Finite Group Databasebeta

← C22×C3×#4179 #14518484

Subgroups — C22×C3×#4179 #14518484

Order 1944.

588 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 146 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×#732C211yesmaximal, characteristic, complemented
2C2×C3×#4179C216yesmaximal, direct product factor
3C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
4C22×C3×(C3⋊D3)⋊C3—31nomaximal
5C22×#4179C313yesmaximal, direct product factor
6C2×C3×#732C2213yescomplemented
7C3×#4179C2214yesdirect product factor
8C22×C3×H(3,𝔽3)—21no—
9C22×C3×H(3,𝔽3)D311yescharacteristic
10C22×C32×C9C2×C311yescharacteristic, complemented
11C2×C3×C3⋊D9C2×C316yescomplemented
12C2×C3×(C3⋊D3)⋊C3—36no—
13C22×#732—23no—
14C22×#732C2×C313yescomplemented
15C2×#4179C2×C3118yesdirect product factor
16C3×#732C2311yescharacteristic, complemented, Sylow
17C22×C3×C3⋊D3—31no—
18C22×C32×D3—91no—
19C22×C3⋊D9C3211yescharacteristic, complemented
20C22×(C3⋊D3)⋊C3—33no—
21C22×C3×D9—91no—
22C2×C3×H(3,𝔽3)—23no—
23C2×C3×H(3,𝔽3)C2×D313yes—
24C2×C32×C9C22×C313yescomplemented
25C3×C3⋊D9C22×C314yescomplemented
26C3×(C3⋊D3)⋊C3—34no—
27C2×#732—29no—
28C2×#732C22×C319yescomplemented
29#4179C22×C3112yesdirect product factor
30C22×C33—31no—
31C22×C33—61no—
32C22×C33C3×D311yescharacteristic
33C2×C3×C3⋊D3—36no—
34C2×C32×D3—96no—
35C22×H(3,𝔽3)—23no—
36C22×H(3,𝔽3)—61no—
37C22×H(3,𝔽3)—62no—
38C22×H(3,𝔽3)C3×D313yes—
39C22×C3×C9—21no—
40C22×C3×C9—31no—
41C22×C3×C9—61no—
42C22×C3×C9C2×C3211yescharacteristic, complemented
43C2×C3⋊D9C2×C3216yescomplemented
44C2×(C3⋊D3)⋊C3—318no—
45C2×C3×D9—96no—
46C3×H(3,𝔽3)—21no—
47C3×H(3,𝔽3)C22×D311yescharacteristic
48C32×C9C23×C311yescharacteristic, complemented
49#732—23no—
50#732C23×C313yescomplemented
51C23×C32—271no—
52C22×C3⋊D3—31no—
53C22×C3×D3—93no—
54C22×C3×D3—91no—
55C22×C3×D3—271no—
56C22×D9—91no—
57C2×C33—33no—
58C2×C33—63no—
59C2×C33C2×C3×D313yes—
60C3×C3⋊D3—34no—
61C32×D3—94no—
62C2×H(3,𝔽3)—29no—
63C2×H(3,𝔽3)—63no—
64C2×H(3,𝔽3)—66no—
65C2×H(3,𝔽3)C2×C3×D319yes—
66C2×C3×C9—23no—
67C2×C3×C9—33no—
68C2×C3×C9—63no—
69C2×C3×C9C22×C3213yescomplemented
70C3⋊D9C22×C3214yescomplemented
71(C3⋊D3)⋊C3—312no—
72C3×D9—94no—
73C22×C32—21no—
74C22×C32—31no—
75C22×C32—33no—
76C22×C32—61no—
77C22×C32—63no—
78C22×C32—91no—
79C22×C32—181no—
80C22×C32—182no—
81C22×C32—181no—
82C22×C32—276no—
83C22×C32(C3⋊D3)⋊C311yescharacteristic
84C22×C32C32×D311yescharacteristic
85C2×C3⋊D3—36no—
86C2×C3×D3—918no—
87C2×C3×D3—96no—
88C2×C3×D3—276no—
89C22×C9—31no—
90C22×C9—61no—
91C2×D9—96no—
92C33—31no—
93C33—61no—
94C33C22×C3×D311yescharacteristic
95H(3,𝔽3)—23no—
96H(3,𝔽3)—61no—
97H(3,𝔽3)—62no—
98H(3,𝔽3)C22×C3×D313yes—
99C3×C9—21no—
100C3×C9—31no—
101C3×C9—61no—
102C3×C9C23×C3211yescharacteristic, complemented
103C23×C3—273no—
104C23×C3—271no—
105C22×D3—91no—
106C22×D3—271no—
107C2×C32—23no—
108C2×C32—33no—
109C2×C32—39no—
110C2×C32—63no—
111C2×C32—69no—
112C2×C32—93no—
113C2×C32—183no—
114C2×C32—186no—
115C2×C32—183no—
116C2×C32—274no—
117C2×C32C2×(C3⋊D3)⋊C313yes—
118C2×C32C2×C32×D313yes—
119C3⋊D3—34no—
120C3×D3—912no—
121C3×D3—94no—
122C3×D3—274no—
123C2×C9—33no—
124C2×C9—63no—
125D9—94no—
126C22×C3—21no—
127C22×C3—31no—
128C22×C3—61no—
129C22×C3—93no—
130C22×C3—183no—
131C22×C3—2718no—
132C22×C3—276no—
133C22×C3#417911yescharacteristic, direct product factor
134C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
135C2×D3—96no—
136C2×D3—276no—
137C32—21no—
138C32—31no—
139C32—33no—
140C32—61no—
141C32—63no—
142C32—91no—
143C32—181no—
144C32—182no—
145C32—181no—
146C32C22×(C3⋊D3)⋊C311yescharacteristic
147C32C22×C32×D311yescharacteristic
148C9—31no—
149C9—61no—
150C23—271noSylow
151C2×C3—23no—
152C2×C3—33no—
153C2×C3—63no—
154C2×C3—99no—
155C2×C3—189no—
156C2×C3—2712no—
157C2×C3—274no—
158C2×C3C2×#417913yesdirect product factor
159C2×C3C2×C3×(C3⋊D3)⋊C313yes—
160D3—94no—
161D3—274no—
162C22—276no—
163C22C3×#417911yescharacteristic, direct product factor
164C3—21no—
165C3—31no—
166C3—61no—
167C3—93no—
168C3—183no—
169C3C22×#417911yescharacteristic, direct product factor
170C3C22×C3×(C3⋊D3)⋊C311yescharacteristic
171C2—274no—
172C2C2×C3×#417913yesdirect product factor
subgroupG/H
center, hypercenterC22×C3#4179
commutator, cosocle, hypocenterC3×C9C23×C32
FrattiniC32C22×C32×D3
FittingC22×C3×#732C2
socleC22×C32(C3⋊D3)⋊C3
LCSG ▷ C3×C9
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#732C2semidirect
2. C2×C3×#4179C2direct (N × H)
3. C22×C3×C3⋊D9C3semidirect
5. C22×#4179C3direct (N × H)
6. C2×C3×#732C22semidirect
7. C3×#4179C22direct (N × H)
10. C22×C32×C9C2×C3semidirect
11. C2×C3×C3⋊D9C2×C3semidirect
14. C22×#732C2×C3semidirect
15. C2×#4179C2×C3direct (N × H)
16. C3×#732C23semidirect
19. C22×C3⋊D9C32semidirect
24. C2×C32×C9C22×C3semidirect
25. C3×C3⋊D9C22×C3semidirect
28. C2×#732C22×C3semidirect
29. #4179C22×C3direct (N × H)
42. C22×C3×C9C2×C32semidirect
43. C2×C3⋊D9C2×C32semidirect
48. C32×C9C23×C3semidirect
50. #732C23×C3semidirect
69. C2×C3×C9C22×C32semidirect
70. C3⋊D9C22×C32semidirect
102. C3×C9C23×C32semidirect
133. C22×C3#4179direct (N × H)
158. C2×C3C2×#4179direct (N × H)
163. C22C3×#4179direct (N × H)
169. C3C22×#4179direct (N × H)
172. C2C2×C3×#4179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7322
C2×C3×#41792
C22×C3×C3⋊D93
C22×C3×(C3⋊D3)⋊C33
C22×#41793