Finite Group Databasebeta

← #1463×C239 #44480233

Subgroups — #1463×C239 #44480233

Order 30592.

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

normal subgroups only

This group has 312 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
1C22×C4⋊C4×C239C211yesmaximal, characteristic
2#407×C239C212yesmaximal
3#324×C239C214yesmaximal, complemented
4C23×C4×C239C411yescharacteristic
5C23×C4×C239C411yescharacteristic
6C23×C4×C239C2211yescharacteristic
7C2×M16×C239—22no—
8C2×C4⋊C4×C239—22no—
9C2×C4⋊C4×C239—22no—
10C2×C4⋊C4×C239C412yes—
11C2×C4⋊C4×C239C2212yes—
12C22⋊C8×C239—22no—
13C22⋊C8×C239C2214yes—
14C24×C239C2×C411yescharacteristic
15C22×C4×C239—21no—
16C22×C4×C239—21no—
17C22×C4×C239—24no—
18C22×C4×C239—21no—
19C22×C4×C239—21no—
20C22×C4×C239—42no—
21C22×C4×C239—42no—
22C22×C4×C239C2×C412yes—
23C22×C4×C239C2×C412yes—
24C22×C4×C239C2×C411yescharacteristic
25C22×C4×C239D412yes—
26C22×C4×C239D412yes—
27C22×C4×C239C2311yescharacteristic
28M16×C239—44no—
29C2×C8×C239—24no—
30C4⋊C4×C239—24no—
31C4⋊C4×C239—24no—
32C23×C239—22no—
33C23×C239—22no—
34C23×C239—22no—
35C23×C239C22⋊C411yescharacteristic
36C23×C239C22⋊C411yescharacteristic
37C23×C239C22×C411yescharacteristic
38C2×C4×C239—24no—
39C2×C4×C239—24no—
40C2×C4×C239—24no—
41C2×C4×C239—22no—
42C2×C4×C239—22no—
43C2×C4×C239—22no—
44C2×C4×C239—41no—
45C2×C4×C239—42no—
46C2×C4×C239—41no—
47C2×C4×C239—42no—
48C2×C4×C239—42no—
49C2×C4×C239—42no—
50C2×C4×C239C22⋊C412yes—
51C2×C4×C239M1614yescomplemented
52C2×C4×C239C2×D412yes—
53C8×C239—44no—
54C22×C239—28no—
55C22×C239—21no—
56C22×C239—21no—
57C22×C239—21no—
58C22×C239—21no—
59C22×C239—21no—
60C22×C239—21no—
61C22×C239#9912yes—
62C22×C239#10112yes—
63C22×C239C2×C22⋊C411yescharacteristic
64C22×C239C2×M1612yes—
65C4×C239—24no—
66C4×C239—22no—
67C4×C239—22no—
68C4×C239—42no—
69C2×C239—22no—
70C2×C239—22no—
71C2×C239—22no—
72C2×C239#40711yescharacteristic
73C2×C239C2×#9911yescharacteristic
74C2×C239C2×#10111yescharacteristic
75C239#146311yescharacteristic, direct product factor, Sylow
76#1463C23911yesmaximal, characteristic, direct product factor, Sylow
77C22×C4⋊C4C2×C23911yescharacteristic
78#407C2×C23912yes—
79#324C2×C23914yescomplemented
80C23×C4C4×C23911yescharacteristic
81C23×C4C4×C23911yescharacteristic
82C23×C4C22×C23911yescharacteristic
83C2×M16—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4C4×C23912yes—
87C2×C4⋊C4C22×C23912yes—
88C22⋊C8—22no—
89C22⋊C8C22×C23914yes—
90C24C2×C4×C23911yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—24no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4C2×C4×C23912yes—
99C22×C4C2×C4×C23912yes—
100C22×C4C2×C4×C23911yescharacteristic
101C22×C4D4×C23912yes—
102C22×C4D4×C23912yes—
103C22×C4C23×C23911yescharacteristic
104M16—44no—
105C2×C8—24no—
106C4⋊C4—24no—
107C4⋊C4—24no—
108C23—22no—
109C23—22no—
110C23—22no—
111C23C22⋊C4×C23911yescharacteristic
112C23C22⋊C4×C23911yescharacteristic
113C23C22×C4×C23911yescharacteristic
114C2×C4—24no—
115C2×C4—24no—
116C2×C4—24no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4C22⋊C4×C23912yes—
127C2×C4M16×C23914yescomplemented
128C2×C4C2×D4×C23912yes—
129C8—44no—
130C22—28no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22#99×C23912yes—
138C22#101×C23912yes—
139C22C2×C22⋊C4×C23911yescharacteristic
140C22C2×M16×C23912yes—
141C4—24no—
142C4—22no—
143C4—22no—
144C4—42no—
145C2—22no—
146C2—22no—
147C2—22no—
148C2#407×C23911yescharacteristic
149C2C2×#99×C23911yescharacteristic
150C2C2×#101×C23911yescharacteristic
subgroupG/H
center, socleC22×C239C2×C22⋊C4
commutatorC23C22×C4×C239
Frattini, cosocleC22×C4C23×C239
prime radicalC24×C239C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C239 ◁ C23×C4×C239 ◁ G

Complements

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

NH ≅ G/Ntype
3. #324×C239C2semidirect
51. C2×C4×C239M16semidirect
75. C239#1463direct (N × H)
76. #1463C239direct (N × H)
79. #324C2×C239semidirect
127. C2×C4M16×C239semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×C2392
#407×C2392
#324×C2392
#1463239