Finite Group Databasebeta

← 3−1+2×C3⋊S4 #14519203

Subgroups — 3−1+2×C3⋊S4 #14519203

Order 1944.

491 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 491 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C3×A4×3−1+2C211yesmaximal, characteristic, complemented
2C32×C3⋊S4C311yesmaximal, characteristic
3C9×C3⋊S4C313yesmaximal, complemented
4S4×3−1+2—33nomaximal
5#67×3−1+2—31nomaximal
6C3⋊D3×3−1+2—41nomaximal
7C33×A4C2×C311yescharacteristic
8C22×C3×3−1+2D311yescharacteristic, complemented
9C2×D3×3−1+2—31no—
10C3×#1094—21no—
11A4×3−1+2—23no—
12A4×3−1+2—29no—
13A4×3−1+2D313yescomplemented
14C3×C9⋊A4—23no—
15C3×C9×A4C2×C313yescomplemented
16Dic3×3−1+2—31no—
17C32×3−1+2—41noSylow
18C3×C3⋊S4—31no—
19C3×C3⋊S4C3211yescharacteristic
20C32×S4—33no—
21C32×#67—31no—
22C9×S4—39no—
23D4×3−1+2—91no—
24C9×#67—33no—
25C32×C3⋊D3—41no—
26C2×C3×3−1+2—31no—
27C9×C3⋊D3—43no—
28D3×3−1+2—61no—
29D3×3−1+2—123no—
30C22×C33C3×D311yescharacteristic
31C2×C32×D3—31no—
32C32×A4—21no—
33C32×A4—23no—
34C32×A4—31no—
35C32×A4—63no—
36C32×A4—61no—
37C32×A4C3×D313yes—
38C32×A4C2×C3211yescharacteristic
39C32×Dic3—31no—
40C22×3−1+2—21no—
41C22×3−1+2—23no—
42C22×3−1+2—91no—
43C22×3−1+2C3⋊D311yescharacteristic, complemented
44C22×C3×C9C3×D313yescomplemented
45C2×D3×C9—33no—
46#1094—26no—
47#1094—23no—
48C3×C22⋊C9—23no—
49C9⋊A4—218no—
50C9⋊A4—29no—
51C9×A4—29no—
52C9×A4C3×D319yescomplemented
53C4×3−1+2—91no—
54C9×Dic3—33no—
55C34—41no—
56C3×3−1+2—43no—
57C3×3−1+2—89no—
58C3×3−1+2—83no—
59C3×3−1+2—81no—
60C3×3−1+2—83no—
61C3×3−1+2S411yescharacteristic, complemented
62C32×C9—43no—
63C3⋊S43−1+211yescharacteristic, direct product factor
64C3×S4—33no—
65C3×S4—93no—
66C32×D4—91no—
67C3×#67—31no—
68C3×#67—91no—
69D4×C9—93no—
70C2×C33—31no—
71C3×C3⋊D3—41no—
72C3×C3⋊D3—121no—
73C32×D3—61no—
74C32×D3—123no—
75C2×3−1+2—31no—
76C2×3−1+2—63no—
77C2×3−1+2—61no—
78C2×3−1+2—181no—
79C2×C3×C9—33no—
80D3×C9—63no—
81D3×C9—129no—
82C22×C32—21no—
83C22×C32—31no—
84C22×C32—61no—
85C22×C32—91no—
86C22×C32C32×D311yescharacteristic
87C22×C32C3×C3⋊D311yescharacteristic
88C2×C3×D3—31no—
89C2×C3×D3—91no—
90C3×A4—21no—
91C3×A4—23no—
92C3×A4—23no—
93C3×A4—33no—
94C3×A4—66no—
95C3×A4—63no—
96C3×A4—62no—
97C3×A4—61no—
98C3×A4—63no—
99C3×A4C2×3−1+211yescharacteristic, complemented
100C3×A4C32×D313yes—
101C32×C4—91no—
102C3×Dic3—31no—
103C3×Dic3—91no—
104C22×C9—23no—
105C22×C9—93no—
106C22×C9C3×C3⋊D313yescomplemented
107C22⋊C9—29no—
108C4×C9—93no—
109C33—41no—
110C33—43no—
111C33—83no—
112C33—81no—
113C33—121no—
114C33—241no—
115C33—243no—
116C33C3×S411yescharacteristic
1173−1+2—21no—
1183−1+2—23no—
1193−1+2—818no—
1203−1+2—86no—
1213−1+2—83no—
1223−1+2—89no—
1233−1+2C3⋊S411yescharacteristic, direct product factor
124C3×C9—49no—
125C3×C9—89no—
126C3×C9—83no—
127C3×C9C3×S413yescomplemented
128S4—33no—
129C3×D4—91no—
130C3×D4—271no—
131#67—31no—
132C2×C32—31no—
133C2×C32—31no—
134C2×C32—61no—
135C2×C32—91no—
136C2×C32—181no—
137C2×C32—181no—
138C3⋊D3—41no—
139C3×D3—61no—
140C3×D3—123no—
141C3×D3—181no—
142C3×D3—363no—
143C2×C9—33no—
144C2×C9—63no—
145C2×C9—183no—
146C22×C3—21no—
147C22×C3—31no—
148C22×C3—61no—
149C22×C3—91no—
150C22×C3—271no—
151C22×C3D3×3−1+211yescharacteristic, complemented
152C22×C3C32×C3⋊D311yescharacteristic
153C2×D3—31no—
154A4—23no—
155A4—63no—
156A4D3×3−1+213yescomplemented
157C3×C4—91no—
158C3×C4—271no—
159Dic3—31no—
160C32—21no—
161C32—31no—
162C32—41no—
163C32—43no—
164C32—61no—
165C32—83no—
166C32—81no—
167C32—83no—
168C32—123no—
169C32—242no—
170C32—243no—
171C32—243no—
172C32—246no—
173C32—241no—
174C32C32×S411yescharacteristic
175C32C3×C3⋊S411yescharacteristic
176C9—23no—
177C9—89no—
178C9C3×C3⋊S413yescomplemented
179D4—91noSylow
180C2×C3—31no—
181C2×C3—31no—
182C2×C3—61no—
183C2×C3—91no—
184C2×C3—181no—
185C2×C3—181no—
186C2×C3—541no—
187D3—61no—
188D3—123no—
189C22—91no—
190C22C3⋊D3×3−1+211yescharacteristic, complemented
191C4—91no—
192C3—21no—
193C3—31no—
194C3—43no—
195C3—61no—
196C3—83no—
197C3—243no—
198C3S4×3−1+211yescharacteristic, complemented
199C3C32×C3⋊S411yescharacteristic
200C2—31no—
201C2—181no—
subgroupG/H
center, FrattiniC3C32×C3⋊S4
commutator, cosocleC32×A4C2×C32
FittingC22×C3×3−1+2D3
socleC22×C32C32×D3
prime radicalC32×C3⋊S4C3
hypercenter3−1+2C3⋊S4
hypocenterC3×A4C2×3−1+2
LCSG ▷ C32×A4 ▷ C3×A4
UCSC1 ◁ C3 ◁ 3−1+2

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2semidirect
3. C9×C3⋊S4C3semidirect
8. C22×C3×3−1+2D3semidirect
13. A4×3−1+2D3semidirect
15. C3×C9×A4C2×C3semidirect
43. C22×3−1+2C3⋊D3semidirect
44. C22×C3×C9C3×D3semidirect
52. C9×A4C3×D3semidirect
61. C3×3−1+2S4semidirect
63. C3⋊S43−1+2direct (N × H)
99. C3×A4C2×3−1+2semidirect
106. C22×C9C3×C3⋊D3semidirect
123. 3−1+2C3⋊S4direct (N × H)
127. C3×C9C3×S4semidirect
151. C22×C3D3×3−1+2semidirect
156. A4D3×3−1+2semidirect
178. C9C3×C3⋊S4semidirect
190. C22C3⋊D3×3−1+2semidirect
198. C3S4×3−1+2semidirect

Maximal subgroups

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

subgroupindex
C3×A4×3−1+22
C32×C3⋊S43
C9×C3⋊S43
S4×3−1+23
#67×3−1+23
C3⋊D3×3−1+24