Finite Group Databasebeta

← #1392×C263 #46778361

Subgroups — #1392×C263 #46778361

Order 33664.

158 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 60 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#413×C263C212yesmaximal
2#408×C263C211yesmaximal, characteristic
3C2×#41×C263C2211yescharacteristic
4C2×M16×C263—22no—
5C2×M16×C263C411yescharacteristic
6C22×C8×C263C411yescharacteristic
7#101×C263—22no—
8#100×C263C414yes—
9C22⋊C8×C263—22no—
10#41×C263—41no—
11#41×C263—41no—
12C2×Q8×C263D411yescharacteristic
13C2×D4×C263C2×C412yes—
14C2×D4×C263Q811yescharacteristic
15C22×C4×C263C2×C411yescharacteristic
16C22×C4×C263D412yes—
17M16×C263—24no—
18M16×C263—42no—
19M16×C263—41no—
20C2×C8×C263—21no—
21C2×C8×C263—21no—
22C2×C8×C263—42no—
23C2×C8×C263—41no—
24C23×C263C4211yescharacteristic
25C23×C263C4⋊C412yes—
26Q8×C263—41no—
27D4×C263—42no—
28D4×C263—41no—
29C2×C4×C263—21no—
30C2×C4×C263—22no—
31C2×C4×C263—21no—
32C2×C4×C263—22no—
33C2×C4×C263C22⋊C412yes—
34C2×C4×C263C22⋊C411yescharacteristic
35C2×C4×C263C4⋊C411yescharacteristic
36C8×C263—44no—
37C8×C263—41no—
38C8×C263—41no—
39C22×C263—21no—
40C22×C263—22no—
41C22×C263—41no—
42C22×C263—42no—
43C22×C263#9511yescharacteristic
44C4×C263—22no—
45C4×C263—21no—
46C4×C263#9911yescharacteristic
47C4×C263#9911yescharacteristic
48C2×C263—21no—
49C2×C263—41no—
50C2×C263—42no—
51C2×C263#34211yescharacteristic
52C263#139211yescharacteristic, direct product factor, Sylow
53#1392C26311yesmaximal, characteristic, direct product factor, Sylow
54#413C2×C26312yes—
55#408C2×C26311yescharacteristic
56C2×#41C22×C26311yescharacteristic
57C2×M16—22no—
58C2×M16C4×C26311yescharacteristic
59C22×C8C4×C26311yescharacteristic
60#101—22no—
61#100C4×C26314yes—
62C22⋊C8—22no—
63#41—41no—
64#41—41no—
65C2×Q8D4×C26311yescharacteristic
66C2×D4C2×C4×C26312yes—
67C2×D4Q8×C26311yescharacteristic
68C22×C4C2×C4×C26311yescharacteristic
69C22×C4D4×C26312yes—
70M16—24no—
71M16—42no—
72M16—41no—
73C2×C8—21no—
74C2×C8—21no—
75C2×C8—42no—
76C2×C8—41no—
77C23C42×C26311yescharacteristic
78C23C4⋊C4×C26312yes—
79Q8—41no—
80D4—42no—
81D4—41no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—21no—
85C2×C4—22no—
86C2×C4C22⋊C4×C26312yes—
87C2×C4C22⋊C4×C26311yescharacteristic
88C2×C4C4⋊C4×C26311yescharacteristic
89C8—44no—
90C8—41no—
91C8—41no—
92C22—21no—
93C22—22no—
94C22—41no—
95C22—42no—
96C22#95×C26311yescharacteristic
97C4—22no—
98C4—21no—
99C4#99×C26311yescharacteristic
100C4#99×C26311yescharacteristic
101C2—21no—
102C2—41no—
103C2—42no—
104C2#342×C26311yescharacteristic
subgroupG/H
centerC4×C263#99
commutatorC23C42×C263
Frattini, cosocleC2×#41C22×C263
socleC2×C263#342
prime radicalC2×#41×C263C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C263 ◁ C2×C4×C263 ◁ C2×#41×C263 ◁ G

Complements

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

NH ≅ G/Ntype
52. C263#1392direct (N × H)
53. #1392C263direct (N × H)

Maximal subgroups

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

subgroupindex
#413×C2632
#408×C2632
#1392263