Finite Group Databasebeta

← C151×#7822 #50312747

Subgroups — C151×#7822 #50312747

Order 38656.

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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#2679×C151C211yesmaximal, characteristic
2#2094×C151C213yesmaximal, complemented
3#1270×C151C213yesmaximal, complemented
4C2×#120×C151—23no—
5C2×#106×C151—23no—
6C2×#102×C151—23no—
7#394×C151—23no—
8#390×C151C2213yes—
9#384×C151C2211yescharacteristic, complemented
10#336×C151C2213yescomplemented
11C25×C151—21no—
12C22×D4×C151—23no—
13C22×D4×C151D413yes—
14C22×C8×C151—23no—
15#120×C151—46no—
16#120×C151—46no—
17C2×C4⋊C4×C151—23no—
18C2×C4⋊C4×C151D413yes—
19C2×C22⋊C4×C151—23no—
20C2×C22⋊C4×C151—26no—
21C2×C42×C151C2311yescharacteristic
22#106×C151—46no—
23#102×C151—46no—
24#95×C151—21no—
25C24×C151—23no—
26C24×C151—46no—
27C24×C151—83no—
28C24×C151—81no—
29C2×D4×C151—23no—
30C2×D4×C151—43no—
31C2×D4×C151—43no—
32C2×D4×C151—412no—
33C2×D4×C151—83no—
34C2×D4×C151SD1616yes—
35C22×C4×C151—23no—
36C22×C4×C151—41no—
37C22×C4×C151C2×D413yes—
38C2×C8×C151—26no—
39C2×C8×C151—43no—
40C2×C8×C151—43no—
41C4⋊C4×C151—43no—
42C4⋊C4×C151—43no—
43C4⋊C4×C151—43no—
44C22⋊C4×C151—46no—
45C22⋊C4×C151—46no—
46C22⋊C4×C151—46no—
47C42×C151—41no—
48C23×C151—26no—
49C23×C151—46no—
50C23×C151—43no—
51C23×C151—46no—
52C23×C151—43no—
53C23×C151—812no—
54C23×C151—812no—
55C23×C151—84no—
56C23×C151#12011yescharacteristic
57D4×C151—46no—
58D4×C151—83no—
59D4×C151—812no—
60C2×C4×C151—23no—
61C2×C4×C151—23no—
62C2×C4×C151—46no—
63C2×C4×C151—43no—
64C2×C4×C151—83no—
65C2×C4×C151C2×SD1613yes—
66C2×C4×C151AGL(1,ℤ/8)13yes—
67C8×C151—46no—
68C22×C151—46no—
69C22×C151—412no—
70C22×C151—816no—
71C22×C151—86no—
72C22×C151—83no—
73C22×C151—83no—
74C22×C151#45013yes—
75C22×C151#45313yes—
76C22×C151#45811yescharacteristic
77C4×C151—23no—
78C4×C151—23no—
79C4×C151—83no—
80C4×C151—161no—
81C2×C151—86no—
82C2×C151#161313yes—
83C2×C151#162913yes—
84C2×C151#165511yescharacteristic
85#7822C15111yesmaximal, characteristic, direct product factor, Sylow
86C151#782211yescharacteristic, direct product factor, Sylow
87#2679C2×C15111yescharacteristic
88#2094C2×C15113yescomplemented
89#1270C2×C15113yescomplemented
90C2×#120—23no—
91C2×#106—23no—
92C2×#102—23no—
93#394—23no—
94#390C22×C15113yes—
95#384C22×C15111yescharacteristic, complemented
96#336C22×C15113yescomplemented
97C25—21no—
98C22×D4—23no—
99C22×D4D4×C15113yes—
100C22×C8—23no—
101#120—46no—
102#120—46no—
103C2×C4⋊C4—23no—
104C2×C4⋊C4D4×C15113yes—
105C2×C22⋊C4—23no—
106C2×C22⋊C4—26no—
107C2×C42C23×C15111yescharacteristic
108#106—46no—
109#102—46no—
110#95—21no—
111C24—23no—
112C24—46no—
113C24—83no—
114C24—81no—
115C2×D4—23no—
116C2×D4—43no—
117C2×D4—43no—
118C2×D4—412no—
119C2×D4—83no—
120C2×D4SD16×C15116yes—
121C22×C4—23no—
122C22×C4—41no—
123C22×C4C2×D4×C15113yes—
124C2×C8—26no—
125C2×C8—43no—
126C2×C8—43no—
127C4⋊C4—43no—
128C4⋊C4—43no—
129C4⋊C4—43no—
130C22⋊C4—46no—
131C22⋊C4—46no—
132C22⋊C4—46no—
133C42—41no—
134C23—26no—
135C23—46no—
136C23—43no—
137C23—46no—
138C23—43no—
139C23—812no—
140C23—812no—
141C23—84no—
142C23#120×C15111yescharacteristic
143D4—46no—
144D4—83no—
145D4—812no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—46no—
149C2×C4—43no—
150C2×C4—83no—
151C2×C4C2×SD16×C15113yes—
152C2×C4AGL(1,ℤ/8)×C15113yes—
153C8—46no—
154C22—46no—
155C22—412no—
156C22—816no—
157C22—86no—
158C22—83no—
159C22—83no—
160C22#450×C15113yes—
161C22#453×C15113yes—
162C22#458×C15111yescharacteristic
163C4—23no—
164C4—23no—
165C4—83no—
166C4—161no—
167C2—86no—
168C2#1613×C15113yes—
169C2#1629×C15113yes—
170C2#1655×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#2679×C151C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2094×C151C2semidirect
3. #1270×C151C2semidirect
9. #384×C151C22semidirect
10. #336×C151C22semidirect
85. #7822C151direct (N × H)
86. C151#7822direct (N × H)
88. #2094C2×C151semidirect
89. #1270C2×C151semidirect
95. #384C22×C151semidirect
96. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
#2679×C1512
#2094×C1512
#1270×C1512
#7822151