Finite Group Databasebeta

← C3×#10588843 #13143330

Subgroups — C3×#10588843 #13143330

Order 1728.

452 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×SD16C211yesmaximal, characteristic, complemented
2C3×Q8×Dic9C211yesmaximal, characteristic, complemented
3C2×C3×#3675C211yesmaximal, characteristic, complemented
4C3×#63502C211yesmaximal, characteristic
5C3×#63392C211yesmaximal, characteristic, complemented
6C3×#63380C211yesmaximal, characteristic, complemented
7C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
8C3×#5163—31nomaximal
9#10588843C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D4×C9C2211yescharacteristic
12C2×C3×#611—21no—
13C2×C3×#611—21no—
14C2×C3×D36C2211yescharacteristic
15C3×C9×SD16—22no—
16C2×C3×C8×C9C2211yescharacteristic
17C3×#3675—22no—
18C3×C4⋊Dic9—21no—
19C3×C4⋊Dic9C2211yescharacteristic
20C3×C4×Dic9—21no—
21C3×C4×Dic9C2211yescharacteristic
22C2×C3×C9⋊C8C2211yescharacteristic
23C2×C32×SD16D311yescharacteristic
24C3×Q8×Dic3—31no—
25C2×C3×#215—31no—
26C3×#940—31no—
27C3×#832—31no—
28C3×#821—31no—
29C3×Dic3⋊C8—31no—
30C2×C9×SD16—21no—
31C2×C9×SD16C2×C311yescharacteristic, complemented
32Q8×Dic9C2×C311yescharacteristic, complemented
33C2×#3675C2×C311yescharacteristic, complemented
34#63502C2×C311yescharacteristic
35#63392C2×C311yescharacteristic, complemented
36#63380C2×C311yescharacteristic, complemented
37Dic9⋊C8C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×C3×D9—21no—
40C3×Q8×C9—21no—
41C3×Q8×C9D412yescomplemented
42C3×D4×C9—21no—
43C3×D4×C9—21no—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9C2311yescharacteristic
46C3×#611—42no—
47C3×#611—42no—
48C2×C3×Dic9—21no—
49C2×C3×Dic9D411yescharacteristic
50C2×C3×Dic9D411yescharacteristic
51C3×D36—21no—
52C3×D36—21no—
53C3×C8×C9—21no—
54C3×C9⋊C8—21no—
55C3×#460—91no—
56#5163—31no—
57C2×C32×Q8C2×D311yescharacteristic
58C2×C32×D4C2×D311yescharacteristic
59C2×C3×#67—61no—
60C2×C3×#67—61no—
61C2×C3×D12—31no—
62C32×SD16—22no—
63C2×C32×C8C2×D311yescharacteristic
64C3×#215—62no—
65C3×C4⋊Dic3—31no—
66C3×C4⋊Dic3—61no—
67C3×C4×Dic3—31no—
68C3×C4×Dic3—61no—
69C2×C3×C3⋊C8—31no—
70C2×Q8×C9—21no—
71C2×Q8×C9C22×C311yescharacteristic
72C2×D4×C9—21no—
73C2×D4×C9C22×C311yescharacteristic
74C2×#611—21no—
75C2×#611—21no—
76C2×D36C22×C311yescharacteristic
77C9×SD16—24no—
78C9×SD16—22no—
79C2×C8×C9—21no—
80C2×C8×C9C22×C311yescharacteristic
81#3675—22no—
82C4⋊Dic9—21no—
83C4⋊Dic9C22×C311yescharacteristic
84C4×Dic9—21no—
85C4×Dic9C22×C311yescharacteristic
86C2×C9⋊C8C22×C311yescharacteristic
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9—41no—
90C22×C3×C9C2×D411yescharacteristic
91C2×C3×D9—41no—
92C2×C3×D9—41no—
93C2×C3×D9—41no—
94C3×C4×C9—22no—
95C3×C4×C9C2×D411yescharacteristic
96C3×C4×C9#4111yescharacteristic
97C3×Dic9—21no—
98C3×Dic9—41no—
99C3×Dic9SD1612yescomplemented
100C2×C3×SD16—21no—
101C2×C3×SD16—91no—
102C2×C3×SD16D911yescharacteristic, complemented
103C2×C3×SD16C3×D311yescharacteristic
104C3×#127—91no—
105C3×C4×Q8—91no—
106Q8×Dic3—31no—
107C2×#215—31no—
108#940—31no—
109C3×C4⋊C8—91no—
110C3×#102—91no—
111C3×#102—91no—
112#832—31no—
113#821—31no—
114Dic3⋊C8—31no—
115C23×C32—21no—
116C22×C3×D3—61no—
117C32×Q8—21no—
118C32×Q8#6712yes—
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C22×D311yescharacteristic
123C3×#67—122no—
124C3×#67—122no—
125C2×C3×Dic3—31no—
126C2×C3×Dic3—31no—
127C2×C3×Dic3—61no—
128C3×D12—61no—
129C3×D12—61no—
130C23×C9—21no—
131C23×C9—41no—
132C22×D9—21no—
133C32×C8—21no—
134C3×C3⋊C8—61no—
135Q8×C9—21no—
136Q8×C9—22no—
137Q8×C9—41no—
138Q8×C9C3×D412yescomplemented
139D4×C9—22no—
140D4×C9—21no—
141D4×C9—21no—
142D4×C9—41no—
143C2×C4×C9—21no—
144C2×C4×C9—21no—
145C2×C4×C9—41no—
146C2×C4×C9C23×C311yescharacteristic
147#611—42no—
148#611—42no—
149C2×Dic9—21no—
150C2×Dic9C3×D411yescharacteristic
151C2×Dic9C3×D411yescharacteristic
152D36—21no—
153D36—21no—
154C8×C9—22no—
155C8×C9—21no—
156C9⋊C8—21no—
157#460—91noSylow
158C2×C3×C9—81no—
159C2×C3×C9#12111yescharacteristic
160C2×C3×C9C2×SD1611yescharacteristic
161C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
162C3×D9—81no—
163C2×C3×Q8—21no—
164C2×C3×Q8C2×D911yescharacteristic
165C2×C3×Q8C2×C3×D311yescharacteristic
166C2×C3×D4—21no—
167C2×C3×D4—91no—
168C2×C3×D4—181no—
169C2×C3×D4—181no—
170C2×C3×D4C2×D911yescharacteristic
171C2×C3×D4C2×C3×D311yescharacteristic
172C2×#67—61no—
173C2×#67—61no—
174C2×D12—31no—
175C3×SD16—24no—
176C3×SD16—22no—
177C3×SD16—22no—
178C3×SD16—182no—
179C2×C3×C8—21no—
180C2×C3×C8—91no—
181C2×C3×C8C2×D911yescharacteristic
182C2×C3×C8C2×C3×D311yescharacteristic
183C3×C4⋊C4—91no—
184C3×C4⋊C4—181no—
185C3×C42—91no—
186C3×C42—181no—
187#215—62no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190C4×Dic3—31no—
191C4×Dic3—61no—
192C2×C3⋊C8—31no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32D3×D411yescharacteristic
197C2×C3×D3—121no—
198C2×C3×D3—121no—
199C2×C3×D3—121no—
200C32×C4—22no—
201C32×C4#23711yescharacteristic
202C32×C4C2×#6711yescharacteristic
203C3×Dic3—32no—
204C3×Dic3—61no—
205C3×Dic3—121no—
206C22×C9—21no—
207C22×C9—42no—
208C22×C9—41no—
209C22×C9—41no—
210C22×C9—41no—
211C22×C9—81no—
212C22×C9—81no—
213C22×C9C2×C3×D411yescharacteristic
214C2×D9—41no—
215C2×D9—41no—
216C2×D9—41no—
217C4×C9—22no—
218C4×C9—21no—
219C4×C9—21no—
220C4×C9—42no—
221C4×C9C2×C3×D411yescharacteristic
222C4×C9C3×#4111yescharacteristic
223Dic9—21no—
224Dic9—41no—
225Dic9C3×SD1612yescomplemented
226C2×SD16—91no—
227C2×SD16C3×D911yescharacteristic, complemented
228#127—91no—
229C4×Q8—91no—
230C4⋊C8—91no—
231#102—91no—
232#102—91no—
233C3×C9#46011yescharacteristic, complemented, Sylow
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—41no—
237C23×C3—181no—
238C22×D3—61no—
239C3×Q8—21no—
240C3×Q8—21no—
241C3×Q8—22no—
242C3×Q8—41no—
243C3×Q8#61112yescomplemented
244C3×Q8C3×#6712yes—
245C3×D4—22no—
246C3×D4—21no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—41no—
251C3×D4—181no—
252C3×D4—181no—
253C3×D4—362no—
254C3×D4—362no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—91no—
260C2×C3×C4—91no—
261C2×C3×C4—181no—
262C2×C3×C4C22×D911yescharacteristic
263C2×C3×C4C22×C3×D311yescharacteristic
264#67—122no—
265#67—122no—
266C2×Dic3—31no—
267C2×Dic3—31no—
268C2×Dic3—61no—
269D12—61no—
270D12—61no—
271C3×C8—22no—
272C3×C8—21no—
273C3×C8—21no—
274C3×C8—181no—
275C3⋊C8—61no—
276C2×C32—81no—
277C2×C32D3×SD1611yescharacteristic
278C2×C32#91411yescharacteristic
279C2×C32#93911yescharacteristic
280C3×D3—241no—
281C2×C9—21no—
282C2×C9—21no—
283C2×C9—21no—
284C2×C9—82no—
285C2×C9—81no—
286C2×C9C3×#12111yescharacteristic
287C2×C9C2×C3×SD1611yescharacteristic
288C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
289D9—81no—
290C2×Q8C2×C3×D911yescharacteristic
291C2×D4—91no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4C2×C3×D911yescharacteristic
295SD16—22no—
296SD16—182no—
297C2×C8—91no—
298C2×C8C2×C3×D911yescharacteristic
299C4⋊C4—91no—
300C4⋊C4—181no—
301C42—91no—
302C42—181no—
303C22×C3—21no—
304C22×C3—42no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—81no—
312C22×C3—81no—
313C22×C3—361no—
314C22×C3—361no—
315C22×C3—361no—
316C22×C3D4×D911yescharacteristic
317C22×C3C3×D3×D411yescharacteristic
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C3×C4—22no—
322C3×C4—22no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—42no—
326C3×C4—92no—
327C3×C4—181no—
328C3×C4—361no—
329C3×C4#369911yescharacteristic
330C3×C4C2×#61111yescharacteristic
331C3×C4C3×#23711yescharacteristic
332C3×C4C2×C3×#6711yescharacteristic
333Dic3—32no—
334Dic3—61no—
335Dic3—121no—
336C32#516311yescharacteristic
337C9—21no—
338C9C3×#46011yescharacteristic, complemented
339C23—21no—
340C23—181no—
341Q8—21no—
342Q8C3×#61112yescomplemented
343D4—21no—
344D4—21no—
345D4—181no—
346D4—181no—
347D4—362no—
348D4—362no—
349C2×C4—21no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—181no—
353C2×C4C22×C3×D911yescharacteristic
354C8—21no—
355C8—181no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—82no—
360C2×C3—81no—
361C2×C3—81no—
362C2×C3—721no—
363C2×C3SD16×D911yescharacteristic
364C2×C3#6347611yescharacteristic
365C2×C3#6350111yescharacteristic
366C2×C3C3×D3×SD1611yescharacteristic
367C2×C3C3×#91411yescharacteristic
368C2×C3C3×#93911yescharacteristic
369D3—241no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—361no—
374C22—361no—
375C22—361no—
376C22C3×D4×D911yescharacteristic
377C4—22no—
378C4—92no—
379C4—181no—
380C4—361no—
381C4C3×#369911yescharacteristic
382C4C2×C3×#61111yescharacteristic
383C3—21no—
384C3#1058884311yescharacteristic, direct product factor
385C3C3×#516311yescharacteristic
386C2—81no—
387C2—721no—
388C2C3×SD16×D911yescharacteristic
389C2C3×#6347611yescharacteristic
390C2C3×#6350111yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C9×SD16C2
socleC22×C32D3×D4
prime radicalC3×#63502C2
hypercenterC2×C3×SD16D9
hypocenterC9C3×#460
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×SD16C2semidirect
2. C3×Q8×Dic9C2semidirect
3. C2×C3×#3675C2semidirect
5. C3×#63392C2semidirect
6. C3×#63380C2semidirect
7. C3×Dic9⋊C8C2semidirect
9. #10588843C3direct (N × H)
31. C2×C9×SD16C2×C3semidirect
32. Q8×Dic9C2×C3semidirect
33. C2×#3675C2×C3semidirect
35. #63392C2×C3semidirect
36. #63380C2×C3semidirect
37. Dic9⋊C8C2×C3semidirect
41. C3×Q8×C9D4semidirect
99. C3×Dic9SD16semidirect
102. C2×C3×SD16D9semidirect
138. Q8×C9C3×D4semidirect
225. Dic9C3×SD16semidirect
227. C2×SD16C3×D9semidirect
233. C3×C9#460semidirect
243. C3×Q8#611semidirect
338. C9C3×#460semidirect
342. Q8C3×#611semidirect
384. C3#10588843direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×SD162
C3×Q8×Dic92
C2×C3×#36752
C3×#635022
C3×#633922
C3×#633802
C3×Dic9⋊C82
C3×#51633
#105888433