Finite Group Databasebeta

← C3×#10588455 #13141740

Subgroups — C3×#10588455 #13141740

Order 1728.

452 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63500C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic, complemented
3C2×C3×C8×D9C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×#63380C211yesmaximal, characteristic, complemented
7C3×#63366C211yesmaximal, characteristic, complemented
8C3×#4775—31nomaximal
9#10588455C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×#611—21no—
12C2×C3×D36—21no—
13C2×C3×D36C2211yescharacteristic
14C2×C3×C4×D9C2211yescharacteristic
15C2×C3×C8×C9C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C3×#3676—21no—
18C3×#3673—22no—
19C3×(C2×D9)⋊C4—21no—
20C3×C4⋊Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×C8×D9—22no—
23C3×#938—31no—
24C2×C3×#213—31no—
25C2×C3×D3×C8—31no—
26C3×#895—31no—
27C32×#102D311yescharacteristic
28C3×#821—31no—
29C3×#807—31no—
30#63500C2×C311yescharacteristic, complemented
31C2×#3673C2×C311yescharacteristic, complemented
32C2×C8×D9C2×C311yescharacteristic, complemented
33#63457C2×C311yescharacteristic, complemented
34C9×#102—21no—
35C9×#102C2×C311yescharacteristic, complemented
36#63380C2×C311yescharacteristic, complemented
37#63366C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×C3×D9—21no—
40C22×C3×D9D411yescharacteristic
41C3×D4×C9—21no—
42C3×D4×C9—21no—
43C2×C3×C4×C9—21no—
44C2×C3×C4×C9C2311yescharacteristic
45C3×#611—42no—
46C2×C3×Dic9—21no—
47C2×C3×Dic9D411yescharacteristic
48C3×D36—21no—
49C3×D36—21no—
50C3×D36—42no—
51C3×C4×D9—21no—
52C3×C4×D9—21no—
53C3×C8×C9—21no—
54C3×C9⋊C8D412yescomplemented
55C3×#466—91no—
56#4775—31no—
57C2×C32×D4C2×D311yescharacteristic
58C2×C3×#67—61no—
59C2×C3×D12—31no—
60C2×C3×D12—61no—
61C2×C3×C4×D3—31no—
62C2×C32×C8C2×D311yescharacteristic
63C32×C4⋊C4C2×D311yescharacteristic
64C3×#217—61no—
65C3×#213—62no—
66C3×(C2×D3)⋊C4—61no—
67C3×C4⋊Dic3—31no—
68C2×C3×C3⋊C8—31no—
69C3×D3×C8—62no—
70C2×D4×C9—21no—
71C2×D4×C9C22×C311yescharacteristic
72C2×#611—21no—
73C2×D36—21no—
74C2×D36C22×C311yescharacteristic
75C2×C4×D9C22×C311yescharacteristic
76C2×C8×C9—21no—
77C2×C8×C9C22×C311yescharacteristic
78C9×C4⋊C4—21no—
79C9×C4⋊C4C22×C311yescharacteristic
80#3676—21no—
81#3673—22no—
82(C2×D9)⋊C4—21no—
83C4⋊Dic9C22×C311yescharacteristic
84C2×C9⋊C8C22×C311yescharacteristic
85C8×D9—22no—
86C22×C3×C9—41no—
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9C2×D411yescharacteristic
90C2×C3×D9—21no—
91C2×C3×D9—21no—
92C2×C3×D9—41no—
93C2×C3×D9—41no—
94C2×C3×D9—41no—
95C2×C3×D9D812yescomplemented
96C3×C4×C9—41no—
97C3×C4×C9C2×D411yescharacteristic
98C3×C4×C9#4111yescharacteristic
99C3×Dic9—21no—
100C3×Dic9—41no—
101C2×C3×D8—91no—
102C22×C3×C8—91no—
103C3×#121—91no—
104C3×#121—91no—
105#938—31no—
106C2×#213—31no—
107C2×D3×C8—31no—
108#895—31no—
109C3×#107—91no—
110C3×#102—21no—
111C3×#102—91no—
112C3×#102D911yescharacteristic, complemented
113C3×#102C3×D311yescharacteristic
114#821—31no—
115#807—31no—
116C23×C32—21no—
117C22×C3×D3—31no—
118C22×C3×D3—61no—
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C22×D311yescharacteristic
123C3×#67—122no—
124C2×C3×Dic3—31no—
125C2×C3×Dic3—61no—
126C3×D12—61no—
127C3×D12—61no—
128C3×D12—122no—
129C3×C4×D3—61no—
130C3×C4×D3—61no—
131C23×C9—21no—
132C23×C9—41no—
133C22×D9—21no—
134C22×D9C3×D411yescharacteristic
135C32×C8—21no—
136C3×C3⋊C8—32no—
137D4×C9—22no—
138D4×C9—21no—
139D4×C9—21no—
140D4×C9—41no—
141C2×C4×C9—21no—
142C2×C4×C9—21no—
143C2×C4×C9—41no—
144C2×C4×C9C23×C311yescharacteristic
145#611—42no—
146C2×Dic9—21no—
147C2×Dic9C3×D411yescharacteristic
148D36—21no—
149D36—21no—
150D36—42no—
151C4×D9—21no—
152C4×D9—21no—
153C8×C9—21no—
154C8×C9—41no—
155C9⋊C8C3×D412yescomplemented
156#466—91noSylow
157C2×C3×C9—81no—
158C2×C3×C9#12111yescharacteristic
159C2×C3×C9C2×D811yescharacteristic
160C2×C3×C9#13511yescharacteristic
161C3×D9—22no—
162C3×D9—81no—
163C2×C3×D4—21no—
164C2×C3×D4—91no—
165C2×C3×D4—181no—
166C2×C3×D4—181no—
167C2×C3×D4C2×D911yescharacteristic
168C2×C3×D4C2×C3×D311yescharacteristic
169C22×C3×C4—91no—
170C2×#67—61no—
171C2×D12—31no—
172C2×D12—61no—
173C2×C4×D3—31no—
174C3×D8—182no—
175C2×C3×C8—21no—
176C2×C3×C8—91no—
177C2×C3×C8—182no—
178C2×C3×C8C2×D911yescharacteristic
179C2×C3×C8C2×C3×D311yescharacteristic
180C3×C4⋊C4—21no—
181C3×C4⋊C4—91no—
182C3×C4⋊C4C2×D911yescharacteristic
183C3×C4⋊C4C2×C3×D311yescharacteristic
184C3×C22⋊C4—181no—
185C3×C22⋊C4—181no—
186#217—61no—
187#213—62no—
188(C2×D3)⋊C4—61no—
189C4⋊Dic3—31no—
190C2×C3⋊C8—31no—
191D3×C8—62no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32D3×D411yescharacteristic
196C2×C3×D3—32no—
197C2×C3×D3—61no—
198C2×C3×D3—61no—
199C2×C3×D3—121no—
200C2×C3×D3—121no—
201C2×C3×D3—121no—
202C32×C4—41no—
203C32×C4#23511yescharacteristic
204C32×C4D3×D411yescharacteristic
205C3×Dic3—61no—
206C3×Dic3—121no—
207C22×C9—21no—
208C22×C9—42no—
209C22×C9—41no—
210C22×C9—41no—
211C22×C9—41no—
212C22×C9—81no—
213C22×C9—81no—
214C22×C9C2×C3×D411yescharacteristic
215C2×D9—21no—
216C2×D9—21no—
217C2×D9—41no—
218C2×D9—41no—
219C2×D9—41no—
220C2×D9C3×D812yescomplemented
221C4×C9—21no—
222C4×C9—21no—
223C4×C9—41no—
224C4×C9—81no—
225C4×C9C2×C3×D411yescharacteristic
226C4×C9C3×#4111yescharacteristic
227Dic9—21no—
228Dic9—41no—
229C2×D8—91no—
230C22×C8—91no—
231#121—91no—
232#121—91no—
233#107—91no—
234#102—91no—
235#102C3×D911yescharacteristic, complemented
236C3×C9#46611yescharacteristic, complemented, Sylow
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C23×C3—91no—
241C23×C3—181no—
242C22×D3—31no—
243C22×D3—61no—
244C3×D4—22no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—41no—
250C3×D4—181no—
251C3×D4—181no—
252C3×D4—362no—
253C3×D4—362no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—91no—
259C2×C3×C4—181no—
260C2×C3×C4—181no—
261C2×C3×C4—181no—
262C2×C3×C4C22×D911yescharacteristic
263C2×C3×C4C22×C3×D311yescharacteristic
264#67—122no—
265C2×Dic3—31no—
266C2×Dic3—61no—
267D12—61no—
268D12—61no—
269D12—122no—
270C4×D3—61no—
271C4×D3—61no—
272C3×C8—21no—
273C3×C8—21no—
274C3×C8—41no—
275C3×C8—92no—
276C3⋊C8—32no—
277C2×C32—81no—
278C2×C32#88411yescharacteristic
279C2×C32D3×D811yescharacteristic
280C2×C32#91611yescharacteristic
281C3×D3—62no—
282C3×D3—241no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—21no—
286C2×C9—82no—
287C2×C9—81no—
288C2×C9C3×#12111yescharacteristic
289C2×C9C2×C3×D811yescharacteristic
290C2×C9C3×#13511yescharacteristic
291D9—22no—
292D9—81no—
293C2×D4—91no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4C2×C3×D911yescharacteristic
297C22×C4—91no—
298D8—182no—
299C2×C8—91no—
300C2×C8—182no—
301C2×C8C2×C3×D911yescharacteristic
302C4⋊C4—91no—
303C4⋊C4C2×C3×D911yescharacteristic
304C22⋊C4—181no—
305C22⋊C4—181no—
306C22×C3—21no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3—92no—
317C22×C3—181no—
318C22×C3—181no—
319C22×C3—361no—
320C22×C3—361no—
321C22×C3—361no—
322C22×C3D4×D911yescharacteristic
323C22×C3C3×D3×D411yescharacteristic
324C2×D3—32no—
325C2×D3—61no—
326C2×D3—61no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—121no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—81no—
335C3×C4—181no—
336C3×C4—361no—
337C3×C4#369711yescharacteristic
338C3×C4D4×D911yescharacteristic
339C3×C4C3×#23511yescharacteristic
340C3×C4C3×D3×D411yescharacteristic
341Dic3—61no—
342Dic3—121no—
343C32#477511yescharacteristic
344C9—21no—
345C9C3×#46611yescharacteristic, complemented
346C23—21no—
347C23—91no—
348C23—181no—
349D4—21no—
350D4—21no—
351D4—181no—
352D4—181no—
353D4—362no—
354D4—362no—
355C2×C4—21no—
356C2×C4—91no—
357C2×C4—181no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4C22×C3×D911yescharacteristic
361C8—21no—
362C8—92no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—82no—
367C2×C3—81no—
368C2×C3—81no—
369C2×C3—182no—
370C2×C3—721no—
371C2×C3#6344611yescharacteristic
372C2×C3D8×D911yescharacteristic
373C2×C3#6347811yescharacteristic
374C2×C3C3×#88411yescharacteristic
375C2×C3C3×D3×D811yescharacteristic
376C2×C3C3×#91611yescharacteristic
377D3—62no—
378D3—241no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—92no—
383C22—181no—
384C22—181no—
385C22—361no—
386C22—361no—
387C22—361no—
388C22C3×D4×D911yescharacteristic
389C4—41no—
390C4—181no—
391C4—361no—
392C4C3×#369711yescharacteristic
393C4C3×D4×D911yescharacteristic
394C3—21no—
395C3#1058845511yescharacteristic, direct product factor
396C3C3×#477511yescharacteristic
397C2—81no—
398C2—182no—
399C2—721no—
400C2C3×#6344611yescharacteristic
401C2C3×D8×D911yescharacteristic
402C2C3×#6347811yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
hypercenterC3×#102D9
hypocenterC9C3×#466
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
1. C3×#63500C2semidirect
2. C2×C3×#3673C2semidirect
3. C2×C3×C8×D9C2semidirect
4. C3×#63457C2semidirect
5. C3×C9×#102C2semidirect
6. C3×#63380C2semidirect
7. C3×#63366C2semidirect
9. #10588455C3direct (N × H)
30. #63500C2×C3semidirect
31. C2×#3673C2×C3semidirect
32. C2×C8×D9C2×C3semidirect
33. #63457C2×C3semidirect
35. C9×#102C2×C3semidirect
36. #63380C2×C3semidirect
37. #63366C2×C3semidirect
54. C3×C9⋊C8D4semidirect
95. C2×C3×D9D8semidirect
112. C3×#102D9semidirect
155. C9⋊C8C3×D4semidirect
220. C2×D9C3×D8semidirect
235. #102C3×D9semidirect
236. C3×C9#466semidirect
345. C9C3×#466semidirect
395. C3#10588455direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635002
C2×C3×#36732
C2×C3×C8×D92
C3×#634572
C3×C9×#1022
C3×#633802
C3×#633662
C3×#47753
#105884553