Finite Group Databasebeta

← C3⋊#91143 #13085370

Subgroups — C3⋊#91143 #13085370

Order 1440.

108 conjugacy classes of subgroups; only the 15 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 15 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
1C2×C3×SL(2,𝔽5)C211yesmaximal, characteristic
2#91143—31nomaximal
3C3×SL(2,𝔽5)C411yescharacteristic, complemented
4C3⋊#859—51nomaximal, Hall
5C2×C3⋊#170—61nomaximal
6C2×SL(2,𝔽5)D311yescharacteristic
7C2×C3×SL(2,𝔽3)—51no—
8Dic3⋊Dic3—101nomaximal
9C2×C3×Dic5—61no—
10C3⋊#170—62no—
11SL(2,𝔽5)Dic311yescharacteristic, complemented
12#859—151no—
13#859—152no—
14#835—151no—
15C2×#170—181no—
16C2×C3⋊Dic3—101no—
17C2×C3×Dic3—101no—
18C2×C3×Dic3—101no—
19C3×SL(2,𝔽3)—51no—
20C22×C3×C5—61no—
21C3×Dic5—61no—
22C3×Dic5—61no—
23C2×C3×Q8—51no—
24C2×SL(2,𝔽3)—51no—
25C2×SL(2,𝔽3)—52no—
26C4⋊Dic3—151no—
27Dic3⋊C4—301no—
28C2×C3⋊C8—151no—
29C2×Dic5—61no—
30#170—182no—
31C22×C32—101no—
32C3⋊Dic3—201no—
33C3×Dic3—101no—
34C3×Dic3—101no—
35C3×Dic3—201no—
36#103—451noSylow
37C2×C3×C5—61no—
38C2×C3×C5—61no—
39C2×C3×C5—61no—
40C3×Q8—51no—
41C3×Q8—151no—
42C2×C3×C4—151no—
43C2×C3×C4—301no—
44C2×Dic3—101no—
45C2×Dic3—101no—
46C2×Dic3—301no—
47C2×Dic3—601no—
48SL(2,𝔽3)—51no—
49SL(2,𝔽3)—52no—
50C3⋊C8—301no—
51C22×C5—61no—
52Dic5—61no—
53Dic5—61no—
54C2×C32—101no—
55C2×C32—101no—
56C2×C32—101no—
57C2×Q8—51no—
58C2×C8—451no—
59C4⋊C4—451no—
60C3×C5—61no—
61C22×C3—101no—
62C22×C3—201no—
63C22×C3S511yescharacteristic
64C3×C4—151no—
65C3×C4—151no—
66C3×C4—601no—
67Dic3—101no—
68Dic3—101no—
69Dic3—201no—
70Dic3—601no—
71Dic3—602no—
72C2×C5—61no—
73C2×C5—61no—
74C2×C5—61no—
75C32—101noSylow
76Q8—51no—
77Q8—151no—
78C2×C4—151no—
79C2×C4—301no—
80C8—901no—
81C2×C3—101no—
82C2×C3—101no—
83C2×C3—101no—
84C2×C3—201no—
85C2×C3—201no—
86C2×C3—201no—
87C2×C3#672811yescharacteristic
88C2×C3#672911yescharacteristic
89C2×C3A5⋊C411yescharacteristic
90C5—61noSylow
91C22ΓL(2,𝔽4)11yescharacteristic
92C4—151no—
93C4—151no—
94C4—601no—
95C3—101no—
96C3—201no—
97C3#9114311yescharacteristic, complemented
98C2C3⋊(A5⋊C4)11yescharacteristic
99C2C3⋊#672811yescharacteristic
100C2C3⋊#672911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22ΓL(2,𝔽4)
commutator, hypocenterC3×SL(2,𝔽5)C4
Fitting, socleC22×C3S5
prime radical, cosocleC2×C3×SL(2,𝔽5)C2
LCSG ▷ C3×SL(2,𝔽5)
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
3. C3×SL(2,𝔽5)C4semidirect
11. SL(2,𝔽5)Dic3semidirect
97. C3#91143semidirect

Maximal subgroups

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

subgroupindex
C2×C3×SL(2,𝔽5)2
#911433
C3⋊#8595
C2×C3⋊#1706
Dic3⋊Dic310