Finite Group Databasebeta

← C151×#7361 #50312286

Subgroups — C151×#7361 #50312286

Order 38656.

184 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 46 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#1994×C151C211yesmaximal, characteristic
2#1327×C151C212yesmaximal
3#533×C151C411yescharacteristic
4#423×C151C2211yescharacteristic
5C43×C151C411yescharacteristic
6#349×C151—22no—
7#339×C151—22no—
8C2×M16×C151D412yes—
9C4⋊Q8×C151—21no—
10#125×C151C812yes—
11C22⋊Q8×C151—41no—
12C4×Q8×C151—41no—
13#117×C151—21no—
14C2×C42×C151—21no—
15C2×C42×C151—41no—
16C2×C42×C151C2×C411yescharacteristic
17M32×C151—42no—
18C4⋊C8×C151—41no—
19C2×Q8×C151—41no—
20C22×C4×C151—21no—
21C22×C4×C151—41no—
22C22×C4×C151C22⋊C411yescharacteristic
23M16×C151—42no—
24C2×C8×C151—22no—
25C4⋊C4×C151—22no—
26C4⋊C4×C151—42no—
27C4⋊C4×C151—41no—
28C22⋊C4×C151—41no—
29C42×C151—21no—
30C42×C151—22no—
31C42×C151—41no—
32C42×C151—44no—
33C42×C151—41no—
34C42×C151C2×C811yescharacteristic
35C42×C151M1611yescharacteristic
36C16×C151—82no—
37C23×C151#10011yescharacteristic
38Q8×C151—82no—
39C2×C4×C151—21no—
40C2×C4×C151—21no—
41C2×C4×C151—21no—
42C2×C4×C151—21no—
43C2×C4×C151—42no—
44C2×C4×C151—42no—
45C2×C4×C151—44no—
46C2×C4×C151—42no—
47C2×C4×C151C22⋊C811yescharacteristic
48C2×C4×C151#9911yescharacteristic
49C8×C151—42no—
50C22×C151—21no—
51C22×C151—41no—
52C22×C151#32311yescharacteristic
53C4×C151—22no—
54C4×C151—21no—
55C4×C151—41no—
56C4×C151—44no—
57C4×C151—82no—
58C4×C151#35411yescharacteristic
59C4×C151#35611yescharacteristic
60C2×C151—21no—
61C2×C151—41no—
62C2×C151#131911yescharacteristic
63#7361C15111yesmaximal, characteristic, direct product factor, Sylow
64C151#736111yescharacteristic, direct product factor, Sylow
65#1994C2×C15111yescharacteristic
66#1327C2×C15112yes—
67#533C4×C15111yescharacteristic
68#423C22×C15111yescharacteristic
69C43C4×C15111yescharacteristic
70#349—22no—
71#339—22no—
72C2×M16D4×C15112yes—
73C4⋊Q8—21no—
74#125C8×C15112yes—
75C22⋊Q8—41no—
76C4×Q8—41no—
77#117—21no—
78C2×C42—21no—
79C2×C42—41no—
80C2×C42C2×C4×C15111yescharacteristic
81M32—42no—
82C4⋊C8—41no—
83C2×Q8—41no—
84C22×C4—21no—
85C22×C4—41no—
86C22×C4C22⋊C4×C15111yescharacteristic
87M16—42no—
88C2×C8—22no—
89C4⋊C4—22no—
90C4⋊C4—42no—
91C4⋊C4—41no—
92C22⋊C4—41no—
93C42—21no—
94C42—22no—
95C42—41no—
96C42—44no—
97C42—41no—
98C42C2×C8×C15111yescharacteristic
99C42M16×C15111yescharacteristic
100C16—82no—
101C23#100×C15111yescharacteristic
102Q8—82no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—44no—
110C2×C4—42no—
111C2×C4C22⋊C8×C15111yescharacteristic
112C2×C4#99×C15111yescharacteristic
113C8—42no—
114C22—21no—
115C22—41no—
116C22#323×C15111yescharacteristic
117C4—22no—
118C4—21no—
119C4—41no—
120C4—44no—
121C4—82no—
122C4#354×C15111yescharacteristic
123C4#356×C15111yescharacteristic
124C2—21no—
125C2—41no—
126C2#1319×C15111yescharacteristic
subgroupG/H
centerC4×C151#354
commutatorC42C2×C8×C151
Frattini, cosocle#423C22×C151
socleC2×C151#1319
prime radicalC23×C151#100
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C2×C4×C151 ◁ C22×C4×C151 ◁ #423×C151 ◁ G

Complements

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

NH ≅ G/Ntype
63. #7361C151direct (N × H)
64. C151#7361direct (N × H)

Maximal subgroups

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

subgroupindex
#1994×C1512
#1327×C1512
#7361151