Finite Group Databasebeta

← D47×#2846 #26422101

Subgroups — D47×#2846 #26422101

Order 12032.

32890 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.

normal subgroups only

This group has 32890 conjugacy classes of subgroups — too many to draw. Only its 1123 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
1C26×D47C211yesmaximal, characteristic, complemented
2C2×#120×D47C217yesmaximal, complemented
3#20251666C217yesmaximal, complemented
4#20251665C211yesmaximal, characteristic, complemented
5#20251664C217yesmaximal, complemented
6#379×D47C217yesmaximal, complemented
7C47×#2846C211yesmaximal, characteristic, complemented
8C25×D47—256no—
9C25×D47C2217yes—
10C25×D47C2217yescomplemented
11C22×D4×D47C2217yescomplemented
12C2×#13093994C22121yescomplemented
13C2×#13093993C2217yescomplemented
14C2×#13093992C22121yescomplemented
15#120×D47—256no—
16C2×C22⋊C4×D47C22121yescomplemented
17#15688979C2217yescomplemented
18#15688978C22142yescomplemented
19C26×C47C2211yescharacteristic, complemented
20C2×#120×C47C2217yescomplemented
21C47×#379C2217yescomplemented
22C24×D47—2896no—
23C24×D47—228no—
24C24×D47—2168no—
25C24×D47—2168no—
26C24×D47D4156yescomplemented
27C24×D47C23121yes—
28C24×D47C2317yes—
29C24×D47C2311yescharacteristic, complemented
30C22×D188C2317yescomplemented
31C22×C22⋊D47C2317yescomplemented
32C22×C22⋊D47C2317yescomplemented
33C2×D4×D47—284no—
34C22×C4×D47C2317yescomplemented
35#13093994—284no—
36#13093993—228no—
37#13093992—284no—
38C2×C22⋊Dic47C23121yescomplemented
39C2×(C2×D47)⋊C4C23142yescomplemented
40C22⋊C4×D47—284no—
41C25×C47—228no—
42C25×C47C2317yes—
43C22×D4×C47C2317yescomplemented
44#120×C47—228no—
45C2×C22⋊C4×C47C23121yescomplemented
46C24×C47—2224no—
47C24×C47—284no—
48C24×C47C2×D4128yescomplemented
49C24×C47C2417yes—
50C24×C47C2411yescharacteristic, complemented
51C23×D47—22048no—
52C23×D47—2672no—
53C23×D47—2896no—
54C23×D47—2896no—
55C23×D47—284no—
56C23×D47—2672no—
57C23×D47—2168no—
58C23×D47—256no—
59C23×D47—214no—
60C23×D47C2×D4184yes—
61C23×D47C2×D4184yescomplemented
62C23×D47C2417yes—
63C23×D47C2411yescharacteristic
64C23×D47C2411yescharacteristic, complemented
65C2×D4×C47—242no—
66C22×C4×C47C2417yescomplemented
67C2×C22⋊D47—242no—
68C2×C22⋊D47—242no—
69C22×Dic47C2417yescomplemented
70D4×D47—4112no—
71C2×D188—242no—
72C2×C4×D47—242no—
73C22⋊C4×C47—242no—
74C22⋊Dic47—242no—
75(C2×D47)⋊C4—284no—
76C23×C47—2256no—
77C23×C47—2224no—
78C23×C47—2168no—
79C23×C47—228no—
80C23×C47—27no—
81C23×C47C22×D4142yes—
82C23×C47C2511yescharacteristic
83C22×D47—21792no—
84C22×D47—2672no—
85C22×D47—21792no—
86C22×D47—2168no—
87C22×D47—228no—
88C22×D47—2336no—
89C22×D47—2336no—
90C22×D47—27no—
91C22×D47—428no—
92C22×D47#1201112yescomplemented
93C22×D47C22×D4142yes—
94C22×D47C22×D4114yes—
95D4×C47—428no—
96C2×C4×C47—221no—
97C22⋊D47—428no—
98C22⋊D47—428no—
99C2×Dic47—221no—
100D188—428no—
101C4×D47—428no—
102C2×#2846—471nomaximal, Sylow
103C22×C47—2224no—
104C22×C47—284no—
105C22×C47—47no—
106C22×C47C2×#120128yescomplemented
107C22×C47C23×D417yes—
108C2×D47—2672no—
109C2×D47—284no—
110C2×D47—2224no—
111C2×D47—47no—
112C2×D47—88no—
113C2×D47C2×#120128yes—
114C2×D47C2×#120128yescomplemented
115C4×C47—47no—
116Dic47—47no—
117C27—471no—
118C22×#120—477no—
119#2846—477no—
120#2846—471no—
121#2846—477no—
122#2846D4711yescharacteristic, direct product factor
123C2×#379—477no—
124C2×C47—228no—
125C2×C47—81no—
126C2×C47C22×#12017yes—
127D47—228no—
128D47—81no—
129D47#284618yesdirect product factor
130C26—477no—
131C26—477no—
132C26—9456no—
133C26C2×D4711yescharacteristic, complemented
134C23×D4—477no—
135C2×#120—477no—
136C2×#120—4721no—
137C2×#120—4721no—
138C2×#120—9456no—
139C2×#120C2×D4717yescomplemented
140C22×C22⋊C4—4721no—
141#379—477no—
142#379—4742no—
143#379C2×D4717yescomplemented
144C47C2×#284611yescharacteristic, complemented, Sylow
145C25—228no—
146C25—477no—
147C25—4756no—
148C25—4721no—
149C25—471no—
150C25—94168no—
151C25—94168no—
152C25—94896no—
153C25—9428no—
154C25C22×D4717yes—
155C22×D4—477no—
156C22×D4—477no—
157C22×D4—477no—
158C22×D4—9484no—
159C22×D4C22×D4717yescomplemented
160C23×C4—477no—
161#120—228no—
162#120—9484no—
163#120—9484no—
164#120—9428no—
165C2×C22⋊C4—4721no—
166C2×C22⋊C4—4742no—
167C2×C22⋊C4—9484no—
168C2×C22⋊C4C22×D47121yescomplemented
169C24—2224no—
170C24—284no—
171C24—471no—
172C24—4784no—
173C24—477no—
174C24—4784no—
175C24—471no—
176C24—94672no—
177C24—9456no—
178C24—94168no—
179C24—9414no—
180C24—94896no—
181C24—94896no—
182C24—942048no—
183C24—94672no—
184C24—9484no—
185C24D4×D47128yescomplemented
186C24C23×D4717yes—
187C24C23×D4711yescharacteristic, complemented
188C2×D4—242no—
189C2×D4—9442no—
190C2×D4—9442no—
191C2×D4—9442no—
192C2×D4—188112no—
193C22×C4—477no—
194C22×C4—9442no—
195C22×C4C23×D4717yescomplemented
196C22⋊C4—242no—
197C22⋊C4—9484no—
198C22⋊C4—9442no—
199C23—2256no—
200C23—2224no—
201C23—2168no—
202C23—228no—
203C23—27no—
204C23—4714no—
205C23—47112no—
206C23—4742no—
207C23—94336no—
208C23—94336no—
209C23—941792no—
210C23—941792no—
211C23—94672no—
212C23—94168no—
213C23—9428no—
214C23—947no—
215C23—18828no—
216C23C2×D4×D47142yes—
217C23C24×D4711yescharacteristic
218D4—428no—
219D4—18828no—
220D4—18828no—
221D4—18828no—
222C2×C4—221no—
223C2×C4—9421no—
224C2×C4—18828no—
225C22—2224no—
226C22—284no—
227C22—47no—
228C22—4728no—
229C22—4728no—
230C22—94224no—
231C22—94672no—
232C22—9484no—
233C22—3768no—
234C22—1887no—
235C22#120×D47128yescomplemented
236C22C22×D4×D4717yes—
237C4—47no—
238C4—1887no—
239C2—228no—
240C2—81no—
241C2—478no—
242C2—9428no—
243C2—3761no—
244C2C2×#120×D4717yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2846C2
hypercenter#2846D47
hypocenterC47C2×#2846
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2846

Complements

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

NH ≅ G/Ntype
1. C26×D47C2semidirect
2. C2×#120×D47C2semidirect
3. #20251666C2semidirect
4. #20251665C2semidirect
5. #20251664C2semidirect
6. #379×D47C2semidirect
7. C47×#2846C2semidirect
10. C25×D47C22semidirect
11. C22×D4×D47C22semidirect
12. C2×#13093994C22semidirect
13. C2×#13093993C22semidirect
14. C2×#13093992C22semidirect
16. C2×C22⋊C4×D47C22semidirect
17. #15688979C22semidirect
18. #15688978C22semidirect
19. C26×C47C22semidirect
20. C2×#120×C47C22semidirect
21. C47×#379C22semidirect
26. C24×D47D4semidirect
29. C24×D47C23semidirect
30. C22×D188C23semidirect
31. C22×C22⋊D47C23semidirect
32. C22×C22⋊D47C23semidirect
34. C22×C4×D47C23semidirect
38. C2×C22⋊Dic47C23semidirect
39. C2×(C2×D47)⋊C4C23semidirect
43. C22×D4×C47C23semidirect
45. C2×C22⋊C4×C47C23semidirect
48. C24×C47C2×D4semidirect
50. C24×C47C24semidirect
61. C23×D47C2×D4semidirect
64. C23×D47C24semidirect
66. C22×C4×C47C24semidirect
69. C22×Dic47C24semidirect
92. C22×D47#120semidirect
106. C22×C47C2×#120semidirect
114. C2×D47C2×#120semidirect
122. #2846D47direct (N × H)
129. D47#2846direct (N × H)
133. C26C2×D47semidirect
139. C2×#120C2×D47semidirect
143. #379C2×D47semidirect
144. C47C2×#2846semidirect
159. C22×D4C22×D47semidirect
168. C2×C22⋊C4C22×D47semidirect
185. C24D4×D47semidirect
187. C24C23×D47semidirect
195. C22×C4C23×D47semidirect
235. C22#120×D47semidirect

Maximal subgroups

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

subgroupindex
C26×D472
C2×#120×D472
#202516662
#202516652
#202516642
#379×D472
C47×#28462
C2×#284647