Finite Group Databasebeta

← C3×#10588453 #13141738

Subgroups — C3×#10588453 #13141738

Order 1728.

644 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D9C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic, complemented
3C2×C3×D72C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic, complemented
8C3×#4773—31nomaximal
9#10588453C311yesmaximal, characteristic, direct product factor
10C23×C3×D9—21no—
11C2×C3×D4×C9C2211yescharacteristic
12C2×C3×#611—21no—
13C3×D4×D9—22no—
14C3×D4×D9—22no—
15C2×C3×D36—21no—
16C2×C3×D36C2211yescharacteristic
17C2×C3×D36C2211yescharacteristic, complemented
18C2×C3×C4×D9C2211yescharacteristic
19C2×C3×C8×C9C2211yescharacteristic, complemented
20C3×C9×C4⋊C4C2211yescharacteristic, complemented
21C3×#3673—22no—
22C3×(C2×D9)⋊C4—21no—
23C2×C3×C9⋊C8C2211yescharacteristic, complemented
24C3×D72—22no—
25C2×C3×D3×D4—31no—
26C2×C3×#213—31no—
27C2×C3×D24—31no—
28C3×#895—31no—
29C2×D4×D9C2×C311yescharacteristic, complemented
30C32×#102D311yescharacteristic
31C3×(C2×D3)⋊C8—31no—
32C3×#809—31no—
33C2×#3673C2×C311yescharacteristic, complemented
34C2×D72C2×C311yescharacteristic, complemented
35#63457C2×C311yescharacteristic, complemented
36C9×#102—21no—
37C9×#102C2×C311yescharacteristic, complemented
38(C2×D9)⋊C8C2×C311yescharacteristic, complemented
39#63369C2×C311yescharacteristic, complemented
40C23×C3×C9—21no—
41C22×C3×D9—24no—
42C22×C3×D9—21no—
43C22×C3×D9—21no—
44C22×C3×D9—42no—
45C22×C3×D9—42no—
46C22×C3×D9D411yescharacteristic
47C3×D4×C9—21no—
48C3×D4×C9D412yescomplemented
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9C2311yescharacteristic
51C3×#611—24no—
52C2×C3×Dic9D411yescharacteristic
53C3×D36—21no—
54C3×D36—21no—
55C3×D36—21no—
56C3×D36—42no—
57C3×D36D412yescomplemented
58C3×C4×D9—21no—
59C3×C4×D9—21no—
60C3×C8×C9—21no—
61C3×C9⋊C8—21no—
62C3×#447—91no—
63#4773—31no—
64C23×C3×D3—61no—
65C2×C32×D4C2×D311yescharacteristic
66C2×C3×#67—61no—
67C3×D3×D4—62no—
68C3×D3×D4—62no—
69C2×C3×D12—31no—
70C2×C3×D12—31no—
71C2×C3×D12—61no—
72C2×C3×C4×D3—31no—
73C23×D9—21no—
74C2×C32×C8C2×D311yescharacteristic
75C32×C4⋊C4C2×D311yescharacteristic
76C3×#213—62no—
77C3×(C2×D3)⋊C4—61no—
78C2×C3×C3⋊C8—31no—
79C3×D24—62no—
80C2×D4×C9—21no—
81C2×D4×C9C22×C311yescharacteristic
82C2×#611—21no—
83D4×D9—22no—
84D4×D9—22no—
85C2×D36—21no—
86C2×D36C22×C311yescharacteristic
87C2×D36C22×C311yescharacteristic, complemented
88C2×C4×D9C22×C311yescharacteristic
89C2×C8×C9—21no—
90C2×C8×C9C22×C311yescharacteristic, complemented
91C9×C4⋊C4—21no—
92C9×C4⋊C4C22×C311yescharacteristic, complemented
93#3673—22no—
94(C2×D9)⋊C4—21no—
95C2×C9⋊C8C22×C311yescharacteristic, complemented
96D72—22no—
97C22×C3×C9—22no—
98C22×C3×C9—41no—
99C22×C3×C9—41no—
100C22×C3×C9C2×D411yescharacteristic
101C2×C3×D9—21no—
102C2×C3×D9—21no—
103C2×C3×D9—22no—
104C2×C3×D9—48no—
105C2×C3×D9—41no—
106C2×C3×D9—41no—
107C2×C3×D9—41no—
108C2×C3×D9—41no—
109C2×C3×D9—41no—
110C2×C3×D9D812yescomplemented
111C3×C4×C9—41no—
112C3×C4×C9C2×D411yescharacteristic
113C3×C4×C9C2×D411yescharacteristic
114C3×Dic9—21no—
115C22×C3×D4—91no—
116C2×D3×D4—31no—
117C2×C3×D8—91no—
118C2×C3×D8—91no—
119C3×#121—91no—
120C2×#213—31no—
121C2×D24—31no—
122#895—31no—
123C3×#102—21no—
124C3×#102—91no—
125C3×#102D911yescharacteristic, complemented
126C3×#102C3×D311yescharacteristic
127C3×C22⋊C8—91no—
128(C2×D3)⋊C8—31no—
129#809—31no—
130C23×C32—21no—
131C22×C3×D3—31no—
132C22×C3×D3—64no—
133C22×C3×D3—61no—
134C22×C3×D3—61no—
135C22×C3×D3—122no—
136C22×C3×D3—122no—
137C32×D4—21no—
138C32×D4D1212yes—
139C2×C32×C4—21no—
140C2×C32×C4C22×D311yescharacteristic
141C3×#67—64no—
142C2×C3×Dic3—31no—
143C3×D12—32no—
144C3×D12—61no—
145C3×D12—61no—
146C3×D12—61no—
147C3×D12—122no—
148C3×C4×D3—61no—
149C3×C4×D3—61no—
150C23×C9—21no—
151C23×C9—41no—
152C22×D9—24no—
153C22×D9—21no—
154C22×D9—21no—
155C22×D9—42no—
156C22×D9—42no—
157C22×D9C3×D411yescharacteristic
158C32×C8—21no—
159C3×C3⋊C8—61no—
160D4×C9—21no—
161D4×C9—22no—
162D4×C9—41no—
163D4×C9C3×D412yescomplemented
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—41no—
167C2×C4×C9C23×C311yescharacteristic
168#611—24no—
169C2×Dic9C3×D411yescharacteristic
170D36—21no—
171D36—21no—
172D36—21no—
173D36—42no—
174D36C3×D412yescomplemented
175C4×D9—21no—
176C4×D9—21no—
177C8×C9—21no—
178C8×C9—41no—
179C9⋊C8—21no—
180#447—91noSylow
181C2×C3×C9—42no—
182C2×C3×C9#12011yescharacteristic
183C2×C3×C9C2×D811yescharacteristic
184C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
185C3×D9—22no—
186C3×D9—42no—
187C3×D9—81no—
188C24×C3—181no—
189C23×D3—61no—
190C2×C3×D4—21no—
191C2×C3×D4—91no—
192C2×C3×D4—91no—
193C2×C3×D4—181no—
194C2×C3×D4—181no—
195C2×C3×D4—182no—
196C2×C3×D4—182no—
197C2×C3×D4C2×D911yescharacteristic
198C2×C3×D4C2×C3×D311yescharacteristic
199C22×C3×C4—91no—
200C2×#67—61no—
201D3×D4—62no—
202D3×D4—62no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—61no—
206C2×C4×D3—31no—
207C3×D8—182no—
208C3×D8—182no—
209C2×C3×C8—21no—
210C2×C3×C8—91no—
211C2×C3×C8C2×D911yescharacteristic, complemented
212C2×C3×C8C2×C3×D311yescharacteristic
213C3×C4⋊C4—21no—
214C3×C4⋊C4C2×D911yescharacteristic, complemented
215C3×C4⋊C4C2×C3×D311yescharacteristic
216C3×C22⋊C4—181no—
217#213—62no—
218(C2×D3)⋊C4—61no—
219C2×C3⋊C8—31no—
220D24—62no—
221C22×C32—22no—
222C22×C32—41no—
223C22×C32—41no—
224C22×C32D3×D411yescharacteristic
225C2×C3×D3—32no—
226C2×C3×D3—61no—
227C2×C3×D3—61no—
228C2×C3×D3—62no—
229C2×C3×D3—128no—
230C2×C3×D3—121no—
231C2×C3×D3—121no—
232C2×C3×D3—121no—
233C2×C3×D3—121no—
234C2×C3×D3—121no—
235C32×C4—41no—
236C32×C4C2×D1211yescharacteristic
237C32×C4D3×D411yescharacteristic
238C3×Dic3—61no—
239C22×C9—22no—
240C22×C9—21no—
241C22×C9—42no—
242C22×C9—41no—
243C22×C9—41no—
244C22×C9—81no—
245C22×C9—81no—
246C22×C9C2×C3×D411yescharacteristic
247C2×D9—21no—
248C2×D9—21no—
249C2×D9—22no—
250C2×D9—48no—
251C2×D9—41no—
252C2×D9—41no—
253C2×D9—41no—
254C2×D9—41no—
255C2×D9—41no—
256C2×D9C3×D812yescomplemented
257C4×C9—21no—
258C4×C9—21no—
259C4×C9—41no—
260C4×C9—81no—
261C4×C9C2×C3×D411yescharacteristic
262C4×C9C2×C3×D411yescharacteristic
263Dic9—21no—
264C22×D4—91no—
265C2×D8—91no—
266C2×D8—91no—
267#121—91no—
268#102—91no—
269#102C3×D911yescharacteristic, complemented
270C22⋊C8—91no—
271C3×C9#44711yescharacteristic, complemented, Sylow
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—41no—
275C23×C3—91no—
276C23×C3—184no—
277C23×C3—181no—
278C23×C3—181no—
279C23×C3—362no—
280C23×C3—362no—
281C22×D3—31no—
282C22×D3—64no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—122no—
286C22×D3—122no—
287C3×D4—21no—
288C3×D4—21no—
289C3×D4—22no—
290C3×D4—41no—
291C3×D4—92no—
292C3×D4—184no—
293C3×D4—181no—
294C3×D4—181no—
295C3×D4—181no—
296C3×D4—362no—
297C3×D4D3612yescomplemented
298C3×D4C3×D1212yes—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—91no—
304C2×C3×C4—181no—
305C2×C3×C4—181no—
306C2×C3×C4C22×D911yescharacteristic
307C2×C3×C4C22×C3×D311yescharacteristic
308#67—64no—
309C2×Dic3—31no—
310D12—32no—
311D12—61no—
312D12—61no—
313D12—61no—
314D12—122no—
315C4×D3—61no—
316C4×D3—61no—
317C3×C8—21no—
318C3×C8—21no—
319C3×C8—41no—
320C3×C8—181no—
321C3⋊C8—61no—
322C2×C32—42no—
323C2×C32#88211yescharacteristic
324C2×C32D3×D811yescharacteristic
325C2×C32#91411yescharacteristic
326C3×D3—62no—
327C3×D3—122no—
328C3×D3—241no—
329C2×C9—21no—
330C2×C9—21no—
331C2×C9—21no—
332C2×C9—42no—
333C2×C9—82no—
334C2×C9C3×#12011yescharacteristic
335C2×C9C2×C3×D811yescharacteristic
336C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
337D9—22no—
338D9—42no—
339D9—81no—
340C24—181no—
341C2×D4—91no—
342C2×D4—91no—
343C2×D4—181no—
344C2×D4—181no—
345C2×D4—182no—
346C2×D4—182no—
347C2×D4C2×C3×D911yescharacteristic
348C22×C4—91no—
349D8—182no—
350D8—182no—
351C2×C8—91no—
352C2×C8C2×C3×D911yescharacteristic, complemented
353C4⋊C4C2×C3×D911yescharacteristic, complemented
354C22⋊C4—181no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—42no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—92no—
366C22×C3—181no—
367C22×C3—181no—
368C22×C3—182no—
369C22×C3—368no—
370C22×C3—361no—
371C22×C3—361no—
372C22×C3—361no—
373C22×C3—361no—
374C22×C3—361no—
375C22×C3D4×D911yescharacteristic
376C22×C3C3×D3×D411yescharacteristic
377C2×D3—32no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—62no—
381C2×D3—128no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—81no—
392C3×C4—181no—
393C3×C4C2×D3611yescharacteristic
394C3×C4D4×D911yescharacteristic
395C3×C4C2×C3×D1211yescharacteristic
396C3×C4C3×D3×D411yescharacteristic
397Dic3—61no—
398C32#477311yescharacteristic
399C9—21no—
400C9C3×#44711yescharacteristic, complemented
401C23—21no—
402C23—91no—
403C23—184no—
404C23—181no—
405C23—181no—
406C23—362no—
407C23—362no—
408D4—21no—
409D4—92no—
410D4—184no—
411D4—181no—
412D4—181no—
413D4—181no—
414D4—362no—
415D4C3×D3612yescomplemented
416C2×C4—21no—
417C2×C4—91no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4C22×C3×D911yescharacteristic
421C8—21no—
422C8—181no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—42no—
427C2×C3—42no—
428C2×C3—82no—
429C2×C3—182no—
430C2×C3—362no—
431C2×C3—721no—
432C2×C3#6344411yescharacteristic
433C2×C3D8×D911yescharacteristic
434C2×C3#6347611yescharacteristic
435C2×C3C3×#88211yescharacteristic
436C2×C3C3×D3×D811yescharacteristic
437C2×C3C3×#91411yescharacteristic
438D3—62no—
439D3—122no—
440D3—241no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—92no—
445C22—181no—
446C22—181no—
447C22—182no—
448C22—368no—
449C22—361no—
450C22—361no—
451C22—361no—
452C22—361no—
453C22—361no—
454C22C3×D4×D911yescharacteristic
455C4—41no—
456C4—181no—
457C4C2×C3×D3611yescharacteristic
458C4C3×D4×D911yescharacteristic
459C3—21no—
460C3#1058845311yescharacteristic, direct product factor
461C3C3×#477311yescharacteristic
462C2—42no—
463C2—182no—
464C2—362no—
465C2—721no—
466C2C3×#6344411yescharacteristic
467C2C3×D8×D911yescharacteristic
468C2C3×#6347611yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
hypercenterC3×#102D9
hypocenterC9C3×#447
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. C2×C3×D4×D9C2semidirect
2. C2×C3×#3673C2semidirect
3. C2×C3×D72C2semidirect
4. C3×#63457C2semidirect
5. C3×C9×#102C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63369C2semidirect
9. #10588453C3direct (N × H)
17. C2×C3×D36C22semidirect
19. C2×C3×C8×C9C22semidirect
20. C3×C9×C4⋊C4C22semidirect
23. C2×C3×C9⋊C8C22semidirect
29. C2×D4×D9C2×C3semidirect
33. C2×#3673C2×C3semidirect
34. C2×D72C2×C3semidirect
35. #63457C2×C3semidirect
37. C9×#102C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63369C2×C3semidirect
48. C3×D4×C9D4semidirect
57. C3×D36D4semidirect
87. C2×D36C22×C3semidirect
90. C2×C8×C9C22×C3semidirect
92. C9×C4⋊C4C22×C3semidirect
95. C2×C9⋊C8C22×C3semidirect
110. C2×C3×D9D8semidirect
125. C3×#102D9semidirect
163. D4×C9C3×D4semidirect
174. D36C3×D4semidirect
211. C2×C3×C8C2×D9semidirect
214. C3×C4⋊C4C2×D9semidirect
256. C2×D9C3×D8semidirect
269. #102C3×D9semidirect
271. C3×C9#447semidirect
297. C3×D4D36semidirect
352. C2×C8C2×C3×D9semidirect
353. C4⋊C4C2×C3×D9semidirect
400. C9C3×#447semidirect
415. D4C3×D36semidirect
460. C3#10588453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C2×C3×#36732
C2×C3×D722
C3×#634572
C3×C9×#1022
C3×(C2×D9)⋊C82
C3×#633692
C3×#47733
#105884533