Finite Group Databasebeta

← #1687×C263 #46778656

Subgroups — #1687×C263 #46778656

Order 33664.

198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 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
1#493×C263C211yesmaximal, characteristic, complemented
2#459×C263C212yesmaximal, complemented
3#436×C263C211yesmaximal, characteristic, complemented
4#334×C263C211yesmaximal, characteristic, complemented
5#331×C263C212yesmaximal, complemented
6C2×D8×C263—22no—
7C2×D8×C263—21no—
8C2×D8×C263—21no—
9C2×M16×C263—21no—
10#127×C263C2212yes—
11C4×D4×C263C2211yescharacteristic
12C4⋊C8×C263C2211yescharacteristic
13C4⋊C8×C263C2212yes—
14#102×C263—22no—
15C22⋊C8×C263—21no—
16C4×C8×C263C2211yescharacteristic
17C2×D4×C263—22no—
18C2×D4×C263—22no—
19C2×D4×C263—22no—
20C2×D4×C263D411yescharacteristic
21C22×C4×C263—21no—
22D8×C263—42no—
23D8×C263—44no—
24D8×C263—42no—
25M16×C263—42no—
26C2×C8×C263—21no—
27C2×C8×C263—22no—
28C2×C8×C263D411yescharacteristic
29C2×C8×C263D411yescharacteristic
30C4⋊C4×C263D411yescharacteristic
31C22⋊C4×C263—21no—
32C42×C263C2311yescharacteristic
33C23×C263—21no—
34C23×C263—42no—
35D4×C263—22no—
36D4×C263—42no—
37D4×C263—42no—
38D4×C263—42no—
39D4×C263—42no—
40D4×C263—82no—
41C2×C4×C263—21no—
42C2×C4×C263—41no—
43C2×C4×C263—41no—
44C2×C4×C263C2×D411yescharacteristic
45C2×C4×C263C2×D411yescharacteristic
46C2×C4×C263#4111yescharacteristic
47C8×C263—21no—
48C8×C263—41no—
49C8×C263—42no—
50C8×C263D812yescomplemented
51C22×C263—41no—
52C22×C263—41no—
53C22×C263—41no—
54C22×C263—82no—
55C22×C263—82no—
56C22×C263—82no—
57C22×C263#12111yescharacteristic
58C4×C263—21no—
59C4×C263—41no—
60C4×C263C2×D811yescharacteristic
61C4×C263AGL(1,ℤ/8)11yescharacteristic
62C4×C263AGL(1,ℤ/8)12yes—
63C2×C263—81no—
64C2×C263—162no—
65C2×C263#45911yescharacteristic
66C2×C263#46911yescharacteristic
67C2×C263#47211yescharacteristic
68C263#168711yescharacteristic, direct product factor, Sylow
69#1687C26311yesmaximal, characteristic, direct product factor, Sylow
70#493C2×C26311yescharacteristic, complemented
71#459C2×C26312yescomplemented
72#436C2×C26311yescharacteristic, complemented
73#334C2×C26311yescharacteristic, complemented
74#331C2×C26312yescomplemented
75C2×D8—22no—
76C2×D8—21no—
77C2×D8—21no—
78C2×M16—21no—
79#127C22×C26312yes—
80C4×D4C22×C26311yescharacteristic
81C4⋊C8C22×C26311yescharacteristic
82C4⋊C8C22×C26312yes—
83#102—22no—
84C22⋊C8—21no—
85C4×C8C22×C26311yescharacteristic
86C2×D4—22no—
87C2×D4—22no—
88C2×D4—22no—
89C2×D4D4×C26311yescharacteristic
90C22×C4—21no—
91D8—42no—
92D8—44no—
93D8—42no—
94M16—42no—
95C2×C8—21no—
96C2×C8—22no—
97C2×C8D4×C26311yescharacteristic
98C2×C8D4×C26311yescharacteristic
99C4⋊C4D4×C26311yescharacteristic
100C22⋊C4—21no—
101C42C23×C26311yescharacteristic
102C23—21no—
103C23—42no—
104D4—22no—
105D4—42no—
106D4—42no—
107D4—42no—
108D4—42no—
109D4—82no—
110C2×C4—21no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4C2×D4×C26311yescharacteristic
114C2×C4C2×D4×C26311yescharacteristic
115C2×C4#41×C26311yescharacteristic
116C8—21no—
117C8—41no—
118C8—42no—
119C8D8×C26312yescomplemented
120C22—41no—
121C22—41no—
122C22—41no—
123C22—82no—
124C22—82no—
125C22—82no—
126C22#121×C26311yescharacteristic
127C4—21no—
128C4—41no—
129C4C2×D8×C26311yescharacteristic
130C4AGL(1,ℤ/8)×C26311yescharacteristic
131C4AGL(1,ℤ/8)×C26312yes—
132C2—81no—
133C2—162no—
134C2#459×C26311yescharacteristic
135C2#469×C26311yescharacteristic
136C2#472×C26311yescharacteristic
subgroupG/H
center, socleC22×C263#121
commutator, Frattini, cosocleC42C23×C263
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ C42×C263 ◁ G

Complements

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

NH ≅ G/Ntype
1. #493×C263C2semidirect
2. #459×C263C2semidirect
3. #436×C263C2semidirect
4. #334×C263C2semidirect
5. #331×C263C2semidirect
50. C8×C263D8semidirect
68. C263#1687direct (N × H)
69. #1687C263direct (N × H)
70. #493C2×C263semidirect
71. #459C2×C263semidirect
72. #436C2×C263semidirect
73. #334C2×C263semidirect
74. #331C2×C263semidirect
119. C8D8×C263semidirect

Maximal subgroups

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

subgroupindex
#493×C2632
#459×C2632
#436×C2632
#334×C2632
#331×C2632
#1687263