Finite Group Databasebeta

← D3×#63368 #13137813

Subgroups — D3×#63368 #13137813

Order 1728.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic18C211yesmaximal, characteristic
2D3×C9×C4⋊C4C211yesmaximal, characteristic
3C2×D3×C9⋊C8C211yesmaximal, characteristic
4#11720527C211yesmaximal, characteristic, complemented
5C3×#63368C211yesmaximal, characteristic, complemented
6#11720269C211yesmaximal, characteristic, complemented
7#11720268C211yesmaximal, characteristic, complemented
8D3×#810—31nomaximal
9C2×#63368—31nomaximal
10C2×#6226C2211yescharacteristic
11C2×C4×D3×C9—21no—
12C2×C4×D3×C9C2211yescharacteristic
13C2×C3×Dic18C2211yescharacteristic
14C2×D3×Dic9—21no—
15C2×#6189—21no—
16D3×Dic18—22no—
17D3×Dic18C414yescomplemented
18C3×C9×C4⋊C4C2211yescharacteristic
19C2×C3⋊(C9⋊C8)C2211yescharacteristic
20C9×C4⋊Dic3C2211yescharacteristic
21C9×Dic3⋊C4—21no—
22C2×C3×C9⋊C8C2211yescharacteristic
23D3×C9⋊C8—22no—
24C2×D3×Dic6—31no—
25C3×D3×C4⋊C4D311yescharacteristic
26C2×D3×C3⋊C8—31no—
27C22×Dic18—31no—
28#63637—31no—
29C3×#810—31no—
30#63567—31no—
31#63565—31no—
32C2×C9×C4⋊C4—31no—
33C22×C9⋊C8—31no—
34#63368—31no—
35#63368—31no—
36#63368—31no—
37#63368—61no—
38#63368D311yescharacteristic, direct product factor
39C22×D3×C9D411yescharacteristic
40C2×C3×C4×C9—21no—
41C2×C3×C4×C9C2311yescharacteristic
42C2×C3⋊Dic9—21no—
43#6226—21no—
44#6226C2×C412yescomplemented
45C2×C9×Dic3—21no—
46C2×C9×Dic3D411yescharacteristic
47C2×C3×Dic9—21no—
48C4×D3×C9—42no—
49C4×D3×C9C2×C412yes—
50C4×D3×C9D412yes—
51C3×Dic18—21no—
52C3×Dic18C2×C412yescomplemented
53D3×Dic9—24no—
54#6189—24no—
55C3⋊(C9⋊C8)—21no—
56C3×C9⋊C8—21no—
57C2×#810—91no—
58D3×#103—91no—
59C2×#634—31no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3C2×D311yescharacteristic
62C2×C3×Dic6—31no—
63C2×#627—61no—
64C2×D3×Dic3—61no—
65D3×Dic6—34no—
66D3×Dic6—62no—
67C32×C4⋊C4C2×D311yescharacteristic
68C2×C3⋊(C3⋊C8)—31no—
69C3×C4⋊Dic3C2×D311yescharacteristic
70C3×Dic3⋊C4—21no—
71C2×C3×C3⋊C8—31no—
72D3×C3⋊C8—62no—
73C22×C4×C9—31no—
74C22×C4×C9—61no—
75C22×Dic9—61no—
76C2×Dic18—31no—
77C2×Dic18—34no—
78C2×Dic18—62no—
79C2×Dic18—61no—
80C2×Dic18—61no—
81C2×Dic18C2×D311yescharacteristic
82C9×C4⋊C4—21no—
83C9×C4⋊C4—31no—
84C9×C4⋊C4—61no—
85C9×C4⋊C4C2×D311yescharacteristic
86C2×C9⋊C8—31no—
87C2×C9⋊C8—62no—
88C2×C9⋊C8—61no—
89C2×C9⋊C8C2×D311yescharacteristic
90C22×C3×C9C2×D411yescharacteristic
91C2×D3×C9C22⋊C412yes—
92C2×D3×C9SD1612yes—
93C2×D3×C9Q1612yes—
94C3×C4×C9—41no—
95C3×C4×C9C22×C411yescharacteristic
96C3×C4×C9C2×D411yescharacteristic
97C3⋊Dic9—22no—
98C9×Dic3—41no—
99C9×Dic3C22⋊C412yes—
100C3×Dic9—22no—
101C2×D3×Q8—91no—
102C22×Dic6—91no—
103C2×C3×C4⋊C4—31no—
104C22×C3⋊C8—91no—
105C2×D3×C8—91no—
106D3×C4⋊C4D911yescharacteristic
107C3×#103—91no—
108#835—91no—
109#816—91no—
110#810—31no—
111#810—91no—
112#810—91no—
113#810—91no—
114#810—91no—
115#810—181no—
116C22×C3×D3#6711yescharacteristic
117C2×C32×C4—21no—
118C2×C32×C4C22×D311yescharacteristic
119C2×C3⋊Dic3—61no—
120#634—32no—
121#634—61no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—61no—
124C2×C3×Dic3#6711yescharacteristic
125C3×C4×D3—42no—
126C3×C4×D3C4×D312yes—
127C3×C4×D3D1212yes—
128C3×Dic6—32no—
129C3×Dic6—61no—
130#627—64no—
131D3×Dic3—64no—
132C23×C9—31no—
133C3⋊(C3⋊C8)—61no—
134C3×C3⋊C8—61no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—31no—
138C2×C4×C9—32no—
139C2×C4×C9—32no—
140C2×C4×C9—41no—
141C2×C4×C9—61no—
142C2×C4×C9—122no—
143C2×C4×C9C22×D311yescharacteristic
144C2×Dic9—21no—
145C2×Dic9—64no—
146C2×Dic9—61no—
147C2×Dic9—121no—
148Dic18—21no—
149Dic18—32no—
150Dic18—62no—
151Dic18—64no—
152Dic18—61no—
153Dic18—121no—
154Dic18C4×D312yescomplemented
155C9⋊C8—21no—
156C9⋊C8—61no—
157C9⋊C8—121no—
158C2×#103—271noSylow
159C2×C3×C9C2×C22⋊C411yescharacteristic
160C2×C3×C9C2×SD1611yescharacteristic
161C2×C3×C9C2×Q1611yescharacteristic
162D3×C9#10314yescomplemented
163C2×C3×Q8—91no—
164C22×C3×C4—31no—
165C22×C3×C4—61no—
166C22×Dic3—181no—
167D3×Q8—94no—
168D3×Q8—182no—
169C2×C4×D3—21no—
170C2×C4×D3—181no—
171C2×C4×D3C2×D911yescharacteristic
172C2×Dic6—31no—
173C2×Dic6—94no—
174C2×Dic6—91no—
175C2×Dic6—91no—
176C2×Dic6—181no—
177C2×Dic6—182no—
178C2×Dic6—181no—
179C2×Dic6—181no—
180C2×C3×C8—91no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4C2×D911yescharacteristic
185C3×C4⋊C4D3211yescharacteristic
186C4⋊Dic3C2×D911yescharacteristic
187Dic3⋊C4—21no—
188C2×C3⋊C8—31no—
189C2×C3⋊C8—91no—
190C2×C3⋊C8—91no—
191C2×C3⋊C8—181no—
192C2×C3⋊C8—182no—
193D3×C8—182no—
194C22×C32C2×#6711yescharacteristic
195C2×C3×D3(C2×D3)⋊C412yes—
196C2×C3×D3#21412yes—
197C2×C3×D3#21612yes—
198C32×C4—41no—
199C32×C4C2×C4×D311yescharacteristic
200C32×C4C2×D1211yescharacteristic
201C3⋊Dic3—62no—
202C3×Dic3—41no—
203C3×Dic3—62no—
204C3×Dic3(C2×D3)⋊C412yes—
205C22×C9—21no—
206C22×C9—32no—
207C22×C9—32no—
208C22×C9—32no—
209C22×C9D3×D411yescharacteristic
210C4×C9—21no—
211C4×C9—21no—
212C4×C9—32no—
213C4×C9—41no—
214C4×C9—81no—
215C4×C9—121no—
216C4×C9C2×C4×D311yescharacteristic
217C4×C9D3×D411yescharacteristic
218Dic9—22no—
219Dic9—62no—
220Dic9—122no—
221C22×Q8—271no—
222C22×C8—271no—
223C2×C4⋊C4—31no—
224#103—91no—
225#103—271no—
226#103—271no—
227#103—271no—
228C3×C9C2×#10311yescharacteristic, complemented, Sylow
229C23×C3—31no—
230C22×D3#61111yescharacteristic
231C3×Q8—92no—
232C3×Q8—181no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—31no—
237C2×C3×C4—32no—
238C2×C3×C4—32no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—122no—
242C2×C3×C4—181no—
243C2×C3×C4C22×D911yescharacteristic
244C2×C3×C4C2×D3211yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—61no—
247C2×Dic3—184no—
248C2×Dic3—181no—
249C2×Dic3—181no—
250C2×Dic3—361no—
251C2×Dic3#61111yescharacteristic
252C4×D3—42no—
253C4×D3—184no—
254C4×D3C4×D912yes—
255C4×D3D3612yes—
256Dic6—32no—
257Dic6—61no—
258Dic6—92no—
259Dic6—92no—
260Dic6—182no—
261Dic6—184no—
262Dic6—181no—
263Dic6—181no—
264Dic6—184no—
265Dic6—361no—
266C3×C8—181no—
267C3⋊C8—61no—
268C3⋊C8—181no—
269C3⋊C8—181no—
270C3⋊C8—361no—
271C2×C32C2×(C2×D3)⋊C411yescharacteristic
272C2×C32C2×#21411yescharacteristic
273C2×C32C2×#21611yescharacteristic
274C3×D3#81014yes—
275C2×C9—21no—
276C2×C9—21no—
277C2×C9—21no—
278C2×C9—34no—
279C2×C9D3×C22⋊C411yescharacteristic
280C2×C9D3×SD1611yescharacteristic
281C2×C9D3×Q1611yescharacteristic
282C2×Q8—91no—
283C2×Q8—274no—
284C2×Q8—271no—
285C2×Q8—541no—
286C2×Q8—542no—
287C22×C4—31no—
288C22×C4—61no—
289C22×C4—541no—
290C2×C8—91no—
291C2×C8—271no—
292C2×C8—542no—
293C4⋊C4—31no—
294C4⋊C4—61no—
295C4⋊C4D3×D911yescharacteristic
296C22×C3—21no—
297C22×C3—32no—
298C22×C3—32no—
299C22×C3—32no—
300C22×C3C2×#61111yescharacteristic
301C22×C3D3×#6711yescharacteristic
302C2×D3(C2×D9)⋊C412yes—
303C2×D3#367212yes—
304C2×D3#367412yes—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—32no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—81no—
311C3×C4—121no—
312C3×C4—182no—
313C3×C4C2×C4×D911yescharacteristic
314C3×C4C2×D3611yescharacteristic
315C3×C4C4×D3211yescharacteristic
316C3×C4D3×D1211yescharacteristic
317Dic3—41no—
318Dic3—62no—
319Dic3—182no—
320Dic3—182no—
321Dic3—362no—
322Dic3(C2×D9)⋊C412yes—
323C32C2×#81011yescharacteristic
324C9—21no—
325C9D3×#10311yescharacteristic, complemented
326C23—31no—
327Q8—92no—
328Q8—181no—
329Q8—272no—
330Q8—544no—
331Q8—541no—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—61no—
337C2×C4—122no—
338C2×C4—181no—
339C2×C4—544no—
340C2×C4—541no—
341C2×C4C2×D3×D911yescharacteristic
342C8—181no—
343C8—541no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—34no—
348C2×C3C2×(C2×D9)⋊C411yescharacteristic
349C2×C3C2×#367211yescharacteristic
350C2×C3C2×#367411yescharacteristic
351C2×C3D3×(C2×D3)⋊C411yescharacteristic
352C2×C3D3×#21411yescharacteristic
353C2×C3D3×#21611yescharacteristic
354D3#6336814yesdirect product factor
355C22—32no—
356C22—32no—
357C22—32no—
358C22D3×#61111yescharacteristic
359C4—32no—
360C4—41no—
361C4—121no—
362C4—182no—
363C4—542no—
364C4C4×D3×D911yescharacteristic
365C4D3×D3611yescharacteristic
366C3—21no—
367C3C2×#6336811yescharacteristic, complemented
368C3D3×#81011yescharacteristic
369C2—34no—
370C2D3×(C2×D9)⋊C411yescharacteristic
371C2D3×#367211yescharacteristic
372C2D3×#367411yescharacteristic
subgroupG/H
centerC22D3×#611
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C2×#67
prime radicalC22×C3×D3#67
cosocleC2×C3×C4×C9C23
hypercenterC4⋊C4D3×D9
hypocenterC3×C9C2×#103
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11720527C2semidirect
5. C3×#63368C2semidirect
6. #11720269C2semidirect
7. #11720268C2semidirect
17. D3×Dic18C4semidirect
38. #63368D3direct (N × H)
44. #6226C2×C4semidirect
52. C3×Dic18C2×C4semidirect
154. Dic18C4×D3semidirect
162. D3×C9#103semidirect
228. C3×C9C2×#103semidirect
325. C9D3×#103semidirect
354. D3#63368direct (N × H)
367. C3C2×#63368semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic182
D3×C9×C4⋊C42
C2×D3×C9⋊C82
#117205272
C3×#633682
#117202692
#117202682
D3×#8103
C2×#633683