Finite Group Databasebeta

← C2×C73×#2846 #32946014

Subgroups — C2×C73×#2846 #32946014

Order 18688.

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×C73C211yesmaximal, characteristic, complemented
2C22×#120×C73C217yesmaximal, complemented
3C73×#2846C2116yesmaximal, direct product factor
4C2×#379×C73C217yesmaximal, complemented
5C26×C73—256no—
6C26×C73C2217yes—
7C26×C73C2218yescomplemented
8C23×D4×C73C2217yescomplemented
9C2×#120×C73—256no—
10C2×#120×C73C22156yescomplemented
11C22×C22⋊C4×C73C22121yescomplemented
12#379×C73C22156yescomplemented
13C25×C73—2896no—
14C25×C73—2168no—
15C25×C73—2224no—
16C25×C73D4156yescomplemented
17C25×C73C23128yes—
18C25×C73C2317yes—
19C25×C73C2311yescharacteristic, complemented
20C22×D4×C73—284no—
21C22×D4×C73C23128yescomplemented
22C23×C4×C73C2317yescomplemented
23#120×C73—2224no—
24C2×C22⋊C4×C73—284no—
25C2×C22⋊C4×C73C23184yescomplemented
26C24×C73—22048no—
27C24×C73—2896no—
28C24×C73—21792no—
29C24×C73—2672no—
30C24×C73—2336no—
31C24×C73—256no—
32C24×C73—214no—
33C24×C73C2×D4184yes—
34C24×C73C2×D41112yescomplemented
35C24×C73C24114yes—
36C24×C73C2411yescharacteristic
37C24×C73C2412yescomplemented
38C2×D4×C73—2168no—
39C2×D4×C73—4112no—
40C22×C4×C73—242no—
41C22×C4×C73C24114yescomplemented
42C22⋊C4×C73—2168no—
43C23×C73—22048no—
44C23×C73—21792no—
45C23×C73—2896no—
46C23×C73—2336no—
47C23×C73—2672no—
48C23×C73—256no—
49C23×C73—214no—
50C23×C73—428no—
51C23×C73#1201112yescomplemented
52C23×C73C22×D4184yes—
53C23×C73C22×D4114yes—
54C23×C73C2511yescharacteristic
55D4×C73—4112no—
56C2×C4×C73—242no—
57C2×C4×C73—428no—
58C22×C73—2896no—
59C22×C73—2224no—
60C22×C73—2168no—
61C22×C73—414no—
62C22×C73—88no—
63C22×C73C2×#120128yes—
64C22×C73C2×#120156yescomplemented
65C22×C73C23×D417yes—
66C4×C73—414no—
67C2×#2846C7311yesmaximal, characteristic, direct product factor, Sylow
68C2×C73—256no—
69C2×C73—82no—
70C2×C73#284618yesdirect product factor
71C2×C73C22×#12017yes—
72C27C2×C7311yescharacteristic, complemented
73C22×#120C2×C7317yescomplemented
74#2846C2×C73116yesdirect product factor
75C2×#379C2×C7317yescomplemented
76C73C2×#284611yescharacteristic, direct product factor, Sylow
77C26—256no—
78C26C22×C7317yes—
79C26C22×C7318yescomplemented
80C23×D4C22×C7317yescomplemented
81C2×#120—256no—
82C2×#120C22×C73156yescomplemented
83C22×C22⋊C4C22×C73121yescomplemented
84#379C22×C73156yescomplemented
85C25—2896no—
86C25—2168no—
87C25—2224no—
88C25D4×C73156yescomplemented
89C25C23×C73128yes—
90C25C23×C7317yes—
91C25C23×C7311yescharacteristic, complemented
92C22×D4—284no—
93C22×D4C23×C73128yescomplemented
94C23×C4C23×C7317yescomplemented
95#120—2224no—
96C2×C22⋊C4—284no—
97C2×C22⋊C4C23×C73184yescomplemented
98C24—22048no—
99C24—2896no—
100C24—21792no—
101C24—2672no—
102C24—2336no—
103C24—256no—
104C24—214no—
105C24C2×D4×C73184yes—
106C24C2×D4×C731112yescomplemented
107C24C24×C73114yes—
108C24C24×C7311yescharacteristic
109C24C24×C7312yescomplemented
110C2×D4—2168no—
111C2×D4—4112no—
112C22×C4—242no—
113C22×C4C24×C73114yescomplemented
114C22⋊C4—2168no—
115C23—22048no—
116C23—21792no—
117C23—2896no—
118C23—2336no—
119C23—2672no—
120C23—256no—
121C23—214no—
122C23—428no—
123C23#120×C731112yescomplemented
124C23C22×D4×C73184yes—
125C23C22×D4×C73114yes—
126C23C25×C7311yescharacteristic
127D4—4112no—
128C2×C4—242no—
129C2×C4—428no—
130C22—2896no—
131C22—2224no—
132C22—2168no—
133C22—414no—
134C22—88no—
135C22C2×#120×C73128yes—
136C22C2×#120×C73156yescomplemented
137C22C23×D4×C7317yes—
138C4—414no—
139C2—256no—
140C2—82no—
141C2C73×#284618yesdirect product factor
142C2C22×#120×C7317yes—
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C73C2semidirect
2. C22×#120×C73C2semidirect
3. C73×#2846C2direct (N × H)
4. C2×#379×C73C2semidirect
7. C26×C73C22semidirect
8. C23×D4×C73C22semidirect
10. C2×#120×C73C22semidirect
11. C22×C22⋊C4×C73C22semidirect
12. #379×C73C22semidirect
16. C25×C73D4semidirect
19. C25×C73C23semidirect
21. C22×D4×C73C23semidirect
22. C23×C4×C73C23semidirect
25. C2×C22⋊C4×C73C23semidirect
34. C24×C73C2×D4semidirect
37. C24×C73C24semidirect
41. C22×C4×C73C24semidirect
51. C23×C73#120semidirect
64. C22×C73C2×#120semidirect
67. C2×#2846C73direct (N × H)
70. C2×C73#2846direct (N × H)
72. C27C2×C73semidirect
73. C22×#120C2×C73semidirect
74. #2846C2×C73direct (N × H)
75. C2×#379C2×C73semidirect
76. C73C2×#2846direct (N × H)
79. C26C22×C73semidirect
80. C23×D4C22×C73semidirect
82. C2×#120C22×C73semidirect
83. C22×C22⋊C4C22×C73semidirect
84. #379C22×C73semidirect
88. C25D4×C73semidirect
91. C25C23×C73semidirect
93. C22×D4C23×C73semidirect
94. C23×C4C23×C73semidirect
97. C2×C22⋊C4C23×C73semidirect
106. C24C2×D4×C73semidirect
109. C24C24×C73semidirect
113. C22×C4C24×C73semidirect
123. C23#120×C73semidirect
136. C22C2×#120×C73semidirect
141. C2C73×#2846direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C732
C22×#120×C732
C73×#28462
C2×#379×C732
C2×#284673