Finite Group Databasebeta

← #2230×C151 #34065562

Subgroups — #2230×C151 #34065562

Order 19328.

126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 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#498×C151C211yesmaximal, characteristic, complemented
2#443×C151C211yesmaximal, characteristic
3#365×C151C212yesmaximal, complemented
4#364×C151C211yesmaximal, characteristic, complemented
5#360×C151C212yesmaximal
6#135×C151C2211yescharacteristic
7#131×C151—21no—
8C4⋊Q8×C151—21no—
9M32×C151C2212yes—
10#108×C151C2211yescharacteristic
11#106×C151—21no—
12#106×C151C2212yes—
13#104×C151—21no—
14C4×C8×C151C2211yescharacteristic
15#41×C151—21no—
16C2×Q8×C151—41no—
17Q16×C151Q811yescharacteristic, complemented
18SD16×C151—21no—
19D8×C151Q811yescharacteristic, complemented
20M16×C151—21no—
21M16×C151—41no—
22C2×C8×C151—41no—
23C2×C8×C151D411yescharacteristic
24C2×C8×C151C2311yescharacteristic
25C4⋊C4×C151—22no—
26C4⋊C4×C151—41no—
27C42×C151D411yescharacteristic
28C16×C151—22no—
29Q8×C151—21no—
30Q8×C151—82no—
31D4×C151—21no—
32D4×C151—41no—
33C2×C4×C151—21no—
34C2×C4×C151—41no—
35C2×C4×C151—42no—
36C2×C4×C151C2×D411yescharacteristic
37C8×C151—41no—
38C8×C151SD1611yescharacteristic
39C8×C151SD1611yescharacteristic
40C8×C151C2×Q811yescharacteristic
41C8×C151#4111yescharacteristic
42C22×C151—41no—
43C22×C151AGL(1,ℤ/8)11yescharacteristic
44C4×C151—22no—
45C4×C151—41no—
46C4×C151—82no—
47C4×C151C22⋊Q811yescharacteristic
48C4×C151C2×SD1611yescharacteristic
49C2×C151—21no—
50C2×C151—81no—
51C2×C151#47611yescharacteristic
52C151#223011yescharacteristic, direct product factor, Sylow
53#2230C15111yesmaximal, characteristic, direct product factor, Sylow
54#498C2×C15111yescharacteristic, complemented
55#443C2×C15111yescharacteristic
56#365C2×C15112yescomplemented
57#364C2×C15111yescharacteristic, complemented
58#360C2×C15112yes—
59#135C22×C15111yescharacteristic
60#131—21no—
61C4⋊Q8—21no—
62M32C22×C15112yes—
63#108C22×C15111yescharacteristic
64#106—21no—
65#106C22×C15112yes—
66#104—21no—
67C4×C8C22×C15111yescharacteristic
68#41—21no—
69C2×Q8—41no—
70Q16Q8×C15111yescharacteristic, complemented
71SD16—21no—
72D8Q8×C15111yescharacteristic, complemented
73M16—21no—
74M16—41no—
75C2×C8—41no—
76C2×C8D4×C15111yescharacteristic
77C2×C8C23×C15111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C42D4×C15111yescharacteristic
81C16—22no—
82Q8—21no—
83Q8—82no—
84D4—21no—
85D4—41no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4C2×D4×C15111yescharacteristic
90C8—41no—
91C8SD16×C15111yescharacteristic
92C8SD16×C15111yescharacteristic
93C8C2×Q8×C15111yescharacteristic
94C8#41×C15111yescharacteristic
95C22—41no—
96C22AGL(1,ℤ/8)×C15111yescharacteristic
97C4—22no—
98C4—41no—
99C4—82no—
100C4C22⋊Q8×C15111yescharacteristic
101C4C2×SD16×C15111yescharacteristic
102C2—21no—
103C2—81no—
104C2#476×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#476
commutator, Frattini, cosocleC2×C8C23×C151
prime radical#135×C151C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #498×C151C2semidirect
3. #365×C151C2semidirect
4. #364×C151C2semidirect
17. Q16×C151Q8semidirect
19. D8×C151Q8semidirect
52. C151#2230direct (N × H)
53. #2230C151direct (N × H)
54. #498C2×C151semidirect
56. #365C2×C151semidirect
57. #364C2×C151semidirect
70. Q16Q8×C151semidirect
72. D8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#498×C1512
#443×C1512
#365×C1512
#364×C1512
#360×C1512
#2230151