Finite Group Databasebeta

← C2×C7×#2846 #13213826

Subgroups — C2×C7×#2846 #13213826

Order 1792.

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×C7C211yesmaximal, characteristic, complemented
2C22×C7×#120C217yesmaximal, complemented
3C7×#2846C2116yesmaximal, direct product factor
4C2×C7×#379C217yesmaximal, complemented
5C26×C7—256no—
6C26×C7C2217yes—
7C26×C7C2218yescomplemented
8C23×C7×D4C2217yescomplemented
9C2×C7×#120—256no—
10C2×C7×#120C22156yescomplemented
11C22×C7×C22⋊C4C22121yescomplemented
12C7×#379C22156yescomplemented
13C2×#2846C711yesmaximal, characteristic, direct product factor, Sylow
14C25×C7—2896no—
15C25×C7—2168no—
16C25×C7—2224no—
17C25×C7D4156yescomplemented
18C25×C7C23128yes—
19C25×C7C2317yes—
20C25×C7C2311yescharacteristic, complemented
21C22×C7×D4—284no—
22C22×C7×D4C23128yescomplemented
23C23×C4×C7C2317yescomplemented
24C7×#120—2224no—
25C2×C7×C22⋊C4—284no—
26C2×C7×C22⋊C4C23184yescomplemented
27C27C2×C711yescharacteristic, complemented
28C22×#120C2×C717yescomplemented
29#2846C2×C7116yesdirect product factor
30C2×#379C2×C717yescomplemented
31C24×C7—22048no—
32C24×C7—2896no—
33C24×C7—21792no—
34C24×C7—2672no—
35C24×C7—2336no—
36C24×C7—256no—
37C24×C7—214no—
38C24×C7C2×D4184yes—
39C24×C7C2×D41112yescomplemented
40C24×C7C24114yes—
41C24×C7C2411yescharacteristic
42C24×C7C2412yescomplemented
43C2×C7×D4—2168no—
44C2×C7×D4—4112no—
45C22×C4×C7—242no—
46C22×C4×C7C24114yescomplemented
47C7×C22⋊C4—2168no—
48C26—256no—
49C26C22×C717yes—
50C26C22×C718yescomplemented
51C23×D4C22×C717yescomplemented
52C2×#120—256no—
53C2×#120C22×C7156yescomplemented
54C22×C22⋊C4C22×C7121yescomplemented
55#379C22×C7156yescomplemented
56C23×C7—22048no—
57C23×C7—21792no—
58C23×C7—2896no—
59C23×C7—2336no—
60C23×C7—2672no—
61C23×C7—256no—
62C23×C7—214no—
63C23×C7—428no—
64C23×C7#1201112yescomplemented
65C23×C7C22×D4184yes—
66C23×C7C22×D4114yes—
67C23×C7C2511yescharacteristic
68C7×D4—4112no—
69C2×C4×C7—242no—
70C2×C4×C7—428no—
71C25—2896no—
72C25—2168no—
73C25—2224no—
74C25C7×D4156yescomplemented
75C25C23×C7128yes—
76C25C23×C717yes—
77C25C23×C711yescharacteristic, complemented
78C22×D4—284no—
79C22×D4C23×C7128yescomplemented
80C23×C4C23×C717yescomplemented
81#120—2224no—
82C2×C22⋊C4—284no—
83C2×C22⋊C4C23×C7184yescomplemented
84C22×C7—2896no—
85C22×C7—2224no—
86C22×C7—2168no—
87C22×C7—414no—
88C22×C7—88no—
89C22×C7C2×#120128yes—
90C22×C7C2×#120156yescomplemented
91C22×C7C23×D417yes—
92C4×C7—414no—
93C24—22048no—
94C24—2896no—
95C24—21792no—
96C24—2672no—
97C24—2336no—
98C24—256no—
99C24—214no—
100C24C2×C7×D4184yes—
101C24C2×C7×D41112yescomplemented
102C24C24×C7114yes—
103C24C24×C711yescharacteristic
104C24C24×C712yescomplemented
105C2×D4—2168no—
106C2×D4—4112no—
107C22×C4—242no—
108C22×C4C24×C7114yescomplemented
109C22⋊C4—2168no—
110C2×C7—256no—
111C2×C7—82no—
112C2×C7#284618yesdirect product factor
113C2×C7C22×#12017yes—
114C23—22048no—
115C23—2896no—
116C23—21792no—
117C23—256no—
118C23—2336no—
119C23—2672no—
120C23—214no—
121C23—428no—
122C23C7×#1201112yescomplemented
123C23C22×C7×D4184yes—
124C23C22×C7×D4114yes—
125C23C25×C711yescharacteristic
126D4—4112no—
127C2×C4—242no—
128C2×C4—428no—
129C7C2×#284611yescharacteristic, direct product factor, Sylow
130C22—2896no—
131C22—2168no—
132C22—2224no—
133C22—414no—
134C22—88no—
135C22C2×C7×#120128yes—
136C22C2×C7×#120156yescomplemented
137C22C23×C7×D417yes—
138C4—414no—
139C2—256no—
140C2—82no—
141C2C7×#284618yesdirect product factor
142C2C22×C7×#12017yes—
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC23C25×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C7C2semidirect
2. C22×C7×#120C2semidirect
3. C7×#2846C2direct (N × H)
4. C2×C7×#379C2semidirect
7. C26×C7C22semidirect
8. C23×C7×D4C22semidirect
10. C2×C7×#120C22semidirect
11. C22×C7×C22⋊C4C22semidirect
12. C7×#379C22semidirect
13. C2×#2846C7direct (N × H)
17. C25×C7D4semidirect
20. C25×C7C23semidirect
22. C22×C7×D4C23semidirect
23. C23×C4×C7C23semidirect
26. C2×C7×C22⋊C4C23semidirect
27. C27C2×C7semidirect
28. C22×#120C2×C7semidirect
29. #2846C2×C7direct (N × H)
30. C2×#379C2×C7semidirect
39. C24×C7C2×D4semidirect
42. C24×C7C24semidirect
46. C22×C4×C7C24semidirect
50. C26C22×C7semidirect
51. C23×D4C22×C7semidirect
53. C2×#120C22×C7semidirect
54. C22×C22⋊C4C22×C7semidirect
55. #379C22×C7semidirect
64. C23×C7#120semidirect
74. C25C7×D4semidirect
77. C25C23×C7semidirect
79. C22×D4C23×C7semidirect
80. C23×C4C23×C7semidirect
83. C2×C22⋊C4C23×C7semidirect
90. C22×C7C2×#120semidirect
101. C24C2×C7×D4semidirect
104. C24C24×C7semidirect
108. C22×C4C24×C7semidirect
112. C2×C7#2846direct (N × H)
122. C23C7×#120semidirect
129. C7C2×#2846direct (N × H)
136. C22C2×C7×#120semidirect
141. C2C7×#2846direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C72
C22×C7×#1202
C7×#28462
C2×C7×#3792
C2×#28467