Finite Group Databasebeta

← D3×Dic3×C3⋊D3 #13049487

Subgroups — D3×Dic3×C3⋊D3 #13049487

Order 1296.

1036 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 146 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×C3×D3×C3⋊D3C211yesmaximal, characteristic
2#10620154C211yesmaximal, characteristic, complemented
3C3⋊D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4Dic3×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5D3×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C3×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
7C32×D3×Dic3C211yesmaximal, characteristic, complemented
8C2×Dic3×C3⋊D3—31nomaximal
9C4×D3×C3⋊D3—31nomaximal
10D32×Dic3—34nomaximal
11C2×C3×C3⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×C3⋊D3C2211yescharacteristic
13C2×C33×D3C2211yescharacteristic
14C3×D3×C3⋊D3C414yescomplemented
15C3⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
16C3×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
17C32×C3⋊Dic3C2211yescharacteristic, complemented
18C33×Dic3C2211yescharacteristic, complemented
19C22×C3×C3⋊D3—31no—
20C2×D3×C3⋊D3D311yescharacteristic
21C2×C3×D32—34no—
22C2×C3⋊(C3⋊Dic3)—31no—
23C4×C3⋊(C3⋊D3)—31no—
24C3×C4×C3⋊D3—31no—
25C2×C32×Dic3—31no—
26C32×C4×D3—31no—
27#6294—34no—
28#6289—31no—
29Dic3×C3⋊D3—31no—
30Dic3×C3⋊D3—31no—
31Dic3×C3⋊D3—31no—
32Dic3×C3⋊D3—31no—
33Dic3×C3⋊D3—34no—
34Dic3×C3⋊D3—64no—
35Dic3×C3⋊D3—61no—
36Dic3×C3⋊D3D311yescharacteristic, direct product factor
37D3×C3⋊Dic3—31no—
38D3×C3⋊Dic3—34no—
39D3×C3⋊Dic3—34no—
40D3×C3⋊Dic3—64no—
41C3×D3×Dic3—34no—
42C3×D3×Dic3D314yescomplemented
43C2×C34C2311yescharacteristic
44C3×C3⋊(C3⋊D3)C2×C412yescomplemented
45C32×C3⋊D3C2×C412yescomplemented
46C33×D3C2×C412yescomplemented
47C2×C4×C3⋊D3—91no—
48C2×D3×Dic3—94no—
49C2×D3×Dic3—91no—
50C4×D32—94no—
51C22×C33—31no—
52C2×C3⋊(C3⋊D3)C2×D311yescharacteristic
53C2×C3×C3⋊D3—21no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—34no—
56C2×C3×C3⋊D3—34no—
57C2×C3×C3⋊D3—64no—
58C2×C3×C3⋊D3C2×D311yescharacteristic
59C2×C3×C3⋊D3C2×D311yescharacteristic
60C2×C32×D3—24no—
61C2×C32×D3—34no—
62C2×C32×D3C2×D314yes—
63C2×C32×D3C2×D311yescharacteristic
64D3×C3⋊D3Dic314yesdirect product factor
65C3×D32—316no—
66C33×C4—31no—
67C3⋊(C3⋊Dic3)—31no—
68C3⋊(C3⋊Dic3)—31no—
69C3⋊(C3⋊Dic3)—34no—
70C3⋊(C3⋊Dic3)—64no—
71C3⋊(C3⋊Dic3)—64no—
72C3⋊(C3⋊Dic3)—61no—
73C3⋊(C3⋊Dic3)—124no—
74C3⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
75C3×C3⋊Dic3—31no—
76C3×C3⋊Dic3—34no—
77C3×C3⋊Dic3—64no—
78C3×C3⋊Dic3C2×D314yescomplemented
79C32×Dic3—24no—
80C32×Dic3—31no—
81C32×Dic3—31no—
82C32×Dic3—61no—
83C32×Dic3C2×D314yescomplemented
84C32×Dic3C2×D311yescharacteristic, complemented
85C34C22×C411yescharacteristic, complemented, Sylow
86C22×C3⋊D3—31no—
87C22×C3×D3—94no—
88C22×C3×D3—91no—
89C2×D32—34no—
90C2×C32×C4—91no—
91C2×C3⋊Dic3—91no—
92C2×C3⋊Dic3—94no—
93C2×C3⋊Dic3—91no—
94C2×C3⋊Dic3—184no—
95C4×C3⋊D3—31no—
96C4×C3⋊D3—91no—
97C4×C3⋊D3—91no—
98C4×C3⋊D3—91no—
99C4×C3⋊D3—94no—
100C4×C3⋊D3—184no—
101C2×C3×Dic3—34no—
102C2×C3×Dic3—91no—
103C3×C4×D3—34no—
104C3×C4×D3—94no—
105#624—94no—
106D3×Dic3—34no—
107D3×Dic3—94no—
108D3×Dic3—94no—
109D3×Dic3—94no—
110D3×Dic3—94no—
111D3×Dic3—91no—
112D3×Dic3—91no—
113D3×Dic3—94no—
114D3×Dic3—91no—
115D3×Dic3—184no—
116D3×Dic3—184no—
117D3×Dic3—184no—
118D3×Dic3C3⋊D311yescharacteristic, direct product factor
119C2×C33—24no—
120C2×C33—21no—
121C2×C33—24no—
122C2×C33—32no—
123C2×C33—44no—
124C2×C33C22×D311yescharacteristic
125C2×C33C22×D311yescharacteristic
126C2×C33C22×D314yes—
127C3⋊(C3⋊D3)C2×Dic312yescomplemented
128C3×C3⋊D3—22no—
129C3×C3⋊D3—32no—
130C3×C3⋊D3—38no—
131C3×C3⋊D3—68no—
132C3×C3⋊D3C4×D312yescomplemented
133C3×C3⋊D3C2×Dic312yescomplemented
134C32×D3—28no—
135C32×D3—38no—
136C32×D3C4×D318yescomplemented
137C32×D3C2×Dic312yescomplemented
138C22×Dic3—271no—
139C2×C4×D3—271no—
140C2×C4×D3—274no—
141C22×C32—31no—
142C22×C32—34no—
143C22×C32—64no—
144C22×C32—91no—
145C2×C3⋊D3—31no—
146C2×C3⋊D3—34no—
147C2×C3⋊D3—34no—
148C2×C3⋊D3—64no—
149C2×C3⋊D3D3211yescharacteristic
150C2×C3×D3—24no—
151C2×C3×D3—34no—
152C2×C3×D3—34no—
153C2×C3×D3—64no—
154C2×C3×D3—916no—
155C2×C3×D3—94no—
156C2×C3×D3—91no—
157C2×C3×D3—94no—
158C2×C3×D3—184no—
159C2×C3×D3D3214yes—
160C2×C3×D3C2×C3⋊D311yescharacteristic
161D32—316no—
162C32×C4—31no—
163C32×C4—34no—
164C32×C4—64no—
165C32×C4—91no—
166C3⋊Dic3—31no—
167C3⋊Dic3—34no—
168C3⋊Dic3—64no—
169C3⋊Dic3—91no—
170C3⋊Dic3—94no—
171C3⋊Dic3—94no—
172C3⋊Dic3—91no—
173C3⋊Dic3—184no—
174C3⋊Dic3—184no—
175C3⋊Dic3—184no—
176C3⋊Dic3—184no—
177C3⋊Dic3—184no—
178C3⋊Dic3—364no—
179C3⋊Dic3—364no—
180C3⋊Dic3—3612no—
181C3⋊Dic3C2×C3⋊D311yescharacteristic, complemented
182C3×Dic3—24no—
183C3×Dic3—34no—
184C3×Dic3—34no—
185C3×Dic3—64no—
186C3×Dic3—94no—
187C3×Dic3—91no—
188C3×Dic3—184no—
189C3×Dic3D3214yescomplemented
190C3×Dic3C2×C3⋊D311yescharacteristic, complemented
191C33—24no—
192C33—24no—
193C33—21no—
194C33—44no—
195C33C2×C4×D311yescharacteristic, complemented
196C33C2×C4×D314yescomplemented
197C33C22×Dic311yescharacteristic, complemented
198C23×C3—271no—
199C22×D3—94no—
200C22×D3—91no—
201C2×C3×C4—94no—
202C2×C3×C4—271no—
203C2×Dic3—31no—
204C2×Dic3—91no—
205C2×Dic3—271no—
206C2×Dic3—271no—
207C2×Dic3—271no—
208C2×Dic3—271no—
209C2×Dic3—274no—
210C2×Dic3—271no—
211C2×Dic3—541no—
212C2×Dic3—544no—
213C4×D3—31no—
214C4×D3—94no—
215C4×D3—271no—
216C4×D3—274no—
217C4×D3—271no—
218C4×D3—274no—
219C4×D3—274no—
220C4×D3—271no—
221C4×D3—544no—
222C2×C32—24no—
223C2×C32—24no—
224C2×C32—24no—
225C2×C32—24no—
226C2×C32—24no—
227C2×C32—32no—
228C2×C32—38no—
229C2×C32—44no—
230C2×C32—412no—
231C2×C32—44no—
232C2×C32—68no—
233C2×C32—92no—
234C2×C32C2×D3214yes—
235C2×C32C2×D3214yes—
236C2×C32C2×D3211yescharacteristic
237C2×C32C22×C3⋊D311yescharacteristic
238C3⋊D3—32no—
239C3⋊D3—38no—
240C3⋊D3—68no—
241C3⋊D3D3×Dic312yesdirect product factor
242C3×D3—28no—
243C3×D3—38no—
244C3×D3—38no—
245C3×D3—68no—
246C3×D3—98no—
247C3×D3—92no—
248C3×D3—188no—
249C3×D3D3×Dic318yescomplemented
250C3×D3C4×C3⋊D312yescomplemented
251C22×C4—811noSylow
252C22×C3—34no—
253C22×C3—31no—
254C22×C3—64no—
255C22×C3—91no—
256C22×C3—91no—
257C22×C3—181no—
258C22×C3—274no—
259C22×C3—271no—
260C2×D3—34no—
261C2×D3—916no—
262C2×D3—94no—
263C2×D3—91no—
264C2×D3—94no—
265C2×D3—184no—
266C2×D3D3×C3⋊D311yescharacteristic
267C3×C4—34no—
268C3×C4—31no—
269C3×C4—64no—
270C3×C4—94no—
271C3×C4—271no—
272Dic3—31no—
273Dic3—31no—
274Dic3—61no—
275Dic3—94no—
276Dic3—91no—
277Dic3—184no—
278Dic3—274no—
279Dic3—271no—
280Dic3—271no—
281Dic3—544no—
282Dic3—541no—
283Dic3—544no—
284Dic3—1084no—
285Dic3D3×C3⋊D311yescharacteristic, direct product factor
286C32—24no—
287C32—24no—
288C32—24no—
289C32—24no—
290C32—24no—
291C32—44no—
292C32—412no—
293C32—44no—
294C32C4×D3214yescomplemented
295C32C2×D3×Dic314yescomplemented
296C32C2×D3×Dic311yescharacteristic, complemented
297C32C2×C4×C3⋊D311yescharacteristic, complemented
298C23—271no—
299C2×C4—91no—
300C2×C4—271no—
301C2×C4—811no—
302C2×C4—811no—
303C2×C4—811no—
304C2×C4—811no—
305C2×C3—21no—
306C2×C3—24no—
307C2×C3—24no—
308C2×C3—38no—
309C2×C3—32no—
310C2×C3—44no—
311C2×C3—68no—
312C2×C3—92no—
313C2×C3—92no—
314C2×C3—182no—
315C2×C3—272no—
316C2×C3D3314yes—
317C2×C3C2×D3×C3⋊D311yescharacteristic
318C2×C3C2×D3×C3⋊D311yescharacteristic
319D3—38no—
320D3—98no—
321D3—92no—
322D3—188no—
323D3Dic3×C3⋊D312yesdirect product factor
324C22—31no—
325C22—91no—
326C22—274no—
327C22—271no—
328C4—31no—
329C4—91no—
330C4—271no—
331C4—811no—
332C3—24no—
333C3—24no—
334C3—21no—
335C3—44no—
336C3D32×Dic314yescomplemented
337C3C4×D3×C3⋊D311yescharacteristic, complemented
338C3C2×Dic3×C3⋊D311yescharacteristic, complemented
339C2—32no—
340C2—92no—
341C2—272no—
342C2D32×C3⋊D311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×C3⋊D3
commutator, hypocenterC34C22×C4
Fitting, socle, cosocleC2×C34C23
prime radicalC2×C3×D3×C3⋊D3C2
LCSG ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #10620154C2semidirect
3. C3⋊D3×C3⋊Dic3C2semidirect
4. Dic3×C3⋊(C3⋊D3)C2semidirect
5. D3×C3⋊(C3⋊Dic3)C2semidirect
6. C3×Dic3×C3⋊D3C2semidirect
7. C32×D3×Dic3C2semidirect
14. C3×D3×C3⋊D3C4semidirect
15. C3⋊(C3⋊(C3⋊Dic3))C22semidirect
16. C3×C3⋊(C3⋊Dic3)C22semidirect
17. C32×C3⋊Dic3C22semidirect
18. C33×Dic3C22semidirect
36. Dic3×C3⋊D3D3direct (N × H)
42. C3×D3×Dic3D3semidirect
44. C3×C3⋊(C3⋊D3)C2×C4semidirect
45. C32×C3⋊D3C2×C4semidirect
46. C33×D3C2×C4semidirect
64. D3×C3⋊D3Dic3direct (N × H)
74. C3⋊(C3⋊Dic3)C2×D3semidirect
78. C3×C3⋊Dic3C2×D3semidirect
83. C32×Dic3C2×D3semidirect
84. C32×Dic3C2×D3semidirect
85. C34C22×C4semidirect
118. D3×Dic3C3⋊D3direct (N × H)
127. C3⋊(C3⋊D3)C2×Dic3semidirect
132. C3×C3⋊D3C4×D3semidirect
133. C3×C3⋊D3C2×Dic3semidirect
136. C32×D3C4×D3semidirect
137. C32×D3C2×Dic3semidirect
181. C3⋊Dic3C2×C3⋊D3semidirect
189. C3×Dic3D32semidirect
190. C3×Dic3C2×C3⋊D3semidirect
195. C33C2×C4×D3semidirect
196. C33C2×C4×D3semidirect
197. C33C22×Dic3semidirect
241. C3⋊D3D3×Dic3direct (N × H)
249. C3×D3D3×Dic3semidirect
250. C3×D3C4×C3⋊D3semidirect
285. Dic3D3×C3⋊D3direct (N × H)
294. C32C4×D32semidirect
295. C32C2×D3×Dic3semidirect
296. C32C2×D3×Dic3semidirect
297. C32C2×C4×C3⋊D3semidirect
323. D3Dic3×C3⋊D3direct (N × H)
336. C3D32×Dic3semidirect
337. C3C4×D3×C3⋊D3semidirect
338. C3C2×Dic3×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C3⋊D32
#106201542
C3⋊D3×C3⋊Dic32
Dic3×C3⋊(C3⋊D3)2
D3×C3⋊(C3⋊Dic3)2
C3×Dic3×C3⋊D32
C32×D3×Dic32
C2×Dic3×C3⋊D33
C4×D3×C3⋊D33
D32×Dic33