Finite Group Databasebeta

← C151×#7370 #50312295

Subgroups — C151×#7370 #50312295

Order 38656.

190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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#1845×C151C211yesmaximal, characteristic
2#1325×C151C212yesmaximal
3C2×#107×C151—22no—
4C2×C4×C8×C151C411yescharacteristic
5#384×C151C411yescharacteristic
6#384×C151C2211yescharacteristic
7#324×C151—22no—
8C22×C8×C151—21no—
9C2×C4⋊C4×C151—21no—
10C2×C4⋊C4×C151—41no—
11C2×C4⋊C4×C151—41no—
12C2×C4⋊C4×C151D412yes—
13C2×C42×C151C2×C411yescharacteristic
14#107×C151—44no—
15C22⋊C8×C151—42no—
16C4×C8×C151—21no—
17C4×C8×C151C812yescomplemented
18C22×C4×C151—21no—
19C22×C4×C151—22no—
20C22×C4×C151—41no—
21C22×C4×C151C22⋊C411yescharacteristic
22C2×C8×C151—22no—
23C2×C8×C151—22no—
24C2×C8×C151—22no—
25C2×C8×C151—82no—
26C4⋊C4×C151—42no—
27C4⋊C4×C151—42no—
28C4⋊C4×C151—82no—
29C4⋊C4×C151—82no—
30C42×C151—21no—
31C42×C151C2×C811yescharacteristic
32C42×C151M1611yescharacteristic
33C23×C151#9911yescharacteristic
34C2×C4×C151—22no—
35C2×C4×C151—22no—
36C2×C4×C151—21no—
37C2×C4×C151—21no—
38C2×C4×C151—21no—
39C2×C4×C151—21no—
40C2×C4×C151—42no—
41C2×C4×C151—82no—
42C2×C4×C151—82no—
43C2×C4×C151—81no—
44C2×C4×C151C22⋊C811yescharacteristic
45C2×C4×C151#10111yescharacteristic
46C8×C151—24no—
47C8×C151—162no—
48C22×C151—21no—
49C22×C151—21no—
50C22×C151#32411yescharacteristic
51C22×C151#35311yescharacteristic
52C22×C151#35611yescharacteristic
53C4×C151—22no—
54C4×C151—22no—
55C4×C151—21no—
56C4×C151—21no—
57C4×C151—82no—
58C4×C151—161no—
59C2×C151—21no—
60C2×C151—21no—
61C2×C151#132511yescharacteristic
62C2×C151#140811yescharacteristic
63C2×C151#141111yescharacteristic
64#7370C15111yesmaximal, characteristic, direct product factor, Sylow
65C151#737011yescharacteristic, direct product factor, Sylow
66#1845C2×C15111yescharacteristic
67#1325C2×C15112yes—
68C2×#107—22no—
69C2×C4×C8C4×C15111yescharacteristic
70#384C4×C15111yescharacteristic
71#384C22×C15111yescharacteristic
72#324—22no—
73C22×C8—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4D4×C15112yes—
78C2×C42C2×C4×C15111yescharacteristic
79#107—44no—
80C22⋊C8—42no—
81C4×C8—21no—
82C4×C8C8×C15112yescomplemented
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—41no—
86C22×C4C22⋊C4×C15111yescharacteristic
87C2×C8—22no—
88C2×C8—22no—
89C2×C8—22no—
90C2×C8—82no—
91C4⋊C4—42no—
92C4⋊C4—42no—
93C4⋊C4—82no—
94C4⋊C4—82no—
95C42—21no—
96C42C2×C8×C15111yescharacteristic
97C42M16×C15111yescharacteristic
98C23#99×C15111yescharacteristic
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—42no—
106C2×C4—82no—
107C2×C4—82no—
108C2×C4—81no—
109C2×C4C22⋊C8×C15111yescharacteristic
110C2×C4#101×C15111yescharacteristic
111C8—24no—
112C8—162no—
113C22—21no—
114C22—21no—
115C22#324×C15111yescharacteristic
116C22#353×C15111yescharacteristic
117C22#356×C15111yescharacteristic
118C4—22no—
119C4—22no—
120C4—21no—
121C4—21no—
122C4—82no—
123C4—161no—
124C2—21no—
125C2—21no—
126C2#1325×C15111yescharacteristic
127C2#1408×C15111yescharacteristic
128C2#1411×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#353
commutatorC42C2×C8×C151
Frattini, cosocle#384C22×C151
prime radicalC23×C151#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C151 ◁ C22×C4×C151 ◁ #384×C151 ◁ G

Complements

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

NH ≅ G/Ntype
17. C4×C8×C151C8semidirect
64. #7370C151direct (N × H)
65. C151#7370direct (N × H)
82. C4×C8C8×C151semidirect

Maximal subgroups

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

subgroupindex
#1845×C1512
#1325×C1512
#7370151