Finite Group Databasebeta

← C3×#10588350 #13141315

Subgroups — C3×#10588350 #13141315

Order 1728.

646 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
2C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
4C2×C3×C4⋊Dic9C211yesmaximal, characteristic, complemented
5C2×C3×C4×Dic9C211yesmaximal, characteristic, complemented
6C3×C9×#95C211yesmaximal, characteristic, complemented
7C3×C9⋊#95C211yesmaximal, characteristic, complemented
8C3×#4670—31nomaximal
9#10588350C311yesmaximal, characteristic, direct product factor
10C23×C3×D9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3×C4×C9C2211yescharacteristic
14C22×C3×Dic9C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C3×(C2×D9)⋊C4—22no—
18C3×(C2×D9)⋊C4—22no—
19C3×(C2×D9)⋊C4C414yescomplemented
20C3×C4⋊Dic9—22no—
21C3×C4×Dic9—22no—
22C2×C3×(C2×D3)⋊C4—31no—
23C2×C3×(C2×D3)⋊C4—31no—
24C2×C3×(C2×D3)⋊C4—31no—
25C2×C3×C4⋊Dic3—31no—
26C2×C3×C4×Dic3—31no—
27C32×#95D311yescharacteristic
28C3×C3⋊#95—31no—
29C2×(C2×D9)⋊C4C2×C311yescharacteristic
30C2×(C2×D9)⋊C4C2×C311yescharacteristic
31C2×(C2×D9)⋊C4C2×C311yescharacteristic
32C2×C4⋊Dic9C2×C311yescharacteristic, complemented
33C2×C4×Dic9C2×C311yescharacteristic, complemented
34C9×#95—21no—
35C9×#95C2×C311yescharacteristic, complemented
36C9⋊#95C2×C311yescharacteristic, complemented
37C23×C3×C9C2311yescharacteristic
38C22×C3×D9—21no—
39C22×C3×D9—21no—
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9—21no—
43C22×C3×D9—21no—
44C22×C3×D9C2×C412yes—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9—21no—
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9—21no—
51C2×C3×C4×C9—21no—
52C2×C3×C4×C9C2×C412yes—
53C2×C3×C4×C9D412yes—
54C2×C3×Dic9—21no—
55C2×C3×Dic9—21no—
56C2×C3×Dic9—21no—
57C2×C3×Dic9—21no—
58C2×C3×Dic9—21no—
59C2×C3×Dic9—21no—
60C2×C3×Dic9—21no—
61C2×C3×Dic9C2×C412yes—
62C2×C3×Dic9D412yes—
63C3×#388—91no—
64#4670—31no—
65C23×C3×D3—31no—
66C22×C32×C4C2×D311yescharacteristic
67C22×C32×C4C2×D311yescharacteristic
68C22×C32×C4C2×D311yescharacteristic
69C22×C3×Dic3—31no—
70C22×C3×Dic3—31no—
71C22×C3×Dic3—31no—
72C23×D9C22×C311yescharacteristic
73C3×(C2×D3)⋊C4—34no—
74C3×(C2×D3)⋊C4—62no—
75C3×(C2×D3)⋊C4—62no—
76C3×C4⋊Dic3—62no—
77C3×C4×Dic3—62no—
78C22×C4×C9—21no—
79C22×C4×C9—21no—
80C22×C4×C9—21no—
81C22×C4×C9C22×C311yescharacteristic
82C22×C4×C9C22×C311yescharacteristic
83C22×C4×C9C22×C311yescharacteristic
84C22×Dic9C22×C311yescharacteristic
85C22×Dic9C22×C311yescharacteristic
86C22×Dic9C22×C311yescharacteristic
87(C2×D9)⋊C4—22no—
88(C2×D9)⋊C4—22no—
89(C2×D9)⋊C4C3×C414yescomplemented
90C4⋊Dic9—22no—
91C4×Dic9—22no—
92C22×C3×C9C22×C411yescharacteristic
93C22×C3×C9C2×D411yescharacteristic
94C22×C3×C9C2×D411yescharacteristic
95C22×C3×C9#4111yescharacteristic
96C22×C3×C9#4111yescharacteristic
97C22×C3×C9#4111yescharacteristic
98C22×C3×C9#4111yescharacteristic
99C2×C3×D9—22no—
100C2×C3×D9—22no—
101C2×C3×D9—22no—
102C2×C3×D9—41no—
103C2×C3×D9—41no—
104C2×C3×D9—41no—
105C2×C3×D9—41no—
106C3×C4×C9—22no—
107C3×C4×C9—22no—
108C3×C4×C9—41no—
109C3×Dic9—22no—
110C3×Dic9—22no—
111C3×Dic9—41no—
112C2×C3×C4⋊C4—91no—
113C2×C3×C22⋊C4—91no—
114C2×C3×C22⋊C4—91no—
115C2×C3×C22⋊C4—91no—
116C2×C3×C42—91no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—31no—
120C2×C4⋊Dic3—31no—
121C2×C4×Dic3—31no—
122C3×#95—21no—
123C3×#95—91no—
124C3×#95D911yescharacteristic, complemented
125C3×#95C3×D311yescharacteristic
126C3⋊#95—31no—
127C23×C32C22×D311yescharacteristic
128C22×C3×D3—32no—
129C22×C3×D3—61no—
130C22×C3×D3—61no—
131C22×C3×D3—61no—
132C22×C3×D3—61no—
133C22×C3×D3—61no—
134C22×C3×D3—61no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4C4×D312yes—
143C2×C32×C4D1212yes—
144C2×C3×Dic3—32no—
145C2×C3×Dic3—32no—
146C2×C3×Dic3—61no—
147C2×C3×Dic3—61no—
148C2×C3×Dic3—61no—
149C2×C3×Dic3—61no—
150C2×C3×Dic3—61no—
151C2×C3×Dic3—61no—
152C2×C3×Dic3—61no—
153C23×C9—21no—
154C23×C9C23×C311yescharacteristic
155C22×D9—21no—
156C22×D9—21no—
157C22×D9—21no—
158C22×D9—21no—
159C22×D9—21no—
160C22×D9—21no—
161C22×D9C2×C3×C412yes—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—22no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—22no—
171C2×C4×C9—22no—
172C2×C4×C9—41no—
173C2×C4×C9—41no—
174C2×C4×C9—41no—
175C2×C4×C9—41no—
176C2×C4×C9—41no—
177C2×C4×C9—41no—
178C2×C4×C9C2×C3×C412yes—
179C2×C4×C9C3×D412yes—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9C2×C3×C412yes—
188C2×Dic9C3×D412yes—
189#388—91noSylow
190C2×C3×C9#11711yescharacteristic
191C2×C3×C9C4×D411yescharacteristic
192C2×C3×C9C4×D411yescharacteristic
193C2×C3×C9#12111yescharacteristic
194C2×C3×C9#12311yescharacteristic
195C2×C3×C9#12411yescharacteristic
196C2×C3×C9#12611yescharacteristic
197C3×D9—42no—
198C24×C3—91no—
199C23×D3—31no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—91no—
204C22×C3×C4—91no—
205C22×C3×C4—91no—
206C22×C3×C4C2×D911yescharacteristic
207C22×C3×C4C2×D911yescharacteristic
208C22×C3×C4C2×D911yescharacteristic
209C22×C3×C4C2×C3×D311yescharacteristic
210C22×C3×C4C2×C3×D311yescharacteristic
211C22×C3×C4C2×C3×D311yescharacteristic
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C3×C4⋊C4—182no—
216C3×C22⋊C4—94no—
217C3×C22⋊C4—182no—
218C3×C22⋊C4—182no—
219C3×C42—182no—
220(C2×D3)⋊C4—34no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223C4⋊Dic3—62no—
224C4×Dic3—62no—
225C22×C32C2×C4×D311yescharacteristic
226C22×C32C2×D1211yescharacteristic
227C22×C32#23511yescharacteristic
228C22×C32D3×D411yescharacteristic
229C22×C32#23711yescharacteristic
230C22×C32#23711yescharacteristic
231C22×C32#23911yescharacteristic
232C2×C3×D3—62no—
233C2×C3×D3—62no—
234C2×C3×D3—62no—
235C2×C3×D3—121no—
236C2×C3×D3—121no—
237C2×C3×D3—121no—
238C2×C3×D3—121no—
239C32×C4—22no—
240C32×C4—22no—
241C32×C4—41no—
242C3×Dic3—62no—
243C3×Dic3—62no—
244C3×Dic3—121no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9—21no—
248C22×C9—21no—
249C22×C9—21no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9C22×C3×C411yescharacteristic
253C22×C9C2×C3×D411yescharacteristic
254C22×C9C2×C3×D411yescharacteristic
255C22×C9C3×#4111yescharacteristic
256C22×C9C3×#4111yescharacteristic
257C22×C9C3×#4111yescharacteristic
258C22×C9C3×#4111yescharacteristic
259C2×D9—22no—
260C2×D9—22no—
261C2×D9—22no—
262C2×D9—41no—
263C2×D9—41no—
264C2×D9—41no—
265C2×D9—41no—
266C4×C9—22no—
267C4×C9—22no—
268C4×C9—42no—
269C4×C9—42no—
270C4×C9—42no—
271C4×C9—41no—
272Dic9—22no—
273Dic9—22no—
274Dic9—41no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C42—91no—
280#95—91no—
281#95C3×D911yescharacteristic, complemented
282C3×C9#38811yescharacteristic, complemented, Sylow
283C23×C3—21no—
284C23×C3—92no—
285C23×C3—181no—
286C23×C3—181no—
287C23×C3—181no—
288C23×C3—181no—
289C23×C3—181no—
290C23×C3—181no—
291C23×C3C22×D911yescharacteristic
292C23×C3C22×C3×D311yescharacteristic
293C22×D3—32no—
294C22×D3—61no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—92no—
324C2×C3×C4—92no—
325C2×C3×C4—181no—
326C2×C3×C4—181no—
327C2×C3×C4—181no—
328C2×C3×C4—181no—
329C2×C3×C4—181no—
330C2×C3×C4—181no—
331C2×C3×C4—181no—
332C2×C3×C4C4×D912yes—
333C2×C3×C4D3612yes—
334C2×C3×C4C3×C4×D312yes—
335C2×C3×C4C3×D1212yes—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×C32C4×D1211yescharacteristic
346C2×C32#67⋊C411yescharacteristic
347C2×C32#88511yescharacteristic
348C2×C32#88611yescharacteristic
349C2×C32#89211yescharacteristic
350C2×C32#89511yescharacteristic
351C2×C32#89811yescharacteristic
352C3×D3—122no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9—21no—
356C2×C9—21no—
357C2×C9—21no—
358C2×C9—21no—
359C2×C9—21no—
360C2×C9C3×#11711yescharacteristic
361C2×C9C3×C4×D411yescharacteristic
362C2×C9C3×C4×D411yescharacteristic
363C2×C9C3×#12111yescharacteristic
364C2×C9C3×#12311yescharacteristic
365C2×C9C3×#12411yescharacteristic
366C2×C9C3×#12611yescharacteristic
367D9—42no—
368C24—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4C2×C3×D911yescharacteristic
373C22×C4C2×C3×D911yescharacteristic
374C22×C4C2×C3×D911yescharacteristic
375C4⋊C4—182no—
376C22⋊C4—94no—
377C22⋊C4—182no—
378C22⋊C4—182no—
379C42—182no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—182no—
388C22×C3—182no—
389C22×C3—182no—
390C22×C3—361no—
391C22×C3—361no—
392C22×C3—361no—
393C22×C3—361no—
394C22×C3C2×C4×D911yescharacteristic
395C22×C3C2×D3611yescharacteristic
396C22×C3#369711yescharacteristic
397C22×C3D4×D911yescharacteristic
398C22×C3#369911yescharacteristic
399C22×C3#369911yescharacteristic
400C22×C3#370111yescharacteristic
401C22×C3C2×C3×C4×D311yescharacteristic
402C22×C3C2×C3×D1211yescharacteristic
403C22×C3C3×#23511yescharacteristic
404C22×C3C3×D3×D411yescharacteristic
405C22×C3C3×#23711yescharacteristic
406C22×C3C3×#23711yescharacteristic
407C22×C3C3×#23911yescharacteristic
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—62no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—121no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—182no—
425C3×C4—182no—
426C3×C4—361no—
427Dic3—62no—
428Dic3—62no—
429Dic3—121no—
430C32#467011yescharacteristic
431C9—21no—
432C9C3×#38811yescharacteristic, complemented
433C23—92no—
434C23—181no—
435C23—181no—
436C23—181no—
437C23—181no—
438C23—181no—
439C23—181no—
440C23C22×C3×D911yescharacteristic
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—92no—
449C2×C4—92no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4C3×C4×D912yes—
458C2×C4C3×D3612yes—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—362no—
467C2×C3C4×D3611yescharacteristic
468C2×C3#611⋊C411yescharacteristic
469C2×C3#6344711yescharacteristic
470C2×C3#6344811yescharacteristic
471C2×C3#6345411yescharacteristic
472C2×C3#6345711yescharacteristic
473C2×C3#6346011yescharacteristic
474C2×C3C3×C4×D1211yescharacteristic
475C2×C3C3×#67⋊C411yescharacteristic
476C2×C3C3×#88511yescharacteristic
477C2×C3C3×#88611yescharacteristic
478C2×C3C3×#89211yescharacteristic
479C2×C3C3×#89511yescharacteristic
480C2×C3C3×#89811yescharacteristic
481D3—122no—
482C22—182no—
483C22—182no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22—361no—
488C22—361no—
489C22C2×C3×C4×D911yescharacteristic
490C22C2×C3×D3611yescharacteristic
491C22C3×#369711yescharacteristic
492C22C3×D4×D911yescharacteristic
493C22C3×#369911yescharacteristic
494C22C3×#369911yescharacteristic
495C22C3×#370111yescharacteristic
496C4—22no—
497C4—22no—
498C4—41no—
499C4—182no—
500C4—182no—
501C4—361no—
502C3—21no—
503C3#1058835011yescharacteristic, direct product factor
504C3C3×#467011yescharacteristic
505C2—362no—
506C2C3×C4×D3611yescharacteristic
507C2C3×#611⋊C411yescharacteristic
508C2C3×#6344711yescharacteristic
509C2C3×#6344811yescharacteristic
510C2C3×#6345411yescharacteristic
511C2C3×#6345711yescharacteristic
512C2C3×#6346011yescharacteristic
subgroupG/H
centerC23×C3C22×D9
commutatorC22×C9C22×C3×C4
FrattiniC23×C3C22×C3×D3
FittingC3×C9×#95C2
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
cosocleC23×C9C23×C3
hypercenterC3×#95D9
hypocenterC9C3×#388
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×C4⋊Dic9C2semidirect
5. C2×C3×C4×Dic9C2semidirect
6. C3×C9×#95C2semidirect
7. C3×C9⋊#95C2semidirect
9. #10588350C3direct (N × H)
19. C3×(C2×D9)⋊C4C4semidirect
32. C2×C4⋊Dic9C2×C3semidirect
33. C2×C4×Dic9C2×C3semidirect
35. C9×#95C2×C3semidirect
36. C9⋊#95C2×C3semidirect
89. (C2×D9)⋊C4C3×C4semidirect
124. C3×#95D9semidirect
281. #95C3×D9semidirect
282. C3×C9#388semidirect
432. C9C3×#388semidirect
503. C3#10588350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C2×D9)⋊C42
C2×C3×C4⋊Dic92
C2×C3×C4×Dic92
C3×C9×#952
C3×C9⋊#952
C3×#46703
#105883503