Finite Group Databasebeta

← D3×#63385 #13139215

Subgroups — D3×#63385 #13139215

Order 1728.

322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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
1D3×C9×D8C211yesmaximal, characteristic, complemented
2D3×D72C211yesmaximal, characteristic, complemented
3#11720563C211yesmaximal, characteristic, complemented
4C3×#63385C211yesmaximal, characteristic, complemented
5#11720239C211yesmaximal, characteristic, complemented
6#11720238C211yesmaximal, characteristic, complemented
7D3×C9⋊C16C211yesmaximal, characteristic, complemented
8D3×#826—31nomaximal
9C2×#63385—31nomaximal
10D3×D4×C9—21no—
11D3×D36—21no—
12C3×C9×D8C2211yescharacteristic, complemented
13#88525C2211yescharacteristic, complemented
14C9×#213—21no—
15C9×D24C2211yescharacteristic, complemented
16D3×C8×C9C2211yescharacteristic
17C3×D72C2211yescharacteristic, complemented
18#88417—21no—
19C3⋊(C9⋊C16)C2211yescharacteristic, complemented
20C3×C9⋊C16C2211yescharacteristic, complemented
21C3×D3×D8D311yescharacteristic
22D3×D24—31no—
23#63653—31no—
24C3×#826—31no—
25#63546—31no—
26#63545—31no—
27D3×C3⋊C16—31no—
28C2×C9×D8—31no—
29C2×D72—31no—
30#63385—31no—
31#63385—31no—
32#63385—31no—
33#63385—61no—
34#63385D311yescharacteristic, direct product factor
35C2×C9⋊C16—31no—
36C22×D3×C9—41no—
37C2×D3×D9—41no—
38C3×D4×C9—21no—
39C4⋊(C3⋊D9)—21no—
40C9×#67—41no—
41C9×D12—21no—
42C4×D3×C9D411yescharacteristic
43C3×D36—21no—
44#6192—41no—
45C3×C8×C9C2311yescharacteristic
46C9×C3⋊C8D411yescharacteristic
47C2×#826—91no—
48D3×D16—91no—
49C3×D3×D4—21no—
50D3×D12—61no—
51C32×D8C2×D311yescharacteristic
52#3745—31no—
53C3×#213—21no—
54C3×D24—31no—
55C3×D24C2×D311yescharacteristic
56C3×D3×C8C2×D311yescharacteristic
57#3714—61no—
58C2×D4×C9—61no—
59C2×D36—61no—
60C3⋊(C3⋊C16)—31no—
61C3×C3⋊C16—31no—
62C9×D8—21no—
63C9×D8—31no—
64C9×D8—61no—
65C9×D8C2×D311yescharacteristic, complemented
66C2×C8×C9—31no—
67D72—31no—
68D72—61no—
69D72—61no—
70D72C2×D311yescharacteristic, complemented
71C9⋊C16—31no—
72C9⋊C16—61no—
73C9⋊C16C2×D311yescharacteristic, complemented
74C22×C3×C9—41no—
75C2×C3⋊D9—41no—
76C2×D3×C9—41no—
77C2×D3×C9—82no—
78C2×D3×C9D811yescharacteristic
79C2×C3×D9—41no—
80D3×D9—82no—
81C3×C4×C9C2×D411yescharacteristic
82C9×Dic3D811yescharacteristic
83C2×C3×D8—31no—
84D3×D8—91no—
85D3×D8D911yescharacteristic, complemented
86C2×D24—91no—
87C3×D16—91no—
88#826—31no—
89#826—91no—
90#826—91no—
91#826—91no—
92#826—91no—
93#826—91no—
94#826—181no—
95C2×C3⋊C16—91no—
96D48—91no—
97D3×C16—91no—
98C22×C3×D3—41no—
99C2×D32—121no—
100C32×D4—21no—
101C4⋊(C3⋊D3)—61no—
102C3×#67—41no—
103C3×D12—21no—
104C3×D12—61no—
105C3×C4×D3#6711yescharacteristic
106#626—121no—
107C23×C9—121no—
108C22×D9—121no—
109C32×C8C22×D311yescharacteristic
110C3×C3⋊C8#6711yescharacteristic
111D4×C9—21no—
112D4×C9—41no—
113D4×C9—61no—
114D4×C9—121no—
115C2×C4×C9—31no—
116D36—21no—
117D36—61no—
118D36—121no—
119D36—121no—
120C8×C9—21no—
121C8×C9—31no—
122C8×C9C22×D311yescharacteristic
123C2×D16—271noSylow
124C2×C3×C9—81no—
125C2×C3×C9C2×D811yescharacteristic
126C3⋊D9—81no—
127D3×C9—81no—
128D3×C9D1612yescomplemented
129C3×D9—81no—
130C2×C3×D4—61no—
131D3×D4—21no—
132D3×D4—181no—
133C2×D12—181no—
134C3×D8—21no—
135C3×D8—31no—
136C3×D8—61no—
137C3×D8—91no—
138C3×D8C2×D911yescharacteristic, complemented
139C3×D8D3211yescharacteristic
140C2×C3×C8—31no—
141#213—21no—
142#213—181no—
143D24—31no—
144D24—91no—
145D24—91no—
146D24—181no—
147D24—181no—
148D24C2×D911yescharacteristic, complemented
149D3×C8C2×D911yescharacteristic
150C3×C16—91no—
151C3⋊C16—31no—
152C3⋊C16—91no—
153C3⋊C16—91no—
154C3⋊C16—181no—
155C22×C32—41no—
156C2×C3⋊D3—121no—
157C2×C3×D3—41no—
158C2×C3×D3—82no—
159C2×C3×D3—121no—
160C2×C3×D3#21311yescharacteristic
161D32—242no—
162C32×C4C2×#6711yescharacteristic
163C3×Dic3#21311yescharacteristic
164C22×C9—31no—
165C22×C9—41no—
166C22×C9—81no—
167C22×C9—121no—
168C22×C9—242no—
169C2×D9—41no—
170C2×D9—121no—
171C2×D9—241no—
172C2×D9—242no—
173C4×C9—21no—
174C4×C9—31no—
175C4×C9D3×D411yescharacteristic
176C2×D8—31no—
177C2×D8—271no—
178D16—91no—
179D16—271no—
180D16—271no—
181D16—271no—
182C2×C16—271no—
183C3×C9C2×D1611yescharacteristic, complemented, Sylow
184C23×C3—121no—
185C22×D3—41no—
186C22×D3—361no—
187C22×D3—361no—
188C3×D4—21no—
189C3×D4—21no—
190C3×D4—41no—
191C3×D4—61no—
192C3×D4—121no—
193C3×D4—181no—
194C2×C3×C4—31no—
195#67—41no—
196#67—361no—
197D12—21no—
198D12—61no—
199D12—181no—
200D12—181no—
201D12—361no—
202D12—361no—
203C4×D3#61111yescharacteristic
204C3×C8—21no—
205C3×C8—31no—
206C3×C8C22×D911yescharacteristic
207C3×C8C2×D3211yescharacteristic
208C3⋊C8#61111yescharacteristic
209C2×C32—81no—
210C2×C32C2×#21311yescharacteristic
211C3⋊D3—241no—
212C3×D3—81no—
213C3×D3—241no—
214C3×D3#82612yes—
215C2×C9—21no—
216C2×C9—32no—
217C2×C9—81no—
218C2×C9—161no—
219C2×C9—241no—
220C2×C9D3×D811yescharacteristic
221D9—81no—
222D9—241no—
223D9—481no—
224C2×D4—61no—
225C2×D4—541no—
226D8—31no—
227D8—61no—
228D8—91no—
229D8—271no—
230D8—541no—
231D8D3×D911yescharacteristic, complemented
232C2×C8—31no—
233C16—91no—
234C16—271no—
235C22×C3—31no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—81no—
239C22×C3—121no—
240C22×C3—242no—
241C22×C3—361no—
242C2×D3—41no—
243C2×D3—82no—
244C2×D3—121no—
245C2×D3—361no—
246C2×D3—361no—
247C2×D3—721no—
248C2×D3—722no—
249C2×D3—722no—
250C2×D3#367311yescharacteristic
251C3×C4—21no—
252C3×C4—31no—
253C3×C4C2×#61111yescharacteristic
254C3×C4D3×#6711yescharacteristic
255Dic3#367311yescharacteristic
256C32C2×#82611yescharacteristic
257C9—21no—
258C9D3×D1611yescharacteristic, complemented
259C23—121no—
260C23—1081no—
261D4—21no—
262D4—61no—
263D4—121no—
264D4—181no—
265D4—541no—
266D4—1081no—
267C2×C4—31no—
268C8—31no—
269C8C2×D3×D911yescharacteristic
270C2×C3—21no—
271C2×C3—32no—
272C2×C3—81no—
273C2×C3—81no—
274C2×C3—161no—
275C2×C3—241no—
276C2×C3—721no—
277C2×C3C2×#367311yescharacteristic
278C2×C3D3×#21311yescharacteristic
279D3—81no—
280D3—241no—
281D3—721no—
282D3—721no—
283D3—1441no—
284D3#6338512yesdirect product factor
285C22—31no—
286C22—41no—
287C22—121no—
288C22—242no—
289C22—361no—
290C22—1081no—
291C22—2162no—
292C4—31no—
293C4D3×#61111yescharacteristic
294C3—21no—
295C3C2×#6338511yescharacteristic, complemented
296C3D3×#82611yescharacteristic
297C2—32no—
298C2—81no—
299C2—241no—
300C2—721no—
301C2—2161no—
302C2D3×#367311yescharacteristic
subgroupG/H
centerC2D3×#3673
commutator, cosocleC3×C8×C9C23
FrattiniC3×C8C2×D32
FittingC3×C9×D8C22
socleC2×C32C2×#213
hypercenterD8D3×D9
hypocenterC3×C9C2×D16
LCSG ▷ C3×C8×C9 ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D3×C9×D8C2semidirect
2. D3×D72C2semidirect
3. #11720563C2semidirect
4. C3×#63385C2semidirect
5. #11720239C2semidirect
6. #11720238C2semidirect
7. D3×C9⋊C16C2semidirect
12. C3×C9×D8C22semidirect
13. #88525C22semidirect
15. C9×D24C22semidirect
17. C3×D72C22semidirect
19. C3⋊(C9⋊C16)C22semidirect
20. C3×C9⋊C16C22semidirect
34. #63385D3direct (N × H)
65. C9×D8C2×D3semidirect
70. D72C2×D3semidirect
73. C9⋊C16C2×D3semidirect
85. D3×D8D9semidirect
128. D3×C9D16semidirect
138. C3×D8C2×D9semidirect
148. D24C2×D9semidirect
183. C3×C9C2×D16semidirect
231. D8D3×D9semidirect
258. C9D3×D16semidirect
284. D3#63385direct (N × H)
295. C3C2×#63385semidirect

Maximal subgroups

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

subgroupindex
D3×C9×D82
D3×D722
#117205632
C3×#633852
#117202392
#117202382
D3×C9⋊C162
D3×#8263
C2×#633853