Finite Group Databasebeta

← D53×#2842 #27590501

Subgroups — D53×#2842 #27590501

Order 13568.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 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#20282980C214yesmaximal, complemented
2#20282979C213yesmaximal, complemented
3#20282978C218yesmaximal, complemented
4#399×D53C214yesmaximal, complemented
5#396×D53C218yesmaximal, complemented
6#379×D53C213yesmaximal
7C53×#2842C211yesmaximal, characteristic, complemented
8C25×D53C2211yescharacteristic
9C2×C4⋊C4×D53C22112yescomplemented
10C2×C22⋊C4×D53C22112yes—
11C2×C22⋊C4×D53C2216yes—
12#16810560C2214yescomplemented
13#16810559C22112yescomplemented
14#16810558C22112yescomplemented
15#16810547C2218yescomplemented
16#16810546C22124yescomplemented
17#16810545C22124yescomplemented
18#16810479C2213yes—
19#16810478C22112yes—
20#16810478C2216yes—
21#95×D53C2214yescomplemented
22C53×#399C2214yescomplemented
23C53×#396C2218yescomplemented
24C53×#379C2213yes—
25C24×D53—412no—
26C24×D53Q818yes—
27C24×D53C2312yes—
28C24×D53C2311yescharacteristic
29C24×D53C2312yes—
30C24×D53C2311yescharacteristic
31C22×C4×D53C23112yes—
32C2×C4⋊Dic53C23112yescomplemented
33C2×#11719919C23124yescomplemented
34C4⋊C4×D53—424no—
35C2×C22⋊Dic53C23112yes—
36C2×C22⋊Dic53C2316yes—
37C2×#11719921C23124yes—
38C2×#11719921C23112yes—
39C22⋊C4×D53—424no—
40C22⋊C4×D53—412no—
41#13133124C23112yescomplemented
42C25×C53C2311yescharacteristic
43C2×C4⋊C4×C53C23112yescomplemented
44C2×C22⋊C4×C53C23112yes—
45C2×C22⋊C4×C53C2316yes—
46#95×C53C2314yescomplemented
47C24×C53—46no—
48C24×C53C2×Q814yes—
49C24×C53C2412yes—
50C24×C53C2411yescharacteristic
51C23×D53—224no—
52C23×D53—212no—
53C23×D53—448no—
54C23×D53—412no—
55C23×D53—46no—
56C23×D53—464no—
57C23×D53C2×Q818yes—
58C23×D53C2×Q814yes—
59C23×D53C2×Q818yes—
60C23×D53C2×Q814yes—
61C23×D53C2412yes—
62C23×D53C2411yescharacteristic
63C23×D53C2411yescharacteristic
64C22×C4×C53C24112yes—
65C22×Dic53C24112yes—
66C2×C4×D53—224no—
67C2×C4×D53—248no—
68C4⋊C4×C53—412no—
69C22⋊C4×C53—412no—
70C22⋊C4×C53—46no—
71C22⋊Dic53—46no—
72C22⋊Dic53—412no—
73#11719921—412no—
74#11719921—424no—
75C4⋊Dic53—412no—
76#11719919—424no—
77C23×C53—212no—
78C23×C53—26no—
79C23×C53—412no—
80C23×C53—416no—
81C23×C53C22×Q814yes—
82C23×C53C22×Q812yes—
83C23×C53C2511yescharacteristic
84C22×D53—212no—
85C22×D53—26no—
86C22×D53—248no—
87C22×D53—224no—
88C22×D53—424no—
89C22×D53—412no—
90C22×D53—432no—
91C22×D53—416no—
92C22×D53—4128no—
93C22×D53—432no—
94C22×D53—416no—
95C22×D53C22×Q814yes—
96C22×D53C22×Q812yes—
97C22×D53C22×Q812yes—
98C22×D53H(5,𝔽2)112yes—
99C2×C4×C53—224no—
100C2×C4×C53—212no—
101C2×Dic53—212no—
102C2×Dic53—224no—
103C4×D53—448no—
104C2×#2842—531nomaximal, Sylow
105C22×C53—212no—
106C22×C53—26no—
107C22×C53—416no—
108C22×C53—48no—
109C22×C53—44no—
110C22×C53C23×Q811yescharacteristic
111C22×C53C2×H(5,𝔽2)16yes—
112C2×D53—212no—
113C2×D53—26no—
114C2×D53—432no—
115C2×D53—416no—
116C2×D53—48no—
117C2×D53—44no—
118C2×D53—432no—
119C2×D53—416no—
120C2×D53#543112yes—
121C2×D53#560116yes—
122C4×C53—412no—
123Dic53—412no—
124#2842—534no—
125#2842—538no—
126#2842—533no—
127#2842D5311yescharacteristic, direct product factor
128C2×#399—534no—
129C2×#396—538no—
130C2×#379—533no—
131C2×C53—44no—
132C2×C53—42no—
133C2×C53C2×#54313yes—
134C2×C53C2×#56014yes—
135D53—44no—
136D53—42no—
137D53#284218yesdirect product factor
138C26—531no—
139C22×C4⋊C4—5312no—
140C22×C22⋊C4—5312no—
141C22×C22⋊C4—536no—
142#399—5312no—
143#399—5312no—
144#399—534no—
145#399C2×D5314yescomplemented
146#396—5324no—
147#396—5324no—
148#396—538no—
149#396C2×D5318yescomplemented
150#379—533no—
151#379—5312no—
152#379—536no—
153#379C2×D5313yes—
154C2×#95—534no—
155C53C2×#284211yescharacteristic, complemented, Sylow
156C25—532no—
157C25—531no—
158C25—538no—
159C25—531no—
160C25—532no—
161C25—21212no—
162C25C22×D5311yescharacteristic
163C23×C4—5312no—
164C2×C4⋊C4—5324no—
165C2×C4⋊C4—5312no—
166C2×C4⋊C4—21224no—
167C2×C4⋊C4C22×D53112yescomplemented
168C2×C22⋊C4—5312no—
169C2×C22⋊C4—536no—
170C2×C22⋊C4—5324no—
171C2×C22⋊C4—5312no—
172C2×C22⋊C4—21224no—
173C2×C22⋊C4—21212no—
174C2×C22⋊C4C22×D53112yes—
175C2×C22⋊C4C22×D5316yes—
176#95—5312no—
177#95C22×D5314yescomplemented
178C24—46no—
179C24—531no—
180C24—538no—
181C24—534no—
182C24—532no—
183C24—531no—
184C24—534no—
185C24—538no—
186C24—10624no—
187C24—10612no—
188C24—21212no—
189C24—2126no—
190C24—21248no—
191C24—21264no—
192C24Q8×D5314yes—
193C24C23×D5312yes—
194C24C23×D5311yescharacteristic
195C22×C4—5312no—
196C22×C4—10648no—
197C22×C4—10624no—
198C22×C4C23×D53112yes—
199C4⋊C4—412no—
200C4⋊C4—21224no—
201C4⋊C4—21212no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—21224no—
205C22⋊C4—21212no—
206C22⋊C4—21212no—
207C22⋊C4—2126no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—532no—
213C23—5312no—
214C23—534no—
215C23—532no—
216C23—10648no—
217C23—10624no—
218C23—10612no—
219C23—1066no—
220C23—21224no—
221C23—21212no—
222C23—21232no—
223C23—21216no—
224C23—212128no—
225C23—21232no—
226C23—21216no—
227C23C2×Q8×D5314yes—
228C23C2×Q8×D5312yes—
229C23C24×D5311yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—10612no—
233C2×C4—10624no—
234C2×C4—21248no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—5316no—
241C22—5312no—
242C22—10612no—
243C22—1066no—
244C22—21232no—
245C22—21216no—
246C22—21232no—
247C22—21216no—
248C22—2128no—
249C22—2124no—
250C22C22×Q8×D5311yescharacteristic
251C22H(5,𝔽2)×D5316yes—
252C4—412no—
253C4—21212no—
254C2—44no—
255C2—42no—
256C2—538no—
257C2—2124no—
258C2—2122no—
259C2#543×D5313yes—
260C2#560×D5314yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2842C2
prime radicalC25×D53C22
hypercenter#2842D53
hypocenterC53C2×#2842
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #20282980C2semidirect
2. #20282979C2semidirect
3. #20282978C2semidirect
4. #399×D53C2semidirect
5. #396×D53C2semidirect
7. C53×#2842C2semidirect
9. C2×C4⋊C4×D53C22semidirect
12. #16810560C22semidirect
13. #16810559C22semidirect
14. #16810558C22semidirect
15. #16810547C22semidirect
16. #16810546C22semidirect
17. #16810545C22semidirect
21. #95×D53C22semidirect
22. C53×#399C22semidirect
23. C53×#396C22semidirect
32. C2×C4⋊Dic53C23semidirect
33. C2×#11719919C23semidirect
41. #13133124C23semidirect
43. C2×C4⋊C4×C53C23semidirect
46. #95×C53C23semidirect
127. #2842D53direct (N × H)
137. D53#2842direct (N × H)
145. #399C2×D53semidirect
149. #396C2×D53semidirect
155. C53C2×#2842semidirect
167. C2×C4⋊C4C22×D53semidirect
177. #95C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202829802
#202829792
#202829782
#399×D532
#396×D532
#379×D532
C53×#28422
C2×#284253