Finite Group Databasebeta

← C3×#10588632 #13142457

Subgroups — C3×#10588632 #13142457

Order 1728.

642 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C22⋊C4C211yesmaximal, characteristic
2C2×C3×#3676C211yesmaximal, characteristic
3C2×C3×#3676C211yesmaximal, characteristic
4C2×C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
5C3×C9⋊#95C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7C3×C9⋊#95C211yesmaximal, characteristic, complemented
8C3×#4952—31nomaximal
9#10588632C311yesmaximal, characteristic, direct product factor
10C24×C3×C9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3×Dic9C2211yescharacteristic
14C22×C3×Dic9C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C3×C9×C22⋊C4—22no—
18C3×#3676—22no—
19C3×#3676—22no—
20C3×Dic9⋊C4—22no—
21C2×C32×C22⋊C4D311yescharacteristic
22C2×C3×#217—31no—
23C2×C3×#217—31no—
24C2×C3×Dic3⋊C4—31no—
25C3×C3⋊#95—31no—
26C3×C3⋊#95—31no—
27C3×C3⋊#95—31no—
28C2×C9×C22⋊C4—21no—
29C2×C9×C22⋊C4C2×C311yescharacteristic
30C2×#3676C2×C311yescharacteristic
31C2×#3676C2×C311yescharacteristic
32C2×Dic9⋊C4C2×C311yescharacteristic, complemented
33C9⋊#95C2×C311yescharacteristic, complemented
34C9⋊#95C2×C311yescharacteristic, complemented
35C9⋊#95C2×C311yescharacteristic, complemented
36C23×C3×C9—21no—
37C23×C3×C9—21no—
38C23×C3×C9—21no—
39C23×C3×C9—21no—
40C23×C3×C9—21no—
41C23×C3×C9—21no—
42C23×C3×C9D412yes—
43C23×C3×C9C2311yescharacteristic
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×Dic9—21no—
51C2×C3×Dic9—21no—
52C2×C3×Dic9—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#4952—31no—
64C24×C32C2×D311yescharacteristic
65C22×C32×C4C2×D311yescharacteristic
66C22×C32×C4C2×D311yescharacteristic
67C22×C3×Dic3—31no—
68C22×C3×Dic3—31no—
69C22×C3×Dic3—31no—
70C22×C3×Dic3—31no—
71C24×C9—21no—
72C24×C9C22×C311yescharacteristic
73C32×C22⋊C4—22no—
74C3×#217—62no—
75C3×#217—62no—
76C3×Dic3⋊C4—62no—
77C22×C4×C9—21no—
78C22×C4×C9—21no—
79C22×C4×C9C22×C311yescharacteristic
80C22×C4×C9C22×C311yescharacteristic
81C22×Dic9C22×C311yescharacteristic
82C22×Dic9C22×C311yescharacteristic
83C22×Dic9C22×C311yescharacteristic
84C22×Dic9C22×C311yescharacteristic
85C9×C22⋊C4—24no—
86C9×C22⋊C4—22no—
87#3676—22no—
88#3676—22no—
89Dic9⋊C4—22no—
90C22×C3×C9—22no—
91C22×C3×C9—22no—
92C22×C3×C9—22no—
93C22×C3×C9—41no—
94C22×C3×C9—41no—
95C22×C3×C9—41no—
96C22×C3×C9—41no—
97C22×C3×C9C2×D411yescharacteristic
98C22×C3×C9C2×D411yescharacteristic
99C22×C3×C9#4111yescharacteristic
100C22×C3×C9#4111yescharacteristic
101C22×C3×C9#4111yescharacteristic
102C22×C3×C9#4111yescharacteristic
103C22×C3×C9#4111yescharacteristic
104C3×C4×C9—41no—
105C3×C4×C9—41no—
106C3×Dic9—22no—
107C3×Dic9—41no—
108C3×Dic9—41no—
109C3×Dic9—41no—
110C2×C3×C4⋊C4—91no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—91no—
113C2×C3×C22⋊C4—91no—
114C2×C3×C22⋊C4D911yescharacteristic
115C2×C3×C22⋊C4C3×D311yescharacteristic
116C2×#217—31no—
117C2×#217—31no—
118C2×Dic3⋊C4—31no—
119C3×#95—91no—
120C3×#95—91no—
121C3×#95—91no—
122C3⋊#95—31no—
123C3⋊#95—31no—
124C3⋊#95—31no—
125C23×C32—21no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32#6712yes—
132C23×C32C22×D311yescharacteristic
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×C3×Dic3—32no—
140C2×C3×Dic3—61no—
141C2×C3×Dic3—61no—
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—
150C2×C3×Dic3—61no—
151C23×C9—22no—
152C23×C9—22no—
153C23×C9—21no—
154C23×C9—21no—
155C23×C9—21no—
156C23×C9—21no—
157C23×C9—21no—
158C23×C9—21no—
159C23×C9—22no—
160C23×C9—21no—
161C23×C9—41no—
162C23×C9—41no—
163C23×C9—41no—
164C23×C9—41no—
165C23×C9C3×D412yes—
166C23×C9C23×C311yescharacteristic
167C2×C4×C9—22no—
168C2×C4×C9—22no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—41no—
176C2×C4×C9—41no—
177C2×C4×C9—41no—
178C2×C4×C9—41no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9C3×D412yes—
191#397—91noSylow
192C2×C3×C9—42no—
193C2×C3×C9#12111yescharacteristic
194C2×C3×C9#12311yescharacteristic
195C2×C3×C9#12311yescharacteristic
196C2×C3×C9#12311yescharacteristic
197C2×C3×C9#12411yescharacteristic
198C2×C3×C9#12611yescharacteristic
199C2×C3×C9#12611yescharacteristic
200C24×C3—21no—
201C24×C3C2×D911yescharacteristic
202C24×C3C2×C3×D311yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—91no—
206C22×C3×C4—91no—
207C22×C3×C4—91no—
208C22×C3×C4—91no—
209C22×C3×C4C2×D911yescharacteristic
210C22×C3×C4C2×D911yescharacteristic
211C22×C3×C4C2×C3×D311yescharacteristic
212C22×C3×C4C2×C3×D311yescharacteristic
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C3×C4⋊C4—182no—
218C3×C22⋊C4—24no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C22⋊C4—182no—
222C3×C22⋊C4—182no—
223#217—62no—
224#217—62no—
225Dic3⋊C4—62no—
226C22×C32—22no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32#23511yescharacteristic
234C22×C32#23511yescharacteristic
235C22×C32D3×D411yescharacteristic
236C22×C32#23711yescharacteristic
237C22×C32#23711yescharacteristic
238C22×C32#23711yescharacteristic
239C22×C32C2×#6711yescharacteristic
240C32×C4—41no—
241C32×C4—41no—
242C3×Dic3—62no—
243C3×Dic3—121no—
244C3×Dic3—121no—
245C3×Dic3—121no—
246C22×C9—24no—
247C22×C9—22no—
248C22×C9—22no—
249C22×C9—22no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9—21no—
253C22×C9—21no—
254C22×C9—21no—
255C22×C9—21no—
256C22×C9—21no—
257C22×C9—42no—
258C22×C9—42no—
259C22×C9—42no—
260C22×C9—42no—
261C22×C9—42no—
262C22×C9—42no—
263C22×C9—41no—
264C22×C9—41no—
265C22×C9—41no—
266C22×C9—41no—
267C22×C9C2×C3×D411yescharacteristic
268C22×C9C2×C3×D411yescharacteristic
269C22×C9C3×#4111yescharacteristic
270C22×C9C3×#4111yescharacteristic
271C22×C9C3×#4111yescharacteristic
272C22×C9C3×#4111yescharacteristic
273C22×C9C3×#4111yescharacteristic
274C4×C9—42no—
275C4×C9—42no—
276C4×C9—41no—
277C4×C9—41no—
278Dic9—22no—
279Dic9—41no—
280Dic9—41no—
281Dic9—41no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—91no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4C3×D911yescharacteristic
286#95—91no—
287#95—91no—
288#95—91no—
289C3×C9#39711yescharacteristic, complemented, Sylow
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3#61112yes—
311C23×C3C22×D911yescharacteristic
312C23×C3C3×#6712yes—
313C23×C3C22×C3×D311yescharacteristic
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—92no—
333C2×C3×C4—181no—
334C2×C3×C4—181no—
335C2×C3×C4—181no—
336C2×C3×C4—181no—
337C2×C3×C4—181no—
338C2×C3×C4—181no—
339C2×C3×C4—181no—
340C2×C3×C4—181no—
341C2×C3×C4—181no—
342C2×C3×C4—181no—
343C2×C3×C4—181no—
344C2×Dic3—32no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×C32—42no—
357C2×C32#87911yescharacteristic
358C2×C32#87911yescharacteristic
359C2×C32#88311yescharacteristic
360C2×C32#88511yescharacteristic
361C2×C32#92911yescharacteristic
362C2×C32#93511yescharacteristic
363C2×C32#93911yescharacteristic
364C2×C9—21no—
365C2×C9—21no—
366C2×C9—21no—
367C2×C9—21no—
368C2×C9—21no—
369C2×C9—21no—
370C2×C9—21no—
371C2×C9—44no—
372C2×C9—42no—
373C2×C9C3×#12111yescharacteristic
374C2×C9C3×#12311yescharacteristic
375C2×C9C3×#12311yescharacteristic
376C2×C9C3×#12311yescharacteristic
377C2×C9C3×#12411yescharacteristic
378C2×C9C3×#12611yescharacteristic
379C2×C9C3×#12611yescharacteristic
380C24C2×C3×D911yescharacteristic
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4C2×C3×D911yescharacteristic
386C22×C4C2×C3×D911yescharacteristic
387C4⋊C4—182no—
388C22⋊C4—22no—
389C22⋊C4—182no—
390C22⋊C4—182no—
391C22×C3—24no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3#369711yescharacteristic
420C22×C3#369711yescharacteristic
421C22×C3D4×D911yescharacteristic
422C22×C3#369911yescharacteristic
423C22×C3#369911yescharacteristic
424C22×C3#369911yescharacteristic
425C22×C3C2×#61111yescharacteristic
426C22×C3C3×#23511yescharacteristic
427C22×C3C3×#23511yescharacteristic
428C22×C3C3×D3×D411yescharacteristic
429C22×C3C3×#23711yescharacteristic
430C22×C3C3×#23711yescharacteristic
431C22×C3C3×#23711yescharacteristic
432C22×C3C2×C3×#6711yescharacteristic
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—182no—
440C3×C4—361no—
441C3×C4—361no—
442C3×C4—361no—
443Dic3—62no—
444Dic3—121no—
445Dic3—121no—
446Dic3—121no—
447C32#495211yescharacteristic
448C9—21no—
449C9C3×#39711yescharacteristic, complemented
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23C3×#61112yes—
457C23C22×C3×D911yescharacteristic
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—92no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—44no—
484C2×C3—42no—
485C2×C3—42no—
486C2×C3#6344111yescharacteristic
487C2×C3#6344111yescharacteristic
488C2×C3#6344511yescharacteristic
489C2×C3#6344711yescharacteristic
490C2×C3#6349111yescharacteristic
491C2×C3#6349711yescharacteristic
492C2×C3#6350111yescharacteristic
493C2×C3C3×#87911yescharacteristic
494C2×C3C3×#87911yescharacteristic
495C2×C3C3×#88311yescharacteristic
496C2×C3C3×#88511yescharacteristic
497C2×C3C3×#92911yescharacteristic
498C2×C3C3×#93511yescharacteristic
499C2×C3C3×#93911yescharacteristic
500C22—22no—
501C22—22no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22C3×#369711yescharacteristic
508C22C3×#369711yescharacteristic
509C22C3×D4×D911yescharacteristic
510C22C3×#369911yescharacteristic
511C22C3×#369911yescharacteristic
512C22C3×#369911yescharacteristic
513C22C2×C3×#61111yescharacteristic
514C4—41no—
515C4—41no—
516C4—182no—
517C4—361no—
518C4—361no—
519C4—361no—
520C3—21no—
521C3#1058863211yescharacteristic, direct product factor
522C3C3×#495211yescharacteristic
523C2—42no—
524C2C3×#6344111yescharacteristic
525C2C3×#6344111yescharacteristic
526C2C3×#6344511yescharacteristic
527C2C3×#6344711yescharacteristic
528C2C3×#6349111yescharacteristic
529C2C3×#6349711yescharacteristic
530C2C3×#6350111yescharacteristic
subgroupG/H
centerC23×C3C22×D9
commutator, cosocleC23×C9C23×C3
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C22⋊C4C2
socleC23×C32C22×D3
prime radicalC24×C32C2×D3
hypercenterC2×C3×C22⋊C4D9
hypocenterC9C3×#397
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

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. #10588632C3direct (N × H)
32. C2×Dic9⋊C4C2×C3semidirect
33. C9⋊#95C2×C3semidirect
34. C9⋊#95C2×C3semidirect
35. C9⋊#95C2×C3semidirect
289. C3×C9#397semidirect
449. C9C3×#397semidirect
521. C3#10588632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×C22⋊C42
C2×C3×#36762
C2×C3×Dic9⋊C42
C3×C9⋊#952
C3×#49523
#105886323