Finite Group Databasebeta

← C3×#10588463 #13141748

Subgroups — C3×#10588463 #13141748

Order 1728.

506 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3699C211yesmaximal, characteristic
2C2×C3×#3672C211yesmaximal, characteristic, complemented
3C2×C3×Dic36C211yesmaximal, characteristic, complemented
4C3×#63459C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63368C211yesmaximal, characteristic, complemented
8C3×#4783—31nomaximal
9#10588463C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×#611—21no—
12C22×C3×Dic9—21no—
13C3×#3699—22no—
14C3×#3699—22no—
15C2×C3×C4×D9C2211yescharacteristic
16C2×C3×Dic18C2211yescharacteristic
17C2×C3×Dic18C2211yescharacteristic
18C2×C3×C8×C9C2211yescharacteristic
19C3×C9×C4⋊C4C2211yescharacteristic
20C3×#3672—22no—
21C3×(C2×D9)⋊C4—21no—
22C3×C4⋊Dic9—21no—
23C2×C3×C9⋊C8C2211yescharacteristic
24C3×Dic36—22no—
25C2×C3×#237—31no—
26C2×C3×#214—31no—
27C2×C3×Dic12—31no—
28C3×#897—31no—
29C2×#3699C2×C311yescharacteristic
30C32×#102D311yescharacteristic
31C3×(C2×D3)⋊C8—31no—
32C3×#810—31no—
33C2×#3672C2×C311yescharacteristic, complemented
34C2×Dic36C2×C311yescharacteristic, complemented
35#63459C2×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×D9D411yescharacteristic
42C3×D4×C9—21no—
43C3×D4×C9D412yes—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9C2311yescharacteristic
46C3×#611—24no—
47C2×C3×Dic9—24no—
48C2×C3×Dic9—21no—
49C2×C3×Dic9—21no—
50C2×C3×Dic9D411yescharacteristic
51C3×C4×D9—21no—
52C3×C4×D9—21no—
53C3×Dic18—21no—
54C3×Dic18—21no—
55C3×Dic18—21no—
56C3×Dic18D412yes—
57C3×C8×C9—21no—
58C3×C9⋊C8—21no—
59C3×#452—91no—
60#4783—31no—
61C2×C32×D4C2×D311yescharacteristic
62C2×C3×#67—61no—
63C22×C3×Dic3—61no—
64C3×#237—62no—
65C3×#237—62no—
66C2×C3×C4×D3—31no—
67C2×C3×Dic6—31no—
68C2×C3×Dic6—31no—
69C2×C32×C8C2×D311yescharacteristic
70C32×C4⋊C4C2×D311yescharacteristic
71C3×#214—62no—
72C3×(C2×D3)⋊C4—61no—
73C3×C4⋊Dic3—61no—
74C2×C3×C3⋊C8—31no—
75C3×Dic12—62no—
76C2×D4×C9—21no—
77C2×D4×C9C22×C311yescharacteristic
78C2×#611—21no—
79C22×Dic9—21no—
80#3699—22no—
81#3699—22no—
82C2×C4×D9C22×C311yescharacteristic
83C2×Dic18C22×C311yescharacteristic
84C2×Dic18C22×C311yescharacteristic
85C2×C8×C9—21no—
86C2×C8×C9C22×C311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4C22×C311yescharacteristic
89#3672—22no—
90(C2×D9)⋊C4—21no—
91C4⋊Dic9—21no—
92C2×C9⋊C8C22×C311yescharacteristic
93Dic36—22no—
94C22×C3×C9—22no—
95C22×C3×C9—41no—
96C22×C3×C9—41no—
97C22×C3×C9C2×D411yescharacteristic
98C2×C3×D9—21no—
99C2×C3×D9—21no—
100C2×C3×D9—21no—
101C3×C4×C9—41no—
102C3×C4×C9C2×D411yescharacteristic
103C3×C4×C9C2×D411yescharacteristic
104C3×Dic9—22no—
105C3×Dic9—21no—
106C3×Dic9—41no—
107C2×C3×#41—91no—
108C2×#237—31no—
109C2×C3×Q16—91no—
110C2×C3×SD16—91no—
111C3×C22⋊Q8—91no—
112C2×#214—31no—
113C2×Dic12—31no—
114#897—31no—
115C3×#103—91no—
116C3×#102—21no—
117C3×#102D911yescharacteristic, complemented
118C3×#102C3×D311yescharacteristic
119C3×C22⋊C8—91no—
120(C2×D3)⋊C8—31no—
121#810—31no—
122C23×C32—21no—
123C22×C3×D3—31no—
124C32×D4—21no—
125C32×D4D1212yes—
126C2×C32×C4—21no—
127C2×C32×C4C22×D311yescharacteristic
128C3×#67—64no—
129C2×C3×Dic3—31no—
130C2×C3×Dic3—64no—
131C2×C3×Dic3—61no—
132C2×C3×Dic3—61no—
133C3×C4×D3—61no—
134C3×C4×D3—61no—
135C3×Dic6—32no—
136C3×Dic6—61no—
137C3×Dic6—61no—
138C3×Dic6—61no—
139C23×C9—21no—
140C23×C9—41no—
141C22×D9C3×D411yescharacteristic
142C32×C8—21no—
143C3×C3⋊C8—61no—
144D4×C9—21no—
145D4×C9—22no—
146D4×C9—41no—
147D4×C9C3×D412yes—
148C2×C4×C9—21no—
149C2×C4×C9—21no—
150C2×C4×C9—41no—
151C2×C4×C9C23×C311yescharacteristic
152#611—24no—
153C2×Dic9—24no—
154C2×Dic9—21no—
155C2×Dic9—21no—
156C2×Dic9C3×D411yescharacteristic
157C4×D9—21no—
158C4×D9—21no—
159Dic18—21no—
160Dic18—21no—
161Dic18—21no—
162Dic18C3×D412yes—
163C8×C9—21no—
164C8×C9—41no—
165C9⋊C8—21no—
166#452—91noSylow
167C2×C3×C9—42no—
168C2×C3×C9#12011yescharacteristic
169C2×C3×C9#13511yescharacteristic
170C2×C3×C9#13711yescharacteristic
171C3×D9—41no—
172C3×#41—182no—
173C3×#41—182no—
174C2×C3×Q8—91no—
175C2×C3×Q8—91no—
176C2×C3×D4—21no—
177C2×C3×D4—181no—
178C2×C3×D4C2×D911yescharacteristic
179C2×C3×D4C2×C3×D311yescharacteristic
180C22×C3×C4—91no—
181C22×C3×C4—181no—
182C2×#67—61no—
183C22×Dic3—61no—
184#237—62no—
185#237—62no—
186C2×C4×D3—31no—
187C2×Dic6—31no—
188C2×Dic6—31no—
189C3×Q16—182no—
190C3×SD16—182no—
191C2×C3×C8—21no—
192C2×C3×C8—91no—
193C2×C3×C8C2×D911yescharacteristic
194C2×C3×C8C2×C3×D311yescharacteristic
195C3×C4⋊C4—21no—
196C3×C4⋊C4—181no—
197C3×C4⋊C4C2×D911yescharacteristic
198C3×C4⋊C4C2×C3×D311yescharacteristic
199C3×C22⋊C4—181no—
200#214—62no—
201(C2×D3)⋊C4—61no—
202C4⋊Dic3—61no—
203C2×C3⋊C8—31no—
204Dic12—62no—
205C22×C32—22no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32D3×D411yescharacteristic
209C2×C3×D3—61no—
210C2×C3×D3—61no—
211C2×C3×D3—61no—
212C32×C4—41no—
213C32×C4C2×D1211yescharacteristic
214C32×C4D3×D411yescharacteristic
215C3×Dic3—62no—
216C3×Dic3—61no—
217C3×Dic3—121no—
218C22×C9—22no—
219C22×C9—21no—
220C22×C9—42no—
221C22×C9—41no—
222C22×C9—41no—
223C22×C9—81no—
224C22×C9—81no—
225C22×C9C2×C3×D411yescharacteristic
226C2×D9—21no—
227C2×D9—21no—
228C2×D9—21no—
229C4×C9—21no—
230C4×C9—21no—
231C4×C9—41no—
232C4×C9—81no—
233C4×C9C2×C3×D411yescharacteristic
234C4×C9C2×C3×D411yescharacteristic
235Dic9—22no—
236Dic9—21no—
237Dic9—41no—
238C2×#41—91no—
239C2×Q16—91no—
240C2×SD16—91no—
241C22⋊Q8—91no—
242#103—91no—
243#102C3×D911yescharacteristic, complemented
244C22⋊C8—91no—
245C3×C9#45211yescharacteristic, complemented, Sylow
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—41no—
249C23×C3—91no—
250C22×D3—31no—
251C3×Q8—92no—
252C3×Q8—181no—
253C3×Q8—181no—
254C3×Q8—181no—
255C3×D4—21no—
256C3×D4—21no—
257C3×D4—22no—
258C3×D4—41no—
259C3×D4—184no—
260C3×D4D3612yes—
261C3×D4C3×D1212yes—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—91no—
267C2×C3×C4—184no—
268C2×C3×C4—181no—
269C2×C3×C4—181no—
270C2×C3×C4—181no—
271C2×C3×C4—181no—
272C2×C3×C4C22×D911yescharacteristic
273C2×C3×C4C22×C3×D311yescharacteristic
274#67—64no—
275C2×Dic3—31no—
276C2×Dic3—64no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C4×D3—61no—
280C4×D3—61no—
281Dic6—32no—
282Dic6—61no—
283Dic6—61no—
284Dic6—61no—
285C3×C8—21no—
286C3×C8—21no—
287C3×C8—41no—
288C3×C8—181no—
289C3⋊C8—61no—
290C2×C32—42no—
291C2×C32#88211yescharacteristic
292C2×C32#91211yescharacteristic
293C2×C32#91511yescharacteristic
294C3×D3—121no—
295C2×C9—21no—
296C2×C9—21no—
297C2×C9—21no—
298C2×C9—42no—
299C2×C9—82no—
300C2×C9C3×#12011yescharacteristic
301C2×C9C3×#13511yescharacteristic
302C2×C9C3×#13711yescharacteristic
303D9—41no—
304#41—182no—
305#41—182no—
306C2×Q8—91no—
307C2×Q8—91no—
308C2×D4—181no—
309C2×D4C2×C3×D911yescharacteristic
310C22×C4—91no—
311C22×C4—181no—
312Q16—182no—
313SD16—182no—
314C2×C8—91no—
315C2×C8C2×C3×D911yescharacteristic
316C4⋊C4—181no—
317C4⋊C4C2×C3×D911yescharacteristic
318C22⋊C4—181no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—42no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3—181no—
330C22×C3—181no—
331C22×C3—181no—
332C22×C3D4×D911yescharacteristic
333C22×C3C3×D3×D411yescharacteristic
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—61no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—81no—
342C3×C4—181no—
343C3×C4—182no—
344C3×C4—361no—
345C3×C4C2×D3611yescharacteristic
346C3×C4D4×D911yescharacteristic
347C3×C4C2×C3×D1211yescharacteristic
348C3×C4C3×D3×D411yescharacteristic
349Dic3—62no—
350Dic3—61no—
351Dic3—121no—
352C32#478311yescharacteristic
353C9—21no—
354C9C3×#45211yescharacteristic, complemented
355C23—21no—
356C23—91no—
357Q8—92no—
358Q8—181no—
359Q8—181no—
360Q8—181no—
361D4—21no—
362D4—184no—
363D4C3×D3612yes—
364C2×C4—21no—
365C2×C4—91no—
366C2×C4—184no—
367C2×C4—181no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4—181no—
371C2×C4C22×C3×D911yescharacteristic
372C8—21no—
373C8—181no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—42no—
378C2×C3—42no—
379C2×C3—82no—
380C2×C3—361no—
381C2×C3#6344411yescharacteristic
382C2×C3#6347411yescharacteristic
383C2×C3#6347711yescharacteristic
384C2×C3C3×#88211yescharacteristic
385C2×C3C3×#91211yescharacteristic
386C2×C3C3×#91511yescharacteristic
387D3—121no—
388C22—22no—
389C22—41no—
390C22—41no—
391C22—181no—
392C22—181no—
393C22—181no—
394C22C3×D4×D911yescharacteristic
395C4—41no—
396C4—181no—
397C4—182no—
398C4—361no—
399C4C2×C3×D3611yescharacteristic
400C4C3×D4×D911yescharacteristic
401C3—21no—
402C3#1058846311yescharacteristic, direct product factor
403C3C3×#478311yescharacteristic
404C2—42no—
405C2—361no—
406C2C3×#6344411yescharacteristic
407C2C3×#6347411yescharacteristic
408C2C3×#6347711yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC2×C3×#3699C2
hypercenterC3×#102D9
hypocenterC9C3×#452
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
2. C2×C3×#3672C2semidirect
3. C2×C3×Dic36C2semidirect
4. C3×#63459C2semidirect
5. C3×C9×#102C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63368C2semidirect
9. #10588463C3direct (N × H)
33. C2×#3672C2×C3semidirect
34. C2×Dic36C2×C3semidirect
35. #63459C2×C3semidirect
37. C9×#102C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63368C2×C3semidirect
117. C3×#102D9semidirect
243. #102C3×D9semidirect
245. C3×C9#452semidirect
354. C9C3×#452semidirect
402. C3#10588463direct (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×#36722
C2×C3×Dic362
C3×#634592
C3×C9×#1022
C3×(C2×D9)⋊C82
C3×#633682
C3×#47833
#105884633