Finite Group Databasebeta

← C2×C19×#442 #14560799

Subgroups — C2×C19×#442 #14560799

Order 2432.

608 conjugacy classes of subgroups; only the 296 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 296 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
1C22×D8×C19C211yesmaximal, characteristic
2C2×C4×D4×C19C212yesmaximal, complemented
3C19×#442C218yesmaximal, direct product factor
4C2×C19×#106C211yesmaximal, characteristic, complemented
5C2×C19×#102C212yesmaximal, complemented
6C2×C19×#97C211yesmaximal, characteristic, complemented
7C22×D4×C19C2212yes—
8C23×C4×C19—22no—
9C2×D8×C19C418yescomplemented
10C2×D8×C19C2214yes—
11C22×C8×C19C2211yescharacteristic
12C22×C8×C19C2211yescharacteristic
13C4×D4×C19—24no—
14C4×D4×C19C2218yescomplemented
15C2×C4⋊C4×C19C2212yes—
16C2×C22⋊C4×C19—22no—
17C2×C42×C19C2211yescharacteristic
18C19×#106C2214yescomplemented
19C19×#102C2218yescomplemented
20C19×#97C2214yescomplemented
21C24×C19—22no—
22C2×D4×C19—22no—
23C2×D4×C19—24no—
24C2×D4×C19C2×C418yescomplemented
25C2×D4×C19C2314yes—
26C22×C4×C19—22no—
27C22×C4×C19—28no—
28C22×C4×C19—48no—
29C22×C4×C19D412yes—
30C22×C4×C19C2311yescharacteristic
31D8×C19C2×C4116yescomplemented
32C2×C8×C19—22no—
33C2×C8×C19C2×C414yescomplemented
34C2×C8×C19C2312yes—
35C2×C8×C19C2312yes—
36C4⋊C4×C19—22no—
37C4⋊C4×C19C2314yes—
38C22⋊C4×C19—28no—
39C42×C19D412yes—
40C42×C19C2312yes—
41C23×C19—28no—
42C23×C19—24no—
43C23×C19—44no—
44C23×C19—44no—
45C23×C19C2×D411yescharacteristic
46D4×C19—28no—
47D4×C19—24no—
48D4×C19C22×C418yescomplemented
49C2×C4×C19—24no—
50C2×C4×C19—24no—
51C2×C4×C19—416no—
52C2×C4×C19—44no—
53C2×C4×C19C22×C412yes—
54C2×C4×C19C2×D414yes—
55C2×C4×C19C2×D411yescharacteristic
56C2×C4×C19#4112yes—
57C2×C4×C19C2411yescharacteristic
58C8×C19—22no—
59C8×C19C22×C414yescomplemented
60C2×#442C1911yesmaximal, characteristic, direct product factor, Sylow
61C22×C19—28no—
62C22×C19—44no—
63C22×C19—44no—
64C22×C19—416no—
65C22×C19C4×D412yes—
66C22×C19AGL(1,ℤ/8)14yes—
67C22×C19C22×D411yescharacteristic
68C4×C19—24no—
69C4×C19—44no—
70C4×C19C4×D412yes—
71C4×C19C23×C411yescharacteristic
72C4×C19C2×#4111yescharacteristic
73C22×D8C2×C1911yescharacteristic
74C2×C4×D4C2×C1912yescomplemented
75#442C2×C1918yesdirect product factor
76C2×#106C2×C1911yescharacteristic, complemented
77C2×#102C2×C1912yescomplemented
78C2×#97C2×C1911yescharacteristic, complemented
79C2×C19—48no—
80C2×C19#44214yesdirect product factor
81C2×C19C2×C4×D411yescharacteristic
82C2×C19C2×AGL(1,ℤ/8)12yes—
83C22×D4C22×C1912yes—
84C23×C4—22no—
85C2×D8C4×C1918yescomplemented
86C2×D8C22×C1914yes—
87C22×C8C22×C1911yescharacteristic
88C22×C8C22×C1911yescharacteristic
89C4×D4—24no—
90C4×D4C22×C1918yescomplemented
91C2×C4⋊C4C22×C1912yes—
92C2×C22⋊C4—22no—
93C2×C42C22×C1911yescharacteristic
94#106C22×C1914yescomplemented
95#102C22×C1918yescomplemented
96#97C22×C1914yescomplemented
97C19C2×#44211yescharacteristic, direct product factor, Sylow
98C24—22no—
99C2×D4—22no—
100C2×D4—24no—
101C2×D4C2×C4×C1918yescomplemented
102C2×D4C23×C1914yes—
103C22×C4—22no—
104C22×C4—28no—
105C22×C4—48no—
106C22×C4D4×C1912yes—
107C22×C4C23×C1911yescharacteristic
108D8C2×C4×C19116yescomplemented
109C2×C8—22no—
110C2×C8C2×C4×C1914yescomplemented
111C2×C8C23×C1912yes—
112C2×C8C23×C1912yes—
113C4⋊C4—22no—
114C4⋊C4C23×C1914yes—
115C22⋊C4—28no—
116C42D4×C1912yes—
117C42C23×C1912yes—
118C23—28no—
119C23—24no—
120C23—44no—
121C23—44no—
122C23C2×D4×C1911yescharacteristic
123D4—28no—
124D4—24no—
125D4C22×C4×C1918yescomplemented
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—416no—
129C2×C4—44no—
130C2×C4C22×C4×C1912yes—
131C2×C4C2×D4×C1914yes—
132C2×C4C2×D4×C1911yescharacteristic
133C2×C4#41×C1912yes—
134C2×C4C24×C1911yescharacteristic
135C8—22no—
136C8C22×C4×C1914yescomplemented
137C22—28no—
138C22—416no—
139C22—44no—
140C22—44no—
141C22C4×D4×C1912yes—
142C22C19×AGL(1,ℤ/8)14yes—
143C22C22×D4×C1911yescharacteristic
144C4—24no—
145C4—44no—
146C4C4×D4×C1912yes—
147C4C23×C4×C1911yescharacteristic
148C4C2×#41×C1911yescharacteristic
149C2—48no—
150C2C19×#44214yesdirect product factor
151C2C2×C4×D4×C1911yescharacteristic
152C2C2×C19×AGL(1,ℤ/8)12yes—
subgroupG/H
center, socleC23×C19C2×D4
commutatorC4C23×C4×C19
Frattini, cosocleC2×C4C24×C19
prime radicalC22×D8×C19C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×C19C2semidirect
3. C19×#442C2direct (N × H)
4. C2×C19×#106C2semidirect
5. C2×C19×#102C2semidirect
6. C2×C19×#97C2semidirect
9. C2×D8×C19C4semidirect
14. C4×D4×C19C22semidirect
18. C19×#106C22semidirect
19. C19×#102C22semidirect
20. C19×#97C22semidirect
24. C2×D4×C19C2×C4semidirect
31. D8×C19C2×C4semidirect
33. C2×C8×C19C2×C4semidirect
48. D4×C19C22×C4semidirect
59. C8×C19C22×C4semidirect
60. C2×#442C19direct (N × H)
74. C2×C4×D4C2×C19semidirect
75. #442C2×C19direct (N × H)
76. C2×#106C2×C19semidirect
77. C2×#102C2×C19semidirect
78. C2×#97C2×C19semidirect
80. C2×C19#442direct (N × H)
85. C2×D8C4×C19semidirect
90. C4×D4C22×C19semidirect
94. #106C22×C19semidirect
95. #102C22×C19semidirect
96. #97C22×C19semidirect
97. C19C2×#442direct (N × H)
101. C2×D4C2×C4×C19semidirect
108. D8C2×C4×C19semidirect
110. C2×C8C2×C4×C19semidirect
125. D4C22×C4×C19semidirect
136. C8C22×C4×C19semidirect
150. C2C19×#442direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D8×C192
C2×C4×D4×C192
C19×#4422
C2×C19×#1062
C2×C19×#1022
C2×C19×#972
C2×#44219