Finite Group Databasebeta

← D47×#2842 #26422687

Subgroups — D47×#2842 #26422687

Order 12032.

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#20251653C214yesmaximal, complemented
2#20251652C213yesmaximal, complemented
3#20251651C218yesmaximal, complemented
4#399×D47C214yesmaximal, complemented
5#396×D47C218yesmaximal, complemented
6#379×D47C213yesmaximal
7C47×#2842C211yesmaximal, characteristic, complemented
8C25×D47C2211yescharacteristic
9C2×C4⋊C4×D47C22112yescomplemented
10C2×C22⋊C4×D47C22112yes—
11C2×C22⋊C4×D47C2216yes—
12#15689060C2214yescomplemented
13#15689059C22112yescomplemented
14#15689058C22112yescomplemented
15#15689047C2218yescomplemented
16#15689046C22124yescomplemented
17#15689045C22124yescomplemented
18#15688979C2213yes—
19#15688978C22112yes—
20#15688978C2216yes—
21#95×D47C2214yescomplemented
22C47×#399C2214yescomplemented
23C47×#396C2218yescomplemented
24C47×#379C2213yes—
25C24×D47—412no—
26C24×D47Q818yes—
27C24×D47C2312yes—
28C24×D47C2311yescharacteristic
29C24×D47C2312yes—
30C24×D47C2311yescharacteristic
31C22×C4×D47C23112yes—
32C2×C4⋊Dic47C23112yescomplemented
33C2×Dic47⋊C4C23124yescomplemented
34C4⋊C4×D47—424no—
35C2×C22⋊Dic47C23112yes—
36C2×C22⋊Dic47C2316yes—
37C2×(C2×D47)⋊C4C23124yes—
38C2×(C2×D47)⋊C4C23112yes—
39C22⋊C4×D47—424no—
40C22⋊C4×D47—412no—
41C47⋊#95C23112yescomplemented
42C25×C47C2311yescharacteristic
43C2×C4⋊C4×C47C23112yescomplemented
44C2×C22⋊C4×C47C23112yes—
45C2×C22⋊C4×C47C2316yes—
46#95×C47C2314yescomplemented
47C24×C47—46no—
48C24×C47C2×Q814yes—
49C24×C47C2412yes—
50C24×C47C2411yescharacteristic
51C23×D47—224no—
52C23×D47—212no—
53C23×D47—448no—
54C23×D47—412no—
55C23×D47—46no—
56C23×D47—464no—
57C23×D47C2×Q818yes—
58C23×D47C2×Q814yes—
59C23×D47C2×Q818yes—
60C23×D47C2×Q814yes—
61C23×D47C2412yes—
62C23×D47C2411yescharacteristic
63C23×D47C2411yescharacteristic
64C22×C4×C47C24112yes—
65C22×Dic47C24112yes—
66C2×C4×D47—224no—
67C2×C4×D47—248no—
68C4⋊C4×C47—412no—
69C22⋊C4×C47—412no—
70C22⋊C4×C47—46no—
71C22⋊Dic47—46no—
72C22⋊Dic47—412no—
73(C2×D47)⋊C4—412no—
74(C2×D47)⋊C4—424no—
75C4⋊Dic47—412no—
76Dic47⋊C4—424no—
77C23×C47—26no—
78C23×C47—212no—
79C23×C47—412no—
80C23×C47—416no—
81C23×C47C22×Q814yes—
82C23×C47C22×Q812yes—
83C23×C47C2511yescharacteristic
84C22×D47—26no—
85C22×D47—212no—
86C22×D47—248no—
87C22×D47—224no—
88C22×D47—424no—
89C22×D47—412no—
90C22×D47—432no—
91C22×D47—416no—
92C22×D47—4128no—
93C22×D47—432no—
94C22×D47—416no—
95C22×D47C22×Q814yes—
96C22×D47C22×Q812yes—
97C22×D47C22×Q812yes—
98C22×D47H(5,𝔽2)112yes—
99C2×C4×C47—224no—
100C2×C4×C47—212no—
101C2×Dic47—212no—
102C2×Dic47—224no—
103C4×D47—448no—
104C2×#2842—471nomaximal, Sylow
105C22×C47—26no—
106C22×C47—212no—
107C22×C47—416no—
108C22×C47—44no—
109C22×C47—48no—
110C22×C47C23×Q811yescharacteristic
111C22×C47C2×H(5,𝔽2)16yes—
112C2×D47—26no—
113C2×D47—212no—
114C2×D47—432no—
115C2×D47—416no—
116C2×D47—44no—
117C2×D47—48no—
118C2×D47—432no—
119C2×D47—416no—
120C2×D47#543112yes—
121C2×D47#560116yes—
122C4×C47—412no—
123Dic47—412no—
124#2842—474no—
125#2842—478no—
126#2842—473no—
127#2842D4711yescharacteristic, direct product factor
128C2×#399—474no—
129C2×#396—478no—
130C2×#379—473no—
131C2×C47—42no—
132C2×C47—44no—
133C2×C47C2×#54313yes—
134C2×C47C2×#56014yes—
135D47—42no—
136D47—44no—
137D47#284218yesdirect product factor
138C26—471no—
139C22×C4⋊C4—4712no—
140C22×C22⋊C4—4712no—
141C22×C22⋊C4—476no—
142#399—4712no—
143#399—4712no—
144#399—474no—
145#399C2×D4714yescomplemented
146#396—4724no—
147#396—4724no—
148#396—478no—
149#396C2×D4718yescomplemented
150#379—473no—
151#379—4712no—
152#379—476no—
153#379C2×D4713yes—
154C2×#95—474no—
155C47C2×#284211yescharacteristic, complemented, Sylow
156C25—472no—
157C25—471no—
158C25—478no—
159C25—471no—
160C25—472no—
161C25—18812no—
162C25C22×D4711yescharacteristic
163C23×C4—4712no—
164C2×C4⋊C4—4724no—
165C2×C4⋊C4—4712no—
166C2×C4⋊C4—18824no—
167C2×C4⋊C4C22×D47112yescomplemented
168C2×C22⋊C4—4712no—
169C2×C22⋊C4—476no—
170C2×C22⋊C4—4724no—
171C2×C22⋊C4—4712no—
172C2×C22⋊C4—18824no—
173C2×C22⋊C4—18812no—
174C2×C22⋊C4C22×D47112yes—
175C2×C22⋊C4C22×D4716yes—
176#95—4712no—
177#95C22×D4714yescomplemented
178C24—46no—
179C24—471no—
180C24—478no—
181C24—474no—
182C24—472no—
183C24—471no—
184C24—474no—
185C24—478no—
186C24—9424no—
187C24—9412no—
188C24—18812no—
189C24—1886no—
190C24—18848no—
191C24—18864no—
192C24Q8×D4714yes—
193C24C23×D4712yes—
194C24C23×D4711yescharacteristic
195C22×C4—4712no—
196C22×C4—9448no—
197C22×C4—9424no—
198C22×C4C23×D47112yes—
199C4⋊C4—412no—
200C4⋊C4—18824no—
201C4⋊C4—18812no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—18824no—
205C22⋊C4—18812no—
206C22⋊C4—18812no—
207C22⋊C4—1886no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—472no—
213C23—4712no—
214C23—474no—
215C23—472no—
216C23—9448no—
217C23—9424no—
218C23—9412no—
219C23—946no—
220C23—18824no—
221C23—18812no—
222C23—18832no—
223C23—18816no—
224C23—188128no—
225C23—18832no—
226C23—18816no—
227C23C2×Q8×D4714yes—
228C23C2×Q8×D4712yes—
229C23C24×D4711yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—9412no—
233C2×C4—9424no—
234C2×C4—18848no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—4712no—
241C22—4716no—
242C22—9412no—
243C22—946no—
244C22—18832no—
245C22—18816no—
246C22—18832no—
247C22—18816no—
248C22—1888no—
249C22—1884no—
250C22C22×Q8×D4711yescharacteristic
251C22H(5,𝔽2)×D4716yes—
252C4—412no—
253C4—18812no—
254C2—44no—
255C2—42no—
256C2—478no—
257C2—1884no—
258C2—1882no—
259C2#543×D4713yes—
260C2#560×D4714yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2842C2
prime radicalC25×D47C22
hypercenter#2842D47
hypocenterC47C2×#2842
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #20251653C2semidirect
2. #20251652C2semidirect
3. #20251651C2semidirect
4. #399×D47C2semidirect
5. #396×D47C2semidirect
7. C47×#2842C2semidirect
9. C2×C4⋊C4×D47C22semidirect
12. #15689060C22semidirect
13. #15689059C22semidirect
14. #15689058C22semidirect
15. #15689047C22semidirect
16. #15689046C22semidirect
17. #15689045C22semidirect
21. #95×D47C22semidirect
22. C47×#399C22semidirect
23. C47×#396C22semidirect
32. C2×C4⋊Dic47C23semidirect
33. C2×Dic47⋊C4C23semidirect
41. C47⋊#95C23semidirect
43. C2×C4⋊C4×C47C23semidirect
46. #95×C47C23semidirect
127. #2842D47direct (N × H)
137. D47#2842direct (N × H)
145. #399C2×D47semidirect
149. #396C2×D47semidirect
155. C47C2×#2842semidirect
167. C2×C4⋊C4C22×D47semidirect
177. #95C22×D47semidirect

Maximal subgroups

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

subgroupindex
#202516532
#202516522
#202516512
#399×D472
#396×D472
#379×D472
C47×#28422
C2×#284247