Finite Group Databasebeta

← C151×#10391 #50315316

Subgroups — C151×#10391 #50315316

Order 38656.

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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#2840×C151C211yesmaximal, characteristic
2#1819×C151C213yesmaximal
3#1304×C151C213yesmaximal
4C22×C22⋊C4×C151C2211yescharacteristic
5#393×C151—26no—
6#379×C151C2213yes—
7#379×C151C2213yes—
8#342×C151—26no—
9C25×C151C2311yescharacteristic
10C22×Q8×C151—22no—
11C23×C4×C151Q812yescomplemented
12C2×C22⋊C4×C151—23no—
13C2×C22⋊C4×C151—23no—
14C2×C22⋊C4×C151—26no—
15C2×C22⋊C4×C151—23no—
16C2×C22⋊C4×C151—26no—
17C2×C22⋊C4×C151D416yes—
18#95×C151—26no—
19C24×C151—42no—
20C24×C151—82no—
21C24×C151C2×D413yes—
22C24×C151C2×Q811yescharacteristic
23C24×C151#4113yes—
24C2×Q8×C151—84no—
25C2×Q8×C151—82no—
26C22×C4×C151—26no—
27C22×C4×C151—26no—
28C22×C4×C151—43no—
29C22×C4×C151—82no—
30C22⋊C4×C151—41no—
31C22⋊C4×C151—43no—
32C22⋊C4×C151—46no—
33C22⋊C4×C151—46no—
34C22⋊C4×C151—86no—
35C22⋊C4×C151—86no—
36C23×C151—26no—
37C23×C151—41no—
38C23×C151—42no—
39C23×C151—43no—
40C23×C151—46no—
41C23×C151—46no—
42C23×C151—88no—
43C23×C151#12011yescharacteristic
44C23×C151C22⋊Q813yes—
45C23×C151#12413yes—
46Q8×C151—88no—
47C2×C4×C151—412no—
48C2×C4×C151—42no—
49C2×C4×C151—46no—
50C2×C4×C151—86no—
51C2×C4×C151—83no—
52C2×C4×C151—86no—
53C22×C151—22no—
54C22×C151—23no—
55C22×C151—23no—
56C22×C151—26no—
57C22×C151—26no—
58C22×C151—44no—
59C22×C151—86no—
60C22×C151—86no—
61C22×C151#39311yescharacteristic
62C22×C151#45812yes—
63C4×C151—86no—
64C4×C151—82no—
65C4×C151—163no—
66C2×C151—22no—
67C2×C151—43no—
68C2×C151—43no—
69C2×C151#203011yescharacteristic
70C2×C151#203212yes—
71#10391C15111yesmaximal, characteristic, direct product factor, Sylow
72C151#1039111yescharacteristic, direct product factor, Sylow
73#2840C2×C15111yescharacteristic
74#1819C2×C15113yes—
75#1304C2×C15113yes—
76C22×C22⋊C4C22×C15111yescharacteristic
77#393—26no—
78#379C22×C15113yes—
79#379C22×C15113yes—
80#342—26no—
81C25C23×C15111yescharacteristic
82C22×Q8—22no—
83C23×C4Q8×C15112yescomplemented
84C2×C22⋊C4—23no—
85C2×C22⋊C4—23no—
86C2×C22⋊C4—23no—
87C2×C22⋊C4—26no—
88C2×C22⋊C4—26no—
89C2×C22⋊C4D4×C15116yes—
90#95—26no—
91C24—42no—
92C24—82no—
93C24C2×D4×C15113yes—
94C24C2×Q8×C15111yescharacteristic
95C24#41×C15113yes—
96C2×Q8—84no—
97C2×Q8—82no—
98C22×C4—26no—
99C22×C4—26no—
100C22×C4—43no—
101C22×C4—82no—
102C22⋊C4—41no—
103C22⋊C4—43no—
104C22⋊C4—46no—
105C22⋊C4—46no—
106C22⋊C4—86no—
107C22⋊C4—86no—
108C23—26no—
109C23—42no—
110C23—41no—
111C23—46no—
112C23—46no—
113C23—43no—
114C23—88no—
115C23#120×C15111yescharacteristic
116C23C22⋊Q8×C15113yes—
117C23#124×C15113yes—
118Q8—88no—
119C2×C4—412no—
120C2×C4—42no—
121C2×C4—46no—
122C2×C4—86no—
123C2×C4—83no—
124C2×C4—86no—
125C22—22no—
126C22—23no—
127C22—23no—
128C22—26no—
129C22—26no—
130C22—44no—
131C22—86no—
132C22—86no—
133C22#393×C15111yescharacteristic
134C22#458×C15112yes—
135C4—86no—
136C4—82no—
137C4—163no—
138C2—22no—
139C2—43no—
140C2—43no—
141C2#2030×C15111yescharacteristic
142C2#2032×C15112yes—
subgroupG/H
center, socleC22×C151#393
commutator, Frattini, cosocleC25C23×C151
prime radicalC25×C151C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
11. C23×C4×C151Q8semidirect
71. #10391C151direct (N × H)
72. C151#10391direct (N × H)
83. C23×C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#2840×C1512
#1819×C1512
#1304×C1512
#10391151