16810859C2211yescharacteristic
15#16810858—21no—
16#16810857—21no—
17#16810856C411yescharacteristic, complemented
18#107×D53C411yescharacteristic, complemented
19#102×D53—21no—
20C22⋊#11719908C2211yescharacteristic, complemented
21#16810402—21no—
22#16810386C2211yescharacteristic, complemented
23#16810385—21no—
24C53×#466C2211yescharacteristic
25C53×C22⋊C16C2211yescharacteristic, complemented
26C53×#340C2211yescharacteristic, complemented
27C2×D4×D53—21no—
28C2×D4×D53—41no—
29C22×C4×D53—41no—
30C22×C4×D53D411yescharacteristic
31C2×D424C2×C411yescharacteristic, complemented
32C2×#11719922—21no—
33D8×D53—42no—
34C22×#88322D411yescharacteristic
35C2×C8×D53—42no—
36C2×C8×D53C2×C411yescharacteristic
37C2×C8×D53C2×C411yescharacteristic
38C2×C8×D53D411yescharacteristic
39C2×C8×D53D411yescharacteristic
40#13133192—21no—
41#13133191—21no—
42#13133190—41no—
43#13133189—41no—
44#13133188—21no—
45C2×C4⋊Dic53—21no—
46C2×#11719919—41no—
47C4⋊C4×D53—24no—
48C4⋊C4×D53—21no—
49C4⋊C4×D53—42no—
50C22⋊C4×D53—41no—
51C2×#11719908—21no—
52C16×D53—42no—
53#13133151C2×C411yescharacteristic, complemented
54#13133150—21no—
55#13133139—21no—
56#13133138—21no—
57#13133137—21no—
58C2×D8×C53C2×C411yescharacteristic, complemented
59C22×C8×C53C2311yescharacteristic
60#121×C53—21no—
61C2×C4⋊C4×C53—21no—
62C2×C16×C53—21no—
63#107×C53C2×C411yescharacteristic, complemented
64#102×C53—21no—
65C23×D53—41no—
66C23×D53D811yescharacteristic
67C2×D4×C53—21no—
68C2×D4×C53—41no—
69C22×C4×C53—41no—
70C22×C4×C53C2×D411yescharacteristic
71C2×C22⋊D53—41no—
72C2×C22⋊D53—41no—
73C2×C22⋊D53—41no—
74C22×Dic53—41no—
75C22×Dic53D811yescharacteristic
76D4×D53—42no—
77D4×D53—42no—
78D4×D53—82no—
79D4×D53—82no—
80C2×D212—21no—
81C2×D212—41no—
82C2×C4×D53—22no—
83C2×C4×D53—22no—
84C2×C4×D53—44no—
85C2×C4×D53—41no—
86C2×C4×D53—82no—
87C2×C4×D53—82no—
88C2×C4×D53C22⋊C411yescharacteristic
89C2×C4×D53C22⋊C411yescharacteristic
90C2×C4×D53SD1611yescharacteristic
91C2×C4×D53SD1611yescharacteristic
92D8×C53—41no—
93C2×C8×C53—41no—
94C2×C8×C53C22×C411yescharacteristic
95C2×C8×C53C2×D411yescharacteristic
96C4⋊C4×C53—22no—
97C4⋊C4×C53—21no—
98C4⋊C4×C53—41no—
99C22⋊C4×C53—41no—
100C22⋊Dic53—41no—
101#11719922—42no—
102#11719921—41no—
103#11719921—41no—
104C4⋊Dic53—22no—
105C4⋊Dic53—21no—
106C4⋊Dic53—41no—
107#11719919—44no—
108#11719919—41no—
109C2×#88322—41no—
110C2×#88322C22⋊C411yescharacteristic
111C2×#88322C22⋊C411yescharacteristic
112D424—41no—
113C8×D53—22no—
114C8×D53—22no—
115C8×D53—41no—
116C8×D53—41no—
117C16×C53—41no—
118#11719908—41no—
119C23×C53—41no—
120C23×C53C2×D811yescharacteristic
121C22×D53—22no—
122C22×D53—22no—
123C22×D53—41no—
124C22×D53—82no—
125C22×D53—82no—
126C22×D53—82no—
127C22×D53#10211yescharacteristic
128C22×D53#10211yescharacteristic
129C22×D53D1612yes—
130C22×D53SD3212yes—
131D4×C53—41no—
132D4×C53—41no—
133D4×C53—81no—
134D4×C53—81no—
135C2×C4×C53—21no—
136C2×C4×C53—21no—
137C2×C4×C53—42no—
138C2×C4×C53—41no—
139C2×C4×C53—81no—
140C2×C4×C53—81no—
141C2×C4×C53C2×C22⋊C411yescharacteristic
142C2×C4×C53C2×SD1611yescharacteristic
143C22⋊D53—81no—
144C22⋊D53—81no—
145C22⋊D53—82no—
146C22⋊D53—82no—
147C2×Dic53—22no—
148C2×Dic53—42no—
149C2×Dic53—41no—
150C2×Dic53—81no—
151C2×Dic53—81no—
152C2×Dic53#10211yescharacteristic
153C2×Dic53#10211yescharacteristic
154D212—41no—
155D212—41no—
156D212—82no—
157C4×D53—22no—
158C4×D53—21no—
159C4×D53—21no—
160C4×D53—22no—
161C4×D53—88no—
162C4×D53—82no—
163C4×D53#9912yes—
164C4×D53#10412yes—
165C8×C53—21no—
166C8×C53—21no—
167#88322—21no—
168#88322—21no—
169C2×#1347—531nomaximal, Sylow
170C22×C53—21no—
171C22×C53—21no—
172C22×C53—81no—
173C22×C53—81no—
174C22×C53—81no—
175C22×C53C2×#10211yescharacteristic
176C22×C53C2×D1611yescharacteristic
177C22×C53C2×SD3211yescharacteristic
178C2×D53—21no—
179C2×D53—21no—
180C2×D53—24no—
181C2×D53—24no—
182C2×D53—81no—
183C2×D53—81no—
184C2×D53—81no—
185C2×D53—164no—
186C2×D53#32712yes—
187C2×D53#35712yes—
188C2×D53#35712yes—
189C2×D53#36012yes—
190C4×C53—21no—
191C4×C53—82no—
192C4×C53—81no—
193C4×C53C2×#9911yescharacteristic
194C4×C53C2×#10411yescharacteristic
195Dic53—21no—
196Dic53—82no—
197Dic53—81no—
198Dic53#32712yes—
199C2×#466—531no—
200C2×C22⋊C16—531no—
201C2×#340—531no—
202#1347—531no—
203#1347—531no—
204#1347—531no—
205#1347D5311yescharacteristic, direct product factor
206C2×C53—21no—
207C2×C53—21no—
208C2×C53—161no—
209C2×C53C2×#32711yescharacteristic
210C2×C53C2×#35711yescharacteristic
211C2×C53C2×#36011yescharacteristic
212D53—22no—
213D53—161no—
214D53#134714yesdirect product factor
215C22×D8—531no—
216C23×C8—531no—
217C2×#121—1061no—
218C22×C4⋊C4—1061no—
219C22×C16—1061no—
220#466—531no—
221#466—531no—
222#466—531no—
223#466—1061no—
224#466—1061no—
225#466C2×D5311yescharacteristic
226C2×#107—531no—
227C2×#102—1061no—
228C22⋊C16—531no—
229C22⋊C16—1061no—
230C22⋊C16C2×D5311yescharacteristic, complemented
231#340—531no—
232#340—1061no—
233#340C2×D5311yescharacteristic, complemented
234C53C2×#134711yescharacteristic, complemented, Sylow
235C22×D4—1061no—
236C22×D4—2121no—
237C23×C4—531no—
238C23×C4—2121no—
239C2×D8—531no—
240C2×D8—1061no—
241C2×D8—2122no—
242C2×D8C4×D5311yescharacteristic, complemented
243C22×C8—531no—
244C22×C8—531no—
245C22×C8—531no—
246C22×C8—531no—
247C22×C8—531no—
248C22×C8—2122no—
249C22×C8C22×D5311yescharacteristic
250#121—21no—
251#121—1061no—
252#121—1061no—
253#121—1061no—
254#121—2121no—
255#121—2121no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—1061no—
258C2×C4⋊C4—1064no—
259C2×C4⋊C4—1061no—
260C2×C4⋊C4—2122no—
261C2×C4⋊C4—2121no—
262C2×C22⋊C4—2121no—
263C2×C16—21no—
264C2×C16—1061no—
265C2×C16—2122no—
266#107—531no—
267#107—1061no—
268#107C4×D5311yescharacteristic, complemented
269#102—21no—
270#102—1061no—
271#102—1061no—
272#102—1061no—
273C24—531no—
274C24—2121no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—1061no—
278C2×D4—4242no—
279C2×D4—4242no—
280C2×D4—2121no—
281C2×D4—2122no—
282C2×D4—2122no—
283C2×D4—2121no—
284C2×D4—2121no—
285C2×D4—2121no—
286C22×C4—41no—
287C22×C4—531no—
288C22×C4—531no—
289C22×C4—531no—
290C22×C4—531no—
291C22×C4—531no—
292C22×C4—1062no—
293C22×C4—1062no—
294C22×C4—4242no—
295C22×C4—4242no—
296C22×C4—2121no—
297C22×C4—2124no—
298C22×C4—2121no—
299C22×C4D4×D5311yescharacteristic
300D8—41no—
301D8—2121no—
302D8—2122no—
303C2×C8—41no—
304C2×C8—531no—
305C2×C8—531no—
306C2×C8—1062no—
307C2×C8—1062no—
308C2×C8—2121no—
309C2×C8—2121no—
310C2×C8—2121no—
311C2×C8C2×C4×D5311yescharacteristic
312C2×C8D4×D5311yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—1062no—
317C4⋊C4—1061no—
318C4⋊C4—2121no—
319C4⋊C4—2121no—
320C4⋊C4—2124no—
321C22⋊C4—41no—
322C22⋊C4—2121no—
323C22⋊C4—2121no—
324C22⋊C4—2121no—
325C16—41no—
326C16—2121no—
327C23—41no—
328C23—531no—
329C23—532no—
330C23—532no—
331C23—531no—
332C23—1062no—
333C23—1062no—
334C23—4242no—
335C23—4242no—
336C23—4242no—
337C23—2121no—
338C23D8×D5311yescharacteristic
339D4—41no—
340D4—41no—
341D4—81no—
342D4—81no—
343D4—4242no—
344D4—4242no—
345D4—4242no—
346D4—4241no—
347D4—4241no—
348D4—2121no—
349D4—2121no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—531no—
357C2×C4—532no—
358C2×C4—532no—
359C2×C4—531no—
360C2×C4—1062no—
361C2×C4—1062no—
362C2×C4—1062no—
363C2×C4—1061no—
364C2×C4—1061no—
365C2×C4—4242no—
366C2×C4—4248no—
367C2×C4—4241no—
368C2×C4—4241no—
369C2×C4—2122no—
370C2×C4—2121no—
371C2×C4C22⋊C4×D5311yescharacteristic
372C2×C4SD16×D5311yescharacteristic
373C8—21no—
374C8—21no—
375C8—1061no—
376C8—1061no—
377C22—21no—
378C22—21no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—532no—
383C22—532no—
384C22—532no—
385C22—532no—
386C22—8484no—
387C22—1064no—
388C22—1064no—
389C22—1061no—
390C22—1061no—
391C22—4241no—
392C22—4241no—
393C22—4241no—
394C22#102×D5311yescharacteristic
395C22D16×D5311yescharacteristic
396C22SD32×D5311yescharacteristic
397C4—21no—
398C4—82no—
399C4—81no—
400C4—532no—
401C4—1061no—
402C4—4242no—
403C4—4241no—
404C4#99×D5311yescharacteristic
405C4#104×D5311yescharacteristic
406C2—21no—
407C2—21no—
408C2—161no—
409C2—534no—
410C2—8481no—
411C2—1062no—
412C2#327×D5311yescharacteristic
413C2#357×D5311yescharacteristic
414C2#360×D5311yescharacteristic
subgroupG/H
centerC22#102×D53
commutatorC2×C8×C53C22×C4
FrattiniC22×C8C22×D53
FittingC53×#1347C2
socleC22×C53C2×#102
prime radical#466×D53C2
cosocleC22×C8×C53C23
hypercenter#1347D53
hypocenterC53C2×#1347
LCSG ▷ C2×C8×C53 ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D53C2semidirect
3. #340×D53C2semidirect
4. #20272725C2semidirect
5. #20272724C2semidirect
6. #20272723C2semidirect
7. C53×#1347C2semidirect
8. C2×D8×D53C4semidirect
13. #16810860C4semidirect
17. #16810856C4semidirect
18. #107×D53C4semidirect
20. C22⋊#11719908C22semidirect
22. #16810386C22semidirect
25. C53×C22⋊C16C22semidirect
26. C53×#340C22semidirect
31. C2×D424C2×C4semidirect
53. #13133151C2×C4semidirect
58. C2×D8×C53C2×C4semidirect
63. #107×C53C2×C4semidirect
205. #1347D53direct (N × H)
214. D53#1347direct (N × H)
230. C22⋊C16C2×D53semidirect
233. #340C2×D53semidirect
234. C53C2×#1347semidirect
242. C2×D8C4×D53semidirect
268. #107C4×D53semidirect

Maximal subgroups

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

subgroupindex
#466×D532
C22⋊C16×D532
#340×D532
#202727252
#202727242
#202727232
C53×#13472
C2×#134753