Finite Group Databasebeta

← D3×#63387 #13139253

Subgroups — D3×#63387 #13139253

Order 1728.

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

normal subgroups only

This group has 296 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×Q16C211yesmaximal, characteristic, complemented
2D3×D72C211yesmaximal, characteristic
3#11720567C211yesmaximal, characteristic, complemented
4C3×#63387C211yesmaximal, characteristic, complemented
5#11720243C211yesmaximal, characteristic, complemented
6#11720242C211yesmaximal, characteristic, complemented
7D3×C9⋊C16C211yesmaximal, characteristic, complemented
8D3×#828—31nomaximal
9C2×#63387—31nomaximal
10D3×Q8×C9—21no—
11D3×D36—21no—
12C3×C9×Q16C2211yescharacteristic, complemented
13#88525C2211yescharacteristic
14C9×#216—21no—
15C9×Dic12C2211yescharacteristic, complemented
16D3×C8×C9C2211yescharacteristic
17C3×D72C2211yescharacteristic
18#88417—21no—
19C3⋊(C9⋊C16)C2211yescharacteristic, complemented
20C3×C9⋊C16C2211yescharacteristic, complemented
21C3×D3×Q16D311yescharacteristic
22D3×D24—31no—
23#63655—31no—
24C3×#828—31no—
25#63549—31no—
26#63547—31no—
27D3×C3⋊C16—31no—
28C2×C9×Q16—31no—
29C2×D72—31no—
30#63387—31no—
31#63387—31no—
32#63387—31no—
33#63387—61no—
34#63387D311yescharacteristic, direct product factor
35C2×C9⋊C16—31no—
36C2×D3×D9—41no—
37C3×Q8×C9—21no—
38C4⋊(C3⋊D9)—21no—
39C4×D3×C9—41no—
40C4×D3×C9D411yescharacteristic
41C3×D36—21no—
42C9×Dic6—21no—
43C9×Dic6—41no—
44#6192—41no—
45C3×C8×C9C2311yescharacteristic
46C9×C3⋊C8D411yescharacteristic
47C2×#828—91no—
48D3×SD32—91no—
49C3×D3×Q8—21no—
50D3×D12—61no—
51C32×Q16C2×D311yescharacteristic
52#3745—31no—
53C3×#216—21no—
54C3×Dic12C2×D311yescharacteristic
55C3×D24—31no—
56C3×D3×C8C2×D311yescharacteristic
57#3714—61no—
58C2×Q8×C9—61no—
59C2×D36—61no—
60C3⋊(C3⋊C16)—31no—
61C3×C3⋊C16—31no—
62C9×Q16—21no—
63C9×Q16—31no—
64C9×Q16—61no—
65C9×Q16C2×D311yescharacteristic, complemented
66C2×C8×C9—31no—
67D72—31no—
68D72—61no—
69D72—61no—
70D72C2×D311yescharacteristic
71C9⋊C16—31no—
72C9⋊C16—61no—
73C9⋊C16C2×D311yescharacteristic, complemented
74C2×C3⋊D9—41no—
75C2×D3×C9D811yescharacteristic
76C2×C3×D9—41no—
77D3×D9—82no—
78C3×C4×C9—41no—
79C3×C4×C9C2×D411yescharacteristic
80C9×Dic3—41no—
81C9×Dic3D811yescharacteristic
82C2×C3×Q16—31no—
83D3×Q16D911yescharacteristic, complemented
84D3×D8—91no—
85C2×D24—91no—
86C3×SD32—91no—
87#828—31no—
88#828—91no—
89#828—91no—
90#828—91no—
91#828—91no—
92#828—181no—
93#827—91no—
94C2×C3⋊C16—91no—
95#800—91no—
96D3×C16—91no—
97C2×D32—121no—
98C32×Q8—21no—
99C4⋊(C3⋊D3)—61no—
100C3×D12—61no—
101C3×C4×D3—41no—
102C3×C4×D3#6711yescharacteristic
103C3×Dic6—21no—
104C3×Dic6—41no—
105#626—121no—
106C22×D9—121no—
107C32×C8C22×D311yescharacteristic
108C3×C3⋊C8#6711yescharacteristic
109Q8×C9—21no—
110Q8×C9—41no—
111Q8×C9—61no—
112Q8×C9—121no—
113C2×C4×C9—31no—
114C2×C4×C9—121no—
115D36—21no—
116D36—61no—
117D36—121no—
118D36—121no—
119C8×C9—21no—
120C8×C9—31no—
121C8×C9C22×D311yescharacteristic
122C2×SD32—271noSylow
123C2×C3×C9C2×D811yescharacteristic
124C3⋊D9—81no—
125D3×C9SD3212yescomplemented
126C3×D9—81no—
127C2×C3×Q8—61no—
128D3×Q8—21no—
129D3×D4—181no—
130C2×D12—181no—
131C3×Q16—21no—
132C3×Q16—31no—
133C3×Q16—61no—
134C3×Q16C2×D911yescharacteristic, complemented
135C3×Q16D3211yescharacteristic
136C3×D8—91no—
137C2×C3×C8—31no—
138#216—21no—
139#213—181no—
140Dic12C2×D911yescharacteristic, complemented
141D24—31no—
142D24—91no—
143D24—91no—
144D24—181no—
145D24—181no—
146D3×C8C2×D911yescharacteristic
147C3×C16—91no—
148C3⋊C16—31no—
149C3⋊C16—91no—
150C3⋊C16—91no—
151C3⋊C16—181no—
152C2×C3⋊D3—121no—
153C2×C3×D3—121no—
154C2×C3×D3#21311yescharacteristic
155D32—242no—
156C32×C4—41no—
157C32×C4C2×#6711yescharacteristic
158C3×Dic3—41no—
159C3×Dic3#21311yescharacteristic
160C22×C9—31no—
161C2×D9—41no—
162C2×D9—121no—
163C2×D9—241no—
164C2×D9—242no—
165C4×C9—21no—
166C4×C9—31no—
167C4×C9—41no—
168C4×C9—81no—
169C4×C9—121no—
170C4×C9D3×D411yescharacteristic
171C2×Q16—31no—
172C2×D8—271no—
173SD32—91no—
174SD32—271no—
175SD32—271no—
176SD32—271no—
177C2×C16—271no—
178C3×C9C2×SD3211yescharacteristic, complemented, Sylow
179C22×D3—361no—
180C22×D3—361no—
181C3×Q8—21no—
182C3×Q8—21no—
183C3×Q8—41no—
184C3×Q8—61no—
185C3×Q8—121no—
186C3×D4—181no—
187C2×C3×C4—31no—
188C2×C3×C4—121no—
189#67—361no—
190D12—61no—
191D12—181no—
192D12—181no—
193D12—361no—
194D12—361no—
195C4×D3—41no—
196C4×D3#61111yescharacteristic
197Dic6—21no—
198Dic6—41no—
199C3×C8—21no—
200C3×C8—31no—
201C3×C8C22×D911yescharacteristic
202C3×C8C2×D3211yescharacteristic
203C3⋊C8#61111yescharacteristic
204C2×C32C2×#21311yescharacteristic
205C3⋊D3—241no—
206C3×D3—241no—
207C3×D3#82812yes—
208C2×C9—21no—
209C2×C9—32no—
210C2×C9D3×D811yescharacteristic
211D9—81no—
212D9—241no—
213D9—481no—
214C2×Q8—61no—
215C2×D4—541no—
216Q16—31no—
217Q16—61no—
218Q16D3×D911yescharacteristic, complemented
219D8—91no—
220D8—271no—
221D8—541no—
222C2×C8—31no—
223C16—91no—
224C16—271no—
225C22×C3—31no—
226C22×C3—361no—
227C2×D3—121no—
228C2×D3—361no—
229C2×D3—361no—
230C2×D3—721no—
231C2×D3—722no—
232C2×D3—722no—
233C2×D3#367311yescharacteristic
234C3×C4—21no—
235C3×C4—31no—
236C3×C4—41no—
237C3×C4—41no—
238C3×C4—81no—
239C3×C4—121no—
240C3×C4C2×#61111yescharacteristic
241C3×C4D3×#6711yescharacteristic
242Dic3—41no—
243Dic3#367311yescharacteristic
244C32C2×#82811yescharacteristic
245C9—21no—
246C9D3×SD3211yescharacteristic, complemented
247C23—1081no—
248Q8—21no—
249Q8—61no—
250Q8—121no—
251D4—181no—
252D4—541no—
253D4—1081no—
254C2×C4—31no—
255C2×C4—121no—
256C8—31no—
257C8C2×D3×D911yescharacteristic
258C2×C3—21no—
259C2×C3—32no—
260C2×C3—721no—
261C2×C3C2×#367311yescharacteristic
262C2×C3D3×#21311yescharacteristic
263D3—241no—
264D3—721no—
265D3—721no—
266D3—1441no—
267D3#6338712yesdirect product factor
268C22—31no—
269C22—361no—
270C22—1081no—
271C22—2162no—
272C4—31no—
273C4—41no—
274C4—121no—
275C4D3×#61111yescharacteristic
276C3—21no—
277C3C2×#6338711yescharacteristic, complemented
278C3D3×#82811yescharacteristic
279C2—32no—
280C2—721no—
281C2—2161no—
282C2D3×#367311yescharacteristic
subgroupG/H
centerC2D3×#3673
commutator, cosocleC3×C8×C9C23
FrattiniC3×C8C2×D32
FittingC3×C9×Q16C22
socleC2×C32C2×#213
prime radicalD3×D72C2
hypercenterQ16D3×D9
hypocenterC3×C9C2×SD32
LCSG ▷ C3×C8×C9 ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. D3×C9×Q16C2semidirect
3. #11720567C2semidirect
4. C3×#63387C2semidirect
5. #11720243C2semidirect
6. #11720242C2semidirect
7. D3×C9⋊C16C2semidirect
12. C3×C9×Q16C22semidirect
15. C9×Dic12C22semidirect
19. C3⋊(C9⋊C16)C22semidirect
20. C3×C9⋊C16C22semidirect
34. #63387D3direct (N × H)
65. C9×Q16C2×D3semidirect
73. C9⋊C16C2×D3semidirect
83. D3×Q16D9semidirect
125. D3×C9SD32semidirect
134. C3×Q16C2×D9semidirect
140. Dic12C2×D9semidirect
178. C3×C9C2×SD32semidirect
218. Q16D3×D9semidirect
246. C9D3×SD32semidirect
267. D3#63387direct (N × H)
277. C3C2×#63387semidirect

Maximal subgroups

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

subgroupindex
D3×C9×Q162
D3×D722
#117205672
C3×#633872
#117202432
#117202422
D3×C9⋊C162
D3×#8283
C2×#633873