Finite Group Databasebeta

← C3×#10588355 #13141319

Subgroups — C3×#10588355 #13141319

Order 1728.

586 conjugacy classes of subgroups.

The subgroup lattice has 508 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×Dic9⋊C4C211yesmaximal, characteristic, complemented
5C3×C9×#95C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7C3×C9⋊#95C211yesmaximal, characteristic, complemented
8C3×#4675—31nomaximal
9#10588355C311yesmaximal, 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)⋊C4—22no—
20C3×Dic9⋊C4—22no—
21C2×C3×(C2×D3)⋊C4—31no—
22C2×C3×(C2×D3)⋊C4—31no—
23C2×C3×(C2×D3)⋊C4—31no—
24C2×C3×Dic3⋊C4—31no—
25C32×#95D311yescharacteristic
26C3×C3⋊#95—31no—
27C3×C3⋊#95—31no—
28C2×(C2×D9)⋊C4C2×C311yescharacteristic
29C2×(C2×D9)⋊C4C2×C311yescharacteristic
30C2×(C2×D9)⋊C4C2×C311yescharacteristic
31C2×Dic9⋊C4C2×C311yescharacteristic, complemented
32C9×#95—21no—
33C9×#95C2×C311yescharacteristic, complemented
34C9⋊#95C2×C311yescharacteristic, complemented
35C9⋊#95C2×C311yescharacteristic, complemented
36C23×C3×C9C2311yescharacteristic
37C22×C3×D9—21no—
38C22×C3×D9—21no—
39C22×C3×D9—21no—
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9—21no—
43C22×C3×D9D412yes—
44C2×C3×C4×C9—21no—
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×C9—21no—
53C2×C3×Dic9—21no—
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×Dic9D412yes—
62C3×#397—91no—
63#4675—31no—
64C23×C3×D3—31no—
65C22×C32×C4C2×D311yescharacteristic
66C22×C32×C4C2×D311yescharacteristic
67C22×C32×C4C2×D311yescharacteristic
68C22×C3×Dic3—31no—
69C22×C3×Dic3—31no—
70C22×C3×Dic3—31no—
71C23×D9C22×C311yescharacteristic
72C3×(C2×D3)⋊C4—62no—
73C3×(C2×D3)⋊C4—62no—
74C3×(C2×D3)⋊C4—62no—
75C3×Dic3⋊C4—62no—
76C22×C4×C9—21no—
77C22×C4×C9—21no—
78C22×C4×C9—21no—
79C22×C4×C9C22×C311yescharacteristic
80C22×C4×C9C22×C311yescharacteristic
81C22×C4×C9C22×C311yescharacteristic
82C22×Dic9C22×C311yescharacteristic
83C22×Dic9C22×C311yescharacteristic
84C22×Dic9C22×C311yescharacteristic
85(C2×D9)⋊C4—22no—
86(C2×D9)⋊C4—22no—
87(C2×D9)⋊C4—22no—
88Dic9⋊C4—22no—
89C22×C3×C9C2×D411yescharacteristic
90C22×C3×C9C2×D411yescharacteristic
91C22×C3×C9#4111yescharacteristic
92C22×C3×C9#4111yescharacteristic
93C22×C3×C9#4111yescharacteristic
94C22×C3×C9#4111yescharacteristic
95C22×C3×C9#4111yescharacteristic
96C2×C3×D9—22no—
97C2×C3×D9—22no—
98C2×C3×D9—22no—
99C2×C3×D9—41no—
100C2×C3×D9—41no—
101C2×C3×D9—41no—
102C2×C3×D9—41no—
103C3×C4×C9—41no—
104C3×C4×C9—41no—
105C3×C4×C9—41no—
106C3×Dic9—22no—
107C3×Dic9—41no—
108C3×Dic9—41no—
109C2×C3×C4⋊C4—91no—
110C2×C3×C22⋊C4—91no—
111C2×C3×C22⋊C4—91no—
112C2×C3×C22⋊C4—91no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C3×#95—21no—
118C3×#95—91no—
119C3×#95—91no—
120C3×#95D911yescharacteristic, complemented
121C3×#95C3×D311yescharacteristic
122C3⋊#95—31no—
123C3⋊#95—31no—
124C23×C32C22×D311yescharacteristic
125C22×C3×D3—32no—
126C22×C3×D3—61no—
127C22×C3×D3—61no—
128C22×C3×D3—61no—
129C22×C3×D3—61no—
130C22×C3×D3—61no—
131C22×C3×D3—61no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
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×C3×Dic3—32no—
142C2×C3×Dic3—61no—
143C2×C3×Dic3—61no—
144C2×C3×Dic3—61no—
145C2×C3×Dic3—61no—
146C2×C3×Dic3—61no—
147C2×C3×Dic3—61no—
148C2×C3×Dic3—61no—
149C2×C3×Dic3—61no—
150C23×C9—21no—
151C23×C9C23×C311yescharacteristic
152C22×D9—21no—
153C22×D9—21no—
154C22×D9—21no—
155C22×D9—21no—
156C22×D9—21no—
157C22×D9—21no—
158C22×D9C3×D412yes—
159C2×C4×C9—22no—
160C2×C4×C9—22no—
161C2×C4×C9—22no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—41no—
172C2×C4×C9—41no—
173C2×C4×C9—41no—
174C2×C4×C9—41no—
175C2×C4×C9—41no—
176C2×C4×C9—41no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9C3×D412yes—
186#397—91noSylow
187C2×C3×C9#12111yescharacteristic
188C2×C3×C9#12311yescharacteristic
189C2×C3×C9#12311yescharacteristic
190C2×C3×C9#12311yescharacteristic
191C2×C3×C9#12411yescharacteristic
192C2×C3×C9#12611yescharacteristic
193C2×C3×C9#12611yescharacteristic
194C3×D9—42no—
195C24×C3—91no—
196C23×D3—31no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—91no—
201C22×C3×C4—91no—
202C22×C3×C4—91no—
203C22×C3×C4C2×D911yescharacteristic
204C22×C3×C4C2×D911yescharacteristic
205C22×C3×C4C2×D911yescharacteristic
206C22×C3×C4C2×C3×D311yescharacteristic
207C22×C3×C4C2×C3×D311yescharacteristic
208C22×C3×C4C2×C3×D311yescharacteristic
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C3×C4⋊C4—182no—
213C3×C22⋊C4—182no—
214C3×C22⋊C4—182no—
215C3×C22⋊C4—182no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219Dic3⋊C4—62no—
220C22×C32#23511yescharacteristic
221C22×C32#23511yescharacteristic
222C22×C32#23511yescharacteristic
223C22×C32D3×D411yescharacteristic
224C22×C32D3×D411yescharacteristic
225C22×C32#23711yescharacteristic
226C22×C32#23911yescharacteristic
227C2×C3×D3—62no—
228C2×C3×D3—62no—
229C2×C3×D3—62no—
230C2×C3×D3—121no—
231C2×C3×D3—121no—
232C2×C3×D3—121no—
233C2×C3×D3—121no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4—41no—
237C3×Dic3—62no—
238C3×Dic3—121no—
239C3×Dic3—121no—
240C22×C9—21no—
241C22×C9—21no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—21no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9C2×C3×D411yescharacteristic
248C22×C9C2×C3×D411yescharacteristic
249C22×C9C3×#4111yescharacteristic
250C22×C9C3×#4111yescharacteristic
251C22×C9C3×#4111yescharacteristic
252C22×C9C3×#4111yescharacteristic
253C22×C9C3×#4111yescharacteristic
254C2×D9—22no—
255C2×D9—22no—
256C2×D9—22no—
257C2×D9—41no—
258C2×D9—41no—
259C2×D9—41no—
260C2×D9—41no—
261C4×C9—42no—
262C4×C9—42no—
263C4×C9—42no—
264C4×C9—41no—
265C4×C9—41no—
266C4×C9—41no—
267Dic9—22no—
268Dic9—41no—
269Dic9—41no—
270C2×C4⋊C4—91no—
271C2×C22⋊C4—91no—
272C2×C22⋊C4—91no—
273C2×C22⋊C4—91no—
274#95—91no—
275#95—91no—
276#95C3×D911yescharacteristic, complemented
277C3×C9#39711yescharacteristic, complemented, Sylow
278C23×C3—21no—
279C23×C3—92no—
280C23×C3—181no—
281C23×C3—181no—
282C23×C3—181no—
283C23×C3—181no—
284C23×C3—181no—
285C23×C3—181no—
286C23×C3C22×D911yescharacteristic
287C23×C3C22×C3×D311yescharacteristic
288C22×D3—32no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—61no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
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—21no—
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—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—92no—
323C2×C3×C4—181no—
324C2×C3×C4—181no—
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×Dic3—32no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×C32#87611yescharacteristic
341C2×C32#88311yescharacteristic
342C2×C32#88411yescharacteristic
343C2×C32#88511yescharacteristic
344C2×C32#89411yescharacteristic
345C2×C32#89411yescharacteristic
346C2×C32#89811yescharacteristic
347C3×D3—122no—
348C2×C9—21no—
349C2×C9—21no—
350C2×C9—21no—
351C2×C9—21no—
352C2×C9—21no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9C3×#12111yescharacteristic
356C2×C9C3×#12311yescharacteristic
357C2×C9C3×#12311yescharacteristic
358C2×C9C3×#12311yescharacteristic
359C2×C9C3×#12411yescharacteristic
360C2×C9C3×#12611yescharacteristic
361C2×C9C3×#12611yescharacteristic
362D9—42no—
363C24—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4C2×C3×D911yescharacteristic
368C22×C4C2×C3×D911yescharacteristic
369C22×C4C2×C3×D911yescharacteristic
370C4⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C22⋊C4—182no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—182no—
382C22×C3—182no—
383C22×C3—182no—
384C22×C3—361no—
385C22×C3—361no—
386C22×C3—361no—
387C22×C3—361no—
388C22×C3#369711yescharacteristic
389C22×C3#369711yescharacteristic
390C22×C3#369711yescharacteristic
391C22×C3D4×D911yescharacteristic
392C22×C3D4×D911yescharacteristic
393C22×C3#369911yescharacteristic
394C22×C3#370111yescharacteristic
395C22×C3C3×#23511yescharacteristic
396C22×C3C3×#23511yescharacteristic
397C22×C3C3×#23511yescharacteristic
398C22×C3C3×D3×D411yescharacteristic
399C22×C3C3×D3×D411yescharacteristic
400C22×C3C3×#23711yescharacteristic
401C22×C3C3×#23911yescharacteristic
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—182no—
419C3×C4—361no—
420C3×C4—361no—
421Dic3—62no—
422Dic3—121no—
423Dic3—121no—
424C32#467511yescharacteristic
425C9—21no—
426C9C3×#39711yescharacteristic, complemented
427C23—92no—
428C23—181no—
429C23—181no—
430C23—181no—
431C23—181no—
432C23—181no—
433C23—181no—
434C23C22×C3×D911yescharacteristic
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—92no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—362no—
461C2×C3#6343811yescharacteristic
462C2×C3#6344511yescharacteristic
463C2×C3#6344611yescharacteristic
464C2×C3#6344711yescharacteristic
465C2×C3#6345611yescharacteristic
466C2×C3#6345611yescharacteristic
467C2×C3#6346011yescharacteristic
468C2×C3C3×#87611yescharacteristic
469C2×C3C3×#88311yescharacteristic
470C2×C3C3×#88411yescharacteristic
471C2×C3C3×#88511yescharacteristic
472C2×C3C3×#89411yescharacteristic
473C2×C3C3×#89411yescharacteristic
474C2×C3C3×#89811yescharacteristic
475D3—122no—
476C22—182no—
477C22—182no—
478C22—182no—
479C22—361no—
480C22—361no—
481C22—361no—
482C22—361no—
483C22C3×#369711yescharacteristic
484C22C3×#369711yescharacteristic
485C22C3×#369711yescharacteristic
486C22C3×D4×D911yescharacteristic
487C22C3×D4×D911yescharacteristic
488C22C3×#369911yescharacteristic
489C22C3×#370111yescharacteristic
490C4—41no—
491C4—41no—
492C4—41no—
493C4—182no—
494C4—361no—
495C4—361no—
496C3—21no—
497C3#1058835511yescharacteristic, direct product factor
498C3C3×#467511yescharacteristic
499C2—362no—
500C2C3×#6343811yescharacteristic
501C2C3×#6344511yescharacteristic
502C2C3×#6344611yescharacteristic
503C2C3×#6344711yescharacteristic
504C2C3×#6345611yescharacteristic
505C2C3×#6345611yescharacteristic
506C2C3×#6346011yescharacteristic
subgroupG/H
centerC23×C3C22×D9
commutator, cosocleC23×C9C23×C3
FrattiniC23×C3C22×C3×D3
FittingC3×C9×#95C2
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
hypercenterC3×#95D9
hypocenterC9C3×#397
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×Dic9⋊C4C2semidirect
5. C3×C9×#95C2semidirect
6. C3×C9⋊#95C2semidirect
7. C3×C9⋊#95C2semidirect
9. #10588355C3direct (N × H)
31. C2×Dic9⋊C4C2×C3semidirect
33. C9×#95C2×C3semidirect
34. C9⋊#95C2×C3semidirect
35. C9⋊#95C2×C3semidirect
120. C3×#95D9semidirect
276. #95C3×D9semidirect
277. C3×C9#397semidirect
426. C9C3×#397semidirect
497. C3#10588355direct (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×Dic9⋊C42
C3×C9×#952
C3×C9⋊#952
C3×#46753
#105883553