Finite Group Databasebeta

← C2×C47×#2846 #26076308

Subgroups — C2×C47×#2846 #26076308

Order 12032.

32890 conjugacy classes of subgroups; only the 1886 normal subgroups are shown.

normal subgroups only

This group has 32890 conjugacy classes of subgroups — too many to draw. Only its 1886 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
1C27×C47C211yesmaximal, characteristic, complemented
2C22×#120×C47C217yesmaximal, complemented
3C47×#2846C2116yesmaximal, direct product factor
4C2×C47×#379C217yesmaximal, complemented
5C26×C47—256no—
6C26×C47C2217yes—
7C26×C47C2218yescomplemented
8C23×D4×C47C2217yescomplemented
9C2×#120×C47—256no—
10C2×#120×C47C22156yescomplemented
11C22×C22⋊C4×C47C22121yescomplemented
12C47×#379C22156yescomplemented
13C25×C47—2896no—
14C25×C47—2168no—
15C25×C47—2224no—
16C25×C47D4156yescomplemented
17C25×C47C23128yes—
18C25×C47C2317yes—
19C25×C47C2311yescharacteristic, complemented
20C22×D4×C47—284no—
21C22×D4×C47C23128yescomplemented
22C23×C4×C47C2317yescomplemented
23#120×C47—2224no—
24C2×C22⋊C4×C47—284no—
25C2×C22⋊C4×C47C23184yescomplemented
26C24×C47—22048no—
27C24×C47—2896no—
28C24×C47—21792no—
29C24×C47—2672no—
30C24×C47—2336no—
31C24×C47—256no—
32C24×C47—214no—
33C24×C47C2×D4184yes—
34C24×C47C2×D41112yescomplemented
35C24×C47C24114yes—
36C24×C47C2411yescharacteristic
37C24×C47C2412yescomplemented
38C2×D4×C47—2168no—
39C2×D4×C47—4112no—
40C22×C4×C47—242no—
41C22×C4×C47C24114yescomplemented
42C22⋊C4×C47—2168no—
43C23×C47—22048no—
44C23×C47—21792no—
45C23×C47—2896no—
46C23×C47—2336no—
47C23×C47—2672no—
48C23×C47—256no—
49C23×C47—214no—
50C23×C47—428no—
51C23×C47#1201112yescomplemented
52C23×C47C22×D4184yes—
53C23×C47C22×D4114yes—
54C23×C47C2511yescharacteristic
55D4×C47—4112no—
56C2×C4×C47—242no—
57C2×C4×C47—428no—
58C2×#2846C4711yesmaximal, characteristic, direct product factor, Sylow
59C22×C47—2896no—
60C22×C47—2224no—
61C22×C47—2168no—
62C22×C47—414no—
63C22×C47—88no—
64C22×C47C2×#120128yes—
65C22×C47C2×#120156yescomplemented
66C22×C47C23×D417yes—
67C4×C47—414no—
68C27C2×C4711yescharacteristic, complemented
69C22×#120C2×C4717yescomplemented
70#2846C2×C47116yesdirect product factor
71C2×#379C2×C4717yescomplemented
72C2×C47—256no—
73C2×C47—82no—
74C2×C47#284618yesdirect product factor
75C2×C47C22×#12017yes—
76C26—256no—
77C26C22×C4717yes—
78C26C22×C4718yescomplemented
79C23×D4C22×C4717yescomplemented
80C2×#120—256no—
81C2×#120C22×C47156yescomplemented
82C22×C22⋊C4C22×C47121yescomplemented
83#379C22×C47156yescomplemented
84C47C2×#284611yescharacteristic, direct product factor, Sylow
85C25—2896no—
86C25—2168no—
87C25—2224no—
88C25D4×C47156yescomplemented
89C25C23×C47128yes—
90C25C23×C4717yes—
91C25C23×C4711yescharacteristic, complemented
92C22×D4—284no—
93C22×D4C23×C47128yescomplemented
94C23×C4C23×C4717yescomplemented
95#120—2224no—
96C2×C22⋊C4—284no—
97C2×C22⋊C4C23×C47184yescomplemented
98C24—22048no—
99C24—2896no—
100C24—21792no—
101C24—2672no—
102C24—2336no—
103C24—256no—
104C24—214no—
105C24C2×D4×C47184yes—
106C24C2×D4×C471112yescomplemented
107C24C24×C47114yes—
108C24C24×C4711yescharacteristic
109C24C24×C4712yescomplemented
110C2×D4—2168no—
111C2×D4—4112no—
112C22×C4—242no—
113C22×C4C24×C47114yescomplemented
114C22⋊C4—2168no—
115C23—22048no—
116C23—21792no—
117C23—2896no—
118C23—2336no—
119C23—2672no—
120C23—256no—
121C23—214no—
122C23—428no—
123C23#120×C471112yescomplemented
124C23C22×D4×C47184yes—
125C23C22×D4×C47114yes—
126C23C25×C4711yescharacteristic
127D4—4112no—
128C2×C4—242no—
129C2×C4—428no—
130C22—2896no—
131C22—2224no—
132C22—2168no—
133C22—414no—
134C22—88no—
135C22C2×#120×C47128yes—
136C22C2×#120×C47156yescomplemented
137C22C23×D4×C4717yes—
138C4—414no—
139C2—256no—
140C2—82no—
141C2C47×#284618yesdirect product factor
142C2C22×#120×C4717yes—
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C47C2semidirect
2. C22×#120×C47C2semidirect
3. C47×#2846C2direct (N × H)
4. C2×C47×#379C2semidirect
7. C26×C47C22semidirect
8. C23×D4×C47C22semidirect
10. C2×#120×C47C22semidirect
11. C22×C22⋊C4×C47C22semidirect
12. C47×#379C22semidirect
16. C25×C47D4semidirect
19. C25×C47C23semidirect
21. C22×D4×C47C23semidirect
22. C23×C4×C47C23semidirect
25. C2×C22⋊C4×C47C23semidirect
34. C24×C47C2×D4semidirect
37. C24×C47C24semidirect
41. C22×C4×C47C24semidirect
51. C23×C47#120semidirect
58. C2×#2846C47direct (N × H)
65. C22×C47C2×#120semidirect
68. C27C2×C47semidirect
69. C22×#120C2×C47semidirect
70. #2846C2×C47direct (N × H)
71. C2×#379C2×C47semidirect
74. C2×C47#2846direct (N × H)
78. C26C22×C47semidirect
79. C23×D4C22×C47semidirect
81. C2×#120C22×C47semidirect
82. C22×C22⋊C4C22×C47semidirect
83. #379C22×C47semidirect
84. C47C2×#2846direct (N × H)
88. C25D4×C47semidirect
91. C25C23×C47semidirect
93. C22×D4C23×C47semidirect
94. C23×C4C23×C47semidirect
97. C2×C22⋊C4C23×C47semidirect
106. C24C2×D4×C47semidirect
109. C24C24×C47semidirect
113. C22×C4C24×C47semidirect
123. C23#120×C47semidirect
136. C22C2×#120×C47semidirect
141. C2C47×#2846direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C472
C22×#120×C472
C47×#28462
C2×C47×#3792
C2×#284647