Finite Group Databasebeta

← C3×#10588461 #13141746

Subgroups — C3×#10588461 #13141746

Order 1728.

536 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3699C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic, complemented
3C2×C3×#3664C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63368C211yesmaximal, characteristic, complemented
8C3×#4781—31nomaximal
9#10588461C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×#611—21no—
12C22×C3×Dic9—21no—
13C3×#3699—22no—
14C3×#3699—22no—
15C2×C3×D36—21no—
16C2×C3×D36C2211yescharacteristic
17C2×C3×C4×D9C2211yescharacteristic
18C2×C3×Dic18C2211yescharacteristic
19C2×C3×C8×C9C2211yescharacteristic
20C3×C9×C4⋊C4C2211yescharacteristic
21C3×#3673—22no—
22C3×(C2×D9)⋊C4—21no—
23C2×C3×C9⋊C8C2211yescharacteristic
24C3×#3664—22no—
25C2×C3×#237—31no—
26C2×C3×#213—31no—
27C2×C3×#204—31no—
28C3×#895—31no—
29C2×#3699C2×C311yescharacteristic, complemented
30C32×#102D311yescharacteristic
31C3×(C2×D3)⋊C8—31no—
32C3×#810—31no—
33C2×#3673C2×C311yescharacteristic, complemented
34C2×#3664C2×C311yescharacteristic, complemented
35#63457C2×C311yescharacteristic, complemented
36C9×#102—21no—
37C9×#102C2×C311yescharacteristic, complemented
38(C2×D9)⋊C8C2×C311yescharacteristic, complemented
39#63368C2×C311yescharacteristic, complemented
40C23×C3×C9—21no—
41C22×C3×D9—21no—
42C22×C3×D9D411yescharacteristic
43C3×D4×C9—21no—
44C3×D4×C9D412yescomplemented
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9C2311yescharacteristic
47C3×#611—24no—
48C2×C3×Dic9—24no—
49C2×C3×Dic9—21no—
50C2×C3×Dic9D411yescharacteristic
51C3×D36—21no—
52C3×D36—21no—
53C3×D36—42no—
54C3×C4×D9—21no—
55C3×C4×D9—21no—
56C3×Dic18—21no—
57C3×Dic18D412yescomplemented
58C3×C8×C9—21no—
59C3×C9⋊C8—21no—
60C3×#449—91no—
61#4781—31no—
62C2×C32×D4C2×D311yescharacteristic
63C2×C3×#67—61no—
64C22×C3×Dic3—61no—
65C3×#237—62no—
66C3×#237—62no—
67C2×C3×D12—31no—
68C2×C3×D12—61no—
69C2×C3×C4×D3—31no—
70C2×C3×Dic6—31no—
71C2×C32×C8C2×D311yescharacteristic
72C32×C4⋊C4C2×D311yescharacteristic
73C3×#213—62no—
74C3×(C2×D3)⋊C4—61no—
75C2×C3×C3⋊C8—31no—
76C3×#204—62no—
77C2×D4×C9—21no—
78C2×D4×C9C22×C311yescharacteristic
79C2×#611—21no—
80C22×Dic9—21no—
81#3699—22no—
82#3699—22no—
83C2×D36—21no—
84C2×D36C22×C311yescharacteristic
85C2×C4×D9C22×C311yescharacteristic
86C2×Dic18C22×C311yescharacteristic
87C2×C8×C9—21no—
88C2×C8×C9C22×C311yescharacteristic
89C9×C4⋊C4—21no—
90C9×C4⋊C4C22×C311yescharacteristic
91#3673—22no—
92(C2×D9)⋊C4—21no—
93C2×C9⋊C8C22×C311yescharacteristic
94#3664—22no—
95C22×C3×C9—22no—
96C22×C3×C9—41no—
97C22×C3×C9—41no—
98C22×C3×C9C2×D411yescharacteristic
99C2×C3×D9—21no—
100C2×C3×D9—21no—
101C2×C3×D9—21no—
102C2×C3×D9—41no—
103C2×C3×D9—41no—
104C2×C3×D9—41no—
105C3×C4×C9—41no—
106C3×C4×C9C2×D411yescharacteristic
107C3×C4×C9C2×D411yescharacteristic
108C3×Dic9—22no—
109C3×Dic9—21no—
110C2×C3×#41—91no—
111C2×#237—31no—
112C2×C3×SD16—91no—
113C2×C3×D8—91no—
114C3×#121—91no—
115C2×#213—31no—
116C2×#204—31no—
117#895—31no—
118C3×#103—91no—
119C3×#102—21no—
120C3×#102D911yescharacteristic, complemented
121C3×#102C3×D311yescharacteristic
122C3×C22⋊C8—91no—
123(C2×D3)⋊C8—31no—
124#810—31no—
125C23×C32—21no—
126C22×C3×D3—31no—
127C22×C3×D3—61no—
128C32×D4—21no—
129C32×D4D1212yes—
130C2×C32×C4—21no—
131C2×C32×C4C22×D311yescharacteristic
132C3×#67—64no—
133C2×C3×Dic3—31no—
134C2×C3×Dic3—64no—
135C2×C3×Dic3—61no—
136C3×D12—61no—
137C3×D12—61no—
138C3×D12—122no—
139C3×C4×D3—61no—
140C3×C4×D3—61no—
141C3×Dic6—32no—
142C3×Dic6—61no—
143C23×C9—21no—
144C23×C9—41no—
145C22×D9—21no—
146C22×D9C3×D411yescharacteristic
147C32×C8—21no—
148C3×C3⋊C8—61no—
149D4×C9—21no—
150D4×C9—22no—
151D4×C9—41no—
152D4×C9C3×D412yescomplemented
153C2×C4×C9—21no—
154C2×C4×C9—21no—
155C2×C4×C9—41no—
156C2×C4×C9C23×C311yescharacteristic
157#611—24no—
158C2×Dic9—24no—
159C2×Dic9—21no—
160C2×Dic9C3×D411yescharacteristic
161D36—21no—
162D36—21no—
163D36—42no—
164C4×D9—21no—
165C4×D9—21no—
166Dic18—21no—
167Dic18C3×D412yescomplemented
168C8×C9—21no—
169C8×C9—41no—
170C9⋊C8—21no—
171#449—91noSylow
172C2×C3×C9—42no—
173C2×C3×C9#12011yescharacteristic
174C2×C3×C9#13511yescharacteristic
175C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
176C3×D9—41no—
177C3×D9—81no—
178C3×#41—182no—
179C3×#41—182no—
180C2×C3×Q8—91no—
181C2×C3×D4—21no—
182C2×C3×D4—91no—
183C2×C3×D4—181no—
184C2×C3×D4—181no—
185C2×C3×D4C2×D911yescharacteristic
186C2×C3×D4C2×C3×D311yescharacteristic
187C22×C3×C4—91no—
188C22×C3×C4—181no—
189C2×#67—61no—
190C22×Dic3—61no—
191#237—62no—
192#237—62no—
193C2×D12—31no—
194C2×D12—61no—
195C2×C4×D3—31no—
196C2×Dic6—31no—
197C3×SD16—182no—
198C3×D8—182no—
199C2×C3×C8—21no—
200C2×C3×C8—91no—
201C2×C3×C8C2×D911yescharacteristic
202C2×C3×C8C2×C3×D311yescharacteristic
203C3×C4⋊C4—21no—
204C3×C4⋊C4C2×D911yescharacteristic
205C3×C4⋊C4C2×C3×D311yescharacteristic
206C3×C22⋊C4—181no—
207#213—62no—
208(C2×D3)⋊C4—61no—
209C2×C3⋊C8—31no—
210#204—62no—
211C22×C32—22no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32D3×D411yescharacteristic
215C2×C3×D3—61no—
216C2×C3×D3—61no—
217C2×C3×D3—61no—
218C2×C3×D3—121no—
219C2×C3×D3—121no—
220C2×C3×D3—121no—
221C32×C4—41no—
222C32×C4C2×D1211yescharacteristic
223C32×C4D3×D411yescharacteristic
224C3×Dic3—62no—
225C3×Dic3—61no—
226C22×C9—22no—
227C22×C9—21no—
228C22×C9—42no—
229C22×C9—41no—
230C22×C9—41no—
231C22×C9—81no—
232C22×C9—81no—
233C22×C9C2×C3×D411yescharacteristic
234C2×D9—21no—
235C2×D9—21no—
236C2×D9—21no—
237C2×D9—41no—
238C2×D9—41no—
239C2×D9—41no—
240C4×C9—21no—
241C4×C9—21no—
242C4×C9—41no—
243C4×C9—81no—
244C4×C9C2×C3×D411yescharacteristic
245C4×C9C2×C3×D411yescharacteristic
246Dic9—22no—
247Dic9—21no—
248C2×#41—91no—
249C2×SD16—91no—
250C2×D8—91no—
251#121—91no—
252#103—91no—
253#102C3×D911yescharacteristic, complemented
254C22⋊C8—91no—
255C3×C9#44911yescharacteristic, complemented, Sylow
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—41no—
259C23×C3—91no—
260C23×C3—181no—
261C22×D3—31no—
262C22×D3—61no—
263C3×Q8—92no—
264C3×Q8—181no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—22no—
268C3×D4—41no—
269C3×D4—184no—
270C3×D4—181no—
271C3×D4—181no—
272C3×D4—362no—
273C3×D4D3612yescomplemented
274C3×D4C3×D1212yes—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—91no—
280C2×C3×C4—184no—
281C2×C3×C4—181no—
282C2×C3×C4—181no—
283C2×C3×C4—181no—
284C2×C3×C4C22×D911yescharacteristic
285C2×C3×C4C22×C3×D311yescharacteristic
286#67—64no—
287C2×Dic3—31no—
288C2×Dic3—64no—
289C2×Dic3—61no—
290D12—61no—
291D12—61no—
292D12—122no—
293C4×D3—61no—
294C4×D3—61no—
295Dic6—32no—
296Dic6—61no—
297C3×C8—21no—
298C3×C8—21no—
299C3×C8—41no—
300C3×C8—181no—
301C3⋊C8—61no—
302C2×C32—42no—
303C2×C32#88211yescharacteristic
304C2×C32#91111yescharacteristic
305C2×C32#91611yescharacteristic
306C3×D3—121no—
307C3×D3—241no—
308C2×C9—21no—
309C2×C9—21no—
310C2×C9—21no—
311C2×C9—42no—
312C2×C9—82no—
313C2×C9C3×#12011yescharacteristic
314C2×C9C3×#13511yescharacteristic
315C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
316D9—41no—
317D9—81no—
318#41—182no—
319#41—182no—
320C2×Q8—91no—
321C2×D4—91no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4C2×C3×D911yescharacteristic
325C22×C4—91no—
326C22×C4—181no—
327SD16—182no—
328D8—182no—
329C2×C8—91no—
330C2×C8C2×C3×D911yescharacteristic
331C4⋊C4C2×C3×D911yescharacteristic
332C22⋊C4—181no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—42no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—81no—
342C22×C3—81no—
343C22×C3—181no—
344C22×C3—181no—
345C22×C3—181no—
346C22×C3—361no—
347C22×C3—361no—
348C22×C3—361no—
349C22×C3D4×D911yescharacteristic
350C22×C3C3×D3×D411yescharacteristic
351C2×D3—61no—
352C2×D3—61no—
353C2×D3—61no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—81no—
362C3×C4—181no—
363C3×C4—182no—
364C3×C4C2×D3611yescharacteristic
365C3×C4D4×D911yescharacteristic
366C3×C4C2×C3×D1211yescharacteristic
367C3×C4C3×D3×D411yescharacteristic
368Dic3—62no—
369Dic3—61no—
370C32#478111yescharacteristic
371C9—21no—
372C9C3×#44911yescharacteristic, complemented
373C23—21no—
374C23—91no—
375C23—181no—
376Q8—92no—
377Q8—181no—
378D4—21no—
379D4—184no—
380D4—181no—
381D4—181no—
382D4—362no—
383D4C3×D3612yescomplemented
384C2×C4—21no—
385C2×C4—91no—
386C2×C4—184no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—181no—
390C2×C4C22×C3×D911yescharacteristic
391C8—21no—
392C8—181no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—42no—
397C2×C3—42no—
398C2×C3—82no—
399C2×C3—361no—
400C2×C3—721no—
401C2×C3#6344411yescharacteristic
402C2×C3#6347311yescharacteristic
403C2×C3#6347811yescharacteristic
404C2×C3C3×#88211yescharacteristic
405C2×C3C3×#91111yescharacteristic
406C2×C3C3×#91611yescharacteristic
407D3—121no—
408D3—241no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—181no—
413C22—181no—
414C22—181no—
415C22—361no—
416C22—361no—
417C22—361no—
418C22C3×D4×D911yescharacteristic
419C4—41no—
420C4—181no—
421C4—182no—
422C4C2×C3×D3611yescharacteristic
423C4C3×D4×D911yescharacteristic
424C3—21no—
425C3#1058846111yescharacteristic, direct product factor
426C3C3×#478111yescharacteristic
427C2—42no—
428C2—361no—
429C2—721no—
430C2C3×#6344411yescharacteristic
431C2C3×#6347311yescharacteristic
432C2C3×#6347811yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
hypercenterC3×#102D9
hypocenterC9C3×#449
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3699C2semidirect
2. C2×C3×#3673C2semidirect
3. C2×C3×#3664C2semidirect
4. C3×#63457C2semidirect
5. C3×C9×#102C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63368C2semidirect
9. #10588461C3direct (N × H)
29. C2×#3699C2×C3semidirect
33. C2×#3673C2×C3semidirect
34. C2×#3664C2×C3semidirect
35. #63457C2×C3semidirect
37. C9×#102C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63368C2×C3semidirect
44. C3×D4×C9D4semidirect
57. C3×Dic18D4semidirect
120. C3×#102D9semidirect
152. D4×C9C3×D4semidirect
167. Dic18C3×D4semidirect
253. #102C3×D9semidirect
255. C3×C9#449semidirect
273. C3×D4D36semidirect
372. C9C3×#449semidirect
383. D4C3×D36semidirect
425. C3#10588461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#36992
C2×C3×#36732
C2×C3×#36642
C3×#634572
C3×C9×#1022
C3×(C2×D9)⋊C82
C3×#633682
C3×#47813
#105884613