Finite Group Databasebeta

← D3×#63545 #13155195

Subgroups — D3×#63545 #13155195

Order 1728.

486 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×D24C212yesmaximal, complemented
2#11722067C211yesmaximal, characteristic, complemented
3#11722004C212yesmaximal, complemented
4D3×C3⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
5C3×#63545C211yesmaximal, characteristic, complemented
6D3×#826—32nomaximal
7C2×#63545—31nomaximal
8C3×D3×D12—22no—
9C3×#3745C2212yescomplemented
10C32×D24C2212yescomplemented
11C32×D3×C8C2211yescharacteristic
12C3×#3714—22no—
13C3⋊(C3⋊(C3⋊C16))C2211yescharacteristic, complemented
14C3×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
15C3×D3×D8—32no—
16C2×C3×D24—32no—
17D3×D24D312yescomplemented
18#63653—32no—
19C2×C3⋊(C3⋊C16)—31no—
20C3×#826—32no—
21#63546—32no—
22#63545—32no—
23#63545—32no—
24#63545—31no—
25#63545—62no—
26#63545D311yescharacteristic, direct product factor
27D3×C3⋊C16—32no—
28D3×C3⋊C16—61no—
29C2×C3×D32—42no—
30C3×C4⋊(C3⋊D3)—22no—
31C32×D12—22no—
32C32×C4×D3D411yescharacteristic
33C3×#626—42no—
34C33×C8C2311yescharacteristic
35C32×C3⋊C8D411yescharacteristic
36C2×#826—92no—
37D3×D16—91no—
38C3×D3×D4—62no—
39C2×C3×D12—62no—
40D3×D12—22no—
41C32×D8—32no—
42C2×C32×C8—31no—
43#3745C2×D312yescomplemented
44C3×#213—62no—
45C3×D24—22no—
46C3×D24—32no—
47C3×D24—32no—
48C3×D24—62no—
49C3×D24—62no—
50C3×D24C2×D312yescomplemented
51C3×D24C2×D312yescomplemented
52C3×D3×C8—21no—
53C3×D3×C8C2×D312yes—
54#3714—22no—
55C3⋊(C3⋊C16)—32no—
56C3⋊(C3⋊C16)—31no—
57C3⋊(C3⋊C16)—61no—
58C3⋊(C3⋊C16)—62no—
59C3⋊(C3⋊C16)—121no—
60C3⋊(C3⋊C16)C2×D311yescharacteristic, complemented
61C3×C3⋊C16—32no—
62C3×C3⋊C16—61no—
63C2×C3×C3⋊D3—42no—
64C2×C32×D3—42no—
65C2×C32×D3D811yescharacteristic
66C3×D32—84no—
67C33×C4C2×D411yescharacteristic
68C32×Dic3D811yescharacteristic
69C2×C3×D8—92no—
70D3×D8—32no—
71C2×D24—32no—
72C3×D16—91no—
73#826—32no—
74#826—92no—
75#826—92no—
76#826—92no—
77#826—92no—
78#826—182no—
79C2×C3⋊C16—92no—
80C2×C3⋊C16—181no—
81D48—91no—
82D3×C16—91no—
83C22×C3×D3—122no—
84C22×C3×D3—122no—
85C2×D32—42no—
86C32×D4—62no—
87C2×C32×C4—31no—
88C4⋊(C3⋊D3)—22no—
89C3×#67—122no—
90C3×D12—22no—
91C3×D12—22no—
92C3×D12—42no—
93C3×D12—62no—
94C3×D12—62no—
95C3×D12—122no—
96C3×D12—122no—
97C3×C4×D3—21no—
98C3×C4×D3#6712yes—
99#626—42no—
100C32×C8—21no—
101C32×C8—22no—
102C32×C8—31no—
103C32×C8—41no—
104C32×C8C22×D311yescharacteristic
105C32×C8C22×D312yes—
106C3×C3⋊C8—21no—
107C3×C3⋊C8#6712yes—
108C2×D16—271noSylow
109C2×C33C2×D811yescharacteristic
110C3×C3⋊D3—82no—
111C32×D3—82no—
112C32×D3D1612yescomplemented
113C2×C3×D4—182no—
114D3×D4—62no—
115C2×D12—62no—
116C3×D8—32no—
117C3×D8—32no—
118C3×D8—62no—
119C3×D8—92no—
120C3×D8—182no—
121C2×C3×C8—32no—
122C2×C3×C8—61no—
123#213—62no—
124D24—32no—
125D24—32no—
126D24—62no—
127D24—62no—
128D24D3212yescomplemented
129D3×C8D3211yescharacteristic
130C3×C16—91no—
131C3⋊C16—32no—
132C3⋊C16—61no—
133C3⋊C16—91no—
134C3⋊C16—92no—
135C3⋊C16—181no—
136C3⋊C16—182no—
137C3⋊C16—361no—
138C22×C32—31no—
139C22×C32—122no—
140C2×C3⋊D3—42no—
141C2×C3×D3—21no—
142C2×C3×D3—42no—
143C2×C3×D3—42no—
144C2×C3×D3—82no—
145C2×C3×D3—122no—
146C2×C3×D3—122no—
147C2×C3×D3—242no—
148C2×C3×D3—244no—
149C2×C3×D3—244no—
150C2×C3×D3#21312yes—
151D32—84no—
152C32×C4—21no—
153C32×C4—22no—
154C32×C4—31no—
155C32×C4—41no—
156C32×C4D3×D411yescharacteristic
157C32×C4C2×#6712yes—
158C3×Dic3—21no—
159C3×Dic3#21312yes—
160C2×D8—92no—
161D16—91no—
162D16—271no—
163D16—272no—
164C2×C16—271no—
165C33C2×D1611yescharacteristic, complemented, Sylow
166C23×C3—362no—
167C22×D3—122no—
168C22×D3—122no—
169C3×D4—62no—
170C3×D4—62no—
171C3×D4—122no—
172C3×D4—182no—
173C3×D4—362no—
174C2×C3×C4—32no—
175C2×C3×C4—61no—
176#67—122no—
177D12—22no—
178D12—62no—
179D12—62no—
180D12—122no—
181D12—122no—
182C4×D3#62511yescharacteristic
183C3×C8—21no—
184C3×C8—22no—
185C3×C8—32no—
186C3×C8—41no—
187C3×C8—61no—
188C3×C8C2×D3211yescharacteristic
189C3×C8C2×D3212yes—
190C3⋊C8#62511yescharacteristic
191C2×C32—21no—
192C2×C32—22no—
193C2×C32—32no—
194C2×C32—41no—
195C2×C32—242no—
196C2×C32D3×D811yescharacteristic
197C2×C32C2×#21312yes—
198C3⋊D3—82no—
199C3×D3—22no—
200C3×D3—82no—
201C3×D3—82no—
202C3×D3—162no—
203C3×D3—242no—
204C3×D3—242no—
205C3×D3—482no—
206C3×D3#82614yescomplemented
207C2×D4—182no—
208D8—32no—
209D8—92no—
210D8—182no—
211C2×C8—31no—
212C16—91no—
213C16—271no—
214C22×C3—32no—
215C22×C3—61no—
216C22×C3—122no—
217C22×C3—122no—
218C22×C3—242no—
219C22×C3—362no—
220C22×C3—724no—
221C2×D3—42no—
222C2×D3—122no—
223C2×D3—122no—
224C2×D3—242no—
225C2×D3—244no—
226C2×D3—244no—
227C2×D3#371311yescharacteristic
228C3×C4—21no—
229C3×C4—22no—
230C3×C4—32no—
231C3×C4—41no—
232C3×C4—61no—
233C3×C4C2×#62511yescharacteristic
234C3×C4D3×#6712yes—
235Dic3#371311yescharacteristic
236C32—22no—
237C32—21no—
238C32—41no—
239C32D3×D1611yescharacteristic, complemented
240C32C2×#82612yescomplemented
241C23—362no—
242D4—62no—
243D4—182no—
244D4—362no—
245C2×C4—31no—
246C8—31no—
247C8D3311yescharacteristic
248C2×C3—21no—
249C2×C3—22no—
250C2×C3—34no—
251C2×C3—41no—
252C2×C3—62no—
253C2×C3—242no—
254C2×C3—242no—
255C2×C3—482no—
256C2×C3—722no—
257C2×C3C2×#371311yescharacteristic
258C2×C3D3×#21312yes—
259D3—82no—
260D3—242no—
261D3—242no—
262D3—482no—
263D3#6354512yesdirect product factor
264C22—31no—
265C22—122no—
266C22—362no—
267C22—724no—
268C4—31no—
269C4D3×#62511yescharacteristic
270C3—22no—
271C3—21no—
272C3—41no—
273C3C2×#6354511yescharacteristic, complemented
274C3D3×#82612yescomplemented
275C2—32no—
276C2—242no—
277C2—722no—
278C2D3×#371311yescharacteristic
subgroupG/H
centerC2D3×#3713
commutator, Fitting, cosocleC33×C8C23
Frattini, hypercenterC8D33
socleC2×C33C2×D8
hypocenterC33C2×D16
LCSG ▷ C33×C8 ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. C3×D3×D24C2semidirect
2. #11722067C2semidirect
3. #11722004C2semidirect
4. D3×C3⋊(C3⋊C16)C2semidirect
5. C3×#63545C2semidirect
9. C3×#3745C22semidirect
10. C32×D24C22semidirect
13. C3⋊(C3⋊(C3⋊C16))C22semidirect
14. C3×C3⋊(C3⋊C16)C22semidirect
17. D3×D24D3semidirect
26. #63545D3direct (N × H)
43. #3745C2×D3semidirect
50. C3×D24C2×D3semidirect
51. C3×D24C2×D3semidirect
60. C3⋊(C3⋊C16)C2×D3semidirect
112. C32×D3D16semidirect
128. D24D32semidirect
165. C33C2×D16semidirect
206. C3×D3#826semidirect
239. C32D3×D16semidirect
240. C32C2×#826semidirect
263. D3#63545direct (N × H)
273. C3C2×#63545semidirect
274. C3D3×#826semidirect

Maximal subgroups

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

subgroupindex
C3×D3×D242
#117220672
#117220042
D3×C3⋊(C3⋊C16)2
C3×#635452
D3×#8263
C2×#635453