Finite Group Databasebeta

← #1687×C151 #34065019

Subgroups — #1687×C151 #34065019

Order 19328.

198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 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#493×C151C211yesmaximal, characteristic, complemented
2#459×C151C212yesmaximal, complemented
3#436×C151C211yesmaximal, characteristic, complemented
4#334×C151C211yesmaximal, characteristic, complemented
5#331×C151C212yesmaximal, complemented
6C2×D8×C151—22no—
7C2×D8×C151—21no—
8C2×D8×C151—21no—
9C2×M16×C151—21no—
10#127×C151C2212yes—
11C4×D4×C151C2211yescharacteristic
12C4⋊C8×C151C2211yescharacteristic
13C4⋊C8×C151C2212yes—
14#102×C151—22no—
15C22⋊C8×C151—21no—
16C4×C8×C151C2211yescharacteristic
17C2×D4×C151—22no—
18C2×D4×C151—22no—
19C2×D4×C151—22no—
20C2×D4×C151D411yescharacteristic
21C22×C4×C151—21no—
22D8×C151—42no—
23D8×C151—44no—
24D8×C151—42no—
25M16×C151—42no—
26C2×C8×C151—21no—
27C2×C8×C151—22no—
28C2×C8×C151D411yescharacteristic
29C2×C8×C151D411yescharacteristic
30C4⋊C4×C151D411yescharacteristic
31C22⋊C4×C151—21no—
32C42×C151C2311yescharacteristic
33C23×C151—21no—
34C23×C151—42no—
35D4×C151—22no—
36D4×C151—42no—
37D4×C151—42no—
38D4×C151—42no—
39D4×C151—42no—
40D4×C151—82no—
41C2×C4×C151—21no—
42C2×C4×C151—41no—
43C2×C4×C151—41no—
44C2×C4×C151C2×D411yescharacteristic
45C2×C4×C151C2×D411yescharacteristic
46C2×C4×C151#4111yescharacteristic
47C8×C151—21no—
48C8×C151—41no—
49C8×C151—42no—
50C8×C151D812yescomplemented
51C22×C151—41no—
52C22×C151—41no—
53C22×C151—41no—
54C22×C151—82no—
55C22×C151—82no—
56C22×C151—82no—
57C22×C151#12111yescharacteristic
58C4×C151—21no—
59C4×C151—41no—
60C4×C151C2×D811yescharacteristic
61C4×C151AGL(1,ℤ/8)11yescharacteristic
62C4×C151AGL(1,ℤ/8)12yes—
63C2×C151—81no—
64C2×C151—162no—
65C2×C151#45911yescharacteristic
66C2×C151#46911yescharacteristic
67C2×C151#47211yescharacteristic
68C151#168711yescharacteristic, direct product factor, Sylow
69#1687C15111yesmaximal, characteristic, direct product factor, Sylow
70#493C2×C15111yescharacteristic, complemented
71#459C2×C15112yescomplemented
72#436C2×C15111yescharacteristic, complemented
73#334C2×C15111yescharacteristic, complemented
74#331C2×C15112yescomplemented
75C2×D8—22no—
76C2×D8—21no—
77C2×D8—21no—
78C2×M16—21no—
79#127C22×C15112yes—
80C4×D4C22×C15111yescharacteristic
81C4⋊C8C22×C15111yescharacteristic
82C4⋊C8C22×C15112yes—
83#102—22no—
84C22⋊C8—21no—
85C4×C8C22×C15111yescharacteristic
86C2×D4—22no—
87C2×D4—22no—
88C2×D4—22no—
89C2×D4D4×C15111yescharacteristic
90C22×C4—21no—
91D8—42no—
92D8—44no—
93D8—42no—
94M16—42no—
95C2×C8—21no—
96C2×C8—22no—
97C2×C8D4×C15111yescharacteristic
98C2×C8D4×C15111yescharacteristic
99C4⋊C4D4×C15111yescharacteristic
100C22⋊C4—21no—
101C42C23×C15111yescharacteristic
102C23—21no—
103C23—42no—
104D4—22no—
105D4—42no—
106D4—42no—
107D4—42no—
108D4—42no—
109D4—82no—
110C2×C4—21no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4C2×D4×C15111yescharacteristic
114C2×C4C2×D4×C15111yescharacteristic
115C2×C4#41×C15111yescharacteristic
116C8—21no—
117C8—41no—
118C8—42no—
119C8D8×C15112yescomplemented
120C22—41no—
121C22—41no—
122C22—41no—
123C22—82no—
124C22—82no—
125C22—82no—
126C22#121×C15111yescharacteristic
127C4—21no—
128C4—41no—
129C4C2×D8×C15111yescharacteristic
130C4AGL(1,ℤ/8)×C15111yescharacteristic
131C4AGL(1,ℤ/8)×C15112yes—
132C2—81no—
133C2—162no—
134C2#459×C15111yescharacteristic
135C2#469×C15111yescharacteristic
136C2#472×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#121
commutator, Frattini, cosocleC42C23×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #493×C151C2semidirect
2. #459×C151C2semidirect
3. #436×C151C2semidirect
4. #334×C151C2semidirect
5. #331×C151C2semidirect
50. C8×C151D8semidirect
68. C151#1687direct (N × H)
69. #1687C151direct (N × H)
70. #493C2×C151semidirect
71. #459C2×C151semidirect
72. #436C2×C151semidirect
73. #334C2×C151semidirect
74. #331C2×C151semidirect
119. C8D8×C151semidirect

Maximal subgroups

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

subgroupindex
#493×C1512
#459×C1512
#436×C1512
#334×C1512
#331×C1512
#1687151