Finite Group Databasebeta

← C47×#3416 #20241026

Subgroups — C47×#3416 #20241026

Order 6016.

360 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C47×#578C211yesmaximal, characteristic, complemented
2C47×#576C211yesmaximal, characteristic, complemented
3C47×#510C213yesmaximal, complemented
4C47×#509C213yesmaximal, complemented
5C47×#508C213yesmaximal, complemented
6C2×SD32×C47C213yesmaximal, complemented
7C47×#504C211yesmaximal, characteristic, complemented
82−1+4×C47—21no—
9H(5,𝔽2)×C47—21no—
10#137×C47—23no—
11AGL(1,ℤ/8)×C47—23no—
12#135×C47C2213yes—
13#135×C47C2213yescomplemented
14C2×Q16×C47C2213yescomplemented
15C2×D8×C47C2213yes—
16#131×C47C2211yescharacteristic
17Q32×C47C2213yescomplemented
18SD32×C47C2213yescomplemented
19SD32×C47C2216yescomplemented
20SD32×C47C2211yescharacteristic, complemented
21D16×C47C2213yescomplemented
22M32×C47C2213yescomplemented
23C2×C16×C47C2213yescomplemented
24#41×C47—23no—
25#41×C47—23no—
26#41×C47—41no—
27#41×C47—43no—
28#41×C47D411yescharacteristic
29C2×Q8×C47—23no—
30C2×Q8×C47—41no—
31C2×D4×C47—23no—
32C2×D4×C47—43no—
33Q16×C47—23no—
34Q16×C47C2313yes—
35Q16×C47C2311yescharacteristic
36SD16×C47—23no—
37SD16×C47—23no—
38D8×C47—23no—
39D8×C47C2311yescharacteristic
40D8×C47C2313yes—
41M16×C47D413yes—
42C2×C8×C47C2313yes—
43C16×C47C2311yescharacteristic
44C16×C47C2313yes—
45C23×C47—43no—
46Q8×C47—21no—
47Q8×C47—23no—
48Q8×C47—43no—
49Q8×C47D811yescharacteristic
50D4×C47—23no—
51D4×C47—21no—
52D4×C47—43no—
53D4×C47—43no—
54D4×C47—43no—
55D4×C47D813yes—
56C2×C4×C47—43no—
57C2×C4×C47—43no—
58C2×C4×C47—43no—
59C2×C4×C47C2×D413yes—
60C8×C47C2×D413yes—
61C8×C47C2411yescharacteristic
62C22×C47—41no—
63C22×C47—43no—
64C22×C47—163no—
65C22×C47C2×D813yes—
66C4×C47—41no—
67C4×C47—43no—
68C4×C47C2×D813yes—
69C4×C47C22×D411yescharacteristic
70#3416C4711yesmaximal, characteristic, direct product factor, Sylow
71C2×C47—23no—
72C2×C47—81no—
73C2×C47—83no—
74C2×C47C22×D811yescharacteristic
75#578C2×C4711yescharacteristic, complemented
76#576C2×C4711yescharacteristic, complemented
77#510C2×C4713yescomplemented
78#509C2×C4713yescomplemented
79#508C2×C4713yescomplemented
80C2×SD32C2×C4713yescomplemented
81#504C2×C4711yescharacteristic, complemented
82C47#341611yescharacteristic, direct product factor, Sylow
832−1+4—21no—
84H(5,𝔽2)—21no—
85#137—23no—
86AGL(1,ℤ/8)—23no—
87#135C22×C4713yes—
88#135C22×C4713yescomplemented
89C2×Q16C22×C4713yescomplemented
90C2×D8C22×C4713yes—
91#131C22×C4711yescharacteristic
92Q32C22×C4713yescomplemented
93SD32C22×C4713yescomplemented
94SD32C22×C4716yescomplemented
95SD32C22×C4711yescharacteristic, complemented
96D16C22×C4713yescomplemented
97M32C22×C4713yescomplemented
98C2×C16C22×C4713yescomplemented
99#41—23no—
100#41—23no—
101#41—41no—
102#41—43no—
103#41D4×C4711yescharacteristic
104C2×Q8—23no—
105C2×Q8—41no—
106C2×D4—23no—
107C2×D4—43no—
108Q16—23no—
109Q16C23×C4713yes—
110Q16C23×C4711yescharacteristic
111SD16—23no—
112SD16—23no—
113D8—23no—
114D8C23×C4711yescharacteristic
115D8C23×C4713yes—
116M16D4×C4713yes—
117C2×C8C23×C4713yes—
118C16C23×C4711yescharacteristic
119C16C23×C4713yes—
120C23—43no—
121Q8—21no—
122Q8—23no—
123Q8—43no—
124Q8D8×C4711yescharacteristic
125D4—23no—
126D4—21no—
127D4—43no—
128D4—43no—
129D4—43no—
130D4D8×C4713yes—
131C2×C4—43no—
132C2×C4—43no—
133C2×C4—43no—
134C2×C4C2×D4×C4713yes—
135C8C2×D4×C4713yes—
136C8C24×C4711yescharacteristic
137C22—41no—
138C22—43no—
139C22—163no—
140C22C2×D8×C4713yes—
141C4—41no—
142C4—43no—
143C4C2×D8×C4713yes—
144C4C22×D4×C4711yescharacteristic
145C2—23no—
146C2—83no—
147C2—81no—
148C2C22×D8×C4711yescharacteristic
subgroupG/H
center, socleC2×C47C22×D8
commutator, Frattini, cosocleC8C24×C47
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ #41×C47 ◁ #131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#578C2semidirect
2. C47×#576C2semidirect
3. C47×#510C2semidirect
4. C47×#509C2semidirect
5. C47×#508C2semidirect
6. C2×SD32×C47C2semidirect
7. C47×#504C2semidirect
13. #135×C47C22semidirect
14. C2×Q16×C47C22semidirect
17. Q32×C47C22semidirect
18. SD32×C47C22semidirect
19. SD32×C47C22semidirect
20. SD32×C47C22semidirect
21. D16×C47C22semidirect
22. M32×C47C22semidirect
23. C2×C16×C47C22semidirect
70. #3416C47direct (N × H)
75. #578C2×C47semidirect
76. #576C2×C47semidirect
77. #510C2×C47semidirect
78. #509C2×C47semidirect
79. #508C2×C47semidirect
80. C2×SD32C2×C47semidirect
81. #504C2×C47semidirect
82. C47#3416direct (N × H)
88. #135C22×C47semidirect
89. C2×Q16C22×C47semidirect
92. Q32C22×C47semidirect
93. SD32C22×C47semidirect
94. SD32C22×C47semidirect
95. SD32C22×C47semidirect
96. D16C22×C47semidirect
97. M32C22×C47semidirect
98. C2×C16C22×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#5782
C47×#5762
C47×#5102
C47×#5092
C47×#5082
C2×SD32×C472
C47×#5042
#341647