Finite Group Databasebeta

← C2×#11757849 #14518439

Subgroups — C2×#11757849 #14518439

Order 1944.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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#11757849C211yesmaximal, characteristic, direct product factor
2C23×C3×3−1+2C311yesmaximal, characteristic, complemented
3C2×C3×C22⋊H(3,𝔽3)C311yesmaximal, characteristic
4C2×C3×#1094C312yesmaximal, complemented
5C2×#66357C319yesmaximal, complemented
6C2×#6910—41nomaximal
7C22×C3×3−1+2—31no—
8C22×C3×3−1+2—31no—
9C22×C3×3−1+2C2×C311yescharacteristic, complemented
10C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic
11C3×#1094C2×C312yescomplemented
12#66357C2×C319yescomplemented
13#6910—41noSylow
14C23×C33C3211yescharacteristic
15C2×C32×A4—31no—
16C23×3−1+2—32no—
17C23×3−1+2—31no—
18C23×C3×C9C3213yescomplemented
19C2×C22⋊H(3,𝔽3)—32no—
20C2×C22⋊H(3,𝔽3)C3213yes—
21C2×#1094—32no—
22C2×#1094—32no—
23C2×#1094C3216yescomplemented
24C2×C3×C22⋊C9—32no—
25C2×C3×3−1+2—31no—
26C2×C3×3−1+2—31no—
27C2×C3×3−1+2—42no—
28C2×C3×3−1+2A411yescharacteristic, complemented
29C2×C3×H(3,𝔽3)—41no—
30C2×#731—49no—
31C22×C33—31no—
32C22×C33—31no—
33C22×C33C2×C3211yescharacteristic
34C32×A4—31no—
35C22×3−1+2—36no—
36C22×3−1+2—33no—
37C22×3−1+2—36no—
38C22×3−1+2—33no—
39C22×3−1+2—32no—
40C22×3−1+2—31no—
41C22×C3×C9—33no—
42C22×C3×C9—33no—
43C22×C3×C9C2×C3213yescomplemented
44C22⋊H(3,𝔽3)—32no—
45C22⋊H(3,𝔽3)C2×C3213yes—
46#1094—32no—
47#1094—32no—
48#1094C2×C3216yescomplemented
49C3×C22⋊C9—32no—
50C3×3−1+2—42no—
51C3×3−1+2C2×A411yescharacteristic, complemented
52C3×H(3,𝔽3)—41no—
53#731—49no—
54C23×C32—91no—
55C23×C32H(3,𝔽3)12yes—
56C23×C32H(3,𝔽3)11yescharacteristic
57C23×C32C3311yescharacteristic
58C2×C3×A4—33no—
59C2×C3×A4—93no—
60C23×C9—33no—
61C2×C22⋊C9—36no—
62C2×C33—31no—
63C2×C33—31no—
64C2×C33—121no—
65C2×C33C3×A411yescharacteristic
66C2×3−1+2—36no—
67C2×3−1+2—33no—
68C2×3−1+2—36no—
69C2×3−1+2—33no—
70C2×3−1+2—32no—
71C2×3−1+2—31no—
72C2×3−1+2—46no—
73C2×3−1+2—122no—
74C2×3−1+2—122no—
75C2×H(3,𝔽3)—43no—
76C2×H(3,𝔽3)—122no—
77C2×C3×C9—33no—
78C2×C3×C9—33no—
79C2×C3×C9—122no—
80C2×C3×C9C3×A413yescomplemented
81C22×C32—31no—
82C22×C32—31no—
83C22×C32—32no—
84C22×C32—31no—
85C22×C32—32no—
86C22×C32—31no—
87C22×C32—91no—
88C22×C32—93no—
89C22×C32—93no—
90C22×C32C2×H(3,𝔽3)12yes—
91C22×C32C2×H(3,𝔽3)11yescharacteristic
92C22×C32C2×C3311yescharacteristic
93C3×A4—33no—
94C3×A4—93no—
95C22×C9—39no—
96C22×C9—39no—
97C22×C9—33no—
98C22⋊C9—36no—
99C33—121no—
100C33C2×C3×A411yescharacteristic
1013−1+2—32no—
1023−1+2—31no—
1033−1+2—46no—
1043−1+2—122no—
1053−1+2—122no—
106H(3,𝔽3)—43no—
107H(3,𝔽3)—122no—
108C3×C9—122no—
109C3×C9C2×C3×A413yescomplemented
110C23×C3—31no—
111C23×C3—31no—
112C23×C3—32no—
113C23×C3C3×H(3,𝔽3)11yescharacteristic
114C2×A4—93no—
115C2×C32—31no—
116C2×C32—31no—
117C2×C32—32no—
118C2×C32—31no—
119C2×C32—32no—
120C2×C32—31no—
121C2×C32—91no—
122C2×C32—93no—
123C2×C32—93no—
124C2×C32—123no—
125C2×C32—363no—
126C2×C32C22⋊H(3,𝔽3)12yes—
127C2×C32C22⋊H(3,𝔽3)11yescharacteristic
128C2×C32C32×A411yescharacteristic
129C2×C9—39no—
130C2×C9—39no—
131C2×C9—33no—
132C2×C9—126no—
133C22×C3—31no—
134C22×C3—33no—
135C22×C3—33no—
136C22×C3—31no—
137C22×C3—31no—
138C22×C3—31no—
139C22×C3—32no—
140C22×C3—91no—
141C22×C3—92no—
142C22×C3—91no—
143C22×C3—92no—
144C22×C3C2×C3×H(3,𝔽3)11yescharacteristic
145A4—93no—
146C32—91no—
147C32—123no—
148C32—363no—
149C32C2×C22⋊H(3,𝔽3)12yes—
150C32C2×C22⋊H(3,𝔽3)11yescharacteristic
151C32C2×C32×A411yescharacteristic
152C9—33no—
153C9—126no—
154C23#691011yescharacteristic, complemented, Sylow
155C2×C3—33no—
156C2×C3—33no—
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—31no—
160C2×C3—31no—
161C2×C3—32no—
162C2×C3—91no—
163C2×C3—92no—
164C2×C3—91no—
165C2×C3—92no—
166C2×C3—363no—
167C2×C3C3×C22⋊H(3,𝔽3)11yescharacteristic
168C22—31no—
169C22—31no—
170C22C2×#691011yescharacteristic, complemented
171C3—31no—
172C3—31no—
173C3—32no—
174C3—363no—
175C3C2×C3×C22⋊H(3,𝔽3)11yescharacteristic
176C2—31no—
177C2—31no—
178C2#1175784911yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C3×C22⋊H(3,𝔽3)
commutator, cosocleC22×C32C2×C33
FrattiniC32C2×C32×A4
FittingC23×C3×3−1+2C3
socleC23×C3C3×H(3,𝔽3)
prime radicalC2×C3×C22⋊H(3,𝔽3)C3
hypercenterC2×C3×3−1+2A4
hypocenterC22C2×#6910
LCSG ▷ C22×C32 ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×C33 ◁ C2×C3×3−1+2

Complements

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

NH ≅ G/Ntype
1. #11757849C2direct (N × H)
2. C23×C3×3−1+2C3semidirect
4. C2×C3×#1094C3semidirect
5. C2×#66357C3semidirect
9. C22×C3×3−1+2C2×C3semidirect
11. C3×#1094C2×C3semidirect
12. #66357C2×C3semidirect
18. C23×C3×C9C32semidirect
23. C2×#1094C32semidirect
28. C2×C3×3−1+2A4semidirect
43. C22×C3×C9C2×C32semidirect
48. #1094C2×C32semidirect
51. C3×3−1+2C2×A4semidirect
80. C2×C3×C9C3×A4semidirect
109. C3×C9C2×C3×A4semidirect
154. C23#6910semidirect
170. C22C2×#6910semidirect
178. C2#11757849direct (N × H)

Maximal subgroups

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

subgroupindex
#117578492
C23×C3×3−1+23
C2×C3×C22⋊H(3,𝔽3)3
C2×C3×#10943
C2×#663573
C2×#69104