Finite Group Databasebeta

← #14518252

Subgroups — #14518252

Order 1944.

398 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 37 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#11757829C211yesmaximal, characteristic, complemented
2C22×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
3C3⋊((C3⋊D3)⋊A4)—31nomaximal
4#10619770—33nomaximal
5#92306—41nomaximal
6C22×C32×C9C2×C311yescharacteristic, complemented
7C2×C3⋊(C3⋊D9)—31no—
8C2×C3⋊(C3⋊D9)—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic
10C3×#1094—21no—
11(C3×A4)⋊C9—23no—
12(C3×A4)⋊C9D313yescomplemented
13#6893—41noSylow
14C22×C3⋊(C3⋊D3)—31no—
15A4×C3⋊D3—91no—
16C22×C3⋊D9—33no—
17C22×C3⋊D9—93no—
18(C3⋊D3)⋊A4—93no—
19C2×C32×C9—31no—
20C3⋊(C3⋊D9)—31no—
21C3⋊(C3⋊D9)A411yescharacteristic, complemented
22C3⋊((C3⋊D3)⋊C3)—121no—
23#4169—123no—
24C22×C33C3×D311yescharacteristic
25C2×C3⋊(C3⋊D3)—91no—
26C2×C3⋊(C3⋊D3)—91no—
27C32×A4—21no—
28C32×A4C3⋊D311yescharacteristic
29C22×C3×C9—33no—
30C22×C3×C9C3×D313yes—
31C2×C3⋊D9—93no—
32C2×C3⋊D9—99no—
33C2×C3⋊D9—99no—
34C2×C3⋊D9—93no—
35C22⋊H(3,𝔽3)—33no—
36#1094—63no—
37C3×C22⋊C9—23no—
38C3×3−1+2—81no—
39C3×H(3,𝔽3)—41no—
40C32×C9C2×A411yescharacteristic, complemented
41C32⋊C9—43no—
42C32⋊C9—83no—
43C22×C3⋊D3—91no—
44C22×C3⋊D3—93no—
45C22×C3⋊D3—273no—
46D3×A4—271no—
47D3×A4—273no—
48C22×D9—273no—
49C2×C33—31no—
50C3⋊(C3⋊D3)—31no—
51C3⋊(C3⋊D3)—91no—
52C3×C3⋊D3—361no—
53C2×C3×C9—39no—
54C2×C3×C9—33no—
55C3⋊D9—33no—
56C3⋊D9—93no—
57C3⋊D9—99no—
58C3⋊D9—93no—
59(C3⋊D3)⋊C3—363no—
60C22×C32—33no—
61C22×C32(C3⋊D3)⋊C313yes—
62C22×C32C3×C3⋊D311yescharacteristic
63C2×C3⋊D3—271no—
64C2×C3⋊D3—273no—
65C2×C3⋊D3—279no—
66C2×C3⋊D3—279no—
67C2×C3⋊D3—273no—
68C2×C3⋊D3—271no—
69C3×A4—31no—
70C3×A4—33no—
71C3×A4—61no—
72C3×A4—63no—
73C22×C9—33no—
74C2×D9—279no—
75C2×D9—279no—
76C22⋊C9—63no—
77C33—41no—
78C33—81no—
79C33D3×A411yescharacteristic
803−1+2—243no—
81H(3,𝔽3)—123no—
82C3×C9—33no—
83C3×C9—83no—
84C3×C9D3×A413yes—
85C22×D3—271no—
86C22×D3—273no—
87C22×D3—813no—
88C2×A4—811no—
89C2×C32—39no—
90C2×C32—33no—
91C2×C32—31no—
92C3⋊D3—91no—
93C3⋊D3—93no—
94C3⋊D3—273no—
95C3⋊D3—279no—
96C3⋊D3—273no—
97C3⋊D3—271no—
98C3×D3—1081no—
99C3×D3—1083no—
100C2×C9—39no—
101D9—273no—
102D9—279no—
103C22×C3—33no—
104C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
105C22×C3#420713yes—
106C2×D3—811no—
107C2×D3—813no—
108C2×D3—819no—
109C2×D3—819no—
110C2×D3—811no—
111C2×D3—813no—
112A4—91no—
113A4—181no—
114C32—33no—
115C32—123no—
116C32—121no—
117C32—243no—
118C32—241no—
119C32(C3⋊D3)⋊A413yes—
120C32A4×C3⋊D311yescharacteristic
121C9—33no—
122C9—243no—
123C23—811noSylow
124C2×C3—39no—
125C2×C3—33no—
126C2×C3—31no—
127C2×C3—3241no—
128D3—273no—
129D3—271no—
130D3—813no—
131D3—819no—
132D3—813no—
133D3—811no—
134C22—2431no—
135C22—2431no—
136C22#9230611yescharacteristic, complemented
137C3—33no—
138C3—361no—
139C3—721no—
140C3#1062007013yes—
141C3C3⋊((C3⋊D3)⋊A4)11yescharacteristic
142C2—31no—
143C2—811no—
144C2—2431no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC22×C32×C9C2×C3
FrattiniC32A4×C3⋊D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C22×C32×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757829C2semidirect
2. C22×C3⋊(C3⋊D9)C3semidirect
6. C22×C32×C9C2×C3semidirect
12. (C3×A4)⋊C9D3semidirect
21. C3⋊(C3⋊D9)A4semidirect
40. C32×C9C2×A4semidirect
136. C22#92306semidirect

Maximal subgroups

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

subgroupindex
#117578292
C22×C3⋊(C3⋊D9)3
C3⋊((C3⋊D3)⋊A4)3
#106197703
#923064