Finite Group Databasebeta

← C151×#12442 #50317367

Subgroups — C151×#12442 #50317367

Order 38656.

244 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 82 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#2246×C151C211yesmaximal, characteristic
2#2183×C151C211yesmaximal, characteristic, complemented
3#1668×C151C212yesmaximal, complemented
4#1372×C151C211yesmaximal, characteristic, complemented
5#1361×C151C212yesmaximal, complemented
6C2×D16×C151—21no—
7C2×D16×C151—21no—
8#493×C151C2212yes—
9#460×C151—22no—
10C8×Q8×C151C2211yescharacteristic
11C4⋊C16×C151—21no—
12C4⋊C16×C151C2211yescharacteristic
13#346×C151—21no—
14C4×C16×C151C2211yescharacteristic
15#335×C151C2212yes—
16#331×C151—22no—
17C2×SD16×C151—42no—
18C2×D8×C151—22no—
19C2×D8×C151—22no—
20#127×C151—22no—
21C4×Q8×C151D411yescharacteristic
22D16×C151—42no—
23D16×C151—42no—
24C2×C16×C151—21no—
25C2×C16×C151D411yescharacteristic
26C2×C16×C151D411yescharacteristic
27C4⋊C8×C151—21no—
28C4⋊C8×C151—22no—
29C4⋊C8×C151D411yescharacteristic
30#102×C151—42no—
31C4×C8×C151—21no—
32C4×C8×C151C2311yescharacteristic
33C2×Q8×C151D811yescharacteristic
34C2×D4×C151—42no—
35C2×D4×C151—42no—
36C2×D4×C151—42no—
37SD16×C151—84no—
38D8×C151—42no—
39D8×C151—42no—
40D8×C151—82no—
41C2×C8×C151—21no—
42C2×C8×C151—42no—
43C2×C8×C151C2×D411yescharacteristic
44C2×C8×C151#4111yescharacteristic
45C4⋊C4×C151—21no—
46C4⋊C4×C151D811yescharacteristic
47C42×C151—21no—
48C42×C151C2×D411yescharacteristic
49C16×C151—21no—
50C16×C151—41no—
51C16×C151SD1612yescomplemented
52C23×C151—82no—
53Q8×C151—22no—
54D4×C151—82no—
55D4×C151—82no—
56D4×C151—82no—
57D4×C151—82no—
58D4×C151—162no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151#12111yescharacteristic
62C2×C4×C151C2×D811yescharacteristic
63C2×C4×C151#13511yescharacteristic
64C8×C151—21no—
65C8×C151—41no—
66C8×C151—82no—
67C8×C151C2×SD1611yescharacteristic
68C8×C151AGL(1,ℤ/8)11yescharacteristic
69C22×C151—162no—
70C22×C151—162no—
71C22×C151—162no—
72C22×C151#46611yescharacteristic
73C4×C151—21no—
74C4×C151—41no—
75C4×C151—41no—
76C4×C151#46011yescharacteristic
77C4×C151#47211yescharacteristic
78C4×C151#50912yes—
79C2×C151—322no—
80C2×C151#166811yescharacteristic
81C2×C151#221811yescharacteristic
82C2×C151#222111yescharacteristic
83#12442C15111yesmaximal, characteristic, direct product factor, Sylow
84C151#1244211yescharacteristic, direct product factor, Sylow
85#2246C2×C15111yescharacteristic
86#2183C2×C15111yescharacteristic, complemented
87#1668C2×C15112yescomplemented
88#1372C2×C15111yescharacteristic, complemented
89#1361C2×C15112yescomplemented
90C2×D16—21no—
91C2×D16—21no—
92#493C22×C15112yes—
93#460—22no—
94C8×Q8C22×C15111yescharacteristic
95C4⋊C16—21no—
96C4⋊C16C22×C15111yescharacteristic
97#346—21no—
98C4×C16C22×C15111yescharacteristic
99#335C22×C15112yes—
100#331—22no—
101C2×SD16—42no—
102C2×D8—22no—
103C2×D8—22no—
104#127—22no—
105C4×Q8D4×C15111yescharacteristic
106D16—42no—
107D16—42no—
108C2×C16—21no—
109C2×C16D4×C15111yescharacteristic
110C2×C16D4×C15111yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—22no—
113C4⋊C8D4×C15111yescharacteristic
114#102—42no—
115C4×C8—21no—
116C4×C8C23×C15111yescharacteristic
117C2×Q8D8×C15111yescharacteristic
118C2×D4—42no—
119C2×D4—42no—
120C2×D4—42no—
121SD16—84no—
122D8—42no—
123D8—42no—
124D8—82no—
125C2×C8—21no—
126C2×C8—42no—
127C2×C8C2×D4×C15111yescharacteristic
128C2×C8#41×C15111yescharacteristic
129C4⋊C4—21no—
130C4⋊C4D8×C15111yescharacteristic
131C42—21no—
132C42C2×D4×C15111yescharacteristic
133C16—21no—
134C16—41no—
135C16SD16×C15112yescomplemented
136C23—82no—
137Q8—22no—
138D4—82no—
139D4—82no—
140D4—82no—
141D4—82no—
142D4—162no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4#121×C15111yescharacteristic
146C2×C4C2×D8×C15111yescharacteristic
147C2×C4#135×C15111yescharacteristic
148C8—21no—
149C8—41no—
150C8—82no—
151C8C2×SD16×C15111yescharacteristic
152C8AGL(1,ℤ/8)×C15111yescharacteristic
153C22—162no—
154C22—162no—
155C22—162no—
156C22#466×C15111yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4#460×C15111yescharacteristic
161C4#472×C15111yescharacteristic
162C4#509×C15112yes—
163C2—322no—
164C2#1668×C15111yescharacteristic
165C2#2218×C15111yescharacteristic
166C2#2221×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#466
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#2246×C151C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2183×C151C2semidirect
3. #1668×C151C2semidirect
4. #1372×C151C2semidirect
5. #1361×C151C2semidirect
51. C16×C151SD16semidirect
83. #12442C151direct (N × H)
84. C151#12442direct (N × H)
86. #2183C2×C151semidirect
87. #1668C2×C151semidirect
88. #1372C2×C151semidirect
89. #1361C2×C151semidirect
135. C16SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#2246×C1512
#2183×C1512
#1668×C1512
#1372×C1512
#1361×C1512
#12442151