Finite Group Databasebeta

← C22×C3×#4174 #14518477

Subgroups — C22×C3×#4174 #14518477

Order 1944.

1233 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 1233 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C22×C3×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
2C2×C3×#4174C216yesmaximal, direct product factor
3C22×C33×D3—31nomaximal
4C22×C3×#272C311yesmaximal, characteristic, complemented
5C22×#4174C313yesmaximal, direct product factor
6C2×C3×AΣL(1,𝔽27)C2213yescomplemented
7C3×#4174C2214yesdirect product factor
8C22×C34D311yescharacteristic, complemented
9C2×C33×D3—36no—
10C22×C3×3−1+2—21no—
11C22×C3×H(3,𝔽3)C2×C311yescharacteristic, complemented
12C2×C3×#272C2×C316yescomplemented
13C22×AΣL(1,𝔽27)—23no—
14C22×AΣL(1,𝔽27)C2×C313yescomplemented
15C2×#4174C2×C3118yesdirect product factor
16C3×AΣL(1,𝔽27)C2311yescharacteristic, complemented, Sylow
17C23×C33—91no—
18C22×C32×D3—39no—
19C22×C32×D3—31no—
20C22×C32×D3—33no—
21C22×C32×D3—91no—
22C22×#272C3211yescharacteristic, complemented
23C2×C34C2×D313yescomplemented
24C33×D3—34no—
25C2×C3×3−1+2—23no—
26C2×C3×H(3,𝔽3)C22×C313yescomplemented
27C3×#272C22×C314yescomplemented
28C2×AΣL(1,𝔽27)—29no—
29C2×AΣL(1,𝔽27)C22×C319yescomplemented
30#4174C22×C3112yesdirect product factor
31C22×C33—31no—
32C22×C33—39no—
33C22×C33—31no—
34C22×C33—61no—
35C22×C33—96no—
36C22×C33C3×D311yescharacteristic
37C22×C33C3×D313yescomplemented
38C2×C32×D3—354no—
39C2×C32×D3—36no—
40C2×C32×D3—318no—
41C2×C32×D3—96no—
42C22×3−1+2—23no—
43C22×3−1+2—62no—
44C22×H(3,𝔽3)—21no—
45C22×H(3,𝔽3)—61no—
46C22×H(3,𝔽3)C2×C3211yescharacteristic, complemented
47C22×C3×C9—61no—
48C2×#272C2×C3216yescomplemented
49C34C22×D311yescharacteristic, complemented
50C3×3−1+2—21no—
51C3×H(3,𝔽3)C23×C311yescharacteristic, complemented
52AΣL(1,𝔽27)—23no—
53AΣL(1,𝔽27)C23×C313yescomplemented
54C23×C32—99no—
55C23×C32—93no—
56C23×C32—91no—
57C22×C3×D3—39no—
58C22×C3×D3—33no—
59C22×C3×D3—31no—
60C22×C3×D3—91no—
61C22×C3×D3—93no—
62C2×C33—33no—
63C2×C33—327no—
64C2×C33—33no—
65C2×C33—63no—
66C2×C33—94no—
67C2×C33C2×C3×D313yes—
68C2×C33C2×C3×D319yescomplemented
69C32×D3—336no—
70C32×D3—34no—
71C32×D3—312no—
72C32×D3—94no—
73C2×3−1+2—29no—
74C2×3−1+2—66no—
75C2×H(3,𝔽3)—23no—
76C2×H(3,𝔽3)—63no—
77C2×H(3,𝔽3)C22×C3213yescomplemented
78C2×C3×C9—63no—
79#272C22×C3214yescomplemented
80C22×C32—21no—
81C22×C32—39no—
82C22×C32—33no—
83C22×C32—39no—
84C22×C32—33no—
85C22×C32—31no—
86C22×C32—69no—
87C22×C32—61no—
88C22×C32—954no—
89C22×C32—918no—
90C22×C32—96no—
91C22×C32—93no—
92C22×C32(C3⋊D3)⋊C311yescharacteristic
93C22×C32C32×D311yescharacteristic
94C2×C3×D3—354no—
95C2×C3×D3—318no—
96C2×C3×D3—36no—
97C2×C3×D3—96no—
98C2×C3×D3—918no—
99C22×C9—63no—
100C33—31no—
101C33—39no—
102C33—31no—
103C33—61no—
104C33C22×C3×D311yescharacteristic
105C33C22×C3×D313yescomplemented
1063−1+2—23no—
1073−1+2—62no—
108H(3,𝔽3)—21no—
109H(3,𝔽3)—61no—
110H(3,𝔽3)C23×C3211yescharacteristic, complemented
111C3×C9—61no—
112C23×C3—99no—
113C23×C3—93no—
114C23×C3—91no—
115C22×D3—31no—
116C22×D3—91no—
117C2×C32—23no—
118C2×C32—327no—
119C2×C32—39no—
120C2×C32—327no—
121C2×C32—39no—
122C2×C32—33no—
123C2×C32—627no—
124C2×C32—63no—
125C2×C32—936no—
126C2×C32—912no—
127C2×C32—94no—
128C2×C32—99no—
129C2×C32C2×(C3⋊D3)⋊C313yes—
130C2×C32C2×C32×D313yes—
131C3×D3—336no—
132C3×D3—312no—
133C3×D3—34no—
134C3×D3—94no—
135C3×D3—912no—
136C2×C9—69no—
137C22×C3—31no—
138C22×C3—39no—
139C22×C3—61no—
140C22×C3—954no—
141C22×C3—918no—
142C22×C3—96no—
143C22×C3—91no—
144C22×C3—181no—
145C22×C3#417413yesdirect product factor
146C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
147C2×D3—36no—
148C2×D3—96no—
149C32—21no—
150C32—39no—
151C32—39no—
152C32—33no—
153C32—33no—
154C32—31no—
155C32—69no—
156C32—61no—
157C32—93no—
158C32C22×(C3⋊D3)⋊C311yescharacteristic
159C32C22×C32×D311yescharacteristic
160C9—63no—
161C23—91noSylow
162C2×C3—33no—
163C2×C3—327no—
164C2×C3—63no—
165C2×C3—936no—
166C2×C3—912no—
167C2×C3—94no—
168C2×C3—93no—
169C2×C3—183no—
170C2×C3C2×#417419yesdirect product factor
171C2×C3C2×C3×(C3⋊D3)⋊C313yes—
172D3—34no—
173D3—94no—
174C22—96no—
175C22C3×#417411yescharacteristic, direct product factor
176C3—31no—
177C3—39no—
178C3—61no—
179C3—91no—
180C3—181no—
181C3C22×#417413yesdirect product factor
182C3C22×C3×(C3⋊D3)⋊C311yescharacteristic
183C2—94no—
184C2C2×C3×#417413yesdirect product factor
subgroupG/H
center, socle, hypercenterC22×C32(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C23×C32
FrattiniC32C22×C32×D3
FittingC22×C3×AΣL(1,𝔽27)C2
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C22×C3×AΣL(1,𝔽27)C2semidirect
2. C2×C3×#4174C2direct (N × H)
4. C22×C3×#272C3semidirect
5. C22×#4174C3direct (N × H)
6. C2×C3×AΣL(1,𝔽27)C22semidirect
7. C3×#4174C22direct (N × H)
8. C22×C34D3semidirect
11. C22×C3×H(3,𝔽3)C2×C3semidirect
12. C2×C3×#272C2×C3semidirect
14. C22×AΣL(1,𝔽27)C2×C3semidirect
15. C2×#4174C2×C3direct (N × H)
16. C3×AΣL(1,𝔽27)C23semidirect
22. C22×#272C32semidirect
23. C2×C34C2×D3semidirect
26. C2×C3×H(3,𝔽3)C22×C3semidirect
27. C3×#272C22×C3semidirect
29. C2×AΣL(1,𝔽27)C22×C3semidirect
30. #4174C22×C3direct (N × H)
37. C22×C33C3×D3semidirect
46. C22×H(3,𝔽3)C2×C32semidirect
48. C2×#272C2×C32semidirect
49. C34C22×D3semidirect
51. C3×H(3,𝔽3)C23×C3semidirect
53. AΣL(1,𝔽27)C23×C3semidirect
68. C2×C33C2×C3×D3semidirect
77. C2×H(3,𝔽3)C22×C32semidirect
79. #272C22×C32semidirect
105. C33C22×C3×D3semidirect
110. H(3,𝔽3)C23×C32semidirect
145. C22×C3#4174direct (N × H)
170. C2×C3C2×#4174direct (N × H)
175. C22C3×#4174direct (N × H)
181. C3C22×#4174direct (N × H)
184. C2C2×C3×#4174direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AΣL(1,𝔽27)2
C2×C3×#41742
C22×C33×D33
C22×C3×#2723
C22×#41743