Finite Group Databasebeta

← C131×#7529 #45693413

Subgroups — C131×#7529 #45693413

Order 33536.

186 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 30 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
1#1712×C131C211yesmaximal, characteristic
2#1408×C131C212yesmaximal, complemented
3#493×C131—22no—
4#493×C131C411yescharacteristic, complemented
5#493×C131C2211yescharacteristic
6#353×C131—22no—
7C82×C131C411yescharacteristic, complemented
8C2×D8×C131—41no—
9C2×D8×C131—44no—
10C2×D8×C131—41no—
11#127×C131—21no—
12#127×C131D412yes—
13#99×C131—42no—
14C4×C8×C131—21no—
15C4×C8×C131C2×C411yescharacteristic
16C2×D4×C131—22no—
17C2×D4×C131—42no—
18C2×D4×C131—42no—
19C2×D4×C131—41no—
20D8×C131—82no—
21D8×C131—88no—
22D8×C131—82no—
23C2×C8×C131—22no—
24C2×C8×C131—21no—
25C22⋊C4×C131—82no—
26C42×C131C22⋊C411yescharacteristic
27C23×C131—42no—
28C23×C131—81no—
29D4×C131—82no—
30D4×C131—84no—
31D4×C131—84no—
32D4×C131—82no—
33C2×C4×C131—21no—
34C2×C4×C131—162no—
35C2×C4×C131#9911yescharacteristic
36C8×C131—24no—
37C8×C131—22no—
38C22×C131—82no—
39C22×C131—162no—
40C22×C131—162no—
41C22×C131—161no—
42C22×C131#35311yescharacteristic
43C4×C131—22no—
44C4×C131—21no—
45C4×C131—322no—
46C2×C131—21no—
47C2×C131—162no—
48C2×C131—321no—
49C2×C131#140811yescharacteristic
50#7529C13111yesmaximal, characteristic, direct product factor, Sylow
51C131#752911yescharacteristic, direct product factor, Sylow
52#1712C2×C13111yescharacteristic
53#1408C2×C13112yescomplemented
54#493—22no—
55#493C4×C13111yescharacteristic, complemented
56#493C22×C13111yescharacteristic
57#353—22no—
58C82C4×C13111yescharacteristic, complemented
59C2×D8—41no—
60C2×D8—41no—
61C2×D8—44no—
62#127—21no—
63#127D4×C13112yes—
64#99—42no—
65C4×C8—21no—
66C4×C8C2×C4×C13111yescharacteristic
67C2×D4—22no—
68C2×D4—42no—
69C2×D4—42no—
70C2×D4—41no—
71D8—82no—
72D8—82no—
73D8—88no—
74C2×C8—22no—
75C2×C8—21no—
76C22⋊C4—82no—
77C42C22⋊C4×C13111yescharacteristic
78C23—42no—
79C23—81no—
80D4—82no—
81D4—84no—
82D4—84no—
83D4—82no—
84C2×C4—21no—
85C2×C4—162no—
86C2×C4#99×C13111yescharacteristic
87C8—24no—
88C8—22no—
89C22—82no—
90C22—162no—
91C22—162no—
92C22—161no—
93C22#353×C13111yescharacteristic
94C4—22no—
95C4—21no—
96C4—322no—
97C2—21no—
98C2—162no—
99C2—321no—
100C2#1408×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1408
commutatorC4×C8C2×C4×C131
Frattini, cosocle#493C22×C131
prime radical#1712×C131C2
LCSG ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C22×C131 ◁ C2×C4×C131 ◁ C42×C131 ◁ #493×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1408×C131C2semidirect
4. #493×C131C4semidirect
7. C82×C131C4semidirect
50. #7529C131direct (N × H)
51. C131#7529direct (N × H)
53. #1408C2×C131semidirect
55. #493C4×C131semidirect
58. C82C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1712×C1312
#1408×C1312
#7529131