Finite Group Databasebeta

← #1270×C263 #46778239

Subgroups — #1270×C263 #46778239

Order 33664.

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

normal subgroups only

This group has 202 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#390×C263C211yesmaximal, characteristic
2#336×C263C212yesmaximal, complemented
3C22×D4×C263C411yescharacteristic
4C22×C8×C263—22no—
5C2×C4⋊C4×C263C411yescharacteristic
6C2×C22⋊C4×C263—22no—
7C2×C42×C263C2211yescharacteristic
8C24×C263—21no—
9C2×D4×C263—21no—
10C2×D4×C263—41no—
11C2×D4×C263—41no—
12C2×D4×C263C812yescomplemented
13C22×C4×C263—21no—
14C22×C4×C263C2×C411yescharacteristic
15C22×C4×C263D412yes—
16C2×C8×C263—24no—
17C2×C8×C263—42no—
18C2×C8×C263—42no—
19C4⋊C4×C263—41no—
20C22⋊C4×C263—42no—
21C22⋊C4×C263—42no—
22C42×C263—41no—
23C23×C263—22no—
24C23×C263—41no—
25C23×C263—41no—
26C23×C263—42no—
27C23×C263—42no—
28C23×C263C22⋊C411yescharacteristic
29D4×C263—42no—
30D4×C263—42no—
31C2×C4×C263—22no—
32C2×C4×C263—21no—
33C2×C4×C263—21no—
34C2×C4×C263—22no—
35C2×C4×C263—41no—
36C2×C4×C263—42no—
37C2×C4×C263C2×C811yescharacteristic
38C2×C4×C263M1611yescharacteristic
39C2×C4×C263D812yes—
40C2×C4×C263SD1612yes—
41C8×C263—44no—
42C22×C263—42no—
43C22×C263—44no—
44C22×C263—82no—
45C22×C263—81no—
46C22×C263—81no—
47C22×C263C22⋊C811yescharacteristic
48C22×C263#9911yescharacteristic
49C22×C263#10011yescharacteristic
50C22×C263#10212yes—
51C22×C263#10412yes—
52C4×C263—21no—
53C4×C263—21no—
54C4×C263—22no—
55C4×C263—22no—
56C4×C263—81no—
57C2×C263—82no—
58C2×C263#32311yescharacteristic
59C2×C263D4⋊C812yes—
60C2×C263#32712yes—
61C2×C263#32911yescharacteristic
62C2×C263#33111yescharacteristic
63C263#127011yescharacteristic, direct product factor, Sylow
64#1270C26311yesmaximal, characteristic, direct product factor, Sylow
65#390C2×C26311yescharacteristic
66#336C2×C26312yescomplemented
67C22×D4C4×C26311yescharacteristic
68C22×C8—22no—
69C2×C4⋊C4C4×C26311yescharacteristic
70C2×C22⋊C4—22no—
71C2×C42C22×C26311yescharacteristic
72C24—21no—
73C2×D4—21no—
74C2×D4—41no—
75C2×D4—41no—
76C2×D4C8×C26312yescomplemented
77C22×C4—21no—
78C22×C4C2×C4×C26311yescharacteristic
79C22×C4D4×C26312yes—
80C2×C8—24no—
81C2×C8—42no—
82C2×C8—42no—
83C4⋊C4—41no—
84C22⋊C4—42no—
85C22⋊C4—42no—
86C42—41no—
87C23—22no—
88C23—41no—
89C23—41no—
90C23—42no—
91C23—42no—
92C23C22⋊C4×C26311yescharacteristic
93D4—42no—
94D4—42no—
95C2×C4—22no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—22no—
99C2×C4—41no—
100C2×C4—42no—
101C2×C4C2×C8×C26311yescharacteristic
102C2×C4M16×C26311yescharacteristic
103C2×C4D8×C26312yes—
104C2×C4SD16×C26312yes—
105C8—44no—
106C22—42no—
107C22—44no—
108C22—82no—
109C22—81no—
110C22—81no—
111C22C22⋊C8×C26311yescharacteristic
112C22#99×C26311yescharacteristic
113C22#100×C26311yescharacteristic
114C22#102×C26312yes—
115C22#104×C26312yes—
116C4—21no—
117C4—21no—
118C4—22no—
119C4—22no—
120C4—81no—
121C2—82no—
122C2#323×C26311yescharacteristic
123C2D4⋊C8×C26312yes—
124C2#327×C26312yes—
125C2#329×C26311yescharacteristic
126C2#331×C26311yescharacteristic
subgroupG/H
center, socleC23×C263C22⋊C4
commutatorC2×C4C2×C8×C263
Frattini, cosocleC2×C42C22×C263
prime radicalC22×D4×C263C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C263 ◁ C2×C42×C263 ◁ G

Complements

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

NH ≅ G/Ntype
2. #336×C263C2semidirect
12. C2×D4×C263C8semidirect
63. C263#1270direct (N × H)
64. #1270C263direct (N × H)
66. #336C2×C263semidirect
76. C2×D4C8×C263semidirect

Maximal subgroups

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

subgroupindex
#390×C2632
#336×C2632
#1270263