Finite Group Databasebeta

← C3×#10588454 #13141739

Subgroups — C3×#10588454 #13141739

Order 1728.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63500C211yesmaximal, characteristic
2C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
3C3×C9×#102C211yesmaximal, characteristic, complemented
4C3×#63392C211yesmaximal, characteristic, complemented
5C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
6C3×#63378C211yesmaximal, characteristic, complemented
7C3×#63366C211yesmaximal, characteristic, complemented
8C3×#4774—31nomaximal
9#10588454C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×#611—21no—
12C2×C3×C4×D9—21no—
13C2×C3×C4×D9C2211yescharacteristic
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×#3676—21no—
17C3×C4⋊Dic9C2211yescharacteristic
18C3×C4⋊Dic9C2211yescharacteristic
19C3×Dic9⋊C4—21no—
20C2×C3×C9⋊C8C2211yescharacteristic
21C3×#938—31no—
22C3×D3×C4⋊C4—31no—
23C32×#102D311yescharacteristic
24C3×#832—31no—
25C3×(C2×D3)⋊C8—31no—
26C3×#818—31no—
27C3×#807—31no—
28#63500C2×C311yescharacteristic
29C4⋊C4×D9C2×C311yescharacteristic, complemented
30C9×#102—21no—
31C9×#102C2×C311yescharacteristic, complemented
32#63392C2×C311yescharacteristic, complemented
33(C2×D9)⋊C8C2×C311yescharacteristic, complemented
34#63378C2×C311yescharacteristic, complemented
35#63366C2×C311yescharacteristic, complemented
36C23×C3×C9—21no—
37C22×C3×D9D411yescharacteristic
38C3×D4×C9—21no—
39C3×D4×C9—21no—
40C2×C3×C4×C9—21no—
41C2×C3×C4×C9C2311yescharacteristic
42C3×#611—42no—
43C2×C3×Dic9—21no—
44C2×C3×Dic9—21no—
45C2×C3×Dic9D411yescharacteristic
46C3×C4×D9—21no—
47C3×C4×D9—21no—
48C3×C4×D9—42no—
49C3×C8×C9—21no—
50C3×C9⋊C8—21no—
51C3×#480—91no—
52#4774—31no—
53C2×C32×D4C2×D311yescharacteristic
54C2×C3×#67—61no—
55C2×C3×C4×D3—31no—
56C2×C3×C4×D3—61no—
57C2×C32×C8C2×D311yescharacteristic
58C32×C4⋊C4C2×D311yescharacteristic
59C3×#217—61no—
60C3×C4⋊Dic3—31no—
61C3×C4⋊Dic3—31no—
62C3×Dic3⋊C4—61no—
63C2×C3×C3⋊C8—31no—
64C2×D4×C9—21no—
65C2×D4×C9C22×C311yescharacteristic
66C2×#611—21no—
67C2×C4×D9—21no—
68C2×C4×D9C22×C311yescharacteristic
69C2×C8×C9—21no—
70C2×C8×C9C22×C311yescharacteristic
71C9×C4⋊C4—21no—
72C9×C4⋊C4C22×C311yescharacteristic
73#3676—21no—
74C4⋊Dic9C22×C311yescharacteristic
75C4⋊Dic9C22×C311yescharacteristic
76Dic9⋊C4—21no—
77C2×C9⋊C8C22×C311yescharacteristic
78C22×C3×C9—41no—
79C22×C3×C9—41no—
80C22×C3×C9—41no—
81C22×C3×C9C2×D411yescharacteristic
82C2×C3×D9—21no—
83C2×C3×D9—21no—
84C2×C3×D9D812yes—
85C3×C4×C9—41no—
86C3×C4×C9#4111yescharacteristic
87C3×C4×C9#4111yescharacteristic
88C3×Dic9—21no—
89C3×Dic9—41no—
90C3×Dic9—41no—
91C3×#121—91no—
92C2×C3×C4⋊C4—91no—
93#938—31no—
94D3×C4⋊C4—31no—
95C3×#107—91no—
96C3×#107—91no—
97C3×#102—21no—
98C3×#102—91no—
99C3×#102D911yescharacteristic, complemented
100C3×#102C3×D311yescharacteristic
101C3×C22⋊C8—91no—
102#832—31no—
103(C2×D3)⋊C8—31no—
104#818—31no—
105#807—31no—
106C23×C32—21no—
107C22×C3×D3—31no—
108C32×D4—21no—
109C32×D4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C22×D311yescharacteristic
112C3×#67—122no—
113C2×C3×Dic3—31no—
114C2×C3×Dic3—61no—
115C2×C3×Dic3—61no—
116C3×C4×D3—61no—
117C3×C4×D3—61no—
118C3×C4×D3—122no—
119C23×C9—21no—
120C23×C9—41no—
121C22×D9C3×D411yescharacteristic
122C32×C8—21no—
123C3×C3⋊C8—61no—
124D4×C9—22no—
125D4×C9—21no—
126D4×C9—21no—
127D4×C9—41no—
128C2×C4×C9—21no—
129C2×C4×C9—21no—
130C2×C4×C9—41no—
131C2×C4×C9C23×C311yescharacteristic
132#611—42no—
133C2×Dic9—21no—
134C2×Dic9—21no—
135C2×Dic9C3×D411yescharacteristic
136C4×D9—21no—
137C4×D9—21no—
138C4×D9—42no—
139C8×C9—21no—
140C8×C9—41no—
141C9⋊C8—21no—
142#480—91noSylow
143C2×C3×C9—81no—
144C2×C3×C9#12311yescharacteristic
145C2×C3×C9C2×D811yescharacteristic
146C2×C3×C9#13711yescharacteristic
147C3×D9—22no—
148C2×C3×D4—21no—
149C2×C3×D4—181no—
150C2×C3×D4C2×D911yescharacteristic
151C2×C3×D4C2×C3×D311yescharacteristic
152C22×C3×C4—91no—
153C22×C3×C4—181no—
154C2×#67—61no—
155C2×C4×D3—31no—
156C2×C4×D3—61no—
157C2×C3×C8—21no—
158C2×C3×C8—91no—
159C2×C3×C8C2×D911yescharacteristic
160C2×C3×C8C2×C3×D311yescharacteristic
161C3×C4⋊C4—21no—
162C3×C4⋊C4—91no—
163C3×C4⋊C4—91no—
164C3×C4⋊C4—181no—
165C3×C4⋊C4C2×D911yescharacteristic
166C3×C4⋊C4C2×C3×D311yescharacteristic
167C3×C22⋊C4—181no—
168#217—61no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171Dic3⋊C4—61no—
172C2×C3⋊C8—31no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32D3×D411yescharacteristic
177C2×C3×D3—32no—
178C2×C3×D3—61no—
179C2×C3×D3—61no—
180C32×C4—41no—
181C32×C4#23511yescharacteristic
182C32×C4#23711yescharacteristic
183C3×Dic3—61no—
184C3×Dic3—121no—
185C3×Dic3—121no—
186C22×C9—21no—
187C22×C9—42no—
188C22×C9—41no—
189C22×C9—41no—
190C22×C9—41no—
191C22×C9—81no—
192C22×C9—81no—
193C22×C9C2×C3×D411yescharacteristic
194C2×D9—21no—
195C2×D9—21no—
196C2×D9C3×D812yes—
197C4×C9—21no—
198C4×C9—21no—
199C4×C9—41no—
200C4×C9—81no—
201C4×C9C3×#4111yescharacteristic
202C4×C9C3×#4111yescharacteristic
203Dic9—21no—
204Dic9—41no—
205Dic9—41no—
206#121—91no—
207C2×C4⋊C4—91no—
208#107—91no—
209#107—91no—
210#102—91no—
211#102C3×D911yescharacteristic, complemented
212C22⋊C8—91no—
213C3×C9#48011yescharacteristic, complemented, Sylow
214C23×C3—21no—
215C23×C3—21no—
216C23×C3—41no—
217C23×C3—91no—
218C22×D3—31no—
219C3×D4—22no—
220C3×D4—21no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—21no—
224C3×D4—41no—
225C3×D4—362no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—41no—
230C2×C3×C4—91no—
231C2×C3×C4—181no—
232C2×C3×C4—181no—
233C2×C3×C4—181no—
234C2×C3×C4—181no—
235C2×C3×C4—362no—
236C2×C3×C4C22×D911yescharacteristic
237C2×C3×C4C22×C3×D311yescharacteristic
238#67—122no—
239C2×Dic3—31no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C4×D3—61no—
243C4×D3—61no—
244C4×D3—122no—
245C3×C8—21no—
246C3×C8—21no—
247C3×C8—41no—
248C3×C8—181no—
249C3⋊C8—61no—
250C2×C32—81no—
251C2×C32#88311yescharacteristic
252C2×C32D3×D811yescharacteristic
253C2×C32#91511yescharacteristic
254C3×D3—62no—
255C2×C9—21no—
256C2×C9—21no—
257C2×C9—21no—
258C2×C9—82no—
259C2×C9—81no—
260C2×C9C3×#12311yescharacteristic
261C2×C9C2×C3×D811yescharacteristic
262C2×C9C3×#13711yescharacteristic
263D9—22no—
264C2×D4—181no—
265C2×D4C2×C3×D911yescharacteristic
266C22×C4—91no—
267C22×C4—181no—
268C2×C8—91no—
269C2×C8C2×C3×D911yescharacteristic
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—181no—
273C4⋊C4C2×C3×D911yescharacteristic
274C22⋊C4—181no—
275C22×C3—21no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3—92no—
286C22×C3—181no—
287C22×C3—181no—
288C22×C3D4×D911yescharacteristic
289C22×C3C3×D3×D411yescharacteristic
290C2×D3—32no—
291C2×D3—61no—
292C2×D3—61no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—181no—
299C3×C4—361no—
300C3×C4—361no—
301C3×C4#369711yescharacteristic
302C3×C4#369911yescharacteristic
303C3×C4C3×#23511yescharacteristic
304C3×C4C3×#23711yescharacteristic
305Dic3—61no—
306Dic3—121no—
307Dic3—121no—
308C32#477411yescharacteristic
309C9—21no—
310C9C3×#48011yescharacteristic, complemented
311C23—21no—
312C23—91no—
313D4—21no—
314D4—21no—
315D4—362no—
316C2×C4—21no—
317C2×C4—91no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—362no—
323C2×C4C22×C3×D911yescharacteristic
324C8—21no—
325C8—181no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—82no—
330C2×C3—81no—
331C2×C3—81no—
332C2×C3—182no—
333C2×C3#6344511yescharacteristic
334C2×C3D8×D911yescharacteristic
335C2×C3#6347711yescharacteristic
336C2×C3C3×#88311yescharacteristic
337C2×C3C3×D3×D811yescharacteristic
338C2×C3C3×#91511yescharacteristic
339D3—62no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—92no—
344C22—181no—
345C22—181no—
346C22C3×D4×D911yescharacteristic
347C4—41no—
348C4—181no—
349C4—361no—
350C4—361no—
351C4C3×#369711yescharacteristic
352C4C3×#369911yescharacteristic
353C3—21no—
354C3#1058845411yescharacteristic, direct product factor
355C3C3×#477411yescharacteristic
356C2—81no—
357C2—182no—
358C2C3×#6344511yescharacteristic
359C2C3×D8×D911yescharacteristic
360C2C3×#6347711yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC3×#63500C2
hypercenterC3×#102D9
hypocenterC9C3×#480
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. C3×C4⋊C4×D9C2semidirect
3. C3×C9×#102C2semidirect
4. C3×#63392C2semidirect
5. C3×(C2×D9)⋊C8C2semidirect
6. C3×#63378C2semidirect
7. C3×#63366C2semidirect
9. #10588454C3direct (N × H)
29. C4⋊C4×D9C2×C3semidirect
31. C9×#102C2×C3semidirect
32. #63392C2×C3semidirect
33. (C2×D9)⋊C8C2×C3semidirect
34. #63378C2×C3semidirect
35. #63366C2×C3semidirect
99. C3×#102D9semidirect
211. #102C3×D9semidirect
213. C3×C9#480semidirect
310. C9C3×#480semidirect
354. C3#10588454direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635002
C3×C4⋊C4×D92
C3×C9×#1022
C3×#633922
C3×(C2×D9)⋊C82
C3×#633782
C3×#633662
C3×#47743
#105884543