Finite Group Databasebeta

← C3×#10588853 #13143351

Subgroups — C3×#10588853 #13143351

Order 1728.

524 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3699C211yesmaximal, characteristic
2C2×C3×C9×SD16C211yesmaximal, characteristic, complemented
3C3×#63508C211yesmaximal, characteristic, complemented
4C2×C3×#3674C211yesmaximal, characteristic, complemented
5C3×#63392C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63376C211yesmaximal, characteristic, complemented
8C3×#5173—31nomaximal
9#10588853C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D4×C9C2211yescharacteristic
12C2×C3×#611—21no—
13C22×C3×Dic9—21no—
14C3×#3699—22no—
15C3×#3699—22no—
16C2×C3×C4×D9C2211yescharacteristic
17C2×C3×Dic18C2211yescharacteristic
18C3×C9×SD16—22no—
19C2×C3×C8×C9C2211yescharacteristic
20C3×#3674—22no—
21C3×(C2×D9)⋊C4—21no—
22C3×C4⋊Dic9C2211yescharacteristic
23C3×Dic9⋊C4—21no—
24C2×C3×C9⋊C8C2211yescharacteristic
25C2×C3×#237—31no—
26C2×C32×SD16D311yescharacteristic
27C3×#946—31no—
28C2×C3×#216—31no—
29C2×#3699C2×C311yescharacteristic
30C3×#832—31no—
31C3×(C2×D3)⋊C8—31no—
32C3×#816—31no—
33C2×C9×SD16—21no—
34C2×C9×SD16C2×C311yescharacteristic, complemented
35#63508C2×C311yescharacteristic, complemented
36C2×#3674C2×C311yescharacteristic, complemented
37#63392C2×C311yescharacteristic, complemented
38(C2×D9)⋊C8C2×C311yescharacteristic, complemented
39#63376C2×C311yescharacteristic, complemented
40C23×C3×C9—21no—
41C22×C3×D9D411yescharacteristic
42C3×Q8×C9—21no—
43C3×Q8×C9—21no—
44C3×D4×C9—21no—
45C3×D4×C9D412yes—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9C2311yescharacteristic
48C3×#611—24no—
49C2×C3×Dic9—24no—
50C2×C3×Dic9—21no—
51C2×C3×Dic9—21no—
52C2×C3×Dic9D411yescharacteristic
53C3×C4×D9—21no—
54C3×C4×D9—21no—
55C3×Dic18—21no—
56C3×Dic18D412yes—
57C3×C8×C9—21no—
58C3×C9⋊C8—21no—
59C3×#452—91no—
60#5173—31no—
61C2×C32×Q8C2×D311yescharacteristic
62C2×C32×D4C2×D311yescharacteristic
63C2×C3×#67—61no—
64C22×C3×Dic3—61no—
65C3×#237—62no—
66C3×#237—62no—
67C2×C3×C4×D3—31no—
68C2×C3×Dic6—31no—
69C32×SD16—22no—
70C2×C32×C8C2×D311yescharacteristic
71C3×#216—62no—
72C3×(C2×D3)⋊C4—61no—
73C3×C4⋊Dic3—31no—
74C3×Dic3⋊C4—61no—
75C2×C3×C3⋊C8—31no—
76C2×Q8×C9—21no—
77C2×Q8×C9C22×C311yescharacteristic
78C2×D4×C9—21no—
79C2×D4×C9C22×C311yescharacteristic
80C2×#611—21no—
81C22×Dic9—21no—
82#3699—22no—
83#3699—22no—
84C2×C4×D9C22×C311yescharacteristic
85C2×Dic18C22×C311yescharacteristic
86C9×SD16—24no—
87C9×SD16—22no—
88C2×C8×C9—21no—
89C2×C8×C9C22×C311yescharacteristic
90#3674—22no—
91(C2×D9)⋊C4—21no—
92C4⋊Dic9C22×C311yescharacteristic
93Dic9⋊C4—21no—
94C2×C9⋊C8C22×C311yescharacteristic
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—
102C3×C4×C9—41no—
103C3×C4×C9C2×D411yescharacteristic
104C3×C4×C9C2×D411yescharacteristic
105C3×Dic9—22no—
106C3×Dic9—21no—
107C3×Dic9—41no—
108C2×C3×#41—91no—
109C2×#237—31no—
110C2×C3×Q16—91no—
111C2×C3×SD16—21no—
112C2×C3×SD16D911yescharacteristic, complemented
113C2×C3×SD16C3×D311yescharacteristic
114C3×C22⋊Q8—91no—
115#946—31no—
116C2×#216—31no—
117C3×#103—91no—
118C3×#102—91no—
119C3×C22⋊C8—91no—
120#832—31no—
121(C2×D3)⋊C8—31no—
122#816—31no—
123C23×C32—21no—
124C22×C3×D3—31no—
125C32×Q8—21no—
126C32×Q8—21no—
127C32×D4—21no—
128C32×D4#6712yes—
129C2×C32×C4—21no—
130C2×C32×C4C22×D311yescharacteristic
131C3×#67—64no—
132C2×C3×Dic3—31no—
133C2×C3×Dic3—64no—
134C2×C3×Dic3—61no—
135C2×C3×Dic3—61no—
136C3×C4×D3—61no—
137C3×C4×D3—61no—
138C3×Dic6—32no—
139C3×Dic6—61no—
140C23×C9—21no—
141C23×C9—41no—
142C22×D9C3×D411yescharacteristic
143C32×C8—21no—
144C3×C3⋊C8—61no—
145Q8×C9—22no—
146Q8×C9—21no—
147Q8×C9—21no—
148Q8×C9—41no—
149D4×C9—21no—
150D4×C9—22no—
151D4×C9—41no—
152D4×C9C3×D412yes—
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×Dic9—21no—
161C2×Dic9C3×D411yescharacteristic
162C4×D9—21no—
163C4×D9—21no—
164Dic18—21no—
165Dic18C3×D412yes—
166C8×C9—22no—
167C8×C9—21no—
168C9⋊C8—21no—
169#452—91noSylow
170C2×C3×C9—42no—
171C2×C3×C9#12011yescharacteristic
172C2×C3×C9#13511yescharacteristic
173C2×C3×C9#13711yescharacteristic
174C3×D9—41no—
175C3×#41—182no—
176C3×#41—182no—
177C2×C3×Q8—21no—
178C2×C3×Q8—91no—
179C2×C3×Q8C2×D911yescharacteristic
180C2×C3×Q8C2×C3×D311yescharacteristic
181C2×C3×D4—21no—
182C2×C3×D4—181no—
183C2×C3×D4C2×D911yescharacteristic
184C2×C3×D4C2×C3×D311yescharacteristic
185C22×C3×C4—91no—
186C22×C3×C4—181no—
187C2×#67—61no—
188C22×Dic3—61no—
189#237—62no—
190#237—62no—
191C2×C4×D3—31no—
192C2×Dic6—31no—
193C3×Q16—182no—
194C3×SD16—24no—
195C3×SD16—22no—
196C3×SD16—22no—
197C2×C3×C8—21no—
198C2×C3×C8—91no—
199C2×C3×C8C2×D911yescharacteristic
200C2×C3×C8C2×C3×D311yescharacteristic
201C3×C4⋊C4—91no—
202C3×C4⋊C4—181no—
203C3×C22⋊C4—181no—
204#216—62no—
205(C2×D3)⋊C4—61no—
206C4⋊Dic3—31no—
207Dic3⋊C4—61no—
208C2×C3⋊C8—31no—
209C22×C32—22no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32D3×D411yescharacteristic
213C2×C3×D3—61no—
214C2×C3×D3—61no—
215C2×C3×D3—61no—
216C32×C4—41no—
217C32×C4D3×D411yescharacteristic
218C32×C4C2×#6711yescharacteristic
219C3×Dic3—62no—
220C3×Dic3—61no—
221C3×Dic3—121no—
222C22×C9—22no—
223C22×C9—21no—
224C22×C9—42no—
225C22×C9—41no—
226C22×C9—41no—
227C22×C9—81no—
228C22×C9—81no—
229C22×C9C2×C3×D411yescharacteristic
230C2×D9—21no—
231C2×D9—21no—
232C2×D9—21no—
233C4×C9—21no—
234C4×C9—21no—
235C4×C9—42no—
236C4×C9—41no—
237C4×C9C2×C3×D411yescharacteristic
238C4×C9C2×C3×D411yescharacteristic
239Dic9—22no—
240Dic9—21no—
241Dic9—41no—
242C2×#41—91no—
243C2×Q16—91no—
244C2×SD16C3×D911yescharacteristic, complemented
245C22⋊Q8—91no—
246#103—91no—
247#102—91no—
248C22⋊C8—91no—
249C3×C9#45211yescharacteristic, complemented, Sylow
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—41no—
253C23×C3—91no—
254C22×D3—31no—
255C3×Q8—22no—
256C3×Q8—21no—
257C3×Q8—21no—
258C3×Q8—21no—
259C3×Q8—21no—
260C3×Q8—41no—
261C3×Q8—92no—
262C3×Q8—181no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—22no—
266C3×D4—41no—
267C3×D4—184no—
268C3×D4#61112yes—
269C3×D4C3×#6712yes—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—91no—
275C2×C3×C4—184no—
276C2×C3×C4—181no—
277C2×C3×C4—181no—
278C2×C3×C4—181no—
279C2×C3×C4—181no—
280C2×C3×C4C22×D911yescharacteristic
281C2×C3×C4C22×C3×D311yescharacteristic
282#67—64no—
283C2×Dic3—31no—
284C2×Dic3—64no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C4×D3—61no—
288C4×D3—61no—
289Dic6—32no—
290Dic6—61no—
291C3×C8—22no—
292C3×C8—21no—
293C3×C8—21no—
294C3×C8—181no—
295C3⋊C8—61no—
296C2×C32—42no—
297C2×C32#91511yescharacteristic
298C2×C32#91611yescharacteristic
299C2×C32#93711yescharacteristic
300C3×D3—121no—
301C2×C9—21no—
302C2×C9—21no—
303C2×C9—21no—
304C2×C9—42no—
305C2×C9—82no—
306C2×C9C3×#12011yescharacteristic
307C2×C9C3×#13511yescharacteristic
308C2×C9C3×#13711yescharacteristic
309D9—41no—
310#41—182no—
311#41—182no—
312C2×Q8—91no—
313C2×Q8C2×C3×D911yescharacteristic
314C2×D4—181no—
315C2×D4C2×C3×D911yescharacteristic
316C22×C4—91no—
317C22×C4—181no—
318Q16—182no—
319SD16—22no—
320C2×C8—91no—
321C2×C8C2×C3×D911yescharacteristic
322C4⋊C4—91no—
323C4⋊C4—181no—
324C22⋊C4—181no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—42no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—81no—
334C22×C3—81no—
335C22×C3—181no—
336C22×C3—181no—
337C22×C3—181no—
338C22×C3D4×D911yescharacteristic
339C22×C3C3×D3×D411yescharacteristic
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—42no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—181no—
349C3×C4—182no—
350C3×C4—361no—
351C3×C4D4×D911yescharacteristic
352C3×C4C2×#61111yescharacteristic
353C3×C4C3×D3×D411yescharacteristic
354C3×C4C2×C3×#6711yescharacteristic
355Dic3—62no—
356Dic3—61no—
357Dic3—121no—
358C32#517311yescharacteristic
359C9—21no—
360C9C3×#45211yescharacteristic, complemented
361C23—21no—
362C23—91no—
363Q8—21no—
364Q8—21no—
365Q8—92no—
366Q8—181no—
367D4—21no—
368D4—184no—
369D4C3×#61112yes—
370C2×C4—21no—
371C2×C4—91no—
372C2×C4—184no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—181no—
377C2×C4C22×C3×D911yescharacteristic
378C8—21no—
379C8—181no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—42no—
384C2×C3—42no—
385C2×C3—82no—
386C2×C3—361no—
387C2×C3#6347711yescharacteristic
388C2×C3#6347811yescharacteristic
389C2×C3#6349911yescharacteristic
390C2×C3C3×#91511yescharacteristic
391C2×C3C3×#91611yescharacteristic
392C2×C3C3×#93711yescharacteristic
393D3—121no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—181no—
398C22—181no—
399C22—181no—
400C22C3×D4×D911yescharacteristic
401C4—41no—
402C4—181no—
403C4—182no—
404C4—361no—
405C4C3×D4×D911yescharacteristic
406C4C2×C3×#61111yescharacteristic
407C3—21no—
408C3#1058885311yescharacteristic, direct product factor
409C3C3×#517311yescharacteristic
410C2—42no—
411C2—361no—
412C2C3×#6347711yescharacteristic
413C2C3×#6347811yescharacteristic
414C2C3×#6349911yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C9×SD16C2
socleC22×C32D3×D4
prime radicalC2×C3×#3699C2
hypercenterC2×C3×SD16D9
hypocenterC9C3×#452
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
2. C2×C3×C9×SD16C2semidirect
3. C3×#63508C2semidirect
4. C2×C3×#3674C2semidirect
5. C3×#63392C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63376C2semidirect
9. #10588853C3direct (N × H)
34. C2×C9×SD16C2×C3semidirect
35. #63508C2×C3semidirect
36. C2×#3674C2×C3semidirect
37. #63392C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63376C2×C3semidirect
112. C2×C3×SD16D9semidirect
244. C2×SD16C3×D9semidirect
249. C3×C9#452semidirect
360. C9C3×#452semidirect
408. C3#10588853direct (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×C9×SD162
C3×#635082
C2×C3×#36742
C3×#633922
C3×(C2×D9)⋊C82
C3×#633762
C3×#51733
#105888533