Finite Group Databasebeta

← D59×#2842 #28795098

Subgroups — D59×#2842 #28795098

Order 15104.

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#21432361C214yesmaximal, complemented
2#21432360C213yesmaximal, complemented
3#21432359C218yesmaximal, complemented
4#399×D59C214yesmaximal, complemented
5#396×D59C218yesmaximal, complemented
6#379×D59C213yesmaximal
7C59×#2842C211yesmaximal, characteristic, complemented
8C25×D59C2211yescharacteristic
9C2×C4⋊C4×D59C22112yescomplemented
10C2×C22⋊C4×D59C22112yes—
11C2×C22⋊C4×D59C2216yes—
12#16837339C2214yescomplemented
13#16837338C22112yescomplemented
14#16837337C22112yescomplemented
15#16837326C2218yescomplemented
16#16837325C22124yescomplemented
17#16837324C22124yescomplemented
18#16837258C2213yes—
19#16837257C22112yes—
20#16837257C2216yes—
21#95×D59C2214yescomplemented
22C59×#399C2214yescomplemented
23C59×#396C2218yescomplemented
24C59×#379C2213yes—
25C24×D59—412no—
26C24×D59Q818yes—
27C24×D59C2312yes—
28C24×D59C2311yescharacteristic
29C24×D59C2312yes—
30C24×D59C2311yescharacteristic
31C22×C4×D59C23112yes—
32C2×C4⋊Dic59C23112yescomplemented
33C2×Dic59⋊C4C23124yescomplemented
34C4⋊C4×D59—424no—
35C2×C22⋊Dic59C23112yes—
36C2×C22⋊Dic59C2316yes—
37C2×(C2×D59)⋊C4C23124yes—
38C2×(C2×D59)⋊C4C23112yes—
39C22⋊C4×D59—424no—
40C22⋊C4×D59—412no—
41C59⋊#95C23112yescomplemented
42C25×C59C2311yescharacteristic
43C2×C4⋊C4×C59C23112yescomplemented
44C2×C22⋊C4×C59C23112yes—
45C2×C22⋊C4×C59C2316yes—
46#95×C59C2314yescomplemented
47C24×C59—46no—
48C24×C59C2×Q814yes—
49C24×C59C2412yes—
50C24×C59C2411yescharacteristic
51C23×D59—224no—
52C23×D59—212no—
53C23×D59—448no—
54C23×D59—412no—
55C23×D59—46no—
56C23×D59—464no—
57C23×D59C2×Q818yes—
58C23×D59C2×Q814yes—
59C23×D59C2×Q818yes—
60C23×D59C2×Q814yes—
61C23×D59C2412yes—
62C23×D59C2411yescharacteristic
63C23×D59C2411yescharacteristic
64C22×C4×C59C24112yes—
65C22×Dic59C24112yes—
66C2×C4×D59—224no—
67C2×C4×D59—248no—
68C4⋊C4×C59—412no—
69C22⋊C4×C59—412no—
70C22⋊C4×C59—46no—
71C22⋊Dic59—46no—
72C22⋊Dic59—412no—
73(C2×D59)⋊C4—412no—
74(C2×D59)⋊C4—424no—
75C4⋊Dic59—412no—
76Dic59⋊C4—424no—
77C23×C59—26no—
78C23×C59—212no—
79C23×C59—412no—
80C23×C59—416no—
81C23×C59C22×Q814yes—
82C23×C59C22×Q812yes—
83C23×C59C2511yescharacteristic
84C22×D59—26no—
85C22×D59—212no—
86C22×D59—248no—
87C22×D59—224no—
88C22×D59—424no—
89C22×D59—412no—
90C22×D59—432no—
91C22×D59—416no—
92C22×D59—4128no—
93C22×D59—432no—
94C22×D59—416no—
95C22×D59C22×Q814yes—
96C22×D59C22×Q812yes—
97C22×D59C22×Q812yes—
98C22×D59H(5,𝔽2)112yes—
99C2×C4×C59—224no—
100C2×C4×C59—212no—
101C2×Dic59—212no—
102C2×Dic59—224no—
103C4×D59—448no—
104C2×#2842—591nomaximal, Sylow
105C22×C59—26no—
106C22×C59—212no—
107C22×C59—416no—
108C22×C59—44no—
109C22×C59—48no—
110C22×C59C23×Q811yescharacteristic
111C22×C59C2×H(5,𝔽2)16yes—
112C2×D59—26no—
113C2×D59—212no—
114C2×D59—432no—
115C2×D59—416no—
116C2×D59—44no—
117C2×D59—48no—
118C2×D59—432no—
119C2×D59—416no—
120C2×D59#543112yes—
121C2×D59#560116yes—
122C4×C59—412no—
123Dic59—412no—
124#2842—594no—
125#2842—598no—
126#2842—593no—
127#2842D5911yescharacteristic, direct product factor
128C2×#399—594no—
129C2×#396—598no—
130C2×#379—593no—
131C2×C59—42no—
132C2×C59—44no—
133C2×C59C2×#54313yes—
134C2×C59C2×#56014yes—
135D59—42no—
136D59—44no—
137D59#284218yesdirect product factor
138C26—591no—
139C22×C4⋊C4—5912no—
140C22×C22⋊C4—5912no—
141C22×C22⋊C4—596no—
142#399—5912no—
143#399—5912no—
144#399—594no—
145#399C2×D5914yescomplemented
146#396—5924no—
147#396—5924no—
148#396—598no—
149#396C2×D5918yescomplemented
150#379—593no—
151#379—5912no—
152#379—596no—
153#379C2×D5913yes—
154C2×#95—594no—
155C59C2×#284211yescharacteristic, complemented, Sylow
156C25—592no—
157C25—591no—
158C25—598no—
159C25—591no—
160C25—592no—
161C25—23612no—
162C25C22×D5911yescharacteristic
163C23×C4—5912no—
164C2×C4⋊C4—5924no—
165C2×C4⋊C4—5912no—
166C2×C4⋊C4—23624no—
167C2×C4⋊C4C22×D59112yescomplemented
168C2×C22⋊C4—5912no—
169C2×C22⋊C4—596no—
170C2×C22⋊C4—5924no—
171C2×C22⋊C4—5912no—
172C2×C22⋊C4—23624no—
173C2×C22⋊C4—23612no—
174C2×C22⋊C4C22×D59112yes—
175C2×C22⋊C4C22×D5916yes—
176#95—5912no—
177#95C22×D5914yescomplemented
178C24—46no—
179C24—591no—
180C24—598no—
181C24—594no—
182C24—592no—
183C24—591no—
184C24—594no—
185C24—598no—
186C24—11824no—
187C24—11812no—
188C24—23612no—
189C24—2366no—
190C24—23648no—
191C24—23664no—
192C24Q8×D5914yes—
193C24C23×D5912yes—
194C24C23×D5911yescharacteristic
195C22×C4—5912no—
196C22×C4—11848no—
197C22×C4—11824no—
198C22×C4C23×D59112yes—
199C4⋊C4—412no—
200C4⋊C4—23624no—
201C4⋊C4—23612no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—23624no—
205C22⋊C4—23612no—
206C22⋊C4—23612no—
207C22⋊C4—2366no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—592no—
213C23—5912no—
214C23—594no—
215C23—592no—
216C23—11848no—
217C23—11824no—
218C23—11812no—
219C23—1186no—
220C23—23624no—
221C23—23612no—
222C23—23632no—
223C23—23616no—
224C23—236128no—
225C23—23632no—
226C23—23616no—
227C23C2×Q8×D5914yes—
228C23C2×Q8×D5912yes—
229C23C24×D5911yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—11812no—
233C2×C4—11824no—
234C2×C4—23648no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—5916no—
241C22—5912no—
242C22—11812no—
243C22—1186no—
244C22—23632no—
245C22—23616no—
246C22—23632no—
247C22—23616no—
248C22—2368no—
249C22—2364no—
250C22C22×Q8×D5911yescharacteristic
251C22H(5,𝔽2)×D5916yes—
252C4—412no—
253C4—23612no—
254C2—44no—
255C2—42no—
256C2—598no—
257C2—2364no—
258C2—2362no—
259C2#543×D5913yes—
260C2#560×D5914yes—
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2842C2
prime radicalC25×D59C22
hypercenter#2842D59
hypocenterC59C2×#2842
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #21432361C2semidirect
2. #21432360C2semidirect
3. #21432359C2semidirect
4. #399×D59C2semidirect
5. #396×D59C2semidirect
7. C59×#2842C2semidirect
9. C2×C4⋊C4×D59C22semidirect
12. #16837339C22semidirect
13. #16837338C22semidirect
14. #16837337C22semidirect
15. #16837326C22semidirect
16. #16837325C22semidirect
17. #16837324C22semidirect
21. #95×D59C22semidirect
22. C59×#399C22semidirect
23. C59×#396C22semidirect
32. C2×C4⋊Dic59C23semidirect
33. C2×Dic59⋊C4C23semidirect
41. C59⋊#95C23semidirect
43. C2×C4⋊C4×C59C23semidirect
46. #95×C59C23semidirect
127. #2842D59direct (N × H)
137. D59#2842direct (N × H)
145. #399C2×D59semidirect
149. #396C2×D59semidirect
155. C59C2×#2842semidirect
167. C2×C4⋊C4C22×D59semidirect
177. #95C22×D59semidirect

Maximal subgroups

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

subgroupindex
#214323612
#214323602
#214323592
#399×D592
#396×D592
#379×D592
C59×#28422
C2×#284259