Finite Group Databasebeta

← C3×#10588738 #13142911

Subgroups — C3×#10588738 #13142911

Order 1728.

448 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#124C211yesmaximal, characteristic, complemented
2C2×C3×#3675C211yesmaximal, characteristic, complemented
3C2×C3×#3673C211yesmaximal, characteristic
4C3×C4×D36C211yesmaximal, characteristic, complemented
5C3×#63395C211yesmaximal, characteristic, complemented
6C3×#63392C211yesmaximal, characteristic, complemented
7C3×C4⋊(C9⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5057—31nomaximal
9#10588738C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D4×C9C2211yescharacteristic
12C2×C3×D36C2211yescharacteristic
13C2×C3×C4×D9—21no—
14C3×C9×C22⋊C4—21no—
15C3×C9×C22⋊C4—21no—
16C3×C42×C9C2211yescharacteristic
17C3×#3675—22no—
18C3×#3673—22no—
19C3×(C2×D9)⋊C4—21no—
20C3×C4⋊Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C2×C3×C9⋊C8C2211yescharacteristic
23C32×#124D311yescharacteristic
24C2×C3×#215—31no—
25C2×C3×#213—31no—
26C3×C4×D12—31no—
27C3×#835—31no—
28C3×#832—31no—
29C3×C4⋊(C3⋊C8)—31no—
30C9×#124—21no—
31C9×#124C2×C311yescharacteristic, complemented
32C2×#3675C2×C311yescharacteristic, complemented
33C2×#3673C2×C311yescharacteristic
34C4×D36C2×C311yescharacteristic, complemented
35#63395C2×C311yescharacteristic, complemented
36#63392C2×C311yescharacteristic, complemented
37C4⋊(C9⋊C8)C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×C3×D9—21no—
40C3×Q8×C9—21no—
41C3×Q8×C9—21no—
42C3×D4×C9—21no—
43C3×D4×C9—21no—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9D411yescharacteristic
46C2×C3×C4×C9D411yescharacteristic
47C2×C3×C4×C9C2311yescharacteristic
48C2×C3×Dic9—21no—
49C3×D36—21no—
50C3×D36D412yes—
51C3×C4×D9—42no—
52C3×C9⋊C8—21no—
53C3×C9⋊C8—21no—
54C3×#463—91no—
55#5057—31no—
56C2×C32×Q8C2×D311yescharacteristic
57C2×C32×D4C2×D311yescharacteristic
58C2×C3×D12—31no—
59C2×C3×C4×D3—61no—
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C42C2×D311yescharacteristic
63C3×#215—62no—
64C3×#213—62no—
65C3×(C2×D3)⋊C4—61no—
66C3×C4⋊Dic3—31no—
67C2×C3×C3⋊C8—31no—
68C2×C3×C3⋊C8—31no—
69C2×Q8×C9—21no—
70C2×Q8×C9C22×C311yescharacteristic
71C2×D4×C9—21no—
72C2×D4×C9C22×C311yescharacteristic
73C2×D36C22×C311yescharacteristic
74C2×C4×D9—21no—
75C9×C22⋊C4—22no—
76C9×C22⋊C4—22no—
77C9×C22⋊C4—21no—
78C9×C22⋊C4—21no—
79C42×C9—21no—
80C42×C9C22×C311yescharacteristic
81#3675—22no—
82#3673—22no—
83(C2×D9)⋊C4—21no—
84C4⋊Dic9C22×C311yescharacteristic
85C2×C9⋊C8C22×C311yescharacteristic
86C2×C9⋊C8C22×C311yescharacteristic
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9—41no—
90C22×C3×C9C2×D411yescharacteristic
91C2×C3×D9—22no—
92C2×C3×D9—41no—
93C2×C3×D9—41no—
94C3×C4×C9—21no—
95C3×C4×C9—21no—
96C3×C4×C9—41no—
97C3×C4×C9C2×D411yescharacteristic
98C3×C4×C9#4111yescharacteristic
99C3×Dic9—41no—
100C2×C3×SD16—91no—
101C2×C3×D8—91no—
102C3×#124—21no—
103C3×#124D911yescharacteristic, complemented
104C3×#124C3×D311yescharacteristic
105C3×C4×D4—91no—
106C2×#215—31no—
107C2×#213—31no—
108C4×D12—31no—
109C3×C4⋊C8—91no—
110C3×#103—91no—
111C3×#102—91no—
112#835—31no—
113#832—31no—
114C4⋊(C3⋊C8)—31no—
115C23×C32—21no—
116C22×C3×D3—61no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—21no—
122C2×C32×C4#6711yescharacteristic
123C2×C32×C4#6711yescharacteristic
124C2×C32×C4C22×D311yescharacteristic
125C2×C3×Dic3—61no—
126C3×D12—32no—
127C3×D12—61no—
128C3×C4×D3—122no—
129C23×C9—22no—
130C23×C9—21no—
131C22×D9—21no—
132C3×C3⋊C8—61no—
133C3×C3⋊C8—61no—
134Q8×C9—21no—
135Q8×C9—21no—
136Q8×C9—41no—
137Q8×C9—41no—
138D4×C9—21no—
139D4×C9—21no—
140D4×C9—41no—
141D4×C9—41no—
142C2×C4×C9—22no—
143C2×C4×C9—21no—
144C2×C4×C9—21no—
145C2×C4×C9—21no—
146C2×C4×C9—21no—
147C2×C4×C9C3×D411yescharacteristic
148C2×C4×C9C3×D411yescharacteristic
149C2×C4×C9C23×C311yescharacteristic
150C2×Dic9—21no—
151D36—21no—
152D36C3×D412yes—
153C4×D9—42no—
154C9⋊C8—21no—
155C9⋊C8—21no—
156#463—91noSylow
157C2×C3×C9—81no—
158C2×C3×C9#12111yescharacteristic
159C2×C3×C9#13511yescharacteristic
160C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
161C3×D9—42no—
162C2×C3×Q8—21no—
163C2×C3×Q8C2×D911yescharacteristic
164C2×C3×Q8C2×C3×D311yescharacteristic
165C2×C3×D4—21no—
166C2×C3×D4—91no—
167C2×C3×D4C2×D911yescharacteristic
168C2×C3×D4C2×C3×D311yescharacteristic
169C22×C3×C4—181no—
170C2×D12—31no—
171C2×C4×D3—61no—
172C3×SD16—182no—
173C3×D8—182no—
174C2×C3×C8—91no—
175C2×C3×C8—91no—
176C3×C4⋊C4—91no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—181no—
184C3×C42—21no—
185C3×C42C2×D911yescharacteristic
186C3×C42C2×C3×D311yescharacteristic
187#215—62no—
188#213—62no—
189(C2×D3)⋊C4—61no—
190C4⋊Dic3—31no—
191C2×C3⋊C8—31no—
192C2×C3⋊C8—31no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32C2×#6711yescharacteristic
197C2×C3×D3—62no—
198C2×C3×D3—121no—
199C2×C3×D3—121no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—41no—
203C32×C4D3×D411yescharacteristic
204C32×C4#23711yescharacteristic
205C3×Dic3—121no—
206C22×C9—21no—
207C22×C9—42no—
208C22×C9—42no—
209C22×C9—42no—
210C22×C9—41no—
211C22×C9—41no—
212C22×C9—41no—
213C22×C9C2×C3×D411yescharacteristic
214C2×D9—22no—
215C2×D9—41no—
216C2×D9—41no—
217C4×C9—21no—
218C4×C9—21no—
219C4×C9—21no—
220C4×C9—21no—
221C4×C9—41no—
222C4×C9—41no—
223C4×C9—42no—
224C4×C9—41no—
225C4×C9C2×C3×D411yescharacteristic
226C4×C9C3×#4111yescharacteristic
227Dic9—41no—
228C2×SD16—91no—
229C2×D8—91no—
230#124C3×D911yescharacteristic, complemented
231C4×D4—91no—
232C4⋊C8—91no—
233#103—91no—
234#102—91no—
235C3×C9#46311yescharacteristic, complemented, Sylow
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—181no—
240C22×D3—61no—
241C3×Q8—21no—
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—21no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—92no—
254C3×D4—181no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—181no—
262C2×C3×C4—362no—
263C2×C3×C4#61111yescharacteristic
264C2×C3×C4#61111yescharacteristic
265C2×C3×C4C22×D911yescharacteristic
266C2×C3×C4C3×#6711yescharacteristic
267C2×C3×C4C3×#6711yescharacteristic
268C2×C3×C4C22×C3×D311yescharacteristic
269C2×Dic3—61no—
270D12—32no—
271D12—61no—
272C4×D3—122no—
273C3×C8—181no—
274C3×C8—181no—
275C3⋊C8—61no—
276C3⋊C8—61no—
277C2×C32—81no—
278C2×C32#93811yescharacteristic
279C2×C32#94911yescharacteristic
280C2×C32#95011yescharacteristic
281C3×D3—122no—
282C2×C9—21no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—82no—
286C2×C9—81no—
287C2×C9C3×#12111yescharacteristic
288C2×C9C3×#13511yescharacteristic
289C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
290D9—42no—
291C2×Q8C2×C3×D911yescharacteristic
292C2×D4—91no—
293C2×D4C2×C3×D911yescharacteristic
294C22×C4—181no—
295SD16—182no—
296D8—182no—
297C2×C8—91no—
298C2×C8—91no—
299C4⋊C4—91no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—181no—
303C42C2×C3×D911yescharacteristic
304C22×C3—21no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—182no—
315C22×C3—361no—
316C22×C3—361no—
317C22×C3C2×#61111yescharacteristic
318C22×C3C2×C3×#6711yescharacteristic
319C2×D3—62no—
320C2×D3—121no—
321C2×D3—121no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—42no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—361no—
334C3×C4D4×D911yescharacteristic
335C3×C4#369911yescharacteristic
336C3×C4C3×D3×D411yescharacteristic
337C3×C4C3×#23711yescharacteristic
338Dic3—121no—
339C32#505711yescharacteristic
340C9—21no—
341C9C3×#46311yescharacteristic, complemented
342C23—21no—
343C23—181no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—92no—
349D4—181no—
350C2×C4—21no—
351C2×C4—181no—
352C2×C4—362no—
353C2×C4C3×#61111yescharacteristic
354C2×C4C3×#61111yescharacteristic
355C2×C4C22×C3×D911yescharacteristic
356C8—181no—
357C8—181no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—82no—
362C2×C3—81no—
363C2×C3—81no—
364C2×C3—362no—
365C2×C3#6350011yescharacteristic
366C2×C3#6351211yescharacteristic
367C2×C3#6351311yescharacteristic
368C2×C3C3×#93811yescharacteristic
369C2×C3C3×#94911yescharacteristic
370C2×C3C3×#95011yescharacteristic
371D3—122no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—182no—
376C22—361no—
377C22—361no—
378C22C2×C3×#61111yescharacteristic
379C4—21no—
380C4—21no—
381C4—41no—
382C4—361no—
383C4C3×D4×D911yescharacteristic
384C4C3×#369911yescharacteristic
385C3—21no—
386C3#1058873811yescharacteristic, direct product factor
387C3C3×#505711yescharacteristic
388C2—81no—
389C2—362no—
390C2C3×#6350011yescharacteristic
391C2C3×#6351211yescharacteristic
392C2C3×#6351311yescharacteristic
subgroupG/H
centerC22×C3C2×#611
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#124C2
socleC22×C32C2×#67
prime radicalC2×C3×#3673C2
hypercenterC3×#124D9
hypocenterC9C3×#463
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#124

Complements

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

NH ≅ G/Ntype
1. C3×C9×#124C2semidirect
2. C2×C3×#3675C2semidirect
4. C3×C4×D36C2semidirect
5. C3×#63395C2semidirect
6. C3×#63392C2semidirect
7. C3×C4⋊(C9⋊C8)C2semidirect
9. #10588738C3direct (N × H)
31. C9×#124C2×C3semidirect
32. C2×#3675C2×C3semidirect
34. C4×D36C2×C3semidirect
35. #63395C2×C3semidirect
36. #63392C2×C3semidirect
37. C4⋊(C9⋊C8)C2×C3semidirect
103. C3×#124D9semidirect
230. #124C3×D9semidirect
235. C3×C9#463semidirect
341. C9C3×#463semidirect
386. C3#10588738direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1242
C2×C3×#36752
C2×C3×#36732
C3×C4×D362
C3×#633952
C3×#633922
C3×C4⋊(C9⋊C8)2
C3×#50573
#105887383