Finite Group Databasebeta

← D3×#63436 #13147707

Subgroups — D3×#63436 #13147707

Order 1728.

1602 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 269 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×D36C216yesmaximal, complemented
2#11721711C211yesmaximal, characteristic, complemented
3C42×D3×C9C211yesmaximal, characteristic, complemented
4C3×#63436C211yesmaximal, characteristic, complemented
5#11721006C216yesmaximal, complemented
6D3×#874—31nomaximal
7C2×#63436—31nomaximal
8C22×D3×D9C2214yes—
9C2×C4⋊(C3⋊D9)C2216yescomplemented
10C2×C4×D3×C9C2213yes—
11C2×C3×D36C2216yescomplemented
12C2×#6192C22112yescomplemented
13D3×D36—224no—
14C3×C42×C9C2211yescharacteristic, complemented
15C4×C9×Dic3C2213yescomplemented
16C2×D3×D12—36no—
17#64083—31no—
18C3×#874—31no—
19C3×C42×D3D311yescharacteristic
20#63911—36no—
21C22×D36—36no—
22C2×C42×C9—31no—
23#63436—36no—
24#63436—31no—
25#63436—61no—
26#63436D311yescharacteristic, direct product factor
27C22×C3⋊D9C2314yes—
28C22×D3×C9C2311yescharacteristic
29C22×C3×D9C2314yes—
30C2×D3×D9—224no—
31C2×C3×C4×C9C2313yes—
32C4⋊(C3⋊D9)—212no—
33C2×C9×Dic3C2313yes—
34C4×D3×C9D4112yescomplemented
35C3×D36—212no—
36#6192—224no—
37D3×#127—91no—
38C2×#874—91no—
39C22×D32—34no—
40C2×C4⋊(C3⋊D3)—36no—
41C2×C3×D12—36no—
42C2×C3×C4×D3C2×D313yes—
43C2×#626—312no—
44D3×D12—624no—
45C23×D9—34no—
46C32×C42C2×D311yescharacteristic
47C3×C4×Dic3C2×D313yes—
48C22×C4×C9—33no—
49C2×D36—312no—
50C2×D36—36no—
51C2×D36—624no—
52C2×D36—66no—
53C2×D36C2×D316yescomplemented
54C42×C9—21no—
55C42×C9—33no—
56C42×C9C2×D311yescharacteristic, complemented
57C22×C3×C9C2411yescharacteristic
58C2×C3⋊D9—212no—
59C2×D3×C9C2×D416yes—
60C2×C3×D9—212no—
61D3×D9—416no—
62C3×C4×C9C2×D416yescomplemented
63C9×Dic3C2×D416yescomplemented
64C2×D3×D4—96no—
65C22×D12—96no—
66C3×#127—91no—
67C2×C3×C42—31no—
68#940—96no—
69#874—31no—
70#874—96no—
71#874—91no—
72#874—91no—
73#874—181no—
74C42×D3D911yescharacteristic, complemented
75C22×C3⋊D3—34no—
76C22×C3×D3—34no—
77C22×C3×D3C22×D311yescharacteristic
78C2×D32—624no—
79C2×C32×C4C22×D313yes—
80C4⋊(C3⋊D3)—612no—
81C2×C3×Dic3C22×D313yes—
82C3×D12—612no—
83C3×C4×D3D12112yes—
84#626—624no—
85C23×C9—31no—
86C22×D9—34no—
87C22×D9—64no—
88C22×D9—624no—
89C22×D9C22×D314yes—
90C2×C4×C9—23no—
91C2×C4×C9—33no—
92C2×C4×C9—312no—
93C2×C4×C9C22×D313yes—
94D36—212no—
95D36—624no—
96D36—612no—
97D36—1212no—
98C2×#127—271noSylow
99C2×C3×C9C22×D413yes—
100C3⋊D9—44no—
101D3×C9#12714yescomplemented
102C3×D9—44no—
103C23×D3—94no—
104C23×D3—94no—
105C2×C3×D4—96no—
106C22×C3×C4—33no—
107C2×#67—912no—
108D3×D4—1824no—
109C2×D12—36no—
110C2×D12—912no—
111C2×D12—96no—
112C2×D12—96no—
113C2×D12—186no—
114C2×D12—1824no—
115C2×C4×D3C2×D913yes—
116C3×C42—21no—
117C3×C42—33no—
118C3×C42C2×D911yescharacteristic, complemented
119C3×C42D3211yescharacteristic
120C4×Dic3C2×D913yescomplemented
121C22×C32C23×D311yescharacteristic
122C2×C3⋊D3—612no—
123C2×C3×D3—612no—
124C2×C3×D3C2×D1216yes—
125D32—1216no—
126C32×C4C2×D1216yes—
127C3×Dic3C2×D1216yes—
128C22×C9—21no—
129C22×C9—36no—
130C22×C9C23×D311yescharacteristic
131C2×D9—212no—
132C2×D9—612no—
133C2×D9—1212no—
134C2×D9—1216no—
135C4×C9—26no—
136C4×C9—36no—
137C4×C9D3×D416yescomplemented
138C22×D4—276no—
139#127—91no—
140#127—276no—
141#127—271no—
142C2×C42—31no—
143C3×C9C2×#12711yescharacteristic, complemented, Sylow
144C23×C3—31no—
145C23×C3—94no—
146C22×D3—34no—
147C22×D3—94no—
148C22×D3—94no—
149C22×D3—184no—
150C22×D3—1824no—
151C22×D3—1824no—
152C22×D3C22×D911yescharacteristic
153C3×D4—1812no—
154C2×C3×C4—23no—
155C2×C3×C4—33no—
156C2×C3×C4—312no—
157C2×C3×C4C22×D913yes—
158C2×C3×C4C2×D3213yes—
159#67—1824no—
160C2×Dic3C22×D913yes—
161D12—612no—
162D12—1824no—
163D12—1812no—
164D12—1812no—
165D12—3612no—
166C4×D3D36112yescomplemented
167C2×C32C22×D1213yes—
168C3⋊D3—124no—
169C3×D3—124no—
170C3×D3#87414yes—
171C2×C9—23no—
172C2×C9—34no—
173C2×C9C2×D3×D413yes—
174D9—44no—
175D9—124no—
176D9—244no—
177C24—274no—
178C2×D4—96no—
179C2×D4—2712no—
180C2×D4—276no—
181C2×D4—5424no—
182C22×C4—33no—
183C42—33no—
184C42D3×D911yescharacteristic, complemented
185C22×C3—21no—
186C22×C3—36no—
187C22×C3—1812no—
188C22×C3C23×D911yescharacteristic
189C22×C3C22×D3211yescharacteristic
190C2×D3—612no—
191C2×D3—1812no—
192C2×D3—1812no—
193C2×D3—3612no—
194C2×D3—3616no—
195C2×D3—3616no—
196C2×D3C2×D3616yes—
197C3×C4—26no—
198C3×C4—36no—
199C3×C4C2×D3616yescomplemented
200C3×C4D3×D1216yes—
201Dic3C2×D3616yescomplemented
202C32C2×#87411yescharacteristic
203C9—21no—
204C9D3×#12711yescharacteristic, complemented
205C23—31no—
206C23—94no—
207C23—274no—
208C23—5424no—
209D4—1812no—
210D4—5424no—
211D4—5412no—
212C2×C4—33no—
213C2×C4—312no—
214C2×C4C2×D3×D913yes—
215C2×C3—23no—
216C2×C3—34no—
217C2×C3—364no—
218C2×C3C22×D3613yes—
219C2×C3C2×D3×D1213yes—
220D3—124no—
221D3—364no—
222D3—364no—
223D3—724no—
224D3#6343614yesdirect product factor
225C22—36no—
226C22—1812no—
227C22—5412no—
228C22—10816no—
229C22C22×D3×D911yescharacteristic
230C4—36no—
231C4D3×D3616yescomplemented
232C3—21no—
233C3C2×#6343611yescharacteristic, complemented
234C3D3×#87411yescharacteristic
235C2—34no—
236C2—364no—
237C2—1084no—
238C2C2×D3×D3613yes—
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
hypercenterC42D3×D9
hypocenterC3×C9C2×#127
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×D3×D36C2semidirect
2. #11721711C2semidirect
3. C42×D3×C9C2semidirect
4. C3×#63436C2semidirect
5. #11721006C2semidirect
9. C2×C4⋊(C3⋊D9)C22semidirect
11. C2×C3×D36C22semidirect
12. C2×#6192C22semidirect
14. C3×C42×C9C22semidirect
15. C4×C9×Dic3C22semidirect
26. #63436D3direct (N × H)
34. C4×D3×C9D4semidirect
53. C2×D36C2×D3semidirect
56. C42×C9C2×D3semidirect
62. C3×C4×C9C2×D4semidirect
63. C9×Dic3C2×D4semidirect
74. C42×D3D9semidirect
101. D3×C9#127semidirect
118. C3×C42C2×D9semidirect
120. C4×Dic3C2×D9semidirect
137. C4×C9D3×D4semidirect
143. C3×C9C2×#127semidirect
166. C4×D3D36semidirect
184. C42D3×D9semidirect
199. C3×C4C2×D36semidirect
201. Dic3C2×D36semidirect
204. C9D3×#127semidirect
224. D3#63436direct (N × H)
231. C4D3×D36semidirect
233. C3C2×#63436semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D362
#117217112
C42×D3×C92
C3×#634362
#117210062
D3×#8743
C2×#634363