Finite Group Databasebeta

← D53⋊#1348 #28308849

Subgroups — D53⋊#1348 #28308849

Order 13568.

506 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D53⋊(C22⋊C16)C211yesmaximal, characteristic
2C2×#16811497C211yesmaximal, characteristic
3#20289704C212yesmaximal, complemented
4#20289703C212yesmaximal, complemented
5#467×D53C211yesmaximal, characteristic
6C22×C4⋊#6157—21no—
7C2×D53⋊C16—21no—
8#16811518C2212yes—
9C22⋊#11719910—21no—
10#16811497—21no—
11#16811497C2212yes—
12C2×Q16×D53C411yescharacteristic, complemented
13C22×C8×D53C2211yescharacteristic
14C22⋊Q8×D53—21no—
15#16810865C2211yescharacteristic
16#16810864C411yescharacteristic, complemented
17#16810863—21no—
18#16810862—21no—
19#16810861C2211yescharacteristic
20#107×D53C411yescharacteristic, complemented
21#103×D53—21no—
22C53×#467C411yescharacteristic, complemented
23C23×#6157—41no—
24C2×C4⋊#6157—24no—
25C2×C4⋊#6157—22no—
26C2×C4⋊#6157—42no—
27C2×C4⋊#6157—41no—
28D53⋊C16—42no—
29C2×#11719910—22no—
30C2×Q8×D53—21no—
31C22×C4×D53D411yescharacteristic
32C2×Dic212C2×C411yescharacteristic, complemented
33C2×#11719925—21no—
34Q16×D53—42no—
35C22×#88322D411yescharacteristic
36C2×C8×D53—42no—
37C2×C8×D53C2×C411yescharacteristic
38C2×C8×D53D411yescharacteristic
39C2×C8×D53D411yescharacteristic
40C2×C8×D53C2311yescharacteristic
41#13133197—21no—
42#13133196—21no—
43#13133195—41no—
44#13133194—41no—
45#13133193—21no—
46C4⋊C4×D53—21no—
47C4⋊C4×D53—41no—
48C22⋊C4×D53—41no—
49#13133151C2×C411yescharacteristic, complemented
50#13133150—21no—
51#13133142—21no—
52#13133141—21no—
53#13133140—21no—
54C2×Q16×C53C2×C411yescharacteristic, complemented
55C22×C8×C53C2×C411yescharacteristic
56C22⋊Q8×C53—21no—
57#107×C53C2×C411yescharacteristic, complemented
58#103×C53—21no—
59C23×D53D811yescharacteristic
60C22×#6157—44no—
61C22×#6157—42no—
62C22×#6157—82no—
63C22×#6157—82no—
64C2×Q8×C53—21no—
65C22×C4×C53C22⋊C411yescharacteristic
66C22×Dic53SD1611yescharacteristic
67Q8×D53—42no—
68Q8×D53—42no—
69C2×C4×D53—22no—
70C2×C4×D53—22no—
71C2×C4×D53—41no—
72C2×C4×D53—41no—
73C2×C4×D53C22⋊C411yescharacteristic
74C2×C4×D53D811yescharacteristic
75C2×C4×D53SD1611yescharacteristic
76C2×C4×D53C2×D411yescharacteristic
77C2×Dic106—21no—
78C2×Dic106—41no—
79C4⋊#6157—24no—
80C4⋊#6157—42no—
81C4⋊#6157—44no—
82Q16×C53—41no—
83C2×C8×C53—41no—
84C2×C8×C53C22⋊C411yescharacteristic
85C2×C8×C53C22×C411yescharacteristic
86C4⋊C4×C53—21no—
87C4⋊C4×C53—41no—
88C22⋊C4×C53—41no—
89C22⋊Dic53—41no—
90#11719925—42no—
91#11719921—41no—
92#11719921—41no—
93C4⋊Dic53—21no—
94C4⋊Dic53—41no—
95#11719919—41no—
96#11719919—41no—
97#11719919—41no—
98C2×#88322—41no—
99C2×#88322C22⋊C411yescharacteristic
100C2×#88322C2×D411yescharacteristic
101Dic212—41no—
102C8×D53—22no—
103C8×D53—22no—
104C8×D53—41no—
105C8×D53—41no—
106#11719910—42no—
107C23×C53#10211yescharacteristic
108C22×D53—22no—
109C22×D53—22no—
110C22×D53#10211yescharacteristic
111C22×D53SD3212yes—
112C22×D53Q3212yes—
113C22×D53C2×D811yescharacteristic
114C2×#6157—44no—
115C2×#6157—82no—
116C2×#6157—88no—
117C2×#6157—82no—
118Q8×C53—41no—
119Q8×C53—41no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—41no—
123C2×C4×C53—41no—
124C2×C4×C53#10211yescharacteristic
125C2×C4×C53C2×C22⋊C411yescharacteristic
126C2×Dic53—22no—
127C2×Dic53—41no—
128C2×Dic53—41no—
129C2×Dic53#10211yescharacteristic
130C2×Dic53C2×SD1611yescharacteristic
131C4×D53—22no—
132C4×D53—21no—
133C4×D53—21no—
134C4×D53—22no—
135C4×D53—82no—
136C4×D53—82no—
137C4×D53#9912yes—
138C4×D53#10412yes—
139Dic106—41no—
140Dic106—41no—
141Dic106—82no—
142C8×C53—21no—
143C8×C53—21no—
144#88322—21no—
145#88322—21no—
146C2×#1348—531nomaximal, Sylow
147C22×C53—21no—
148C22×C53—21no—
149C22×C53#35812yes—
150C22×C53C2×#10211yescharacteristic
151C2×D53—21no—
152C2×D53—21no—
153C2×D53—24no—
154C2×D53—24no—
155C2×D53#32712yes—
156C2×D53#35812yes—
157C2×D53#36012yes—
158C2×D53C2×SD3211yescharacteristic
159C2×D53C2×Q3211yescharacteristic
160#6157—84no—
161C4×C53—21no—
162C4×C53—81no—
163C4×C53—81no—
164C4×C53C2×#9911yescharacteristic
165C4×C53C2×#10411yescharacteristic
166Dic53—21no—
167Dic53—81no—
168Dic53—81no—
169Dic53#32712yes—
170C2×#467—531no—
171C2×C22⋊C16—531no—
172C2×#340—531no—
173#1348—532no—
174#1348—532no—
175C2×C53—22no—
176C2×C53C2×#32711yescharacteristic
177C2×C53C2×#35811yescharacteristic
178C2×C53C2×#36011yescharacteristic
179D53—21no—
180D53—21no—
181D53#134814yescomplemented
182C22×Q16—531no—
183C23×C8—531no—
184C2×C22⋊Q8—1061no—
185C22×C4⋊C4—1061no—
186C22×C16—1061no—
187#467—531no—
188#467—531no—
189#467—531no—
190#467—1061no—
191#467—1061no—
192#467#615711yescharacteristic, complemented
193C2×#107—531no—
194C2×#103—1061no—
195C22⋊C16—532no—
196C22⋊C16—1061no—
197#340—532no—
198#340—1061no—
199C53C2×#134811yescharacteristic, complemented, Sylow
200C22×Q8—1061no—
201C23×C4—531no—
202C23×C4—2121no—
203C2×Q16—531no—
204C2×Q16—1061no—
205C2×Q16—2122no—
206C2×Q16C2×#615711yescharacteristic, complemented
207C22×C8—531no—
208C22×C8—531no—
209C22×C8—531no—
210C22×C8—531no—
211C22×C8—531no—
212C22×C8—2122no—
213C22×C8C2×#615711yescharacteristic
214C22⋊Q8—21no—
215C22⋊Q8—1061no—
216C22⋊Q8—1061no—
217C22⋊Q8—1061no—
218C22⋊Q8—2121no—
219C22⋊Q8—2121no—
220C2×C4⋊C4—1061no—
221C2×C4⋊C4—1062no—
222C2×C4⋊C4—1064no—
223C2×C4⋊C4—2121no—
224C2×C4⋊C4—2121no—
225C2×C4⋊C4—2122no—
226C2×C22⋊C4—2121no—
227C2×C16—1062no—
228C2×C16—2122no—
229#107—531no—
230#107—1061no—
231#107C2×#615711yescharacteristic, complemented
232#103—21no—
233#103—1061no—
234#103—1061no—
235#103—1061no—
236C24—531no—
237C2×Q8—21no—
238C2×Q8—1061no—
239C2×Q8—2121no—
240C2×Q8—2122no—
241C2×Q8—2122no—
242C22×C4—531no—
243C22×C4—531no—
244C22×C4—531no—
245C22×C4—531no—
246C22×C4—531no—
247C22×C4—1062no—
248C22×C4—1062no—
249C22×C4—4242no—
250C22×C4—4242no—
251C22×C4—2121no—
252C22×C4—2121no—
253C22×C4—2122no—
254C22×C4—2124no—
255C22×C4C22⋊#615711yescharacteristic
256Q16—41no—
257Q16—2121no—
258Q16—2122no—
259C2×C8—41no—
260C2×C8—531no—
261C2×C8—531no—
262C2×C8—1062no—
263C2×C8—1062no—
264C2×C8—2121no—
265C2×C8—2121no—
266C2×C8—2121no—
267C2×C8C22⋊#615711yescharacteristic
268C2×C8C22×#615711yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—1064no—
272C4⋊C4—1061no—
273C4⋊C4—2121no—
274C4⋊C4—2121no—
275C4⋊C4—2121no—
276C4⋊C4—2124no—
277C4⋊C4—2122no—
278C4⋊C4—2121no—
279C22⋊C4—41no—
280C22⋊C4—2121no—
281C22⋊C4—2121no—
282C22⋊C4—2121no—
283C16—2122no—
284C23—531no—
285C23—532no—
286C23—532no—
287C23—531no—
288C23—1062no—
289C23—1062no—
290C23#1313327911yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—4242no—
294Q8—2121no—
295Q8—2121no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—531no—
301C2×C4—532no—
302C2×C4—532no—
303C2×C4—531no—
304C2×C4—1062no—
305C2×C4—1062no—
306C2×C4—1062no—
307C2×C4—1061no—
308C2×C4—1061no—
309C2×C4—4242no—
310C2×C4—4242no—
311C2×C4—4242no—
312C2×C4—4248no—
313C2×C4—4242no—
314C2×C4—2124no—
315C2×C4—2121no—
316C2×C4—2121no—
317C2×C4#1313327911yescharacteristic
318C2×C4C2×C22⋊#615711yescharacteristic
319C8—21no—
320C8—21no—
321C8—1061no—
322C8—1061no—
323C22—21no—
324C22—21no—
325C22—532no—
326C22—532no—
327C22—532no—
328C22—531no—
329C22—531no—
330C22—1064no—
331C22—1064no—
332C22—1061no—
333C22—1061no—
334C22#1681153612yes—
335C22C2×#1313327911yescharacteristic
336C4—21no—
337C4—81no—
338C4—81no—
339C4—532no—
340C4—1061no—
341C4—4244no—
342C4—4241no—
343C4—4241no—
344C4D53⋊#9911yescharacteristic
345C4D53⋊#10411yescharacteristic
346C2—22no—
347C2—534no—
348C2—1061no—
349C2—1061no—
350C2D53⋊#32711yescharacteristic
351C2C2×#1681153611yescharacteristic
352C2D53⋊#36011yescharacteristic
subgroupG/H
centerC22C2×#13133279
commutatorC2×C8×C53C22×C4
FrattiniC2×C8C22×#6157
FittingC53×#467C4
socleC22×C53C2×#102
prime radicalC23×D53D8
cosocleC2×C8×D53C23
hypercenter#467#6157
hypocenterC53C2×#1348
LCSG ▷ C2×C8×C53 ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #20289704C2semidirect
4. #20289703C2semidirect
12. C2×Q16×D53C4semidirect
16. #16810864C4semidirect
20. #107×D53C4semidirect
22. C53×#467C4semidirect
32. C2×Dic212C2×C4semidirect
49. #13133151C2×C4semidirect
54. C2×Q16×C53C2×C4semidirect
57. #107×C53C2×C4semidirect
181. D53#1348semidirect
192. #467#6157semidirect
199. C53C2×#1348semidirect
206. C2×Q16C2×#6157semidirect
231. #107C2×#6157semidirect

Maximal subgroups

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

subgroupindex
D53⋊(C22⋊C16)2
C2×#168114972
#202897042
#202897032
#467×D532
C2×#134853