Finite Group Databasebeta

← #93802

Subgroups — #93802

Order 512.

119 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 119 conjugacy classes of subgroups — too many to draw. Only its 28 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#13496C211yesmaximal, characteristic
2#7337C211yesmaximal, characteristic
3#7228C211yesmaximal, characteristic
4C2×#367C411yescharacteristic, complemented
5#2113C2211yescharacteristic
6#1816—21no—
7#1812—21no—
8#1400—21no—
9#1387—21no—
10#1381C411yescharacteristic, complemented
11C2×#131D411yescharacteristic
12C2×M32D411yescharacteristic
13C22×C16C2×C411yescharacteristic
14C2×#108—21no—
15#427—41no—
16C2×#107—21no—
17#417—41no—
18#410—41no—
19M64—41no—
20#367—41no—
21C22⋊C16—41no—
22#343—41no—
23H(3,ℤ/4)—22no—
24C2×#41D811yescharacteristic
25#131—41no—
26#131—41no—
27C2×M16—21no—
28C2×M16—41no—
29C2×M16SD1611yescharacteristic
30C22×C8—21no—
31C22×C8C22⋊C411yescharacteristic
32#117—42no—
33C2×C4⋊C4—41no—
34M32—41no—
35C2×C16—21no—
36C2×C16—21no—
37C2×C16—41no—
38#108—41no—
39#108—41no—
40#107—41no—
41#107—41no—
42#107—81no—
43#106—81no—
44#103—81no—
45#102—81no—
46#99—81no—
47#99—81no—
48C32—81no—
49#41—41no—
50#41—41no—
51C2×Q8SD3211yescharacteristic
52C2×D4—21no—
53C2×D4D1611yescharacteristic
54C22×C4—21no—
55C22×C4—81no—
56C22×C4#10211yescharacteristic
57M16—41no—
58M16—81no—
59M16—81no—
60M16—81no—
61C2×C8—21no—
62C2×C8—21no—
63C2×C8—21no—
64C2×C8—41no—
65C2×C8—41no—
66C2×C8—81no—
67C2×C8#9911yescharacteristic
68C2×C8#10411yescharacteristic
69C4⋊C4—82no—
70C4⋊C4—81no—
71C4⋊C4—81no—
72C22⋊C4—82no—
73C42—82no—
74C16—41no—
75C16—41no—
76C23—21no—
77C23#36011yescharacteristic
78Q8—41no—
79D4—41no—
80D4—81no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—162no—
87C2×C4—161no—
88C2×C4—321no—
89C2×C4#32711yescharacteristic
90C2×C4#35711yescharacteristic
91C8—21no—
92C8—41no—
93C8—161no—
94C8#35211yescharacteristic
95C8#35411yescharacteristic
96C22—21no—
97C22—41no—
98C22—41no—
99C22—81no—
100C22#134711yescharacteristic
101C4—21no—
102C4—41no—
103C4—321no—
104C4—322no—
105C4#134011yescharacteristic
106C4#134411yescharacteristic
107C2—21no—
108C2—41no—
109C2—81no—
110C2#707911yescharacteristic
subgroupG/H
center, socleC2#7079
commutatorC22×C16C2×C4
Frattini, cosocle#2113C22
prime radicalC2×#41D8
LCSG ▷ C22×C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ #2113 ◁ G
LECSG ▷ #2113 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#367C4semidirect
10. #1381C4semidirect

Maximal subgroups

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

subgroupindex
#134962
#73372
#72282