Finite Group Databasebeta

← #1490×C239 #44480260

Subgroups — #1490×C239 #44480260

Order 30592.

316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×C4×D4×C239C211yesmaximal, characteristic
2#432×C239C211yesmaximal, characteristic, complemented
3C4×M16×C239C211yesmaximal, characteristic, complemented
4D4⋊C8×C239C214yesmaximal, complemented
5C22×D4×C239C411yescharacteristic
6C23×C4×C239—21no—
7C2×M16×C239—21no—
8C4×D4×C239—21no—
9C4×D4×C239—21no—
10C4×D4×C239C412yes—
11C4×D4×C239C2212yes—
12C2×C4⋊C4×C239C411yescharacteristic
13C2×C22⋊C4×C239—21no—
14C2×C42×C239C2211yescharacteristic
15C4⋊C8×C239C2212yescomplemented
16C22⋊C8×C239—21no—
17#97×C239—21no—
18#97×C239—21no—
19C4×C8×C239C2212yescomplemented
20C24×C239—21no—
21C2×D4×C239—24no—
22C2×D4×C239—21no—
23C2×D4×C239C2×C412yes—
24C22×C4×C239—21no—
25C22×C4×C239—22no—
26C22×C4×C239—22no—
27C22×C4×C239—44no—
28C22×C4×C239C2×C411yescharacteristic
29C22×C4×C239D411yescharacteristic
30C22×C4×C239D411yescharacteristic
31M16×C239—24no—
32C2×C8×C239—22no—
33C2×C8×C239—22no—
34C4⋊C4×C239—21no—
35C4⋊C4×C239C2×C412yes—
36C22⋊C4×C239—22no—
37C22⋊C4×C239—22no—
38C42×C239C2×C411yescharacteristic
39C42×C239D411yescharacteristic
40C42×C239D411yescharacteristic
41C42×C239C2311yescharacteristic
42C23×C239—24no—
43C23×C239—22no—
44C23×C239—42no—
45C23×C239—42no—
46C23×C239C22⋊C411yescharacteristic
47D4×C239—24no—
48D4×C239—22no—
49D4×C239M1614yescomplemented
50C2×C4×C239—22no—
51C2×C4×C239—22no—
52C2×C4×C239—22no—
53C2×C4×C239—22no—
54C2×C4×C239—44no—
55C2×C4×C239—42no—
56C2×C4×C239—44no—
57C2×C4×C239C22⋊C411yescharacteristic
58C2×C4×C239C22⋊C411yescharacteristic
59C2×C4×C239C22⋊C411yescharacteristic
60C2×C4×C239C22×C411yescharacteristic
61C2×C4×C239C2×D411yescharacteristic
62C2×C4×C239C2×D411yescharacteristic
63C8×C239—24no—
64C8×C239—42no—
65C22×C239—21no—
66C22×C239—21no—
67C22×C239—24no—
68C22×C239—48no—
69C22×C239—42no—
70C22×C239—42no—
71C22×C239#10412yes—
72C22×C239C2×C22⋊C411yescharacteristic
73C4×C239—21no—
74C4×C239—21no—
75C4×C239—21no—
76C4×C239—21no—
77C4×C239—42no—
78C4×C239C2×M1612yes—
79C4×C239AGL(1,ℤ/8)12yes—
80C2×C239—22no—
81C2×C239—44no—
82C2×C239#40711yescharacteristic
83C2×C239#41811yescharacteristic
84C2×C239C2×#10411yescharacteristic
85C239#149011yescharacteristic, direct product factor, Sylow
86#1490C23911yesmaximal, characteristic, direct product factor, Sylow
87C2×C4×D4C2×C23911yescharacteristic
88#432C2×C23911yescharacteristic, complemented
89C4×M16C2×C23911yescharacteristic, complemented
90D4⋊C8C2×C23914yescomplemented
91C22×D4C4×C23911yescharacteristic
92C23×C4—21no—
93C2×M16—21no—
94C4×D4—21no—
95C4×D4—21no—
96C4×D4C4×C23912yes—
97C4×D4C22×C23912yes—
98C2×C4⋊C4C4×C23911yescharacteristic
99C2×C22⋊C4—21no—
100C2×C42C22×C23911yescharacteristic
101C4⋊C8C22×C23912yescomplemented
102C22⋊C8—21no—
103#97—21no—
104#97—21no—
105C4×C8C22×C23912yescomplemented
106C24—21no—
107C2×D4—24no—
108C2×D4—21no—
109C2×D4C2×C4×C23912yes—
110C22×C4—21no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—44no—
114C22×C4C2×C4×C23911yescharacteristic
115C22×C4D4×C23911yescharacteristic
116C22×C4D4×C23911yescharacteristic
117M16—24no—
118C2×C8—22no—
119C2×C8—22no—
120C4⋊C4—21no—
121C4⋊C4C2×C4×C23912yes—
122C22⋊C4—22no—
123C22⋊C4—22no—
124C42C2×C4×C23911yescharacteristic
125C42D4×C23911yescharacteristic
126C42D4×C23911yescharacteristic
127C42C23×C23911yescharacteristic
128C23—24no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C22⋊C4×C23911yescharacteristic
133D4—24no—
134D4—22no—
135D4M16×C23914yescomplemented
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—44no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4C22⋊C4×C23911yescharacteristic
144C2×C4C22⋊C4×C23911yescharacteristic
145C2×C4C22⋊C4×C23911yescharacteristic
146C2×C4C22×C4×C23911yescharacteristic
147C2×C4C2×D4×C23911yescharacteristic
148C2×C4C2×D4×C23911yescharacteristic
149C8—24no—
150C8—42no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—48no—
155C22—42no—
156C22—42no—
157C22#104×C23912yes—
158C22C2×C22⋊C4×C23911yescharacteristic
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4C2×M16×C23912yes—
165C4AGL(1,ℤ/8)×C23912yes—
166C2—22no—
167C2—44no—
168C2#407×C23911yescharacteristic
169C2#418×C23911yescharacteristic
170C2C2×#104×C23911yescharacteristic
subgroupG/H
centerC2×C4×C239C2×D4
commutatorC2×C4C22×C4×C239
Frattini, cosocleC42C23×C239
socleC22×C239C2×C22⋊C4
prime radicalC22×D4×C239C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C239 ◁ C2×C42×C239 ◁ G

Complements

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

NH ≅ G/Ntype
2. #432×C239C2semidirect
3. C4×M16×C239C2semidirect
4. D4⋊C8×C239C2semidirect
15. C4⋊C8×C239C22semidirect
19. C4×C8×C239C22semidirect
49. D4×C239M16semidirect
85. C239#1490direct (N × H)
86. #1490C239direct (N × H)
88. #432C2×C239semidirect
89. C4×M16C2×C239semidirect
90. D4⋊C8C2×C239semidirect
101. C4⋊C8C22×C239semidirect
105. C4×C8C22×C239semidirect
135. D4M16×C239semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C2392
#432×C2392
C4×M16×C2392
D4⋊C8×C2392
#1490239