Finite Group Databasebeta

← D3×#626 #88951

Subgroups — D3×#626 #88951

Order 432.

290 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×D32C211yesmaximal, characteristic, complemented
3#6295C211yesmaximal, characteristic, complemented
4#6292C211yesmaximal, characteristic, complemented
5#6291C211yesmaximal, characteristic, complemented
6C3×#626C211yesmaximal, characteristic, complemented
7C3×D3×Dic3C211yesmaximal, characteristic, complemented
8D3×#67—31nomaximal
9C2×#626—31nomaximal
10D3×D12—31nomaximal
11C2×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
12C2×C3×C3⋊D3C2211yescharacteristic, complemented
13C2×C3×C3⋊D3C2211yescharacteristic, complemented
14C2×C32×D3C2211yescharacteristic
15C2×C32×D3C2211yescharacteristic, complemented
16D3×C3⋊D3—22no—
17C3×D32—22no—
18C3×C3⋊Dic3C2211yescharacteristic, complemented
19C32×Dic3C2211yescharacteristic, complemented
20C22×C3⋊D3—31no—
21C22×C3×D3—31no—
22C22×C3×D3—31no—
23C2×D32—31no—
24C2×D32—31no—
25C2×D32—61no—
26C2×D32D311yescharacteristic, complemented
27#638—31no—
28C4⋊(C3⋊D3)—31no—
29C3×#67—31no—
30C2×C3×Dic3—31no—
31C3×D12—31no—
32C3×C4×D3—31no—
33#626—31no—
34#626—31no—
35#626—31no—
36#626—31no—
37#626—31no—
38#626—31no—
39#626—61no—
40#626—61no—
41#626D311yescharacteristic, direct product factor
42#625—31no—
43D3×Dic3D311yescharacteristic, complemented
44C2×C33C2311yescharacteristic
45C3⋊(C3⋊D3)—21no—
46C3×C3⋊D3—21no—
47C3×C3⋊D3—21no—
48C32×D3—21no—
49C32×D3D412yescomplemented
50C2×#67—91no—
51D3×D4—91no—
52C2×D12—91no—
53C22×C32—31no—
54C22×C32—31no—
55C2×C3⋊D3—31no—
56C2×C3⋊D3—31no—
57C2×C3⋊D3—31no—
58C2×C3⋊D3—61no—
59C2×C3⋊D3—61no—
60C2×C3⋊D3—61no—
61C2×C3⋊D3—62no—
62C2×C3⋊D3—121no—
63C2×C3⋊D3C2×D311yescharacteristic, complemented
64C2×C3⋊D3C2×D311yescharacteristic, complemented
65C2×C3×D3—21no—
66C2×C3×D3—21no—
67C2×C3×D3—31no—
68C2×C3×D3—31no—
69C2×C3×D3—31no—
70C2×C3×D3—31no—
71C2×C3×D3—61no—
72C2×C3×D3—61no—
73C2×C3×D3—62no—
74C2×C3×D3—62no—
75C2×C3×D3C2×D311yescharacteristic
76C2×C3×D3C2×D311yescharacteristic
77C2×C3×D3C2×D311yescharacteristic, complemented
78C2×C3×D3C2×D311yescharacteristic, complemented
79D32—22no—
80D32—64no—
81D32—62no—
82D32—62no—
83C32×C4—31no—
84C3⋊Dic3C2×D311yescharacteristic, complemented
85C3×Dic3—21no—
86C3×Dic3—31no—
87C3×Dic3—31no—
88C3×Dic3—61no—
89C3×Dic3C2×D311yescharacteristic, complemented
90C3×Dic3C2×D311yescharacteristic, complemented
91C33C2×D411yescharacteristic, complemented, Sylow
92C23×C3—91no—
93C22×D3—31no—
94C22×D3—31no—
95C22×D3—91no—
96C22×D3—91no—
97C22×D3—91no—
98C22×D3—181no—
99C3×D4—91no—
100C2×C3×C4—91no—
101#67—31no—
102#67—91no—
103#67—91no—
104#67—91no—
105#67—91no—
106#67—91no—
107#67—181no—
108C2×Dic3—31no—
109D12—31no—
110D12—91no—
111D12—91no—
112D12—91no—
113D12—91no—
114D12—181no—
115C4×D3—31no—
116C2×C32—21no—
117C2×C32—21no—
118C2×C32—21no—
119C2×C32—32no—
120C2×C32—41no—
121C2×C32—61no—
122C2×C32C22×D311yescharacteristic
123C2×C32C22×D311yescharacteristic
124C2×C32C22×D311yescharacteristic
125C3⋊D3—21no—
126C3⋊D3—21no—
127C3⋊D3—61no—
128C3⋊D3—62no—
129C3⋊D3—61no—
130C3⋊D3—61no—
131C3⋊D3—121no—
132C3⋊D3—121no—
133C3⋊D3—122no—
134C3×D3—21no—
135C3×D3—21no—
136C3×D3—22no—
137C3×D3—41no—
138C3×D3—62no—
139C3×D3—61no—
140C3×D3—61no—
141C3×D3—61no—
142C3×D3—61no—
143C3×D3—121no—
144C3×D3D1212yescomplemented
145C3×D3#6712yescomplemented
146C2×D4—271noSylow
147C22×C3—31no—
148C22×C3—31no—
149C22×C3—31no—
150C22×C3—31no—
151C22×C3—61no—
152C22×C3—61no—
153C22×C3—91no—
154C22×C3—91no—
155C22×C3—182no—
156C2×D3—31no—
157C2×D3—31no—
158C2×D3—31no—
159C2×D3—31no—
160C2×D3—61no—
161C2×D3—61no—
162C2×D3—62no—
163C2×D3—62no—
164C2×D3—91no—
165C2×D3—91no—
166C2×D3—91no—
167C2×D3—181no—
168C2×D3—181no—
169C2×D3—181no—
170C2×D3—182no—
171C2×D3—182no—
172C2×D3—184no—
173C2×D3—182no—
174C2×D3—361no—
175C2×D3D3211yescharacteristic
176C2×D3D3211yescharacteristic, complemented
177C3×C4—31no—
178C3×C4—31no—
179C3×C4—61no—
180C3×C4—91no—
181Dic3—31no—
182Dic3—31no—
183Dic3—61no—
184Dic3D3211yescharacteristic, complemented
185C32—21no—
186C32—21no—
187C32—21no—
188C32—41no—
189C32C2×D1211yescharacteristic, complemented
190C32D3×D411yescharacteristic, complemented
191C32C2×#6711yescharacteristic, complemented
192C23—91no—
193C23—271no—
194D4—91no—
195D4—271no—
196D4—271no—
197D4—271no—
198C2×C4—91no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—32no—
203C2×C3—32no—
204C2×C3—41no—
205C2×C3—62no—
206C2×C3—61no—
207C2×C3—61no—
208C2×C3—121no—
209C2×C3—181no—
210C2×C3—181no—
211C2×C3C2×D3211yescharacteristic
212C2×C3C2×D3211yescharacteristic
213C2×C3C2×D3211yescharacteristic
214D3—21no—
215D3—62no—
216D3—61no—
217D3—61no—
218D3—61no—
219D3—61no—
220D3—121no—
221D3—182no—
222D3—181no—
223D3—181no—
224D3—181no—
225D3—361no—
226D3—361no—
227D3—362no—
228D3#62612yesdirect product factor
229C22—31no—
230C22—31no—
231C22—91no—
232C22—91no—
233C22—182no—
234C22—271no—
235C22—542no—
236C4—31no—
237C4—91no—
238C3—21no—
239C3—21no—
240C3—21no—
241C3—41no—
242C3D3×D1211yescharacteristic, complemented
243C3C2×#62611yescharacteristic, complemented
244C3D3×#6711yescharacteristic, complemented
245C2—32no—
246C2—61no—
247C2—181no—
248C2—181no—
249C2—541no—
250C2D3311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D33
commutator, Fitting, socle, cosocleC2×C33C23
hypocenterC33C2×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D3×C3⋊D3C2semidirect
2. C2×C3×D32C2semidirect
3. #6295C2semidirect
4. #6292C2semidirect
5. #6291C2semidirect
6. C3×#626C2semidirect
7. C3×D3×Dic3C2semidirect
11. C2×C3⋊(C3⋊D3)C22semidirect
12. C2×C3×C3⋊D3C22semidirect
13. C2×C3×C3⋊D3C22semidirect
15. C2×C32×D3C22semidirect
18. C3×C3⋊Dic3C22semidirect
19. C32×Dic3C22semidirect
26. C2×D32D3semidirect
41. #626D3direct (N × H)
43. D3×Dic3D3semidirect
49. C32×D3D4semidirect
63. C2×C3⋊D3C2×D3semidirect
64. C2×C3⋊D3C2×D3semidirect
77. C2×C3×D3C2×D3semidirect
78. C2×C3×D3C2×D3semidirect
84. C3⋊Dic3C2×D3semidirect
89. C3×Dic3C2×D3semidirect
90. C3×Dic3C2×D3semidirect
91. C33C2×D4semidirect
144. C3×D3D12semidirect
145. C3×D3#67semidirect
176. C2×D3D32semidirect
184. Dic3D32semidirect
189. C32C2×D12semidirect
190. C32D3×D4semidirect
191. C32C2×#67semidirect
228. D3#626direct (N × H)
242. C3D3×D12semidirect
243. C3C2×#626semidirect
244. C3D3×#67semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊D32
C2×C3×D322
#62952
#62922
#62912
C3×#6262
C3×D3×Dic32
D3×#673
C2×#6263
D3×D123