Finite Group Databasebeta

← C2×C11×#2846 #14613803

Subgroups — C2×C11×#2846 #14613803

Order 2816.

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×C11C211yesmaximal, characteristic, complemented
2C22×C11×#120C217yesmaximal, complemented
3C11×#2846C2116yesmaximal, direct product factor
4C2×C11×#379C217yesmaximal, complemented
5C26×C11—256no—
6C26×C11C2217yes—
7C26×C11C2218yescomplemented
8C23×D4×C11C2217yescomplemented
9C2×C11×#120—256no—
10C2×C11×#120C22156yescomplemented
11C22×C11×C22⋊C4C22121yescomplemented
12C11×#379C22156yescomplemented
13C25×C11—2896no—
14C25×C11—2168no—
15C25×C11—2224no—
16C25×C11D4156yescomplemented
17C25×C11C23128yes—
18C25×C11C2317yes—
19C25×C11C2311yescharacteristic, complemented
20C22×D4×C11—284no—
21C22×D4×C11C23128yescomplemented
22C23×C4×C11C2317yescomplemented
23C11×#120—2224no—
24C2×C11×C22⋊C4—284no—
25C2×C11×C22⋊C4C23184yescomplemented
26C2×#2846C1111yesmaximal, characteristic, direct product factor, Sylow
27C24×C11—22048no—
28C24×C11—2896no—
29C24×C11—21792no—
30C24×C11—2672no—
31C24×C11—2336no—
32C24×C11—256no—
33C24×C11—214no—
34C24×C11C2×D4184yes—
35C24×C11C2×D41112yescomplemented
36C24×C11C24114yes—
37C24×C11C2411yescharacteristic
38C24×C11C2412yescomplemented
39C2×D4×C11—2168no—
40C2×D4×C11—4112no—
41C22×C4×C11—242no—
42C22×C4×C11C24114yescomplemented
43C11×C22⋊C4—2168no—
44C27C2×C1111yescharacteristic, complemented
45C22×#120C2×C1117yescomplemented
46#2846C2×C11116yesdirect product factor
47C2×#379C2×C1117yescomplemented
48C23×C11—22048no—
49C23×C11—21792no—
50C23×C11—2896no—
51C23×C11—2336no—
52C23×C11—2672no—
53C23×C11—256no—
54C23×C11—214no—
55C23×C11—428no—
56C23×C11#1201112yescomplemented
57C23×C11C22×D4184yes—
58C23×C11C22×D4114yes—
59C23×C11C2511yescharacteristic
60D4×C11—4112no—
61C2×C4×C11—242no—
62C2×C4×C11—428no—
63C26—256no—
64C26C22×C1117yes—
65C26C22×C1118yescomplemented
66C23×D4C22×C1117yescomplemented
67C2×#120—256no—
68C2×#120C22×C11156yescomplemented
69C22×C22⋊C4C22×C11121yescomplemented
70#379C22×C11156yescomplemented
71C22×C11—2896no—
72C22×C11—2224no—
73C22×C11—2168no—
74C22×C11—414no—
75C22×C11—88no—
76C22×C11C2×#120128yes—
77C22×C11C2×#120156yescomplemented
78C22×C11C23×D417yes—
79C4×C11—414no—
80C25—2896no—
81C25—2168no—
82C25—2224no—
83C25D4×C11156yescomplemented
84C25C23×C11128yes—
85C25C23×C1117yes—
86C25C23×C1111yescharacteristic, complemented
87C22×D4—284no—
88C22×D4C23×C11128yescomplemented
89C23×C4C23×C1117yescomplemented
90#120—2224no—
91C2×C22⋊C4—284no—
92C2×C22⋊C4C23×C11184yescomplemented
93C2×C11—256no—
94C2×C11—82no—
95C2×C11#284618yesdirect product factor
96C2×C11C22×#12017yes—
97C24—22048no—
98C24—2896no—
99C24—21792no—
100C24—2672no—
101C24—2336no—
102C24—256no—
103C24—214no—
104C24C2×D4×C11184yes—
105C24C2×D4×C111112yescomplemented
106C24C24×C11114yes—
107C24C24×C1111yescharacteristic
108C24C24×C1112yescomplemented
109C2×D4—2168no—
110C2×D4—4112no—
111C22×C4—242no—
112C22×C4C24×C11114yescomplemented
113C22⋊C4—2168no—
114C11C2×#284611yescharacteristic, direct product factor, Sylow
115C23—22048no—
116C23—2896no—
117C23—21792no—
118C23—2336no—
119C23—2672no—
120C23—256no—
121C23—214no—
122C23—428no—
123C23C11×#1201112yescomplemented
124C23C22×D4×C11184yes—
125C23C22×D4×C11114yes—
126C23C25×C1111yescharacteristic
127D4—4112no—
128C2×C4—242no—
129C2×C4—428no—
130C22—2896no—
131C22—2168no—
132C22—2224no—
133C22—414no—
134C22—88no—
135C22C2×C11×#120128yes—
136C22C2×C11×#120156yescomplemented
137C22C23×D4×C1117yes—
138C4—414no—
139C2—256no—
140C2—82no—
141C2C11×#284618yesdirect product factor
142C2C22×C11×#12017yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C27×C11C2semidirect
2. C22×C11×#120C2semidirect
3. C11×#2846C2direct (N × H)
4. C2×C11×#379C2semidirect
7. C26×C11C22semidirect
8. C23×D4×C11C22semidirect
10. C2×C11×#120C22semidirect
11. C22×C11×C22⋊C4C22semidirect
12. C11×#379C22semidirect
16. C25×C11D4semidirect
19. C25×C11C23semidirect
21. C22×D4×C11C23semidirect
22. C23×C4×C11C23semidirect
25. C2×C11×C22⋊C4C23semidirect
26. C2×#2846C11direct (N × H)
35. C24×C11C2×D4semidirect
38. C24×C11C24semidirect
42. C22×C4×C11C24semidirect
44. C27C2×C11semidirect
45. C22×#120C2×C11semidirect
46. #2846C2×C11direct (N × H)
47. C2×#379C2×C11semidirect
56. C23×C11#120semidirect
65. C26C22×C11semidirect
66. C23×D4C22×C11semidirect
68. C2×#120C22×C11semidirect
69. C22×C22⋊C4C22×C11semidirect
70. #379C22×C11semidirect
77. C22×C11C2×#120semidirect
83. C25D4×C11semidirect
86. C25C23×C11semidirect
88. C22×D4C23×C11semidirect
89. C23×C4C23×C11semidirect
92. C2×C22⋊C4C23×C11semidirect
95. C2×C11#2846direct (N × H)
105. C24C2×D4×C11semidirect
108. C24C24×C11semidirect
112. C22×C4C24×C11semidirect
114. C11C2×#2846direct (N × H)
123. C23C11×#120semidirect
136. C22C2×C11×#120semidirect
141. C2C11×#2846direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C112
C22×C11×#1202
C11×#28462
C2×C11×#3792
C2×#284611