Finite Group Databasebeta

← C2×C59×#2846 #28448719

Subgroups — C2×C59×#2846 #28448719

Order 15104.

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×C59C211yesmaximal, characteristic, complemented
2C22×#120×C59C217yesmaximal, complemented
3C59×#2846C2116yesmaximal, direct product factor
4C2×C59×#379C217yesmaximal, complemented
5C26×C59—256no—
6C26×C59C2217yes—
7C26×C59C2218yescomplemented
8C23×D4×C59C2217yescomplemented
9C2×#120×C59—256no—
10C2×#120×C59C22156yescomplemented
11C22×C22⋊C4×C59C22121yescomplemented
12C59×#379C22156yescomplemented
13C25×C59—2896no—
14C25×C59—2168no—
15C25×C59—2224no—
16C25×C59D4156yescomplemented
17C25×C59C23128yes—
18C25×C59C2317yes—
19C25×C59C2311yescharacteristic, complemented
20C22×D4×C59—284no—
21C22×D4×C59C23128yescomplemented
22C23×C4×C59C2317yescomplemented
23#120×C59—2224no—
24C2×C22⋊C4×C59—284no—
25C2×C22⋊C4×C59C23184yescomplemented
26C24×C59—22048no—
27C24×C59—2896no—
28C24×C59—21792no—
29C24×C59—2672no—
30C24×C59—2336no—
31C24×C59—256no—
32C24×C59—214no—
33C24×C59C2×D4184yes—
34C24×C59C2×D41112yescomplemented
35C24×C59C24114yes—
36C24×C59C2411yescharacteristic
37C24×C59C2412yescomplemented
38C2×D4×C59—2168no—
39C2×D4×C59—4112no—
40C22×C4×C59—242no—
41C22×C4×C59C24114yescomplemented
42C22⋊C4×C59—2168no—
43C23×C59—22048no—
44C23×C59—21792no—
45C23×C59—2896no—
46C23×C59—2336no—
47C23×C59—2672no—
48C23×C59—256no—
49C23×C59—214no—
50C23×C59—428no—
51C23×C59#1201112yescomplemented
52C23×C59C22×D4184yes—
53C23×C59C22×D4114yes—
54C23×C59C2511yescharacteristic
55D4×C59—4112no—
56C2×C4×C59—242no—
57C2×C4×C59—428no—
58C2×#2846C5911yesmaximal, characteristic, direct product factor, Sylow
59C22×C59—2896no—
60C22×C59—2224no—
61C22×C59—2168no—
62C22×C59—414no—
63C22×C59—88no—
64C22×C59C2×#120128yes—
65C22×C59C2×#120156yescomplemented
66C22×C59C23×D417yes—
67C4×C59—414no—
68C27C2×C5911yescharacteristic, complemented
69C22×#120C2×C5917yescomplemented
70#2846C2×C59116yesdirect product factor
71C2×#379C2×C5917yescomplemented
72C2×C59—256no—
73C2×C59—82no—
74C2×C59#284618yesdirect product factor
75C2×C59C22×#12017yes—
76C26—256no—
77C26C22×C5917yes—
78C26C22×C5918yescomplemented
79C23×D4C22×C5917yescomplemented
80C2×#120—256no—
81C2×#120C22×C59156yescomplemented
82C22×C22⋊C4C22×C59121yescomplemented
83#379C22×C59156yescomplemented
84C59C2×#284611yescharacteristic, direct product factor, Sylow
85C25—2896no—
86C25—2168no—
87C25—2224no—
88C25D4×C59156yescomplemented
89C25C23×C59128yes—
90C25C23×C5917yes—
91C25C23×C5911yescharacteristic, complemented
92C22×D4—284no—
93C22×D4C23×C59128yescomplemented
94C23×C4C23×C5917yescomplemented
95#120—2224no—
96C2×C22⋊C4—284no—
97C2×C22⋊C4C23×C59184yescomplemented
98C24—22048no—
99C24—2896no—
100C24—21792no—
101C24—2672no—
102C24—2336no—
103C24—256no—
104C24—214no—
105C24C2×D4×C59184yes—
106C24C2×D4×C591112yescomplemented
107C24C24×C59114yes—
108C24C24×C5911yescharacteristic
109C24C24×C5912yescomplemented
110C2×D4—2168no—
111C2×D4—4112no—
112C22×C4—242no—
113C22×C4C24×C59114yescomplemented
114C22⋊C4—2168no—
115C23—22048no—
116C23—21792no—
117C23—2896no—
118C23—2336no—
119C23—2672no—
120C23—256no—
121C23—214no—
122C23—428no—
123C23#120×C591112yescomplemented
124C23C22×D4×C59184yes—
125C23C22×D4×C59114yes—
126C23C25×C5911yescharacteristic
127D4—4112no—
128C2×C4—242no—
129C2×C4—428no—
130C22—2896no—
131C22—2224no—
132C22—2168no—
133C22—414no—
134C22—88no—
135C22C2×#120×C59128yes—
136C22C2×#120×C59156yescomplemented
137C22C23×D4×C5917yes—
138C4—414no—
139C2—256no—
140C2—82no—
141C2C59×#284618yesdirect product factor
142C2C22×#120×C5917yes—
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC23C25×C59
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C59C2semidirect
2. C22×#120×C59C2semidirect
3. C59×#2846C2direct (N × H)
4. C2×C59×#379C2semidirect
7. C26×C59C22semidirect
8. C23×D4×C59C22semidirect
10. C2×#120×C59C22semidirect
11. C22×C22⋊C4×C59C22semidirect
12. C59×#379C22semidirect
16. C25×C59D4semidirect
19. C25×C59C23semidirect
21. C22×D4×C59C23semidirect
22. C23×C4×C59C23semidirect
25. C2×C22⋊C4×C59C23semidirect
34. C24×C59C2×D4semidirect
37. C24×C59C24semidirect
41. C22×C4×C59C24semidirect
51. C23×C59#120semidirect
58. C2×#2846C59direct (N × H)
65. C22×C59C2×#120semidirect
68. C27C2×C59semidirect
69. C22×#120C2×C59semidirect
70. #2846C2×C59direct (N × H)
71. C2×#379C2×C59semidirect
74. C2×C59#2846direct (N × H)
78. C26C22×C59semidirect
79. C23×D4C22×C59semidirect
81. C2×#120C22×C59semidirect
82. C22×C22⋊C4C22×C59semidirect
83. #379C22×C59semidirect
84. C59C2×#2846direct (N × H)
88. C25D4×C59semidirect
91. C25C23×C59semidirect
93. C22×D4C23×C59semidirect
94. C23×C4C23×C59semidirect
97. C2×C22⋊C4C23×C59semidirect
106. C24C2×D4×C59semidirect
109. C24C24×C59semidirect
113. C22×C4C24×C59semidirect
123. C23#120×C59semidirect
136. C22C2×#120×C59semidirect
141. C2C59×#2846direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C592
C22×#120×C592
C59×#28462
C2×C59×#3792
C2×#284659