Finite Group Databasebeta

← #72269091

Subgroups — #72269091

Order 2592.

286 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 21 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#13049408C212yesmaximal
2#13049399C211yesmaximal, characteristic
3#10620150C2211yescharacteristic
4C3⋊(C3⋊#622)C411yescharacteristic
5C3×C3⋊#622—22no—
6C32×#622C411yescharacteristic
7#88926—62no—
8#88924—62no—
9C2×C3⋊(C3⋊(C3⋊D3))Q811yescharacteristic
10C32×C3⋊Dic3C2×C411yescharacteristic
11C32×C3⋊Dic3D411yescharacteristic
12#63771—91nomaximal
13#63733—91nomaximal
14#6289—62no—
15#6289—62no—
16C3⋊#622—22no—
17C3⋊#622—62no—
18C3×#622—22no—
19C3×#622—62no—
20C2×C34C4⋊C411yescharacteristic
21C3⋊(C3⋊(C3⋊D3))—21no—
22#3788—92no—
23#3787—91no—
24C8×C3⋊D3—91no—
25#3712—92no—
26C2×C3⋊(C3⋊D3)—62no—
27C2×C3⋊(C3⋊D3)—62no—
28C2×C3⋊(C3⋊D3)—244no—
29C3×C3⋊Dic3—22no—
30C3×C3⋊Dic3—22no—
31C32×Dic3—62no—
32C32×Dic3—62no—
33C34#10811yescharacteristic, complemented, Sylow
34C4×C3⋊D3—91no—
35C4×C3⋊D3—91no—
36#624—364no—
37#622—62no—
38#622—91no—
39#622#15711yescharacteristic
40C32×C8—91no—
41C3⋊(C3⋊C8)—91no—
42C3×C3⋊C8—182no—
43C2×C33—22no—
44C2×C33—22no—
45C2×C33—84no—
46C3⋊(C3⋊D3)—64no—
47C3⋊(C3⋊D3)—122no—
48C3⋊(C3⋊D3)—248no—
49ΓL(1,𝔽25)—542no—
50D3×C8—542no—
51C2×C3⋊D3—91no—
52C2×C3⋊D3—91no—
53C2×C3⋊D3—364no—
54C2×C3⋊D3—724no—
55C2×C3⋊D3—724no—
56C2×C3⋊D3—724no—
57C2×C3⋊D3—722no—
58C32×C4—91no—
59C32×C4—91no—
60C3⋊Dic3GO+(4,𝔽2)11yescharacteristic
61C3⋊Dic3C2×#15711yescharacteristic
62C3×Dic3—124no—
63C3×Dic3—124no—
64#108—811noSylow
65C33—22no—
66C33—22no—
67C33—84no—
68C4×D3—542no—
69C4×D3—542no—
70C3×C8—182no—
71C3×C8—542no—
72C3⋊C8—182no—
73C3⋊C8—542no—
74C2×C32—44no—
75C2×C32—84no—
76C2×C32—84no—
77C2×C32—84no—
78C2×C32—82no—
79C2×C32#377311yescharacteristic
80C2×C32C4⋊#15711yescharacteristic
81C3⋊D3—181no—
82C3⋊D3—181no—
83C3⋊D3—368no—
84C3⋊D3—728no—
85C3⋊D3—728no—
86C3⋊D3—724no—
87C3⋊D3—728no—
88M16—812no—
89C2×C8—811no—
90C2×D3—542no—
91C2×D3—542no—
92C2×D3—2164no—
93C3×C4—182no—
94C3×C4—182no—
95Dic3—62no—
96Dic3—62no—
97C32—44no—
98C32—84no—
99C32—84no—
100C32—82no—
101C32—84no—
102C32#6373311yescharacteristic, complemented
103C32#6377111yescharacteristic, complemented
104C2×C4—811no—
105C8—91no—
106C8—542no—
107C8—811no—
108C2×C3—22no—
109C2×C3—22no—
110C2×C3—84no—
111D3—544no—
112D3—1082no—
113D3—2168no—
114C22—811no—
115C4—91no—
116C4—91no—
117C3—22no—
118C3—22no—
119C3—84no—
120C2—1621no—
121C2#1304978211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#13049782
commutatorC32×C3⋊Dic3C2×C4
Fitting, socleC2×C34C4⋊C4
prime radicalC2×C3⋊(C3⋊(C3⋊D3))Q8
cosocle#10620150C22
hypocenterC34#108
LCSG ▷ C32×C3⋊Dic3 ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
33. C34#108semidirect
102. C32#63733semidirect
103. C32#63771semidirect

Maximal subgroups

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

subgroupindex
#130494082
#130493992
#637719
#637339