Finite Group Databasebeta

← C3×#10588465 #13141750

Subgroups — C3×#10588465 #13141750

Order 1728.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic9C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic
3C3×#63455C211yesmaximal, characteristic, complemented
4C3×C9×#102C211yesmaximal, characteristic, complemented
5C3×#63380C211yesmaximal, characteristic, complemented
6C3×#63375C211yesmaximal, characteristic, complemented
7C3×#63367C211yesmaximal, characteristic, complemented
8C3×#4785—31nomaximal
9#10588465C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C22×C3×Dic9—21no—
12C2×C3×D36C2211yescharacteristic
13C2×C3×C4×D9—21no—
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×#3676—21no—
17C3×#3673C414yescomplemented
18C3×(C2×D9)⋊C4—21no—
19C3×C4⋊Dic9C2211yescharacteristic
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×D4×Dic3—31no—
23C2×C3×#213—31no—
24C3×#893—31no—
25C32×#102D311yescharacteristic
26C3×#821—31no—
27C3×#815—31no—
28C3×#808—31no—
29D4×Dic9C2×C311yescharacteristic, complemented
30C2×#3673C2×C311yescharacteristic
31#63455C2×C311yescharacteristic, complemented
32C9×#102—21no—
33C9×#102C2×C311yescharacteristic, complemented
34#63380C2×C311yescharacteristic, complemented
35#63375C2×C311yescharacteristic, complemented
36#63367C2×C311yescharacteristic, complemented
37C23×C3×C9—21no—
38C22×C3×D9—21no—
39C3×D4×C9—21no—
40C3×D4×C9C2×C412yescomplemented
41C2×C3×C4×C9—21no—
42C2×C3×C4×C9C2311yescharacteristic
43C2×C3×Dic9—21no—
44C2×C3×Dic9—42no—
45C2×C3×Dic9D411yescharacteristic
46C2×C3×Dic9D411yescharacteristic
47C3×D36—21no—
48C3×D36C2×C412yescomplemented
49C3×C4×D9—42no—
50C3×C8×C9—21no—
51C3×C9⋊C8C2×C412yescomplemented
52C3×#442—91no—
53#4785—31no—
54C2×C32×D4C2×D311yescharacteristic
55C22×C3×Dic3—61no—
56C2×C3×D12—31no—
57C2×C3×C4×D3—61no—
58C2×C32×C8C2×D311yescharacteristic
59C32×C4⋊C4C2×D311yescharacteristic
60C3×#217—61no—
61C3×#213—34no—
62C3×(C2×D3)⋊C4—61no—
63C3×C4⋊Dic3—31no—
64C3×C4×Dic3—31no—
65C2×C3×C3⋊C8—31no—
66C2×D4×C9—21no—
67C2×D4×C9C22×C311yescharacteristic
68C22×Dic9—21no—
69C2×D36C22×C311yescharacteristic
70C2×C4×D9—21no—
71C2×C8×C9—21no—
72C2×C8×C9C22×C311yescharacteristic
73C9×C4⋊C4—21no—
74C9×C4⋊C4C22×C311yescharacteristic
75#3676—21no—
76#3673C3×C414yescomplemented
77(C2×D9)⋊C4—21no—
78C4⋊Dic9C22×C311yescharacteristic
79C4×Dic9C22×C311yescharacteristic
80C2×C9⋊C8C22×C311yescharacteristic
81C22×C3×C9—22no—
82C22×C3×C9—41no—
83C22×C3×C9—41no—
84C22×C3×C9C2×D411yescharacteristic
85C2×C3×D9—22no—
86C2×C3×D9—41no—
87C2×C3×D9—41no—
88C3×C4×C9—41no—
89C3×C4×C9C22×C411yescharacteristic
90C3×C4×C9#4111yescharacteristic
91C3×Dic9—21no—
92C3×Dic9—21no—
93C3×Dic9—41no—
94C2×C3×D8—91no—
95C3×C4×D4—91no—
96C3×C4×D4—91no—
97D4×Dic3—31no—
98C2×#213—31no—
99#893—31no—
100C3×#106—91no—
101C3×#102—21no—
102C3×#102—91no—
103C3×#102D911yescharacteristic, complemented
104C3×#102C3×D311yescharacteristic
105C3×#97—91no—
106#821—31no—
107#815—31no—
108#808—31no—
109C23×C32—21no—
110C22×C3×D3—61no—
111C32×D4—21no—
112C32×D4C4×D312yes—
113C2×C32×C4—21no—
114C2×C32×C4C22×D311yescharacteristic
115C2×C3×Dic3—31no—
116C2×C3×Dic3—31no—
117C2×C3×Dic3—61no—
118C2×C3×Dic3—122no—
119C3×D12—32no—
120C3×D12—61no—
121C3×C4×D3—122no—
122C23×C9—21no—
123C23×C9—41no—
124C22×D9—21no—
125C32×C8—21no—
126C3×C3⋊C8—32no—
127D4×C9—21no—
128D4×C9—22no—
129D4×C9—41no—
130D4×C9C2×C3×C412yescomplemented
131C2×C4×C9—21no—
132C2×C4×C9—21no—
133C2×C4×C9—41no—
134C2×C4×C9C23×C311yescharacteristic
135C2×Dic9—21no—
136C2×Dic9—42no—
137C2×Dic9C3×D411yescharacteristic
138C2×Dic9C3×D411yescharacteristic
139D36—21no—
140D36C2×C3×C412yescomplemented
141C4×D9—42no—
142C8×C9—21no—
143C8×C9—41no—
144C9⋊C8C2×C3×C412yescomplemented
145#442—91noSylow
146C2×C3×C9—42no—
147C2×C3×C9C4×D411yescharacteristic
148C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
149C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
150C3×D9—42no—
151C2×C3×D4—21no—
152C2×C3×D4—91no—
153C2×C3×D4C2×D911yescharacteristic
154C2×C3×D4C2×C3×D311yescharacteristic
155C22×C3×C4—181no—
156C22×C3×C4—181no—
157C22×Dic3—61no—
158C2×D12—31no—
159C2×C4×D3—61no—
160C3×D8—94no—
161C2×C3×C8—21no—
162C2×C3×C8—91no—
163C2×C3×C8C2×D911yescharacteristic
164C2×C3×C8C2×C3×D311yescharacteristic
165C3×C4⋊C4—21no—
166C3×C4⋊C4—91no—
167C3×C4⋊C4C2×D911yescharacteristic
168C3×C4⋊C4C2×C3×D311yescharacteristic
169C3×C22⋊C4—181no—
170C3×C22⋊C4—181no—
171C3×C42—91no—
172#217—61no—
173#213—34no—
174(C2×D3)⋊C4—61no—
175C4⋊Dic3—31no—
176C4×Dic3—31no—
177C2×C3⋊C8—31no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32D3×D411yescharacteristic
182C2×C3×D3—62no—
183C2×C3×D3—121no—
184C2×C3×D3—121no—
185C32×C4—41no—
186C32×C4C2×C4×D311yescharacteristic
187C32×C4#23711yescharacteristic
188C3×Dic3—61no—
189C3×Dic3—61no—
190C3×Dic3—121no—
191C22×C9—22no—
192C22×C9—21no—
193C22×C9—42no—
194C22×C9—41no—
195C22×C9—41no—
196C22×C9—81no—
197C22×C9—81no—
198C22×C9C2×C3×D411yescharacteristic
199C2×D9—22no—
200C2×D9—41no—
201C2×D9—41no—
202C4×C9—21no—
203C4×C9—21no—
204C4×C9—41no—
205C4×C9—81no—
206C4×C9C22×C3×C411yescharacteristic
207C4×C9C3×#4111yescharacteristic
208Dic9—21no—
209Dic9—21no—
210Dic9—41no—
211C2×D8—91no—
212C4×D4—91no—
213C4×D4—91no—
214#106—91no—
215#102—91no—
216#102C3×D911yescharacteristic, complemented
217#97—91no—
218C3×C9#44211yescharacteristic, complemented, Sylow
219C23×C3—21no—
220C23×C3—21no—
221C23×C3—41no—
222C23×C3—181no—
223C22×D3—61no—
224C3×D4—21no—
225C3×D4—21no—
226C3×D4—22no—
227C3×D4—41no—
228C3×D4—92no—
229C3×D4—181no—
230C3×D4C4×D912yescomplemented
231C3×D4C3×C4×D312yes—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—91no—
237C2×C3×C4—91no—
238C2×C3×C4—181no—
239C2×C3×C4—362no—
240C2×C3×C4—362no—
241C2×C3×C4C22×D911yescharacteristic
242C2×C3×C4C22×C3×D311yescharacteristic
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—61no—
246C2×Dic3—122no—
247D12—32no—
248D12—61no—
249C4×D3—122no—
250C3×C8—21no—
251C3×C8—21no—
252C3×C8—41no—
253C3×C8—92no—
254C3⋊C8—32no—
255C2×C32—42no—
256C2×C32#67⋊C411yescharacteristic
257C2×C32#91111yescharacteristic
258C2×C32#91411yescharacteristic
259C3×D3—122no—
260C2×C9—21no—
261C2×C9—21no—
262C2×C9—21no—
263C2×C9—42no—
264C2×C9—82no—
265C2×C9C3×C4×D411yescharacteristic
266C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
267C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
268D9—42no—
269C2×D4—91no—
270C2×D4C2×C3×D911yescharacteristic
271C22×C4—181no—
272C22×C4—181no—
273D8—94no—
274C2×C8—91no—
275C2×C8C2×C3×D911yescharacteristic
276C4⋊C4—91no—
277C4⋊C4C2×C3×D911yescharacteristic
278C22⋊C4—181no—
279C22⋊C4—181no—
280C42—91no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—42no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—182no—
292C22×C3—361no—
293C22×C3—361no—
294C22×C3D4×D911yescharacteristic
295C22×C3C3×D3×D411yescharacteristic
296C2×D3—62no—
297C2×D3—121no—
298C2×D3—121no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—81no—
304C3×C4—181no—
305C3×C4—181no—
306C3×C4—361no—
307C3×C4C2×C4×D911yescharacteristic
308C3×C4#369911yescharacteristic
309C3×C4C2×C3×C4×D311yescharacteristic
310C3×C4C3×#23711yescharacteristic
311Dic3—61no—
312Dic3—61no—
313Dic3—121no—
314C32#478511yescharacteristic
315C9—21no—
316C9C3×#44211yescharacteristic, complemented
317C23—21no—
318C23—181no—
319D4—21no—
320D4—92no—
321D4—181no—
322D4C3×C4×D912yescomplemented
323C2×C4—21no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—181no—
327C2×C4—362no—
328C2×C4—362no—
329C2×C4C22×C3×D911yescharacteristic
330C8—21no—
331C8—92no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—42no—
336C2×C3—42no—
337C2×C3—82no—
338C2×C3—362no—
339C2×C3#611⋊C411yescharacteristic
340C2×C3#6347311yescharacteristic
341C2×C3#6347611yescharacteristic
342C2×C3C3×#67⋊C411yescharacteristic
343C2×C3C3×#91111yescharacteristic
344C2×C3C3×#91411yescharacteristic
345D3—122no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—182no—
350C22—361no—
351C22—361no—
352C22C3×D4×D911yescharacteristic
353C4—41no—
354C4—181no—
355C4—181no—
356C4—361no—
357C4C2×C3×C4×D911yescharacteristic
358C4C3×#369911yescharacteristic
359C3—21no—
360C3#1058846511yescharacteristic, direct product factor
361C3C3×#478511yescharacteristic
362C2—42no—
363C2—362no—
364C2C3×#611⋊C411yescharacteristic
365C2C3×#6347311yescharacteristic
366C2C3×#6347611yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC2×C3×#3673C2
cosocleC2×C4×C9C23×C3
hypercenterC3×#102D9
hypocenterC9C3×#442
LCSG ▷ 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
1. C3×D4×Dic9C2semidirect
3. C3×#63455C2semidirect
4. C3×C9×#102C2semidirect
5. C3×#63380C2semidirect
6. C3×#63375C2semidirect
7. C3×#63367C2semidirect
9. #10588465C3direct (N × H)
17. C3×#3673C4semidirect
29. D4×Dic9C2×C3semidirect
31. #63455C2×C3semidirect
33. C9×#102C2×C3semidirect
34. #63380C2×C3semidirect
35. #63375C2×C3semidirect
36. #63367C2×C3semidirect
40. C3×D4×C9C2×C4semidirect
48. C3×D36C2×C4semidirect
51. C3×C9⋊C8C2×C4semidirect
76. #3673C3×C4semidirect
103. C3×#102D9semidirect
130. D4×C9C2×C3×C4semidirect
140. D36C2×C3×C4semidirect
144. C9⋊C8C2×C3×C4semidirect
216. #102C3×D9semidirect
218. C3×C9#442semidirect
230. C3×D4C4×D9semidirect
316. C9C3×#442semidirect
322. D4C3×C4×D9semidirect
360. C3#10588465direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D4×Dic92
C2×C3×#36732
C3×#634552
C3×C9×#1022
C3×#633802
C3×#633752
C3×#633672
C3×#47853
#105884653