Finite Group Databasebeta

← #10619895⋊C3 #14518739

Subgroups — #10619895⋊C3 #14518739

Order 1944.

372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 55 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
13−1+2×C3⋊Dic3C211yesmaximal, characteristic
2C3×C3⋊(3−1+2⋊C4)C212yesmaximal
3C3×#6296—31nomaximal
4#10619895C311yesmaximal, characteristic, complemented
5#6189⋊C3—32nomaximal
6C2×C32×3−1+2C2211yescharacteristic
7C32×C3⋊Dic3—32no—
8C32×C3⋊Dic3D311yescharacteristic
9C3⋊(3−1+2⋊C4)—22no—
10C3⋊(3−1+2⋊C4)D312yes—
11C9×C3⋊Dic3—21no—
12C9×C3⋊Dic3C2×C311yescharacteristic
13C3×C3⋊Dic9C2×C312yes—
14Dic3×3−1+2—32no—
15Dic3×3−1+2—61no—
16C3×3−1+2⋊C4—32no—
17C3×3−1+2⋊C4—62no—
18C32×3−1+2Q811yescharacteristic, complemented, Sylow
19#6296—31no—
20C3×#627—92no—
21C3×#627—91no—
223−1+2⋊Q8—91no—
23#6189—32no—
24C2×C34C2×D311yescharacteristic
25C2×C3×3−1+2—21no—
26C2×C3×3−1+2—22no—
27C2×C3×3−1+2—22no—
28C2×C3×3−1+2—42no—
29C2×C3×3−1+2—42no—
30C2×C3×3−1+2—41no—
31C2×C3×3−1+2—41no—
32C2×C3×3−1+2C2×D312yes—
33C2×C32×C9—21no—
34C2×C32×C9C22×C311yescharacteristic
35C3×C3⋊Dic3—31no—
36C3×C3⋊Dic3—32no—
37C3×C3⋊Dic3—32no—
38C3×C3⋊Dic3—62no—
39C3×C3⋊Dic3C3×D311yescharacteristic
40C32×Dic3—32no—
41C32×Dic3—61no—
42C32×Dic3—92no—
43C32×Dic3—92no—
44C32×Dic3—182no—
45C4×3−1+2—91no—
46C3⋊Dic9C3×D312yes—
473−1+2⋊C4—32no—
483−1+2⋊C4—62no—
493−1+2⋊C4—62no—
503−1+2⋊C4—64no—
51C9×Dic3—32no—
52C9×Dic3—61no—
53C9×Dic3—62no—
54C9×Dic3—62no—
55C3×Dic9—32no—
56C3×Dic9—62no—
57C34Dic611yescharacteristic
58C3×3−1+2—21no—
59C3×3−1+2—22no—
60C3×3−1+2—22no—
61C3×3−1+2—42no—
62C3×3−1+2—42no—
63C3×3−1+2—41no—
64C3×3−1+2—41no—
65C3×3−1+2Dic612yescomplemented
66C32×C9—21no—
67C32×C9C3×Q811yescharacteristic, complemented
68C3×Dic6—271no—
69C3×Dic6—272no—
70#627—92no—
71#627—91no—
72Dic18—91no—
73C2×C33—22no—
74C2×C33—21no—
75C2×C33—31no—
76C2×C33—41no—
77C2×C33—62no—
78C2×C33—121no—
79C2×C33D3212yes—
80C2×C33C2×C3×D311yescharacteristic
81C2×3−1+2—24no—
82C2×3−1+2—22no—
83C2×3−1+2—22no—
84C2×3−1+2—42no—
85C2×3−1+2—42no—
86C2×3−1+2—44no—
87C2×3−1+2—44no—
88C2×3−1+2—42no—
89C2×3−1+2—41no—
90C2×3−1+2—41no—
91C2×3−1+2D3211yescharacteristic
92C2×C3×C9—22no—
93C2×C3×C9—22no—
94C2×C3×C9—22no—
95C2×C3×C9—21no—
96C2×C3×C9—41no—
97C2×C3×C9—42no—
98C2×C3×C9—42no—
99C2×C3×C9C2×C3×D312yes—
100C32×C4—91no—
101C32×C4—272no—
102C3⋊Dic3—32no—
103C3⋊Dic3AGL(1,ℤ/9)11yescharacteristic
104C3×Dic3—32no—
105C3×Dic3—61no—
106C3×Dic3—92no—
107C3×Dic3—92no—
108C3×Dic3—92no—
109C3×Dic3—92no—
110C3×Dic3—92no—
111C3×Dic3—181no—
112C3×Dic3—182no—
113C3×Dic3—182no—
114C3×Dic3—182no—
115C3×Dic3—182no—
116C3×Dic3—184no—
117C4×C9—91no—
118C4×C9—181no—
119Dic9—32no—
120Dic9—62no—
121C33—22no—
122C33—21no—
123C33—31no—
124C33—41no—
125C33—62no—
126C33—121no—
127C33#62712yes—
128C33C3×Dic611yescharacteristic
1293−1+2—24no—
1303−1+2—22no—
1313−1+2—22no—
1323−1+2—42no—
1333−1+2—42no—
1343−1+2—44no—
1353−1+2—44no—
1363−1+2—42no—
1373−1+2—41no—
1383−1+2—41no—
1393−1+2#62711yescharacteristic, complemented
140C3×C9—22no—
141C3×C9—22no—
142C3×C9—22no—
143C3×C9—21no—
144C3×C9—41no—
145C3×C9—42no—
146C3×C9—42no—
147C3×C9C3×Dic612yescomplemented
148C3×Q8—811no—
149Dic6—272no—
150Dic6—271no—
151C2×C32—22no—
152C2×C32—21no—
153C2×C32—22no—
154C2×C32—32no—
155C2×C32—41no—
156C2×C32—41no—
157C2×C32—62no—
158C2×C32—61no—
159C2×C32—64no—
160C2×C32—62no—
161C2×C32—121no—
162C2×C32—121no—
163C2×C32—122no—
164C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
165C2×C32C3×D3212yes—
166C2×C32#111311yescharacteristic
167C2×C9—21no—
168C2×C9—22no—
169C2×C9—41no—
170C2×C9—42no—
171C2×C9—42no—
172C2×C9C3×D3211yescharacteristic
173C3×C4—91no—
174C3×C4—271no—
175C3×C4—272no—
176C3×C4—272no—
177C3×C4—542no—
178Dic3—32no—
179Dic3—61no—
180Dic3—92no—
181Dic3—92no—
182Dic3—182no—
183C32—22no—
184C32—21no—
185C32—22no—
186C32—32no—
187C32—41no—
188C32—41no—
189C32—62no—
190C32—61no—
191C32—64no—
192C32—62no—
193C32—121no—
194C32—121no—
195C32—122no—
196C323−1+2⋊Q811yescharacteristic, complemented
197C32C3×#62712yes—
198C32#629611yescharacteristic
199C9—21no—
200C9—22no—
201C9—41no—
202C9—42no—
203C9—42no—
204C9C3×#62711yescharacteristic, complemented
205Q8—811noSylow
206C2×C3—21no—
207C2×C3—22no—
208C2×C3—31no—
209C2×C3—41no—
210C2×C3—62no—
211C2×C3—121no—
212C2×C3D3×AGL(1,ℤ/9)12yes—
213C2×C3C3×#111311yescharacteristic
214C4—91no—
215C4—272no—
216C3—22no—
217C3—21no—
218C3—31no—
219C3—41no—
220C3—62no—
221C3—121no—
222C3#6189⋊C312yescomplemented
223C3C3×#629611yescharacteristic
224C2#66431⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#66431⋊C3
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C3×#1113
FittingC2×C32×3−1+2C22
socleC2×C33C2×C3×D3
prime radicalC2×C34C2×D3
hypocenterC32×C9C3×Q8
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #10619895C3semidirect
18. C32×3−1+2Q8semidirect
65. C3×3−1+2Dic6semidirect
67. C32×C9C3×Q8semidirect
139. 3−1+2#627semidirect
147. C3×C9C3×Dic6semidirect
196. C323−1+2⋊Q8semidirect
204. C9C3×#627semidirect
222. C3#6189⋊C3semidirect

Maximal subgroups

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

subgroupindex
3−1+2×C3⋊Dic32
C3×C3⋊(3−1+2⋊C4)2
C3×#62963
#106198953
#6189⋊C33