Finite Group Databasebeta

← D3×#63395 #13140783

Subgroups — D3×#63395 #13140783

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×Q8×C9C211yesmaximal, characteristic
2D3×C4⋊Dic9C211yesmaximal, characteristic
3C2×D3×C9⋊C8C211yesmaximal, characteristic
4#11720582C211yesmaximal, characteristic, complemented
5C3×#63395C211yesmaximal, characteristic, complemented
6#11720298C211yesmaximal, characteristic, complemented
7#11720297C211yesmaximal, characteristic, complemented
8D3×#835—31nomaximal
9C2×#63395—31nomaximal
10C2×C3×Q8×C9C2211yescharacteristic
11D3×Q8×C9—22no—
12D3×Q8×C9C414yescomplemented
13C2×C4×D3×C9—21no—
14C2×C4×D3×C9C2211yescharacteristic
15C2×C9×Dic6—21no—
16C2×C9×Dic6C2211yescharacteristic
17C2×D3×Dic9—21no—
18C4⋊(C3⋊Dic9)C2211yescharacteristic
19C2×C3⋊(C9⋊C8)C2211yescharacteristic
20C3×C4⋊Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22Dic3⋊Dic9—21no—
23D3×C9⋊C8—22no—
24C2×C3×D3×Q8D311yescharacteristic
25D3×C4⋊Dic3—31no—
26C2×D3×C3⋊C8—31no—
27C22×Q8×C9—31no—
28#63662—31no—
29C3×#835—31no—
30#63566—31no—
31#63565—31no—
32C2×C4⋊Dic9—31no—
33C22×C9⋊C8—31no—
34#63395—31no—
35#63395—31no—
36#63395—31no—
37#63395—61no—
38#63395D311yescharacteristic, direct product factor
39C22×D3×C9D411yescharacteristic
40C3×Q8×C9—21no—
41C3×Q8×C9C2×C412yescomplemented
42C2×C3×C4×C9—21no—
43C2×C3×C4×C9C2311yescharacteristic
44C2×C3⋊Dic9—21no—
45C2×C9×Dic3—21no—
46C2×C9×Dic3D411yescharacteristic
47C2×C3×Dic9—21no—
48C4×D3×C9—24no—
49C4×D3×C9C2×C412yes—
50C4×D3×C9D412yes—
51C9×Dic6—21no—
52C9×Dic6—24no—
53C9×Dic6C2×C412yescomplemented
54D3×Dic9—42no—
55C3⋊(C9⋊C8)—21no—
56C3×C9⋊C8—21no—
57C2×#835—91no—
58D3×#103—91no—
59C2×C32×Q8C2×D311yescharacteristic
60C3×D3×Q8—22no—
61C3×D3×Q8Dic314yes—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3C2×D311yescharacteristic
64C2×C3×Dic6—21no—
65C2×C3×Dic6C2×D311yescharacteristic
66C2×D3×Dic3—61no—
67C4⋊(C3⋊Dic3)—31no—
68C2×C3⋊(C3⋊C8)—31no—
69C3×C4⋊Dic3—31no—
70C2×C3×C3⋊C8—31no—
71Dic3⋊Dic3—61no—
72D3×C3⋊C8—62no—
73C2×Q8×C9—21no—
74C2×Q8×C9—34no—
75C2×Q8×C9—31no—
76C2×Q8×C9—61no—
77C2×Q8×C9—62no—
78C2×Q8×C9C2×D311yescharacteristic
79C22×C4×C9—31no—
80C22×C4×C9—61no—
81C22×Dic9—61no—
82C4⋊Dic9—31no—
83C4⋊Dic9—61no—
84C4⋊Dic9—61no—
85C4⋊Dic9C2×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—22no—
95C3×C4×C9C22×C411yescharacteristic
96C3×C4×C9C2×D411yescharacteristic
97C3⋊Dic9—41no—
98C9×Dic3—22no—
99C9×Dic3C22⋊C412yes—
100C3×Dic9—41no—
101C22×C3×Q8—31no—
102C2×D3×Q8D911yescharacteristic
103C2×C4⋊Dic3—91no—
104C22×C3⋊C8—91no—
105C2×D3×C8—91no—
106D3×C4⋊C4—91no—
107C3×#103—91no—
108#835—31no—
109#835—91no—
110#835—91no—
111#835—91no—
112#835—91no—
113#835—181no—
114#816—91no—
115#810—91no—
116C22×C3×D3#6711yescharacteristic
117C32×Q8—21no—
118C32×Q8C2×Dic312yes—
119C2×C32×C4—21no—
120C2×C32×C4C22×D311yescharacteristic
121C2×C3⋊Dic3—61no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—61no—
124C2×C3×Dic3#6711yescharacteristic
125C3×C4×D3—24no—
126C3×C4×D3C2×Dic312yes—
127C3×C4×D3#6712yes—
128C3×Dic6—21no—
129C3×Dic6—24no—
130C3×Dic6C2×Dic312yes—
131D3×Dic3—122no—
132C23×C9—31no—
133C3⋊(C3⋊C8)—61no—
134C3×C3⋊C8—61no—
135Q8×C9—21no—
136Q8×C9—22no—
137Q8×C9—32no—
138Q8×C9—41no—
139Q8×C9—64no—
140Q8×C9—61no—
141Q8×C9C4×D312yescomplemented
142C2×C4×C9—21no—
143C2×C4×C9—21no—
144C2×C4×C9—31no—
145C2×C4×C9—32no—
146C2×C4×C9—32no—
147C2×C4×C9—41no—
148C2×C4×C9—64no—
149C2×C4×C9—61no—
150C2×C4×C9C22×D311yescharacteristic
151C2×Dic9—21no—
152C2×Dic9—61no—
153C2×Dic9—121no—
154C2×Dic9—122no—
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—21no—
164C2×C3×Q8—34no—
165C2×C3×Q8—31no—
166C2×C3×Q8—61no—
167C2×C3×Q8—62no—
168C2×C3×Q8C2×D911yescharacteristic
169C2×C3×Q8D3211yescharacteristic
170C22×C3×C4—31no—
171C22×C3×C4—61no—
172C22×Dic3—181no—
173D3×Q8—22no—
174D3×Q8Dic914yescomplemented
175C2×C4×D3—21no—
176C2×C4×D3—181no—
177C2×C4×D3C2×D911yescharacteristic
178C2×Dic6—21no—
179C2×Dic6C2×D911yescharacteristic
180C2×C3×C8—91no—
181C3×C4⋊C4—91no—
182C4⋊Dic3—31no—
183C4⋊Dic3—91no—
184C4⋊Dic3—91no—
185C4⋊Dic3—181no—
186C4⋊Dic3—181no—
187Dic3⋊C4—181no—
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#21512yes—
196C2×C3×D3#21612yes—
197C2×C3×D3#21712yes—
198C32×C4—22no—
199C32×C4C22×Dic311yescharacteristic
200C32×C4C2×#6711yescharacteristic
201C3⋊Dic3—121no—
202C3×Dic3—22no—
203C3×Dic3—121no—
204C3×Dic3#21712yes—
205C22×C9—21no—
206C22×C9—32no—
207C22×C9—32no—
208C22×C9—32no—
209C22×C9D3×D411yescharacteristic
210C4×C9—22no—
211C4×C9—21no—
212C4×C9—21no—
213C4×C9—32no—
214C4×C9—42no—
215C4×C9—62no—
216C4×C9C2×C4×D311yescharacteristic
217C4×C9D3×D411yescharacteristic
218Dic9—41no—
219Dic9—121no—
220Dic9—241no—
221C22×Q8—31no—
222C22×C8—271no—
223C2×C4⋊C4—271no—
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—21no—
232C3×Q8—21no—
233C3×Q8—22no—
234C3×Q8—32no—
235C3×Q8—41no—
236C3×Q8—64no—
237C3×Q8—61no—
238C3×Q8C2×Dic912yescomplemented
239C3×Q8D3×Dic312yes—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—31no—
244C2×C3×C4—32no—
245C2×C3×C4—32no—
246C2×C3×C4—41no—
247C2×C3×C4—64no—
248C2×C3×C4—61no—
249C2×C3×C4—181no—
250C2×C3×C4C22×D911yescharacteristic
251C2×C3×C4C2×D3211yescharacteristic
252C2×Dic3—21no—
253C2×Dic3—61no—
254C2×Dic3—181no—
255C2×Dic3—181no—
256C2×Dic3—361no—
257C2×Dic3—362no—
258C2×Dic3#61111yescharacteristic
259C4×D3—24no—
260C4×D3—362no—
261C4×D3C2×Dic912yes—
262C4×D3#61112yes—
263Dic6—21no—
264Dic6—24no—
265Dic6C2×Dic912yescomplemented
266C3×C8—181no—
267C3⋊C8—61no—
268C3⋊C8—181no—
269C3⋊C8—181no—
270C3⋊C8—361no—
271C2×C32C2×#21511yescharacteristic
272C2×C32C2×#21611yescharacteristic
273C2×C32C2×#21711yescharacteristic
274C3×D3#83514yes—
275C2×C9—21no—
276C2×C9—21no—
277C2×C9—21no—
278C2×C9—34no—
279C2×C9D3×C22⋊C411yescharacteristic
280C2×C9D3×SD1611yescharacteristic
281C2×C9D3×Q1611yescharacteristic
282C2×Q8—34no—
283C2×Q8—31no—
284C2×Q8—61no—
285C2×Q8—62no—
286C2×Q8D3×D911yescharacteristic
287C22×C4—31no—
288C22×C4—61no—
289C22×C4—541no—
290C2×C8—91no—
291C2×C8—271no—
292C2×C8—542no—
293C4⋊C4—91no—
294C4⋊C4—271no—
295C4⋊C4—541no—
296C22×C3—21no—
297C22×C3—32no—
298C22×C3—32no—
299C22×C3—32no—
300C22×C3C2×#61111yescharacteristic
301C22×C3D3×#6711yescharacteristic
302C2×D3#367412yes—
303C2×D3#367512yes—
304C2×D3#367612yes—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—32no—
310C3×C4—42no—
311C3×C4—62no—
312C3×C4—361no—
313C3×C4C22×Dic911yescharacteristic
314C3×C4C2×#61111yescharacteristic
315C3×C4C2×D3×Dic311yescharacteristic
316C3×C4D3×#6711yescharacteristic
317Dic3—22no—
318Dic3—121no—
319Dic3—361no—
320Dic3—361no—
321Dic3—721no—
322Dic3#367612yes—
323C32C2×#83511yescharacteristic
324C9—21no—
325C9D3×#10311yescharacteristic, complemented
326C23—31no—
327Q8—21no—
328Q8—32no—
329Q8—64no—
330Q8—61no—
331Q8D3×Dic912yescomplemented
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—64no—
337C2×C4—61no—
338C2×C4—181no—
339C2×C4—541no—
340C2×C4—1082no—
341C2×C4C2×D3×D911yescharacteristic
342C8—181no—
343C8—541no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—34no—
348C2×C3C2×#367411yescharacteristic
349C2×C3C2×#367511yescharacteristic
350C2×C3C2×#367611yescharacteristic
351C2×C3D3×#21511yescharacteristic
352C2×C3D3×#21611yescharacteristic
353C2×C3D3×#21711yescharacteristic
354D3#6339514yesdirect product factor
355C22—32no—
356C22—32no—
357C22—32no—
358C22D3×#61111yescharacteristic
359C4—22no—
360C4—32no—
361C4—62no—
362C4—361no—
363C4—1081no—
364C4C2×D3×Dic911yescharacteristic
365C4D3×#61111yescharacteristic
366C3—21no—
367C3C2×#6339511yescharacteristic, complemented
368C3D3×#83511yescharacteristic
369C2—34no—
370C2D3×#367411yescharacteristic
371C2D3×#367511yescharacteristic
372C2D3×#367611yescharacteristic
subgroupG/H
centerC22D3×#611
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC2×C3×Q8×C9C22
socleC22×C32C2×#67
prime radicalC22×C3×D3#67
cosocleC2×C3×C4×C9C23
hypercenterC2×Q8D3×D9
hypocenterC3×C9C2×#103
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. #11720582C2semidirect
5. C3×#63395C2semidirect
6. #11720298C2semidirect
7. #11720297C2semidirect
12. D3×Q8×C9C4semidirect
38. #63395D3direct (N × H)
41. C3×Q8×C9C2×C4semidirect
53. C9×Dic6C2×C4semidirect
141. Q8×C9C4×D3semidirect
162. D3×C9#103semidirect
174. D3×Q8Dic9semidirect
228. C3×C9C2×#103semidirect
238. C3×Q8C2×Dic9semidirect
265. Dic6C2×Dic9semidirect
325. C9D3×#103semidirect
331. Q8D3×Dic9semidirect
354. D3#63395direct (N × H)
367. C3C2×#63395semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q8×C92
D3×C4⋊Dic92
C2×D3×C9⋊C82
#117205822
C3×#633952
#117202982
#117202972
D3×#8353
C2×#633953