Finite Group Databasebeta

← C2×#11758104 #14519346

Subgroups — C2×#11758104 #14519346

Order 1944.

1072 conjugacy classes of subgroups; only the 484 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 484 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#11758104C211yesmaximal, characteristic, direct product factor
2C23×C3×3−1+2C311yesmaximal, characteristic, complemented
3C2×C3×C22⋊H(3,𝔽3)C311yesmaximal, characteristic
4C2×C3×#1094C312yesmaximal, complemented
5C2×#66440C3118yesmaximal, complemented
6C2×A4×3−1+2C319yesmaximal, complemented
7C2×#66436C319yesmaximal, complemented
8C2×3−1+4—41nomaximal
9C22×C3×3−1+2—31no—
10C22×C3×3−1+2—31no—
11C22×C3×3−1+2C2×C311yescharacteristic, complemented
12C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic
13C3×#1094C2×C312yescomplemented
14#66440C2×C3118yescomplemented
15A4×3−1+2C2×C319yescomplemented
16#66436C2×C319yescomplemented
173−1+4—41noSylow
18C23×C33C3211yescharacteristic
19C2×C32×A4C3213yes—
20C23×3−1+2C3213yes—
21C23×3−1+2C3216yescomplemented
22C23×C3×C9C3213yescomplemented
23C2×C22⋊H(3,𝔽3)C3213yes—
24C2×C22⋊H(3,𝔽3)C3216yes—
25C2×#1094C3216yes—
26C2×#1094C3216yescomplemented
27C2×#1094C3216yescomplemented
28C2×C3×C22⋊C9C3216yescomplemented
29C2×C9⋊A4C32154yescomplemented
30C2×C9×A4C32127yescomplemented
31C2×#737—418no—
32C2×#737—49no—
33C2×C3×3−1+2—31no—
34C2×C3×3−1+2—31no—
35C2×C3×3−1+2—42no—
36C2×C3×3−1+2—49no—
37C2×C3×3−1+2A411yescharacteristic, complemented
38C2×C3×H(3,𝔽3)—41no—
39C22×C33—31no—
40C22×C33—31no—
41C22×C33C2×C3211yescharacteristic
42C32×A4C2×C3213yes—
43C22×3−1+2—33no—
44C22×3−1+2—36no—
45C22×3−1+2—33no—
46C22×3−1+2—36no—
47C22×3−1+2C2×C3213yes—
48C22×3−1+2C2×C3216yescomplemented
49C22×C3×C9—33no—
50C22×C3×C9—33no—
51C22×C3×C9C2×C3213yescomplemented
52C22⋊H(3,𝔽3)C2×C3213yes—
53C22⋊H(3,𝔽3)C2×C3216yes—
54#1094C2×C3216yes—
55#1094C2×C3216yescomplemented
56#1094C2×C3216yescomplemented
57C3×C22⋊C9C2×C3216yescomplemented
58C9⋊A4C2×C32154yescomplemented
59C9×A4C2×C32127yescomplemented
60#737—418no—
61#737—49no—
62C3×3−1+2—42no—
63C3×3−1+2—49no—
64C3×3−1+2C2×A411yescharacteristic, complemented
65C3×H(3,𝔽3)—41no—
66C23×C32—91no—
67C23×C32C3312yes—
68C23×C32C3311yescharacteristic
69C23×C32C3311yescharacteristic
70C2×C3×A4—93no—
71C2×C3×A4C3319yes—
72C23×C9C3319yes—
73C2×C22⋊C9C33118yes—
74C2×C33—31no—
75C2×C33—31no—
76C2×C33—43no—
77C2×C33C3×A411yescharacteristic
78C2×3−1+2—33no—
79C2×3−1+2—33no—
80C2×3−1+2—36no—
81C2×3−1+2—36no—
82C2×3−1+2—46no—
83C2×3−1+2—46no—
84C2×3−1+2—46no—
85C2×3−1+2—454no—
86C2×3−1+2C3×A413yes—
87C2×3−1+2C3×A416yescomplemented
88C2×H(3,𝔽3)—46no—
89C2×H(3,𝔽3)—43no—
90C2×C3×C9—33no—
91C2×C3×C9—33no—
92C2×C3×C9—46no—
93C2×C3×C9—427no—
94C2×C3×C9C3×A413yescomplemented
95C22×C32—31no—
96C22×C32—31no—
97C22×C32—31no—
98C22×C32—32no—
99C22×C32—32no—
100C22×C32—31no—
101C22×C32—91no—
102C22×C32—93no—
103C22×C32—93no—
104C22×C32C2×C3312yes—
105C22×C32C2×C3311yescharacteristic
106C22×C32C2×C3311yescharacteristic
107C3×A4—93no—
108C3×A4C2×C3319yes—
109C22×C9—39no—
110C22×C9—39no—
111C22×C9C2×C3319yes—
112C22⋊C9C2×C33118yes—
113C33—43no—
114C33C2×C3×A411yescharacteristic
1153−1+2—46no—
1163−1+2—46no—
1173−1+2—46no—
1183−1+2—454no—
1193−1+2C2×C3×A413yes—
1203−1+2C2×C3×A416yescomplemented
121H(3,𝔽3)—46no—
122H(3,𝔽3)—43no—
123C3×C9—46no—
124C3×C9—427no—
125C3×C9C2×C3×A413yescomplemented
126C23×C3—31no—
127C23×C3—31no—
128C23×C3—32no—
129C23×C3C3411yescharacteristic
130C2×A4—39no—
131C2×C32—31no—
132C2×C32—31no—
133C2×C32—32no—
134C2×C32—31no—
135C2×C32—32no—
136C2×C32—31no—
137C2×C32—49no—
138C2×C32—91no—
139C2×C32—93no—
140C2×C32—93no—
141C2×C32—363no—
142C2×C32C32×A412yes—
143C2×C32C32×A411yescharacteristic
144C2×C32C32×A411yescharacteristic
145C2×C9—39no—
146C2×C9—39no—
147C2×C9—418no—
148C2×C9C32×A419yes—
149C22×C3—31no—
150C22×C3—33no—
151C22×C3—33no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—32no—
156C22×C3—91no—
157C22×C3—92no—
158C22×C3—91no—
159C22×C3—92no—
160C22×C3C2×C3411yescharacteristic
161A4—39no—
162C32—49no—
163C32—91no—
164C32—363no—
165C32C2×C32×A412yes—
166C32C2×C32×A411yescharacteristic
167C32C2×C32×A411yescharacteristic
168C9—418no—
169C9C2×C32×A419yes—
170C233−1+411yescharacteristic, complemented, Sylow
171C2×C3—33no—
172C2×C3—33no—
173C2×C3—31no—
174C2×C3—31no—
175C2×C3—31no—
176C2×C3—31no—
177C2×C3—32no—
178C2×C3—91no—
179C2×C3—92no—
180C2×C3—91no—
181C2×C3—92no—
182C2×C3—129no—
183C2×C3C33×A411yescharacteristic
184C22—31no—
185C22—31no—
186C22C2×3−1+411yescharacteristic, complemented
187C3—31no—
188C3—31no—
189C3—32no—
190C3—129no—
191C3C2×C33×A411yescharacteristic
192C2—31no—
193C2—31no—
194C2#1175810411yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C33×A4
commutator, cosocleC22×C3C2×C34
FrattiniC3C2×C33×A4
FittingC23×C3×3−1+2C3
socleC23×C3C34
prime radicalC2×C3×C22⋊H(3,𝔽3)C3
hypercenterC2×C3×3−1+2A4
hypocenterC22C2×3−1+4
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×C3×3−1+2

Complements

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

NH ≅ G/Ntype
1. #11758104C2direct (N × H)
2. C23×C3×3−1+2C3semidirect
4. C2×C3×#1094C3semidirect
5. C2×#66440C3semidirect
6. C2×A4×3−1+2C3semidirect
7. C2×#66436C3semidirect
11. C22×C3×3−1+2C2×C3semidirect
13. C3×#1094C2×C3semidirect
14. #66440C2×C3semidirect
15. A4×3−1+2C2×C3semidirect
16. #66436C2×C3semidirect
21. C23×3−1+2C32semidirect
22. C23×C3×C9C32semidirect
26. C2×#1094C32semidirect
27. C2×#1094C32semidirect
28. C2×C3×C22⋊C9C32semidirect
29. C2×C9⋊A4C32semidirect
30. C2×C9×A4C32semidirect
37. C2×C3×3−1+2A4semidirect
48. C22×3−1+2C2×C32semidirect
51. C22×C3×C9C2×C32semidirect
55. #1094C2×C32semidirect
56. #1094C2×C32semidirect
57. C3×C22⋊C9C2×C32semidirect
58. C9⋊A4C2×C32semidirect
59. C9×A4C2×C32semidirect
64. C3×3−1+2C2×A4semidirect
87. C2×3−1+2C3×A4semidirect
94. C2×C3×C9C3×A4semidirect
120. 3−1+2C2×C3×A4semidirect
125. C3×C9C2×C3×A4semidirect
170. C233−1+4semidirect
186. C22C2×3−1+4semidirect
194. C2#11758104direct (N × H)

Maximal subgroups

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

subgroupindex
#117581042
C23×C3×3−1+23
C2×C3×C22⋊H(3,𝔽3)3
C2×C3×#10943
C2×#664403
C2×A4×3−1+23
C2×#664363
C2×3−1+44