Finite Group Databasebeta

← D53×#1348 #27294313

Subgroups — D53×#1348 #27294313

Order 13568.

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

normal subgroups only

This group has 506 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#467×D53C211yesmaximal, characteristic
2C22⋊C16×D53C211yesmaximal, characteristic
3#340×D53C211yesmaximal, characteristic
4#20272728C211yesmaximal, characteristic, complemented
5#20272727C211yesmaximal, characteristic, complemented
6#20272726C211yesmaximal, characteristic, complemented
7C53×#1348C211yesmaximal, characteristic, complemented
8C2×Q16×D53C411yescharacteristic, complemented
9C22×C8×D53C2211yescharacteristic
10C22⋊Q8×D53—21no—
11C2×C4⋊C4×D53—21no—
12C2×C16×D53—21no—
13#16810865C411yescharacteristic, complemented
14#16810864C2211yescharacteristic
15#16810863—21no—
16#16810862—21no—
17#16810861C411yescharacteristic, complemented
18#107×D53C411yescharacteristic, complemented
19#103×D53—21no—
20C22⋊#11719908C2211yescharacteristic
21#16810402—21no—
22#16810386C2211yescharacteristic
23#16810385—21no—
24C53×#467C2211yescharacteristic
25C53×C22⋊C16C2211yescharacteristic
26C53×#340C2211yescharacteristic
27C2×Q8×D53—21no—
28C22×C4×D53—41no—
29C22×C4×D53D411yescharacteristic
30C2×Dic212C2×C411yescharacteristic, complemented
31C2×#11719925—21no—
32Q16×D53—42no—
33C22×#88322D411yescharacteristic
34C2×C8×D53—42no—
35C2×C8×D53C2×C411yescharacteristic
36C2×C8×D53C2×C411yescharacteristic
37C2×C8×D53D411yescharacteristic
38C2×C8×D53D411yescharacteristic
39#13133197—21no—
40#13133196—21no—
41#13133195—41no—
42#13133194—41no—
43#13133193—21no—
44C2×C4⋊Dic53—21no—
45C2×#11719919—41no—
46C4⋊C4×D53—24no—
47C4⋊C4×D53—21no—
48C4⋊C4×D53—42no—
49C4⋊C4×D53—41no—
50C22⋊C4×D53—41no—
51C2×#11719908—21no—
52C16×D53—42no—
53#13133151C2×C411yescharacteristic, complemented
54#13133150—21no—
55#13133142—21no—
56#13133141—21no—
57#13133140—21no—
58C2×Q16×C53C2×C411yescharacteristic, complemented
59C22×C8×C53C2311yescharacteristic
60C22⋊Q8×C53—21no—
61C2×C4⋊C4×C53—21no—
62C2×C16×C53—21no—
63#107×C53C2×C411yescharacteristic, complemented
64#103×C53—21no—
65C23×D53D811yescharacteristic
66C2×Q8×C53—21no—
67C22×C4×C53—41no—
68C22×C4×C53C2×D411yescharacteristic
69C22×Dic53—41no—
70C22×Dic53D811yescharacteristic
71Q8×D53—42no—
72Q8×D53—42no—
73C2×C4×D53—22no—
74C2×C4×D53—22no—
75C2×C4×D53—44no—
76C2×C4×D53—41no—
77C2×C4×D53—41no—
78C2×C4×D53—82no—
79C2×C4×D53—82no—
80C2×C4×D53C22⋊C411yescharacteristic
81C2×C4×D53C22⋊C411yescharacteristic
82C2×C4×D53SD1611yescharacteristic
83C2×C4×D53SD1611yescharacteristic
84C2×Dic106—21no—
85C2×Dic106—41no—
86Q16×C53—41no—
87C2×C8×C53—41no—
88C2×C8×C53C22×C411yescharacteristic
89C2×C8×C53C2×D411yescharacteristic
90C4⋊C4×C53—22no—
91C4⋊C4×C53—21no—
92C4⋊C4×C53—41no—
93C4⋊C4×C53—41no—
94C22⋊C4×C53—41no—
95C22⋊Dic53—41no—
96#11719925—42no—
97#11719921—41no—
98#11719921—41no—
99C4⋊Dic53—22no—
100C4⋊Dic53—21no—
101C4⋊Dic53—41no—
102C4⋊Dic53—41no—
103#11719919—44no—
104#11719919—41no—
105#11719919—41no—
106#11719919—41no—
107C2×#88322—41no—
108C2×#88322C22⋊C411yescharacteristic
109C2×#88322C22⋊C411yescharacteristic
110Dic212—41no—
111C8×D53—22no—
112C8×D53—22no—
113C8×D53—41no—
114C8×D53—41no—
115C16×C53—41no—
116#11719908—41no—
117C23×C53C2×D811yescharacteristic
118C22×D53—22no—
119C22×D53—22no—
120C22×D53#10211yescharacteristic
121C22×D53#10211yescharacteristic
122C22×D53SD3212yes—
123C22×D53Q3212yes—
124Q8×C53—41no—
125Q8×C53—41no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—42no—
129C2×C4×C53—41no—
130C2×C4×C53—41no—
131C2×C4×C53—81no—
132C2×C4×C53—81no—
133C2×C4×C53C2×C22⋊C411yescharacteristic
134C2×C4×C53C2×SD1611yescharacteristic
135C2×Dic53—22no—
136C2×Dic53—42no—
137C2×Dic53—41no—
138C2×Dic53—41no—
139C2×Dic53—81no—
140C2×Dic53—81no—
141C2×Dic53#10211yescharacteristic
142C2×Dic53#10211yescharacteristic
143C4×D53—22no—
144C4×D53—21no—
145C4×D53—21no—
146C4×D53—22no—
147C4×D53—88no—
148C4×D53—82no—
149C4×D53—82no—
150C4×D53#9912yes—
151C4×D53#10412yes—
152Dic106—41no—
153Dic106—41no—
154Dic106—82no—
155C8×C53—21no—
156C8×C53—21no—
157#88322—21no—
158#88322—21no—
159C2×#1348—531nomaximal, Sylow
160C22×C53—21no—
161C22×C53—21no—
162C22×C53C2×#10211yescharacteristic
163C22×C53C2×SD3211yescharacteristic
164C22×C53C2×Q3211yescharacteristic
165C2×D53—21no—
166C2×D53—21no—
167C2×D53—24no—
168C2×D53—24no—
169C2×D53#32712yes—
170C2×D53#35812yes—
171C2×D53#35812yes—
172C2×D53#36012yes—
173C4×C53—21no—
174C4×C53—82no—
175C4×C53—81no—
176C4×C53—81no—
177C4×C53C2×#9911yescharacteristic
178C4×C53C2×#10411yescharacteristic
179Dic53—21no—
180Dic53—82no—
181Dic53—81no—
182Dic53—81no—
183Dic53#32712yes—
184C2×#467—531no—
185C2×C22⋊C16—531no—
186C2×#340—531no—
187#1348—531no—
188#1348—531no—
189#1348—531no—
190#1348D5311yescharacteristic, direct product factor
191C2×C53—21no—
192C2×C53—21no—
193C2×C53C2×#32711yescharacteristic
194C2×C53C2×#35811yescharacteristic
195C2×C53C2×#36011yescharacteristic
196D53—22no—
197D53#134814yesdirect product factor
198C22×Q16—531no—
199C23×C8—531no—
200C2×C22⋊Q8—1061no—
201C22×C4⋊C4—1061no—
202C22×C16—1061no—
203#467—531no—
204#467—531no—
205#467—531no—
206#467—1061no—
207#467—1061no—
208#467C2×D5311yescharacteristic
209C2×#107—531no—
210C2×#103—1061no—
211C22⋊C16—531no—
212C22⋊C16—1061no—
213C22⋊C16C2×D5311yescharacteristic
214#340—531no—
215#340—1061no—
216#340C2×D5311yescharacteristic
217C53C2×#134811yescharacteristic, complemented, Sylow
218C22×Q8—1061no—
219C23×C4—531no—
220C23×C4—2121no—
221C2×Q16—531no—
222C2×Q16—1061no—
223C2×Q16—2122no—
224C2×Q16C4×D5311yescharacteristic, complemented
225C22×C8—531no—
226C22×C8—531no—
227C22×C8—531no—
228C22×C8—531no—
229C22×C8—531no—
230C22×C8—2122no—
231C22×C8C22×D5311yescharacteristic
232C22⋊Q8—21no—
233C22⋊Q8—1061no—
234C22⋊Q8—1061no—
235C22⋊Q8—1061no—
236C22⋊Q8—2121no—
237C22⋊Q8—2121no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—1061no—
240C2×C4⋊C4—1064no—
241C2×C4⋊C4—1061no—
242C2×C4⋊C4—2121no—
243C2×C4⋊C4—2122no—
244C2×C4⋊C4—2121no—
245C2×C22⋊C4—2121no—
246C2×C16—21no—
247C2×C16—1061no—
248C2×C16—2122no—
249#107—531no—
250#107—1061no—
251#107C4×D5311yescharacteristic, complemented
252#103—21no—
253#103—1061no—
254#103—1061no—
255#103—1061no—
256C24—531no—
257C2×Q8—21no—
258C2×Q8—1061no—
259C2×Q8—2121no—
260C2×Q8—2122no—
261C2×Q8—2122no—
262C22×C4—41no—
263C22×C4—531no—
264C22×C4—531no—
265C22×C4—531no—
266C22×C4—531no—
267C22×C4—531no—
268C22×C4—1062no—
269C22×C4—1062no—
270C22×C4—4242no—
271C22×C4—4242no—
272C22×C4—2121no—
273C22×C4—2121no—
274C22×C4—2124no—
275C22×C4—2121no—
276C22×C4D4×D5311yescharacteristic
277Q16—41no—
278Q16—2121no—
279Q16—2122no—
280C2×C8—41no—
281C2×C8—531no—
282C2×C8—531no—
283C2×C8—1062no—
284C2×C8—1062no—
285C2×C8—2121no—
286C2×C8—2121no—
287C2×C8—2121no—
288C2×C8C2×C4×D5311yescharacteristic
289C2×C8D4×D5311yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—1062no—
295C4⋊C4—1061no—
296C4⋊C4—2121no—
297C4⋊C4—2121no—
298C4⋊C4—2121no—
299C4⋊C4—2121no—
300C4⋊C4—2124no—
301C4⋊C4—2121no—
302C22⋊C4—41no—
303C22⋊C4—2121no—
304C22⋊C4—2121no—
305C22⋊C4—2121no—
306C16—41no—
307C16—2121no—
308C23—531no—
309C23—532no—
310C23—532no—
311C23—531no—
312C23—1062no—
313C23—1062no—
314C23D8×D5311yescharacteristic
315Q8—41no—
316Q8—41no—
317Q8—4242no—
318Q8—2121no—
319Q8—2121no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—531no—
328C2×C4—532no—
329C2×C4—532no—
330C2×C4—531no—
331C2×C4—1062no—
332C2×C4—1062no—
333C2×C4—1062no—
334C2×C4—1061no—
335C2×C4—1061no—
336C2×C4—4242no—
337C2×C4—4242no—
338C2×C4—4248no—
339C2×C4—4241no—
340C2×C4—4241no—
341C2×C4—2122no—
342C2×C4—2121no—
343C2×C4—2121no—
344C2×C4C22⋊C4×D5311yescharacteristic
345C2×C4SD16×D5311yescharacteristic
346C8—21no—
347C8—21no—
348C8—1061no—
349C8—1061no—
350C22—21no—
351C22—21no—
352C22—532no—
353C22—532no—
354C22—532no—
355C22—532no—
356C22—1064no—
357C22—1064no—
358C22—1061no—
359C22—1061no—
360C22#102×D5311yescharacteristic
361C22SD32×D5311yescharacteristic
362C22Q32×D5311yescharacteristic
363C4—21no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—532no—
368C4—1061no—
369C4—4242no—
370C4—4241no—
371C4—4241no—
372C4#99×D5311yescharacteristic
373C4#104×D5311yescharacteristic
374C2—21no—
375C2—21no—
376C2—534no—
377C2—1062no—
378C2#327×D5311yescharacteristic
379C2#358×D5311yescharacteristic
380C2#360×D5311yescharacteristic
subgroupG/H
centerC22#102×D53
commutatorC2×C8×C53C22×C4
FrattiniC22×C8C22×D53
FittingC53×#1348C2
socleC22×C53C2×#102
prime radicalC23×D53D8
cosocleC22×C8×C53C23
hypercenter#1348D53
hypocenterC53C2×#1348
LCSG ▷ C2×C8×C53 ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
4. #20272728C2semidirect
5. #20272727C2semidirect
6. #20272726C2semidirect
7. C53×#1348C2semidirect
8. C2×Q16×D53C4semidirect
13. #16810865C4semidirect
17. #16810861C4semidirect
18. #107×D53C4semidirect
30. C2×Dic212C2×C4semidirect
53. #13133151C2×C4semidirect
58. C2×Q16×C53C2×C4semidirect
63. #107×C53C2×C4semidirect
190. #1348D53direct (N × H)
197. D53#1348direct (N × H)
217. C53C2×#1348semidirect
224. C2×Q16C4×D53semidirect
251. #107C4×D53semidirect

Maximal subgroups

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

subgroupindex
#467×D532
C22⋊C16×D532
#340×D532
#202727282
#202727272
#202727262
C53×#13482
C2×#134853