Finite Group Databasebeta

← C3×#10588490 #13141879

Subgroups — C3×#10588490 #13141879

Order 1728.

528 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3701C211yesmaximal, characteristic, complemented
2C2×C3×#3675C211yesmaximal, characteristic, complemented
3C2×C3×D72C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic, complemented
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic, complemented
8C3×#4810—31nomaximal
9#10588490C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C3×#3701—22no—
12C3×#3701—22no—
13C2×C3×D36—21no—
14C2×C3×D36—21no—
15C2×C3×D36C2211yescharacteristic
16C2×C3×D36C2211yescharacteristic
17C2×C3×C4×D9—21no—
18C2×C3×C4×D9C2211yescharacteristic
19C2×C3×C8×C9C2211yescharacteristic
20C3×C9×C4⋊C4C2211yescharacteristic
21C3×#3675—22no—
22C3×(C2×D9)⋊C4—21no—
23C2×C3×C9⋊C8C2211yescharacteristic
24C3×D72—22no—
25C2×C3×#239—31no—
26C2×C3×#215—31no—
27C2×C3×D24—31no—
28C3×#895—31no—
29C2×#3701C2×C311yescharacteristic, complemented
30C32×#103D311yescharacteristic
31C3×(C2×D3)⋊C8—31no—
32C3×#809—31no—
33C2×#3675C2×C311yescharacteristic, complemented
34C2×D72C2×C311yescharacteristic, complemented
35#63457C2×C311yescharacteristic, complemented
36C9×#103—21no—
37C9×#103C2×C311yescharacteristic, complemented
38(C2×D9)⋊C8C2×C311yescharacteristic, complemented
39#63369C2×C311yescharacteristic, complemented
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9D411yescharacteristic
43C3×Q8×C9—21no—
44C3×Q8×C9D412yescomplemented
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9C2311yescharacteristic
48C2×C3×Dic9D411yescharacteristic
49C3×D36—24no—
50C3×D36—21no—
51C3×D36—21no—
52C3×D36—21no—
53C3×D36—42no—
54C3×D36D412yescomplemented
55C3×C4×D9—24no—
56C3×C4×D9—21no—
57C3×C4×D9—21no—
58C3×C8×C9—21no—
59C3×C9⋊C8—21no—
60C3×#449—91no—
61#4810—31no—
62C2×C32×Q8C2×D311yescharacteristic
63C3×#239—62no—
64C3×#239—62no—
65C2×C3×D12—31no—
66C2×C3×D12—31no—
67C2×C3×D12—61no—
68C2×C3×D12—61no—
69C2×C3×C4×D3—31no—
70C2×C3×C4×D3—61no—
71C2×C32×C8C2×D311yescharacteristic
72C32×C4⋊C4C2×D311yescharacteristic
73C3×#215—62no—
74C3×(C2×D3)⋊C4—61no—
75C2×C3×C3⋊C8—31no—
76C3×D24—62no—
77C2×Q8×C9—21no—
78C2×Q8×C9C22×C311yescharacteristic
79#3701—22no—
80#3701—22no—
81C2×D36—21no—
82C2×D36—21no—
83C2×D36C22×C311yescharacteristic
84C2×D36C22×C311yescharacteristic
85C2×C4×D9—21no—
86C2×C4×D9C22×C311yescharacteristic
87C2×C8×C9—21no—
88C2×C8×C9C22×C311yescharacteristic
89C9×C4⋊C4—21no—
90C9×C4⋊C4C22×C311yescharacteristic
91#3675—22no—
92(C2×D9)⋊C4—21no—
93C2×C9⋊C8C22×C311yescharacteristic
94D72—22no—
95C22×C3×C9C2×D411yescharacteristic
96C2×C3×D9—21no—
97C2×C3×D9—22no—
98C2×C3×D9—21no—
99C2×C3×D9—21no—
100C2×C3×D9—41no—
101C2×C3×D9—41no—
102C2×C3×D9—41no—
103C2×C3×D9—41no—
104C2×C3×D9—41no—
105C3×C4×C9—22no—
106C3×C4×C9—41no—
107C3×C4×C9C2×D411yescharacteristic
108C3×C4×C9C2×D411yescharacteristic
109C3×Dic9—21no—
110C2×C3×#41—91no—
111C2×#239—31no—
112C2×C3×SD16—91no—
113C2×C3×D8—91no—
114C3×#121—91no—
115C2×#215—31no—
116C2×D24—31no—
117#895—31no—
118C3×#103—21no—
119C3×#103D911yescharacteristic, complemented
120C3×#103C3×D311yescharacteristic
121C3×#102—91no—
122C3×C22⋊C8—91no—
123(C2×D3)⋊C8—31no—
124#809—31no—
125C22×C3×D3—31no—
126C22×C3×D3—61no—
127C22×C3×D3—61no—
128C32×Q8—21no—
129C32×Q8D1212yes—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4C22×D311yescharacteristic
133C2×C3×Dic3—31no—
134C3×D12—32no—
135C3×D12—64no—
136C3×D12—61no—
137C3×D12—61no—
138C3×D12—61no—
139C3×D12—122no—
140C3×C4×D3—64no—
141C3×C4×D3—61no—
142C3×C4×D3—61no—
143C22×D9—21no—
144C22×D9—21no—
145C22×D9C3×D411yescharacteristic
146C32×C8—21no—
147C3×C3⋊C8—61no—
148Q8×C9—21no—
149Q8×C9—22no—
150Q8×C9—41no—
151Q8×C9C3×D412yescomplemented
152C2×C4×C9—21no—
153C2×C4×C9—21no—
154C2×C4×C9—21no—
155C2×C4×C9—41no—
156C2×C4×C9—41no—
157C2×C4×C9C23×C311yescharacteristic
158C2×Dic9C3×D411yescharacteristic
159D36—24no—
160D36—21no—
161D36—21no—
162D36—21no—
163D36—42no—
164D36C3×D412yescomplemented
165C4×D9—24no—
166C4×D9—21no—
167C4×D9—21no—
168C8×C9—21no—
169C8×C9—41no—
170C9⋊C8—21no—
171#449—91noSylow
172C2×C3×C9#12011yescharacteristic
173C2×C3×C9#13511yescharacteristic
174C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
175C3×D9—41no—
176C3×D9—42no—
177C3×D9—81no—
178C3×#41—182no—
179C3×#41—182no—
180C2×C3×Q8—21no—
181C2×C3×Q8C2×D911yescharacteristic
182C2×C3×Q8C2×C3×D311yescharacteristic
183C2×C3×D4—91no—
184C2×C3×D4—91no—
185C2×C3×D4—181no—
186C2×C3×D4—181no—
187C22×C3×C4—91no—
188C22×C3×C4—181no—
189#239—62no—
190#239—62no—
191C2×D12—31no—
192C2×D12—31no—
193C2×D12—61no—
194C2×D12—61no—
195C2×C4×D3—31no—
196C2×C4×D3—61no—
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#215—62no—
208(C2×D3)⋊C4—61no—
209C2×C3⋊C8—31no—
210D24—62no—
211C22×C32D3×D411yescharacteristic
212C2×C3×D3—62no—
213C2×C3×D3—61no—
214C2×C3×D3—61no—
215C2×C3×D3—61no—
216C2×C3×D3—121no—
217C2×C3×D3—121no—
218C2×C3×D3—121no—
219C2×C3×D3—121no—
220C2×C3×D3—121no—
221C32×C4—22no—
222C32×C4—41no—
223C32×C4C2×D1211yescharacteristic
224C32×C4D3×D411yescharacteristic
225C3×Dic3—61no—
226C22×C9—21no—
227C22×C9C2×C3×D411yescharacteristic
228C2×D9—21no—
229C2×D9—22no—
230C2×D9—21no—
231C2×D9—21no—
232C2×D9—41no—
233C2×D9—41no—
234C2×D9—41no—
235C2×D9—41no—
236C2×D9—41no—
237C4×C9—22no—
238C4×C9—21no—
239C4×C9—21no—
240C4×C9—42no—
241C4×C9—41no—
242C4×C9—81no—
243C4×C9C2×C3×D411yescharacteristic
244C4×C9C2×C3×D411yescharacteristic
245Dic9—21no—
246C2×#41—91no—
247C2×SD16—91no—
248C2×D8—91no—
249#121—91no—
250#103C3×D911yescharacteristic, complemented
251#102—91no—
252C22⋊C8—91no—
253C3×C9#44911yescharacteristic, complemented, Sylow
254C23×C3—91no—
255C23×C3—181no—
256C23×C3—181no—
257C22×D3—31no—
258C22×D3—61no—
259C22×D3—61no—
260C3×Q8—21no—
261C3×Q8—21no—
262C3×Q8—22no—
263C3×Q8—41no—
264C3×Q8D3612yescomplemented
265C3×Q8C3×D1212yes—
266C3×D4—92no—
267C3×D4—184no—
268C3×D4—181no—
269C3×D4—181no—
270C3×D4—181no—
271C3×D4—362no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—91no—
280C2×C3×C4—184no—
281C2×C3×C4—181no—
282C2×C3×C4—181no—
283C2×C3×C4C22×D911yescharacteristic
284C2×C3×C4C22×C3×D311yescharacteristic
285C2×Dic3—31no—
286D12—32no—
287D12—64no—
288D12—61no—
289D12—61no—
290D12—61no—
291D12—122no—
292C4×D3—64no—
293C4×D3—61no—
294C4×D3—61no—
295C3×C8—21no—
296C3×C8—21no—
297C3×C8—41no—
298C3×C8—181no—
299C3⋊C8—61no—
300C2×C32#88211yescharacteristic
301C2×C32#91411yescharacteristic
302C2×C32#91911yescharacteristic
303C3×D3—121no—
304C3×D3—122no—
305C3×D3—241no—
306C2×C9—21no—
307C2×C9—21no—
308C2×C9—21no—
309C2×C9C3×#12011yescharacteristic
310C2×C9C3×#13511yescharacteristic
311C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
312D9—41no—
313D9—42no—
314D9—81no—
315#41—182no—
316#41—182no—
317C2×Q8C2×C3×D911yescharacteristic
318C2×D4—91no—
319C2×D4—91no—
320C2×D4—181no—
321C2×D4—181no—
322C22×C4—91no—
323C22×C4—181no—
324SD16—182no—
325D8—182no—
326C2×C8—91no—
327C2×C8C2×C3×D911yescharacteristic
328C4⋊C4C2×C3×D911yescharacteristic
329C22⋊C4—181no—
330C22×C3—21no—
331C22×C3—182no—
332C22×C3—181no—
333C22×C3—181no—
334C22×C3—181no—
335C22×C3—361no—
336C22×C3—361no—
337C22×C3—361no—
338C22×C3—361no—
339C22×C3—361no—
340C22×C3D4×D911yescharacteristic
341C22×C3C3×D3×D411yescharacteristic
342C2×D3—62no—
343C2×D3—61no—
344C2×D3—61no—
345C2×D3—61no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C3×C4—22no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—42no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—81no—
359C3×C4—181no—
360C3×C4C2×D3611yescharacteristic
361C3×C4D4×D911yescharacteristic
362C3×C4C2×C3×D1211yescharacteristic
363C3×C4C3×D3×D411yescharacteristic
364Dic3—61no—
365C32#481011yescharacteristic
366C9—21no—
367C9C3×#44911yescharacteristic, complemented
368C23—91no—
369C23—181no—
370C23—181no—
371Q8—21no—
372Q8C3×D3612yescomplemented
373D4—92no—
374D4—184no—
375D4—181no—
376D4—181no—
377D4—181no—
378D4—362no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—91no—
382C2×C4—184no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4C22×C3×D911yescharacteristic
386C8—21no—
387C8—181no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—361no—
392C2×C3—362no—
393C2×C3—721no—
394C2×C3#6344411yescharacteristic
395C2×C3#6347611yescharacteristic
396C2×C3#6348111yescharacteristic
397C2×C3C3×#88211yescharacteristic
398C2×C3C3×#91411yescharacteristic
399C2×C3C3×#91911yescharacteristic
400D3—121no—
401D3—122no—
402D3—241no—
403C22—181no—
404C22—181no—
405C22—182no—
406C22—181no—
407C22—361no—
408C22—361no—
409C22—361no—
410C22—361no—
411C22—361no—
412C22C3×D4×D911yescharacteristic
413C4—22no—
414C4—41no—
415C4—181no—
416C4C2×C3×D3611yescharacteristic
417C4C3×D4×D911yescharacteristic
418C3—21no—
419C3#1058849011yescharacteristic, direct product factor
420C3C3×#481011yescharacteristic
421C2—361no—
422C2—362no—
423C2—721no—
424C2C3×#6344411yescharacteristic
425C2C3×#6347611yescharacteristic
426C2C3×#6348111yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#103C2
socleC22×C32D3×D4
hypercenterC3×#103D9
hypocenterC9C3×#449
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3701C2semidirect
2. C2×C3×#3675C2semidirect
3. C2×C3×D72C2semidirect
4. C3×#63457C2semidirect
5. C3×C9×#103C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63369C2semidirect
9. #10588490C3direct (N × H)
29. C2×#3701C2×C3semidirect
33. C2×#3675C2×C3semidirect
34. C2×D72C2×C3semidirect
35. #63457C2×C3semidirect
37. C9×#103C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63369C2×C3semidirect
44. C3×Q8×C9D4semidirect
54. C3×D36D4semidirect
119. C3×#103D9semidirect
151. Q8×C9C3×D4semidirect
164. D36C3×D4semidirect
250. #103C3×D9semidirect
253. C3×C9#449semidirect
264. C3×Q8D36semidirect
367. C9C3×#449semidirect
372. Q8C3×D36semidirect
419. C3#10588490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37012
C2×C3×#36752
C2×C3×D722
C3×#634572
C3×C9×#1032
C3×(C2×D9)⋊C82
C3×#633692
C3×#48103
#105884903