Finite Group Databasebeta

← C151×#13693 #50318618

Subgroups — C151×#13693 #50318618

Order 38656.

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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#2264×C151C212yesmaximal
2#2247×C151C211yesmaximal, characteristic, complemented
3#2178×C151C211yesmaximal, characteristic
4#1422×C151C211yesmaximal, characteristic, complemented
5#1420×C151C212yesmaximal, complemented
6#508×C151C2211yescharacteristic
7C2×Q32×C151—21no—
8C2×Q32×C151C2212yes—
9#494×C151—21no—
10#443×C151—21no—
11Q64×C151—22no—
12SD64×C151—22no—
13M64×C151C2212yes—
14#368×C151C2211yescharacteristic
15#359×C151—21no—
16C4×C16×C151C2211yescharacteristic
17#135×C151—21no—
18C2×Q16×C151—22no—
19C2×Q16×C151—41no—
20#131×C151—41no—
21C4⋊Q8×C151—41no—
22Q32×C151—22no—
23Q32×C151—22no—
24Q32×C151—42no—
25Q32×C151D411yescharacteristic
26SD32×C151—21no—
27D16×C151D411yescharacteristic
28C2×C16×C151D411yescharacteristic
29C2×C16×C151C2311yescharacteristic
30#108×C151—21no—
31#104×C151—41no—
32C4×C8×C151D411yescharacteristic
33C32×C151—22no—
34#41×C151—41no—
35C2×Q8×C151—42no—
36Q16×C151—21no—
37Q16×C151—42no—
38Q16×C151—42no—
39Q16×C151—81no—
40Q16×C151—81no—
41SD16×C151—41no—
42D8×C151—21no—
43M16×C151—41no—
44M16×C151—81no—
45C2×C8×C151—81no—
46C2×C8×C151D811yescharacteristic
47C2×C8×C151C2×D411yescharacteristic
48C4⋊C4×C151—82no—
49C42×C151D811yescharacteristic
50C16×C151—21no—
51C16×C151C2×D411yescharacteristic
52C16×C151#4111yescharacteristic
53Q8×C151—41no—
54Q8×C151—82no—
55Q8×C151—82no—
56D4×C151—41no—
57D4×C151—81no—
58C2×C4×C151—21no—
59C2×C4×C151—81no—
60C2×C4×C151—82no—
61C2×C4×C151C2×D811yescharacteristic
62C8×C151—81no—
63C8×C151D1611yescharacteristic
64C8×C151D1611yescharacteristic
65C8×C151#12111yescharacteristic
66C8×C151AGL(1,ℤ/8)11yescharacteristic
67C22×C151—81no—
68C22×C151#50911yescharacteristic
69C4×C151—22no—
70C4×C151—81no—
71C4×C151—162no—
72C4×C151#45911yescharacteristic
73C4×C151C2×D1611yescharacteristic
74C2×C151—21no—
75C2×C151—161no—
76C2×C151#220611yescharacteristic
77#13693C15111yesmaximal, characteristic, direct product factor, Sylow
78C151#1369311yescharacteristic, direct product factor, Sylow
79#2264C2×C15112yes—
80#2247C2×C15111yescharacteristic, complemented
81#2178C2×C15111yescharacteristic
82#1422C2×C15111yescharacteristic, complemented
83#1420C2×C15112yescomplemented
84#508C22×C15111yescharacteristic
85C2×Q32—21no—
86C2×Q32C22×C15112yes—
87#494—21no—
88#443—21no—
89Q64—22no—
90SD64—22no—
91M64C22×C15112yes—
92#368C22×C15111yescharacteristic
93#359—21no—
94C4×C16C22×C15111yescharacteristic
95#135—21no—
96C2×Q16—22no—
97C2×Q16—41no—
98#131—41no—
99C4⋊Q8—41no—
100Q32—22no—
101Q32—22no—
102Q32—42no—
103Q32D4×C15111yescharacteristic
104SD32—21no—
105D16D4×C15111yescharacteristic
106C2×C16D4×C15111yescharacteristic
107C2×C16C23×C15111yescharacteristic
108#108—21no—
109#104—41no—
110C4×C8D4×C15111yescharacteristic
111C32—22no—
112#41—41no—
113C2×Q8—42no—
114Q16—21no—
115Q16—42no—
116Q16—42no—
117Q16—81no—
118Q16—81no—
119SD16—41no—
120D8—21no—
121M16—41no—
122M16—81no—
123C2×C8—81no—
124C2×C8D8×C15111yescharacteristic
125C2×C8C2×D4×C15111yescharacteristic
126C4⋊C4—82no—
127C42D8×C15111yescharacteristic
128C16—21no—
129C16C2×D4×C15111yescharacteristic
130C16#41×C15111yescharacteristic
131Q8—41no—
132Q8—82no—
133Q8—82no—
134D4—41no—
135D4—81no—
136C2×C4—21no—
137C2×C4—81no—
138C2×C4—82no—
139C2×C4C2×D8×C15111yescharacteristic
140C8—81no—
141C8D16×C15111yescharacteristic
142C8D16×C15111yescharacteristic
143C8#121×C15111yescharacteristic
144C8AGL(1,ℤ/8)×C15111yescharacteristic
145C22—81no—
146C22#509×C15111yescharacteristic
147C4—22no—
148C4—81no—
149C4—162no—
150C4#459×C15111yescharacteristic
151C4C2×D16×C15111yescharacteristic
152C2—21no—
153C2—161no—
154C2#2206×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2206
commutator, Frattini, cosocleC2×C16C23×C151
prime radical#508×C151C22
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C4×C8×C151 ◁ C4×C16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2247×C151C2semidirect
4. #1422×C151C2semidirect
5. #1420×C151C2semidirect
77. #13693C151direct (N × H)
78. C151#13693direct (N × H)
80. #2247C2×C151semidirect
82. #1422C2×C151semidirect
83. #1420C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2264×C1512
#2247×C1512
#2178×C1512
#1422×C1512
#1420×C1512
#13693151