Finite Group Databasebeta

← C19×#3416 #14561273

Subgroups — C19×#3416 #14561273

Order 2432.

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
1C19×#578C211yesmaximal, characteristic, complemented
2C19×#576C211yesmaximal, characteristic, complemented
3C19×#510C213yesmaximal, complemented
4C19×#509C213yesmaximal, complemented
5C19×#508C213yesmaximal, complemented
6C2×C19×SD32C213yesmaximal, complemented
7C19×#504C211yesmaximal, characteristic, complemented
8C19×2−1+4—21no—
9C19×H(5,𝔽2)—21no—
10C19×#137—23no—
11C19×AGL(1,ℤ/8)—23no—
12C19×#135C2213yes—
13C19×#135C2213yescomplemented
14C2×Q16×C19C2213yescomplemented
15C2×D8×C19C2213yes—
16C19×#131C2211yescharacteristic
17C19×Q32C2213yescomplemented
18C19×SD32C2213yescomplemented
19C19×SD32C2216yescomplemented
20C19×SD32C2211yescharacteristic, complemented
21C19×D16C2213yescomplemented
22C19×M32C2213yescomplemented
23C2×C16×C19C2213yescomplemented
24#41×C19—23no—
25#41×C19—23no—
26#41×C19—41no—
27#41×C19—43no—
28#41×C19D411yescharacteristic
29C2×Q8×C19—23no—
30C2×Q8×C19—41no—
31C2×D4×C19—23no—
32C2×D4×C19—43no—
33Q16×C19—23no—
34Q16×C19C2313yes—
35Q16×C19C2311yescharacteristic
36SD16×C19—23no—
37SD16×C19—23no—
38D8×C19—23no—
39D8×C19C2313yes—
40D8×C19C2311yescharacteristic
41M16×C19D413yes—
42C2×C8×C19C2313yes—
43C16×C19C2311yescharacteristic
44C16×C19C2313yes—
45C23×C19—43no—
46Q8×C19—21no—
47Q8×C19—23no—
48Q8×C19—43no—
49Q8×C19D811yescharacteristic
50D4×C19—23no—
51D4×C19—21no—
52D4×C19—43no—
53D4×C19—43no—
54D4×C19—43no—
55D4×C19D813yes—
56C2×C4×C19—43no—
57C2×C4×C19—43no—
58C2×C4×C19—43no—
59C2×C4×C19C2×D413yes—
60C8×C19C2×D413yes—
61C8×C19C2411yescharacteristic
62#3416C1911yesmaximal, characteristic, direct product factor, Sylow
63C22×C19—41no—
64C22×C19—43no—
65C22×C19—163no—
66C22×C19C2×D813yes—
67C4×C19—41no—
68C4×C19—43no—
69C4×C19C2×D813yes—
70C4×C19C22×D411yescharacteristic
71#578C2×C1911yescharacteristic, complemented
72#576C2×C1911yescharacteristic, complemented
73#510C2×C1913yescomplemented
74#509C2×C1913yescomplemented
75#508C2×C1913yescomplemented
76C2×SD32C2×C1913yescomplemented
77#504C2×C1911yescharacteristic, complemented
78C2×C19—23no—
79C2×C19—81no—
80C2×C19—83no—
81C2×C19C22×D811yescharacteristic
822−1+4—21no—
83H(5,𝔽2)—21no—
84#137—23no—
85AGL(1,ℤ/8)—23no—
86#135C22×C1913yes—
87#135C22×C1913yescomplemented
88C2×Q16C22×C1913yescomplemented
89C2×D8C22×C1913yes—
90#131C22×C1911yescharacteristic
91Q32C22×C1913yescomplemented
92SD32C22×C1913yescomplemented
93SD32C22×C1916yescomplemented
94SD32C22×C1911yescharacteristic, complemented
95D16C22×C1913yescomplemented
96M32C22×C1913yescomplemented
97C2×C16C22×C1913yescomplemented
98C19#341611yescharacteristic, direct product factor, Sylow
99#41—23no—
100#41—23no—
101#41—41no—
102#41—43no—
103#41D4×C1911yescharacteristic
104C2×Q8—23no—
105C2×Q8—41no—
106C2×D4—23no—
107C2×D4—43no—
108Q16—23no—
109Q16C23×C1913yes—
110Q16C23×C1911yescharacteristic
111SD16—23no—
112SD16—23no—
113D8—23no—
114D8C23×C1911yescharacteristic
115D8C23×C1913yes—
116M16D4×C1913yes—
117C2×C8C23×C1913yes—
118C16C23×C1911yescharacteristic
119C16C23×C1913yes—
120C23—43no—
121Q8—21no—
122Q8—23no—
123Q8—43no—
124Q8D8×C1911yescharacteristic
125D4—23no—
126D4—21no—
127D4—43no—
128D4—43no—
129D4—43no—
130D4D8×C1913yes—
131C2×C4—43no—
132C2×C4—43no—
133C2×C4—43no—
134C2×C4C2×D4×C1913yes—
135C8C2×D4×C1913yes—
136C8C24×C1911yescharacteristic
137C22—41no—
138C22—43no—
139C22—163no—
140C22C2×D8×C1913yes—
141C4—41no—
142C4—43no—
143C4C2×D8×C1913yes—
144C4C22×D4×C1911yescharacteristic
145C2—23no—
146C2—83no—
147C2—81no—
148C2C22×D8×C1911yescharacteristic
subgroupG/H
center, socleC2×C19C22×D8
commutator, Frattini, cosocleC8C24×C19
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ #41×C19 ◁ C19×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#578C2semidirect
2. C19×#576C2semidirect
3. C19×#510C2semidirect
4. C19×#509C2semidirect
5. C19×#508C2semidirect
6. C2×C19×SD32C2semidirect
7. C19×#504C2semidirect
13. C19×#135C22semidirect
14. C2×Q16×C19C22semidirect
17. C19×Q32C22semidirect
18. C19×SD32C22semidirect
19. C19×SD32C22semidirect
20. C19×SD32C22semidirect
21. C19×D16C22semidirect
22. C19×M32C22semidirect
23. C2×C16×C19C22semidirect
62. #3416C19direct (N × H)
71. #578C2×C19semidirect
72. #576C2×C19semidirect
73. #510C2×C19semidirect
74. #509C2×C19semidirect
75. #508C2×C19semidirect
76. C2×SD32C2×C19semidirect
77. #504C2×C19semidirect
87. #135C22×C19semidirect
88. C2×Q16C22×C19semidirect
91. Q32C22×C19semidirect
92. SD32C22×C19semidirect
93. SD32C22×C19semidirect
94. SD32C22×C19semidirect
95. D16C22×C19semidirect
96. M32C22×C19semidirect
97. C2×C16C22×C19semidirect
98. C19#3416direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#5782
C19×#5762
C19×#5102
C19×#5092
C19×#5082
C2×C19×SD322
C19×#5042
#341619