Finite Group Databasebeta

← C3×#10588669 #13142588

Subgroups — C3×#10588669 #13142588

Order 1728.

794 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D9C211yesmaximal, characteristic
2C2×C3×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
5C2×C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7C3×C9⋊#95C211yesmaximal, characteristic, complemented
8C3×#4989—31nomaximal
9#10588669C311yesmaximal, 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
17C2×C3×C4×D9—22no—
18C2×C3×C4×D9—22no—
19C2×C3×C4×D9—22no—
20C3×C9×C4⋊C4—22no—
21C3×(C2×D9)⋊C4—22no—
22C3×(C2×D9)⋊C4C414yescomplemented
23C3×Dic9⋊C4—22no—
24C22×C3×C4×D3—31no—
25C2×C32×C4⋊C4D311yescharacteristic
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×(C2×D3)⋊C4—31no—
28C2×C3×Dic3⋊C4—31no—
29C22×C4×D9C2×C311yescharacteristic
30C3×C3⋊#95—31no—
31C3×C3⋊#95—31no—
32C2×C9×C4⋊C4—21no—
33C2×C9×C4⋊C4C2×C311yescharacteristic, complemented
34C2×(C2×D9)⋊C4C2×C311yescharacteristic
35C2×(C2×D9)⋊C4C2×C311yescharacteristic
36C2×Dic9⋊C4C2×C311yescharacteristic, complemented
37C9⋊#95C2×C311yescharacteristic, complemented
38C9⋊#95C2×C311yescharacteristic, complemented
39C23×C3×C9C2311yescharacteristic
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9—21no—
43C22×C3×D9—21no—
44C22×C3×D9C2×C412yes—
45C22×C3×D9D412yes—
46C22×C3×D9Q812yes—
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×C4×C9—21no—
54C2×C3×C4×C9C2×C412yescomplemented
55C2×C3×C4×C9D412yes—
56C2×C3×Dic9—21no—
57C2×C3×Dic9—21no—
58C2×C3×Dic9—21no—
59C2×C3×Dic9—21no—
60C2×C3×Dic9—21no—
61C2×C3×Dic9—21no—
62C2×C3×Dic9—21no—
63C2×C3×Dic9C2×C412yescomplemented
64C2×C3×Dic9D412yes—
65C3×C4×D9—28no—
66C3×#385—91no—
67#4989—31no—
68C23×C3×D3—31no—
69C22×C32×C4C2×D311yescharacteristic
70C22×C32×C4C2×D311yescharacteristic
71C22×C32×C4C2×D311yescharacteristic
72C22×C3×Dic3—31no—
73C22×C3×Dic3—31no—
74C22×C3×Dic3—31no—
75C2×C3×C4×D3—62no—
76C2×C3×C4×D3—62no—
77C2×C3×C4×D3—62no—
78C23×D9C22×C311yescharacteristic
79C32×C4⋊C4—22no—
80C3×(C2×D3)⋊C4—34no—
81C3×(C2×D3)⋊C4—62no—
82C3×Dic3⋊C4—62no—
83C22×C4×C9—21no—
84C22×C4×C9—21no—
85C22×C4×C9—21no—
86C22×C4×C9C22×C311yescharacteristic
87C22×C4×C9C22×C311yescharacteristic
88C22×C4×C9C22×C311yescharacteristic
89C22×Dic9C22×C311yescharacteristic
90C22×Dic9C22×C311yescharacteristic
91C22×Dic9C22×C311yescharacteristic
92C2×C4×D9—22no—
93C2×C4×D9—22no—
94C2×C4×D9—22no—
95C9×C4⋊C4—24no—
96C9×C4⋊C4—22no—
97(C2×D9)⋊C4—22no—
98(C2×D9)⋊C4C3×C414yescomplemented
99Dic9⋊C4—22no—
100C22×C3×C9C22×C411yescharacteristic
101C22×C3×C9C2×D411yescharacteristic
102C22×C3×C9C2×D411yescharacteristic
103C22×C3×C9C2×D411yescharacteristic
104C22×C3×C9C2×Q811yescharacteristic
105C22×C3×C9#4111yescharacteristic
106C22×C3×C9#4111yescharacteristic
107C2×C3×D9—22no—
108C2×C3×D9—22no—
109C2×C3×D9—22no—
110C2×C3×D9—22no—
111C2×C3×D9—22no—
112C2×C3×D9—22no—
113C2×C3×D9C4⋊C414yescomplemented
114C3×C4×C9—22no—
115C3×C4×C9—22no—
116C3×C4×C9—41no—
117C3×Dic9—22no—
118C3×Dic9—22no—
119C3×Dic9—41no—
120C23×C3×C4—91no—
121C22×C4×D3—31no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—91no—
124C2×C3×C4⋊C4D911yescharacteristic, complemented
125C2×C3×C4⋊C4C3×D311yescharacteristic
126C2×C3×C22⋊C4—91no—
127C2×C3×C22⋊C4—91no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C3×#95—91no—
132C3×#95—91no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C23×C32C22×D311yescharacteristic
136C22×C3×D3—32no—
137C22×C3×D3—32no—
138C22×C3×D3—32no—
139C22×C3×D3—61no—
140C22×C3×D3—61no—
141C22×C3×D3—61no—
142C22×C3×D3—61no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C4×D312yes—
151C2×C32×C4#6712yes—
152C2×C3×Dic3—32no—
153C2×C3×Dic3—32no—
154C2×C3×Dic3—61no—
155C2×C3×Dic3—61no—
156C2×C3×Dic3—61no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3—61no—
159C2×C3×Dic3—61no—
160C2×C3×Dic3—61no—
161C3×C4×D3—68no—
162C23×C9—21no—
163C23×C9C23×C311yescharacteristic
164C22×D9—21no—
165C22×D9—21no—
166C22×D9—21no—
167C22×D9—21no—
168C22×D9C2×C3×C412yes—
169C22×D9C3×D412yes—
170C22×D9C3×Q812yes—
171C2×C4×C9—22no—
172C2×C4×C9—22no—
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—22no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—22no—
182C2×C4×C9—22no—
183C2×C4×C9—41no—
184C2×C4×C9—41no—
185C2×C4×C9—41no—
186C2×C4×C9—41no—
187C2×C4×C9C2×C3×C412yescomplemented
188C2×C4×C9C3×D412yes—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9C2×C3×C412yescomplemented
197C2×Dic9C3×D412yes—
198C4×D9—28no—
199#385—91noSylow
200C2×C3×C9C2×C4⋊C411yescharacteristic
201C2×C3×C9C4×D411yescharacteristic
202C2×C3×C9C4×D411yescharacteristic
203C2×C3×C9#12011yescharacteristic
204C2×C3×C9C22⋊Q811yescharacteristic
205C2×C3×C9C22⋊Q811yescharacteristic
206C2×C3×C9#12311yescharacteristic
207C3×D9—24no—
208C24×C3—91no—
209C23×D3—31no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—91no—
214C22×C3×C4—91no—
215C22×C3×C4—91no—
216C22×C3×C4—182no—
217C22×C3×C4—182no—
218C22×C3×C4—182no—
219C22×C3×C4C2×D911yescharacteristic
220C22×C3×C4C2×D911yescharacteristic
221C22×C3×C4C2×D911yescharacteristic
222C22×C3×C4C2×C3×D311yescharacteristic
223C22×C3×C4C2×C3×D311yescharacteristic
224C22×C3×C4C2×C3×D311yescharacteristic
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C3×C4⋊C4—24no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—182no—
235C3×C22⋊C4—94no—
236C3×C22⋊C4—182no—
237(C2×D3)⋊C4—34no—
238(C2×D3)⋊C4—62no—
239Dic3⋊C4—62no—
240C22×C32C2×C4×D311yescharacteristic
241C22×C32#23511yescharacteristic
242C22×C32D3×D411yescharacteristic
243C22×C32D3×D411yescharacteristic
244C22×C32D3×Q811yescharacteristic
245C22×C32#23911yescharacteristic
246C22×C32C2×#6711yescharacteristic
247C2×C3×D3—34no—
248C2×C3×D3—62no—
249C2×C3×D3—62no—
250C2×C3×D3—62no—
251C2×C3×D3—62no—
252C2×C3×D3—62no—
253C2×C3×D3—62no—
254C32×C4—22no—
255C32×C4—22no—
256C32×C4—41no—
257C3×Dic3—62no—
258C3×Dic3—62no—
259C3×Dic3—121no—
260C22×C9—21no—
261C22×C9—21no—
262C22×C9—21no—
263C22×C9—21no—
264C22×C9—21no—
265C22×C9—21no—
266C22×C9—21no—
267C22×C9C22×C3×C411yescharacteristic
268C22×C9C2×C3×D411yescharacteristic
269C22×C9C2×C3×D411yescharacteristic
270C22×C9C2×C3×D411yescharacteristic
271C22×C9C2×C3×Q811yescharacteristic
272C22×C9C3×#4111yescharacteristic
273C22×C9C3×#4111yescharacteristic
274C2×D9—22no—
275C2×D9—22no—
276C2×D9—22no—
277C2×D9—22no—
278C2×D9—22no—
279C2×D9—22no—
280C2×D9C3×C4⋊C414yescomplemented
281C4×C9—24no—
282C4×C9—22no—
283C4×C9—22no—
284C4×C9—42no—
285C4×C9—42no—
286C4×C9—41no—
287Dic9—22no—
288Dic9—22no—
289Dic9—41no—
290C23×C4—91no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4C3×D911yescharacteristic, complemented
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295#95—91no—
296#95—91no—
297C3×C9#38511yescharacteristic, complemented, Sylow
298C23×C3—21no—
299C23×C3—92no—
300C23×C3—92no—
301C23×C3—92no—
302C23×C3—181no—
303C23×C3—181no—
304C23×C3—181no—
305C23×C3—181no—
306C23×C3C22×D911yescharacteristic
307C23×C3C22×C3×D311yescharacteristic
308C22×D3—32no—
309C22×D3—32no—
310C22×D3—32no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—61no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
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—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—92no—
339C2×C3×C4—92no—
340C2×C3×C4—188no—
341C2×C3×C4—181no—
342C2×C3×C4—181no—
343C2×C3×C4—181no—
344C2×C3×C4—181no—
345C2×C3×C4—181no—
346C2×C3×C4—181no—
347C2×C3×C4—181no—
348C2×C3×C4C4×D912yescomplemented
349C2×C3×C4#61112yes—
350C2×C3×C4C3×C4×D312yes—
351C2×C3×C4C3×#6712yes—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C4×D3—68no—
362C2×C32D3×C4⋊C411yescharacteristic
363C2×C32#89311yescharacteristic
364C2×C32#89411yescharacteristic
365C2×C32#89611yescharacteristic
366C2×C32C4×#6711yescharacteristic
367C2×C32#93711yescharacteristic
368C2×C32#94611yescharacteristic
369C3×D3—64no—
370C2×C9—21no—
371C2×C9—21no—
372C2×C9—21no—
373C2×C9—21no—
374C2×C9—21no—
375C2×C9—21no—
376C2×C9—21no—
377C2×C9C2×C3×C4⋊C411yescharacteristic
378C2×C9C3×C4×D411yescharacteristic
379C2×C9C3×C4×D411yescharacteristic
380C2×C9C3×#12011yescharacteristic
381C2×C9C3×C22⋊Q811yescharacteristic
382C2×C9C3×C22⋊Q811yescharacteristic
383C2×C9C3×#12311yescharacteristic
384D9—24no—
385C24—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—182no—
390C22×C4—182no—
391C22×C4—182no—
392C22×C4C2×C3×D911yescharacteristic
393C22×C4C2×C3×D911yescharacteristic
394C22×C4C2×C3×D911yescharacteristic
395C4⋊C4—22no—
396C4⋊C4—182no—
397C22⋊C4—94no—
398C22⋊C4—182no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—94no—
407C22×C3—182no—
408C22×C3—182no—
409C22×C3—182no—
410C22×C3—182no—
411C22×C3—182no—
412C22×C3—182no—
413C22×C3C2×C4×D911yescharacteristic
414C22×C3#369711yescharacteristic
415C22×C3D4×D911yescharacteristic
416C22×C3D4×D911yescharacteristic
417C22×C3Q8×D911yescharacteristic
418C22×C3#370111yescharacteristic
419C22×C3C2×#61111yescharacteristic
420C22×C3C2×C3×C4×D311yescharacteristic
421C22×C3C3×#23511yescharacteristic
422C22×C3C3×D3×D411yescharacteristic
423C22×C3C3×D3×D411yescharacteristic
424C22×C3C3×D3×Q811yescharacteristic
425C22×C3C3×#23911yescharacteristic
426C22×C3C2×C3×#6711yescharacteristic
427C2×D3—34no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C3×C4—24no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—182no—
444C3×C4—182no—
445C3×C4—361no—
446Dic3—62no—
447Dic3—62no—
448Dic3—121no—
449C32#498911yescharacteristic
450C9—21no—
451C9C3×#38511yescharacteristic, complemented
452C23—92no—
453C23—92no—
454C23—92no—
455C23—181no—
456C23—181no—
457C23—181no—
458C23—181no—
459C23C22×C3×D911yescharacteristic
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—188no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4C3×C4×D912yescomplemented
478C2×C4C3×#61112yes—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—184no—
487C2×C3C4⋊C4×D911yescharacteristic
488C2×C3#6345511yescharacteristic
489C2×C3#6345611yescharacteristic
490C2×C3#6345811yescharacteristic
491C2×C3C4×#61111yescharacteristic
492C2×C3#6349911yescharacteristic
493C2×C3#6350811yescharacteristic
494C2×C3C3×D3×C4⋊C411yescharacteristic
495C2×C3C3×#89311yescharacteristic
496C2×C3C3×#89411yescharacteristic
497C2×C3C3×#89611yescharacteristic
498C2×C3C3×C4×#6711yescharacteristic
499C2×C3C3×#93711yescharacteristic
500C2×C3C3×#94611yescharacteristic
501D3—64no—
502C22—94no—
503C22—182no—
504C22—182no—
505C22—182no—
506C22—182no—
507C22—182no—
508C22—182no—
509C22C2×C3×C4×D911yescharacteristic
510C22C3×#369711yescharacteristic
511C22C3×D4×D911yescharacteristic
512C22C3×D4×D911yescharacteristic
513C22C3×Q8×D911yescharacteristic
514C22C3×#370111yescharacteristic
515C22C2×C3×#61111yescharacteristic
516C4—22no—
517C4—22no—
518C4—41no—
519C4—182no—
520C4—182no—
521C4—361no—
522C3—21no—
523C3#1058866911yescharacteristic, direct product factor
524C3C3×#498911yescharacteristic
525C2—184no—
526C2C3×C4⋊C4×D911yescharacteristic
527C2C3×#6345511yescharacteristic
528C2C3×#6345611yescharacteristic
529C2C3×#6345811yescharacteristic
530C2C3×C4×#61111yescharacteristic
531C2C3×#6349911yescharacteristic
532C2C3×#6350811yescharacteristic
subgroupG/H
centerC23×C3C22×D9
commutatorC22×C9C22×C3×C4
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C4⋊C4C2
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
cosocleC23×C9C23×C3
hypercenterC2×C3×C4⋊C4D9
hypocenterC9C3×#385
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C9×C4⋊C4C2semidirect
5. C2×C3×Dic9⋊C4C2semidirect
6. C3×C9⋊#95C2semidirect
7. C3×C9⋊#95C2semidirect
9. #10588669C3direct (N × H)
22. C3×(C2×D9)⋊C4C4semidirect
33. C2×C9×C4⋊C4C2×C3semidirect
36. C2×Dic9⋊C4C2×C3semidirect
37. C9⋊#95C2×C3semidirect
38. C9⋊#95C2×C3semidirect
54. C2×C3×C4×C9C2×C4semidirect
63. C2×C3×Dic9C2×C4semidirect
98. (C2×D9)⋊C4C3×C4semidirect
113. C2×C3×D9C4⋊C4semidirect
124. C2×C3×C4⋊C4D9semidirect
187. C2×C4×C9C2×C3×C4semidirect
196. C2×Dic9C2×C3×C4semidirect
280. C2×D9C3×C4⋊C4semidirect
292. C2×C4⋊C4C3×D9semidirect
297. C3×C9#385semidirect
348. C2×C3×C4C4×D9semidirect
451. C9C3×#385semidirect
477. C2×C4C3×C4×D9semidirect
523. C3#10588669direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D92
C2×C3×C9×C4⋊C42
C2×C3×(C2×D9)⋊C42
C2×C3×Dic9⋊C42
C3×C9⋊#952
C3×#49893
#105886693