Finite Group Databasebeta

← #88960

Subgroups — #88960

Order 432.

210 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 46 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#6295C211yesmaximal, characteristic, complemented
2#6293C211yesmaximal, characteristic, complemented
3#6290C211yesmaximal, characteristic, complemented
4Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
5C3×#626C211yesmaximal, characteristic, complemented
6C3×#624C211yesmaximal, characteristic, complemented
7C3×D3×Dic3C211yesmaximal, characteristic, complemented
8#3804—31nomaximal
9#3798—31nomaximal
10#3795—31nomaximal
11C2×C3×C3⋊D3C2211yescharacteristic
12C2×C3×C3⋊D3C2211yescharacteristic
13C2×C32×D3C2211yescharacteristic
14C3⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C3⋊Dic3C2211yescharacteristic
16C32×Dic3C2211yescharacteristic
17C32×Dic3C2211yescharacteristic
18#638—31no—
19C4×C3⋊D3—31no—
20#634—31no—
21C3×#67—31no—
22C2×C3×Dic3—31no—
23C3×D12—31no—
24C3×C4×D3—31no—
25C3×C4×D3—31no—
26C3×C4×D3—31no—
27#627—31no—
28#627—31no—
29#627—61no—
30#626—31no—
31#626—31no—
32#626D311yescharacteristic, complemented
33#625—31no—
34#625—31no—
35#625—31no—
36#625—61no—
37#624D311yescharacteristic, complemented
38D3×Dic3—31no—
39D3×Dic3—31no—
40D3×Dic3—61no—
41D3×Dic3D311yescharacteristic, complemented
42C2×C33C2311yescharacteristic
43C3×C3⋊D3—21no—
44C3×C3⋊D3—21no—
45C32×D3—21no—
46#237—91no—
47#235—91no—
48#235—91no—
49C22×C32—31no—
50C2×C3⋊D3C2×D311yescharacteristic
51C2×C3⋊D3C2×D311yescharacteristic
52C2×C3×D3—21no—
53C2×C3×D3—31no—
54C2×C3×D3—31no—
55C2×C3×D3—31no—
56C2×C3×D3—31no—
57C2×C3×D3—61no—
58C2×C3×D3—61no—
59C2×C3×D3C2×D311yescharacteristic
60C2×C3×D3C2×D311yescharacteristic
61C32×C4—31no—
62C32×C4—31no—
63C3⋊Dic3—31no—
64C3⋊Dic3—31no—
65C3⋊Dic3—31no—
66C3⋊Dic3—61no—
67C3⋊Dic3—61no—
68C3⋊Dic3—61no—
69C3⋊Dic3—121no—
70C3⋊Dic3C2×D311yescharacteristic
71C3×Dic3—21no—
72C3×Dic3—21no—
73C3×Dic3—31no—
74C3×Dic3—31no—
75C3×Dic3—61no—
76C3×Dic3C2×D311yescharacteristic
77C3×Dic3C2×D311yescharacteristic
78C3×Dic3C2×D311yescharacteristic
79C3×Dic3C2×D311yescharacteristic
80C33#4111yescharacteristic, complemented, Sylow
81C3×D4—91no—
82C2×C3×C4—91no—
83C2×C3×C4—91no—
84#67—31no—
85#67—91no—
86#67—91no—
87#67—91no—
88#67—91no—
89#67—91no—
90#67—181no—
91C2×Dic3—31no—
92C2×Dic3—91no—
93D12—31no—
94D12—91no—
95C4×D3—31no—
96C4×D3—31no—
97C4×D3—31no—
98C4×D3—91no—
99C4×D3—91no—
100C4×D3—181no—
101Dic6—91no—
102Dic6—91no—
103Dic6—91no—
104Dic6—181no—
105C2×C32—21no—
106C2×C32—21no—
107C2×C32—21no—
108C2×C32—41no—
109C2×C32—61no—
110C2×C32C22×D311yescharacteristic
111C2×C32C22×D311yescharacteristic
112C2×C32C22×D311yescharacteristic
113C3⋊D3—21no—
114C3⋊D3—21no—
115C3×D3—21no—
116C3×D3—21no—
117C3×D3—41no—
118C3×D3—62no—
119C3×D3—61no—
120C3×D3—61no—
121C3×D3—61no—
122C3×D3—61no—
123C3×D3—121no—
124#41—271noSylow
125C22×C3—31no—
126C22×C3—31no—
127C22×C3—61no—
128C22×C3—91no—
129C22×C3—91no—
130C2×D3—31no—
131C2×D3—31no—
132C2×D3—31no—
133C2×D3—31no—
134C2×D3—61no—
135C2×D3—61no—
136C2×D3D3211yescharacteristic
137C3×C4—31no—
138C3×C4—31no—
139C3×C4—31no—
140C3×C4—31no—
141C3×C4—61no—
142C3×C4—61no—
143C3×C4—91no—
144Dic3—31no—
145Dic3—31no—
146Dic3—61no—
147Dic3—91no—
148Dic3—91no—
149Dic3—91no—
150Dic3—181no—
151Dic3—181no—
152Dic3—181no—
153Dic3—361no—
154Dic3D3211yescharacteristic
155Dic3D3211yescharacteristic
156C32—21no—
157C32—21no—
158C32—21no—
159C32—41no—
160C32#23511yescharacteristic, complemented
161C32#23511yescharacteristic, complemented
162C32#23711yescharacteristic, complemented
163Q8—271no—
164D4—91no—
165D4—271no—
166D4—271no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—271no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—41no—
174C2×C3—61no—
175C2×C3—61no—
176C2×C3—121no—
177C2×C3—181no—
178C2×C3—181no—
179C2×C3C2×D3211yescharacteristic
180C2×C3C2×D3211yescharacteristic
181C2×C3C2×D3211yescharacteristic
182D3—21no—
183D3—62no—
184D3—61no—
185D3—61no—
186D3—61no—
187D3—61no—
188D3—121no—
189C22—31no—
190C22—91no—
191C22—91no—
192C4—31no—
193C4—31no—
194C4—91no—
195C4—271no—
196C3—21no—
197C3—21no—
198C3—21no—
199C3—41no—
200C3#379511yescharacteristic, complemented
201C3#379811yescharacteristic, complemented
202C3#380411yescharacteristic, complemented
203C2—61no—
204C2—181no—
205C2—181no—
206C2D3311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D33
commutator, Fitting, socle, cosocleC2×C33C23
hypocenterC33#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #6295C2semidirect
2. #6293C2semidirect
3. #6290C2semidirect
4. Dic3×C3⋊D3C2semidirect
5. C3×#626C2semidirect
6. C3×#624C2semidirect
7. C3×D3×Dic3C2semidirect
32. #626D3semidirect
37. #624D3semidirect
41. D3×Dic3D3semidirect
80. C33#41semidirect
160. C32#235semidirect
161. C32#235semidirect
162. C32#237semidirect
200. C3#3795semidirect
201. C3#3798semidirect
202. C3#3804semidirect

Maximal subgroups

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

subgroupindex
#62952
#62932
#62902
Dic3×C3⋊D32
C3×#6262
C3×#6242
C3×D3×Dic32
#38043
#37983
#37953