Finite Group Databasebeta

← C3×#10588507 #13141971

Subgroups — C3×#10588507 #13141971

Order 1728.

482 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63716C211yesmaximal, characteristic, complemented
2C3×#63512C211yesmaximal, characteristic, complemented
3C3×#63470C211yesmaximal, characteristic, complemented
4C3×#63437C211yesmaximal, characteristic, complemented
5C3×C9×#104C211yesmaximal, characteristic, complemented
6C3×#63382C211yesmaximal, characteristic, complemented
7C3×#63364C211yesmaximal, characteristic, complemented
8C3×#4827—31nomaximal
9#10588507C311yesmaximal, characteristic, direct product factor
10C3×C9×#41C2211yescharacteristic
11C3×Q8×D9—21no—
12C3×#3699—21no—
13C3×#3699—22no—
14C3×#3697—21no—
15C3×#3697C2211yescharacteristic
16C2×C3×D36C2211yescharacteristic
17C2×C3×Dic18—21no—
18C2×C3×Dic18C2211yescharacteristic
19C3×C9×M16C2211yescharacteristic
20C3×C42×C9C2211yescharacteristic
21C3×#3675—21no—
22C3×#3673—21no—
23C3×(C2×D9)⋊C4—22no—
24C3×#3667C2211yescharacteristic
25C3×D72—21no—
26C3×#3664—21no—
27C3×#1010—31no—
28C3×#949—31no—
29C3×#908—31no—
30C3×#875—31no—
31#63716C2×C311yescharacteristic, complemented
32C32×#104D311yescharacteristic
33C3×#824—31no—
34C3×#805—31no—
35#63512C2×C311yescharacteristic, complemented
36#63470C2×C311yescharacteristic, complemented
37#63437C2×C311yescharacteristic, complemented
38C9×#104—21no—
39C9×#104C2×C311yescharacteristic, complemented
40#63382C2×C311yescharacteristic, complemented
41#63364C2×C311yescharacteristic, complemented
42C22×C3×D9—21no—
43C3×Q8×C9D411yescharacteristic
44C3×D4×C9—21no—
45C3×D4×C9D411yescharacteristic
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9C2311yescharacteristic
49C3×#611—22no—
50C3×#611—21no—
51C2×C3×Dic9—22no—
52C2×C3×Dic9D412yes—
53C3×D36—21no—
54C3×D36—21no—
55C3×D36D411yescharacteristic
56C3×C4×D9—22no—
57C3×C4×D9—21no—
58C3×Dic18—22no—
59C3×Dic18—21no—
60C3×Dic18—21no—
61C3×Dic18D411yescharacteristic
62C3×C8×C9—21no—
63C3×C9⋊C8—21no—
64C3×#454—91no—
65#4827—31no—
66C32×#41C2×D311yescharacteristic
67C3×D3×Q8—61no—
68C3×#237—62no—
69C3×#237—61no—
70C3×#235—31no—
71C3×#235—61no—
72C2×C3×D12—31no—
73C2×C3×Dic6—31no—
74C2×C3×Dic6—61no—
75C32×M16C2×D311yescharacteristic
76C32×C42C2×D311yescharacteristic
77C3×#215—61no—
78C3×#213—61no—
79C3×(C2×D3)⋊C4—62no—
80C3×#208—31no—
81C3×D24—61no—
82C3×#204—61no—
83C9×#41—21no—
84C9×#41C22×C311yescharacteristic
85Q8×D9—21no—
86#3699—21no—
87#3699—22no—
88#3697—21no—
89#3697C22×C311yescharacteristic
90C2×D36C22×C311yescharacteristic
91C2×Dic18—21no—
92C2×Dic18C22×C311yescharacteristic
93C9×M16—21no—
94C9×M16C22×C311yescharacteristic
95C42×C9—21no—
96C42×C9C22×C311yescharacteristic
97#3675—21no—
98#3673—21no—
99(C2×D9)⋊C4—22no—
100#3667C22×C311yescharacteristic
101D72—21no—
102#3664—21no—
103C22×C3×C9—21no—
104C22×C3×C9C2×D411yescharacteristic
105C2×C3×D9—21no—
106C2×C3×D9—42no—
107C2×C3×D9—41no—
108C3×C4×C9—21no—
109C3×C4×C9—41no—
110C3×C4×C9C2×D411yescharacteristic
111C3×C4×C9C2×D411yescharacteristic
112C3×Dic9—22no—
113C3×Dic9—21no—
114C3×2−1+4—91no—
115#1010—31no—
116C3×AGL(1,ℤ/8)—91no—
117C3×AGL(1,ℤ/8)—91no—
118C3×#124—91no—
119#949—31no—
120#908—31no—
121#875—31no—
122C3×#104—21no—
123C3×#104—91no—
124C3×#104D911yescharacteristic, complemented
125C3×#104C3×D311yescharacteristic
126C3×#101—91no—
127#824—31no—
128#805—31no—
129C22×C3×D3—61no—
130C32×Q8D1211yescharacteristic
131C32×D4—21no—
132C32×D4D1211yescharacteristic
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4C22×D311yescharacteristic
136C3×#67—62no—
137C3×#67—61no—
138C2×C3×Dic3—32no—
139C2×C3×Dic3—62no—
140C3×D12—31no—
141C3×D12—61no—
142C3×D12—61no—
143C3×C4×D3—62no—
144C3×C4×D3—61no—
145C3×Dic6—31no—
146C3×Dic6—62no—
147C3×Dic6—61no—
148C3×Dic6—61no—
149C22×D9—21no—
150C32×C8—21no—
151C3×C3⋊C8—61no—
152Q8×C9—21no—
153Q8×C9C3×D411yescharacteristic
154D4×C9—21no—
155D4×C9—21no—
156D4×C9—41no—
157D4×C9C3×D411yescharacteristic
158C2×C4×C9—21no—
159C2×C4×C9—21no—
160C2×C4×C9—21no—
161C2×C4×C9—41no—
162C2×C4×C9—41no—
163C2×C4×C9C23×C311yescharacteristic
164#611—22no—
165#611—21no—
166C2×Dic9—22no—
167C2×Dic9C3×D412yes—
168D36—21no—
169D36—21no—
170D36C3×D411yescharacteristic
171C4×D9—22no—
172C4×D9—21no—
173Dic18—22no—
174Dic18—21no—
175Dic18—21no—
176Dic18C3×D411yescharacteristic
177C8×C9—21no—
178C8×C9—41no—
179C9⋊C8—21no—
180#454—91noSylow
181C2×C3×C9—21no—
182C2×C3×C9—41no—
183C2×C3×C9#12011yescharacteristic
184C3×D9—41no—
185C3×D9—81no—
186C3×#41—21no—
187C3×#41—91no—
188C3×#41—181no—
189C3×#41—182no—
190C3×#41—181no—
191C3×#41C2×D911yescharacteristic
192C3×#41C2×C3×D311yescharacteristic
193C2×C3×Q8—91no—
194C2×C3×Q8—181no—
195C2×C3×Q8—181no—
196C2×C3×D4—91no—
197D3×Q8—61no—
198#237—62no—
199#237—61no—
200#235—31no—
201#235—61no—
202C2×D12—31no—
203C2×Dic6—31no—
204C2×Dic6—61no—
205C3×SD16—181no—
206C3×SD16—181no—
207C3×D8—181no—
208C3×D8—181no—
209C3×M16—21no—
210C3×M16—91no—
211C3×M16C2×D911yescharacteristic
212C3×M16C2×C3×D311yescharacteristic
213C3×C22⋊C4—182no—
214C3×C42—21no—
215C3×C42C2×D911yescharacteristic
216C3×C42C2×C3×D311yescharacteristic
217#215—61no—
218#213—61no—
219(C2×D3)⋊C4—62no—
220#208—31no—
221D24—61no—
222#204—61no—
223C22×C32—21no—
224C22×C32D3×D411yescharacteristic
225C2×C3×D3—61no—
226C2×C3×D3—122no—
227C2×C3×D3—121no—
228C32×C4—21no—
229C32×C4—41no—
230C32×C4C2×D1211yescharacteristic
231C32×C4D3×D411yescharacteristic
232C3×Dic3—61no—
233C3×Dic3—62no—
234C22×C9—21no—
235C22×C9—21no—
236C22×C9—41no—
237C22×C9C2×C3×D411yescharacteristic
238C2×D9—21no—
239C2×D9—42no—
240C2×D9—41no—
241C4×C9—21no—
242C4×C9—21no—
243C4×C9—21no—
244C4×C9—41no—
245C4×C9—41no—
246C4×C9—42no—
247C4×C9C2×C3×D411yescharacteristic
248C4×C9C2×C3×D411yescharacteristic
249Dic9—22no—
250Dic9—21no—
2512−1+4—91no—
252AGL(1,ℤ/8)—91no—
253AGL(1,ℤ/8)—91no—
254#124—91no—
255#104—91no—
256#104C3×D911yescharacteristic, complemented
257#101—91no—
258C3×C9#45411yescharacteristic, complemented, Sylow
259C23×C3—181no—
260C22×D3—61no—
261C3×Q8—21no—
262C3×Q8—91no—
263C3×Q8—182no—
264C3×Q8—181no—
265C3×Q8—181no—
266C3×Q8D3611yescharacteristic
267C3×Q8C3×D1211yescharacteristic
268C3×D4—21no—
269C3×D4—21no—
270C3×D4—21no—
271C3×D4—41no—
272C3×D4—91no—
273C3×D4—182no—
274C3×D4—181no—
275C3×D4—181no—
276C3×D4—181no—
277C3×D4D3611yescharacteristic
278C3×D4C3×D1211yescharacteristic
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—92no—
287C2×C3×C4—182no—
288C2×C3×C4—182no—
289C2×C3×C4—181no—
290C2×C3×C4C22×D911yescharacteristic
291C2×C3×C4C22×C3×D311yescharacteristic
292#67—62no—
293#67—61no—
294C2×Dic3—32no—
295C2×Dic3—62no—
296D12—31no—
297D12—61no—
298D12—61no—
299C4×D3—62no—
300C4×D3—61no—
301Dic6—31no—
302Dic6—62no—
303Dic6—61no—
304Dic6—61no—
305C3×C8—21no—
306C3×C8—21no—
307C3×C8—41no—
308C3×C8—181no—
309C3⋊C8—61no—
310C2×C32—21no—
311C2×C32—41no—
312C2×C32#88211yescharacteristic
313C3×D3—121no—
314C3×D3—241no—
315C2×C9—21no—
316C2×C9—21no—
317C2×C9—41no—
318C2×C9—41no—
319C2×C9—81no—
320C2×C9C3×#12011yescharacteristic
321D9—41no—
322D9—81no—
323#41—91no—
324#41—181no—
325#41—182no—
326#41—181no—
327#41C2×C3×D911yescharacteristic
328C2×Q8—91no—
329C2×Q8—181no—
330C2×Q8—181no—
331C2×D4—91no—
332SD16—181no—
333SD16—181no—
334D8—181no—
335D8—181no—
336M16—91no—
337M16C2×C3×D911yescharacteristic
338C22⋊C4—182no—
339C42C2×C3×D911yescharacteristic
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—181no—
345C22×C3—362no—
346C22×C3—361no—
347C22×C3D4×D911yescharacteristic
348C22×C3C3×D3×D411yescharacteristic
349C2×D3—61no—
350C2×D3—122no—
351C2×D3—121no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—42no—
360C3×C4—182no—
361C3×C4—181no—
362C3×C4C2×D3611yescharacteristic
363C3×C4D4×D911yescharacteristic
364C3×C4C2×C3×D1211yescharacteristic
365C3×C4C3×D3×D411yescharacteristic
366Dic3—61no—
367Dic3—62no—
368C32#482711yescharacteristic
369C9—21no—
370C9C3×#45411yescharacteristic, complemented
371C23—181no—
372Q8—91no—
373Q8—182no—
374Q8—181no—
375Q8—181no—
376Q8C3×D3611yescharacteristic
377D4—21no—
378D4—91no—
379D4—182no—
380D4—181no—
381D4—181no—
382D4—181no—
383D4C3×D3611yescharacteristic
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—92no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—181no—
390C2×C4C22×C3×D911yescharacteristic
391C8—21no—
392C8—181no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—81no—
400C2×C3—361no—
401C2×C3—721no—
402C2×C3#6344411yescharacteristic
403C2×C3C3×#88211yescharacteristic
404D3—121no—
405D3—241no—
406C22—21no—
407C22—181no—
408C22—362no—
409C22—361no—
410C22C3×D4×D911yescharacteristic
411C4—21no—
412C4—41no—
413C4—182no—
414C4—181no—
415C4C2×C3×D3611yescharacteristic
416C4C3×D4×D911yescharacteristic
417C3—21no—
418C3#1058850711yescharacteristic, direct product factor
419C3C3×#482711yescharacteristic
420C2—21no—
421C2—41no—
422C2—361no—
423C2—721no—
424C2C3×#6344411yescharacteristic
subgroupG/H
centerC2×C3#63444
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#104C2
socleC2×C32#882
hypercenterC3×#104D9
hypocenterC9C3×#454
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#104

Complements

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

NH ≅ G/Ntype
1. C3×#63716C2semidirect
2. C3×#63512C2semidirect
3. C3×#63470C2semidirect
4. C3×#63437C2semidirect
5. C3×C9×#104C2semidirect
6. C3×#63382C2semidirect
7. C3×#63364C2semidirect
9. #10588507C3direct (N × H)
31. #63716C2×C3semidirect
35. #63512C2×C3semidirect
36. #63470C2×C3semidirect
37. #63437C2×C3semidirect
39. C9×#104C2×C3semidirect
40. #63382C2×C3semidirect
41. #63364C2×C3semidirect
124. C3×#104D9semidirect
256. #104C3×D9semidirect
258. C3×C9#454semidirect
370. C9C3×#454semidirect
418. C3#10588507direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#637162
C3×#635122
C3×#634702
C3×#634372
C3×C9×#1042
C3×#633822
C3×#633642
C3×#48273
#105885073