Finite Group Databasebeta

← C3×#10619750 #14518042

Subgroups — C3×#10619750 #14518042

Order 1944.

286 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C3×#66358C211yesmaximal, characteristic, complemented
2C3×(C3⋊S4)⋊C3—33nomaximal
3C32×#611—31nomaximal
4#10619750C311yesmaximal, characteristic, direct product factor
5C3×#4185—41nomaximal
6C22×C32×C9D311yescharacteristic, complemented
7C2×C32×D9—31no—
8C3×C22⋊H(3,𝔽3)D313yescomplemented
9C32×Dic9—31no—
10#66358—21no—
11#66358—23no—
12#66358C2×C311yescharacteristic, complemented
13C3×#732—41noSylow
14C3×C3⋊S4—33no—
15C32×#67—91no—
16(C3⋊S4)⋊C3—36no—
17(C3⋊S4)⋊C3—33no—
18C3×#611—32no—
19C3×#611—31no—
20C3×#611—31no—
21C2×C32×C9—31no—
22C3×(C3⋊D3)⋊C3—123no—
23C32×D9—61no—
24#4185—41no—
25C22×C33C3⋊D311yescharacteristic
26C2×C32×D3—91no—
27C32×A4—33no—
28C32×Dic3—91no—
29C22×C3×C9—21no—
30C22×C3×C9—31no—
31C22×C3×C9—32no—
32C22×C3×C9C3×D311yescharacteristic, complemented
33C2×C3×D9—32no—
34C2×C3×D9—31no—
35C2×C3×D9—31no—
36C22⋊H(3,𝔽3)—23no—
37C22⋊H(3,𝔽3)—36no—
38C22⋊H(3,𝔽3)C3×D313yescomplemented
39C3×Dic9—32no—
40C3×Dic9—31no—
41C3×Dic9—31no—
42C3×H(3,𝔽3)—43no—
43C32×C9S411yescharacteristic, complemented
44#732—41no—
45#732—83no—
46#732—81no—
47C3⋊S4—33no—
48C3×S4—273no—
49C32×D4—271no—
50C3×#67—92no—
51C3×#67—91no—
52C3×#67—91no—
53#611—31no—
54C2×C33—31no—
55C3×C3⋊D3—123no—
56C32×D3—181no—
57C2×C3×C9—32no—
58C2×C3×C9—31no—
59C2×C3×C9—31no—
60C2×C3×C9—61no—
61C2×C3×C9—62no—
62C2×C3×C9—61no—
63(C3⋊D3)⋊C3—123no—
64(C3⋊D3)⋊C3—126no—
65C3×D9—62no—
66C3×D9—61no—
67C3×D9—61no—
68C22×C32—31no—
69C22×C32—61no—
70C22×C32—271no—
71C22×C32#27211yescharacteristic
72C22×C32#27212yes—
73C22×C32C3×C3⋊D311yescharacteristic
74C2×C3×D3—92no—
75C2×C3×D3—91no—
76C2×C3×D3—91no—
77C3×A4—33no—
78C3×A4—63no—
79C3×A4—93no—
80C3×A4—183no—
81C32×C4—271no—
82C3×Dic3—92no—
83C3×Dic3—91no—
84C3×Dic3—91no—
85C22×C9—31no—
86C22×C9—61no—
87C2×D9—31no—
88Dic9—31no—
89C33—123no—
90C33C3⋊S411yescharacteristic
91H(3,𝔽3)—43no—
92H(3,𝔽3)—83no—
93H(3,𝔽3)—126no—
94C3×C9—21no—
95C3×C9—31no—
96C3×C9—32no—
97C3×C9C3×S411yescharacteristic, complemented
98S4—273no—
99C3×D4—272no—
100C3×D4—271no—
101C3×D4—271no—
102#67—91no—
103C2×C32—31no—
104C2×C32—32no—
105C2×C32—31no—
106C2×C32—31no—
107C2×C32—61no—
108C2×C32—62no—
109C2×C32—61no—
110C2×C32—541no—
111C3⋊D3—123no—
112C3×D3—182no—
113C3×D3—181no—
114C3×D3—181no—
115C3×D3—1083no—
116C2×C9—31no—
117C2×C9—61no—
118C2×C9—62no—
119C2×C9—61no—
120D9—61no—
121C22×C3—21no—
122C22×C3—32no—
123C22×C3—31no—
124C22×C3—272no—
125C22×C3—271no—
126C22×C3—271no—
127C22×C3#418511yescharacteristic, complemented
128C22×C3C3×#27211yescharacteristic
129C2×D3—91no—
130A4—93no—
131A4—183no—
132C3×C4—272no—
133C3×C4—271no—
134C3×C4—271no—
135Dic3—91no—
136C32—31no—
137C32—61no—
138C32—123no—
139C32—243no—
140C32—363no—
141C32—723no—
142C32#625811yescharacteristic
143C32#625812yes—
144C32C3×C3⋊S411yescharacteristic
145C9—31no—
146C9—61no—
147D4—271noSylow
148C2×C3—32no—
149C2×C3—31no—
150C2×C3—31no—
151C2×C3—31no—
152C2×C3—61no—
153C2×C3—62no—
154C2×C3—61no—
155C2×C3—542no—
156C2×C3—541no—
157C2×C3—541no—
158D3—181no—
159D3—1083no—
160C22—271no—
161C22C3×#418511yescharacteristic, complemented
162C4—271no—
163C3—21no—
164C3—32no—
165C3—31no—
166C3—363no—
167C3—723no—
168C3#1061975011yescharacteristic, direct product factor
169C3C3×#625811yescharacteristic
170C2—31no—
171C2—541no—
subgroupG/H
center, hypercenterC3#10619750
commutator, cosocle, hypocenter#66358C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C32×C9D3
socleC22×C32#272
LCSG ▷ #66358
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66358C2semidirect
4. #10619750C3direct (N × H)
6. C22×C32×C9D3semidirect
8. C3×C22⋊H(3,𝔽3)D3semidirect
12. #66358C2×C3semidirect
32. C22×C3×C9C3×D3semidirect
38. C22⋊H(3,𝔽3)C3×D3semidirect
43. C32×C9S4semidirect
97. C3×C9C3×S4semidirect
127. C22×C3#4185semidirect
161. C22C3×#4185semidirect
168. C3#10619750direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#663582
C3×(C3⋊S4)⋊C33
C32×#6113
#106197503
C3×#41854