Finite Group Databasebeta

← C22×#4175⋊C3 #14518489

Subgroups — C22×#4175⋊C3 #14518489

Order 1944.

590 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 141 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×#6909C211yesmaximal, characteristic, complemented
2C2×#4175⋊C3C216yesmaximal, direct product factor
3C22×C3⋊((C3⋊D3)⋊C3)C311yesmaximal, characteristic, complemented
4C22×C3×(C3⋊D3)⋊C3—31nomaximal
5C22×#4175C313yesmaximal, complemented
6C2×#6909C2213yescomplemented
7#4175⋊C3C2214yesdirect product factor
8C22×C3×3−1+2—21no—
9C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
10C22×C3×H(3,𝔽3)C2×C311yescharacteristic, complemented
11C2×C3⋊((C3⋊D3)⋊C3)C2×C316yescomplemented
12C2×C3×(C3⋊D3)⋊C3—36no—
13C22×AΣL(1,𝔽27)—23no—
14C22×AΣL(1,𝔽27)C2×C313yescomplemented
15C2×#4175C2×C3118yescomplemented
16#6909C2311yescharacteristic, complemented, Sylow
17C22×C3⋊(C3⋊D3)C3211yescharacteristic, complemented
18C22×C3×C3⋊D3—31no—
19C22×C32×D3—91no—
20C22×(C3⋊D3)⋊C3—33no—
21C22×(C3⋊D3)⋊C3—91no—
22C2×C3×3−1+2—23no—
23C2×C3×H(3,𝔽3)C2×D313yescomplemented
24C2×C3×H(3,𝔽3)C22×C313yescomplemented
25C3⋊((C3⋊D3)⋊C3)C22×C314yescomplemented
26C3×(C3⋊D3)⋊C3—34no—
27C2×AΣL(1,𝔽27)—29no—
28C2×AΣL(1,𝔽27)C22×C319yescomplemented
29#4175C22×C3112yescomplemented
30C22×C33—21no—
31C22×C33—31no—
32C22×C33C3×D311yescharacteristic
33C22×C33C2×C3211yescharacteristic, complemented
34C2×C3⋊(C3⋊D3)C2×C3216yescomplemented
35C2×C3×C3⋊D3—36no—
36C2×C32×D3—96no—
37C22×3−1+2—23no—
38C22×3−1+2—61no—
39C22×3−1+2—61no—
40C22×H(3,𝔽3)—31no—
41C22×H(3,𝔽3)—61no—
42C22×H(3,𝔽3)—61no—
43C22×H(3,𝔽3)C3×D313yes—
44C22×C3×C9—61no—
45C2×(C3⋊D3)⋊C3—318no—
46C2×(C3⋊D3)⋊C3—96no—
47C3×3−1+2—21no—
48C3×H(3,𝔽3)C22×D311yescharacteristic, complemented
49C3×H(3,𝔽3)C23×C311yescharacteristic, complemented
50AΣL(1,𝔽27)—23no—
51AΣL(1,𝔽27)C23×C313yescomplemented
52C23×C32—271no—
53C22×C3⋊D3—31no—
54C22×C3⋊D3—91no—
55C22×C3⋊D3—271no—
56C22×C3×D3—93no—
57C22×C3×D3—91no—
58C22×C3×D3—271no—
59C2×C33—23no—
60C2×C33—33no—
61C2×C33C2×C3×D313yes—
62C2×C33C22×C3213yescomplemented
63C3⋊(C3⋊D3)C22×C3214yescomplemented
64C3×C3⋊D3—34no—
65C32×D3—94no—
66C2×3−1+2—29no—
67C2×3−1+2—63no—
68C2×3−1+2—63no—
69C2×H(3,𝔽3)—33no—
70C2×H(3,𝔽3)—63no—
71C2×H(3,𝔽3)—63no—
72C2×H(3,𝔽3)C2×C3×D319yes—
73C2×C3×C9—63no—
74(C3⋊D3)⋊C3—312no—
75(C3⋊D3)⋊C3—94no—
76C22×C32—21no—
77C22×C32—31no—
78C22×C32—33no—
79C22×C32—61no—
80C22×C32—91no—
81C22×C32—91no—
82C22×C32—91no—
83C22×C32—181no—
84C22×C32—181no—
85C22×C32—276no—
86C22×C32(C3⋊D3)⋊C311yescharacteristic
87C22×C32C32×D311yescharacteristic
88C2×C3⋊D3—36no—
89C2×C3⋊D3—96no—
90C2×C3⋊D3—276no—
91C2×C3×D3—918no—
92C2×C3×D3—96no—
93C2×C3×D3—276no—
94C22×C9—63no—
95C33—21no—
96C33—31no—
97C33C22×C3×D311yescharacteristic
98C33C23×C3211yescharacteristic, complemented
993−1+2—23no—
1003−1+2—61no—
1013−1+2—61no—
102H(3,𝔽3)—31no—
103H(3,𝔽3)—61no—
104H(3,𝔽3)—61no—
105H(3,𝔽3)C22×C3×D313yes—
106C3×C9—61no—
107C23×C3—271no—
108C23×C3—273no—
109C22×D3—91no—
110C22×D3—271no—
111C22×D3—811no—
112C2×C32—23no—
113C2×C32—33no—
114C2×C32—39no—
115C2×C32—63no—
116C2×C32—93no—
117C2×C32—93no—
118C2×C32—93no—
119C2×C32—183no—
120C2×C32—183no—
121C2×C32—274no—
122C2×C32C2×(C3⋊D3)⋊C313yes—
123C2×C32C2×C32×D313yes—
124C3⋊D3—34no—
125C3⋊D3—94no—
126C3⋊D3—274no—
127C3×D3—912no—
128C3×D3—94no—
129C3×D3—274no—
130C2×C9—69no—
131C22×C3—31no—
132C22×C3—31no—
133C22×C3—61no—
134C22×C3—91no—
135C22×C3—93no—
136C22×C3—181no—
137C22×C3—276no—
138C22×C3—2718no—
139C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
140C2×D3—96no—
141C2×D3—276no—
142C2×D3—816no—
143C32—21no—
144C32—33no—
145C32—31no—
146C32—61no—
147C32—91no—
148C32—91no—
149C32—91no—
150C32—181no—
151C32—181no—
152C32C22×(C3⋊D3)⋊C311yescharacteristic
153C32C22×C32×D311yescharacteristic
154C9—63no—
155C23—271noSylow
156C2×C3—33no—
157C2×C3—33no—
158C2×C3—63no—
159C2×C3—93no—
160C2×C3—99no—
161C2×C3—183no—
162C2×C3—274no—
163C2×C3—2712no—
164C2×C3C2×C3×(C3⋊D3)⋊C313yes—
165D3—94no—
166D3—274no—
167D3—814no—
168C22—276no—
169C22#4175⋊C311yescharacteristic, direct product factor
170C3—31no—
171C3—31no—
172C3—61no—
173C3—91no—
174C3—93no—
175C3—181no—
176C3C22×C3×(C3⋊D3)⋊C311yescharacteristic
177C2—274no—
178C2C2×#4175⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22#4175⋊C3
commutator, cosocle, hypocenterC33C23×C32
FrattiniC32C22×C32×D3
FittingC22×#6909C2
socleC22×C3C3×(C3⋊D3)⋊C3
LCSG ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6909C2semidirect
2. C2×#4175⋊C3C2direct (N × H)
3. C22×C3⋊((C3⋊D3)⋊C3)C3semidirect
5. C22×#4175C3semidirect
6. C2×#6909C22semidirect
7. #4175⋊C3C22direct (N × H)
9. C22×C3×H(3,𝔽3)D3semidirect
10. C22×C3×H(3,𝔽3)C2×C3semidirect
11. C2×C3⋊((C3⋊D3)⋊C3)C2×C3semidirect
14. C22×AΣL(1,𝔽27)C2×C3semidirect
15. C2×#4175C2×C3semidirect
16. #6909C23semidirect
17. C22×C3⋊(C3⋊D3)C32semidirect
23. C2×C3×H(3,𝔽3)C2×D3semidirect
24. C2×C3×H(3,𝔽3)C22×C3semidirect
25. C3⋊((C3⋊D3)⋊C3)C22×C3semidirect
28. C2×AΣL(1,𝔽27)C22×C3semidirect
29. #4175C22×C3semidirect
33. C22×C33C2×C32semidirect
34. C2×C3⋊(C3⋊D3)C2×C32semidirect
48. C3×H(3,𝔽3)C22×D3semidirect
49. C3×H(3,𝔽3)C23×C3semidirect
51. AΣL(1,𝔽27)C23×C3semidirect
62. C2×C33C22×C32semidirect
63. C3⋊(C3⋊D3)C22×C32semidirect
98. C33C23×C32semidirect
169. C22#4175⋊C3direct (N × H)
178. C2C2×#4175⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69092
C2×#4175⋊C32
C22×C3⋊((C3⋊D3)⋊C3)3
C22×C3×(C3⋊D3)⋊C33
C22×#41753