Finite Group Databasebeta

← C3×#10588348 #13141313

Subgroups — C3×#10588348 #13141313

Order 1728.

778 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
1C22×C3×C4×D9C211yesmaximal, characteristic
2C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
4C2×C3×C4⋊Dic9C211yesmaximal, characteristic, complemented
5C2×C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
6C3×C9×#95C211yesmaximal, characteristic, complemented
7C3×C9⋊#95C211yesmaximal, characteristic, complemented
8C3×#4668—31nomaximal
9#10588348C311yesmaximal, 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×(C2×D9)⋊C4—22no—
21C3×(C2×D9)⋊C4C414yescomplemented
22C3×C4⋊Dic9—22no—
23C3×Dic9⋊C4—22no—
24C22×C3×C4×D3—31no—
25C2×C3×(C2×D3)⋊C4—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×C4⋊Dic3—31no—
28C2×C3×Dic3⋊C4—31no—
29C22×C4×D9C2×C311yescharacteristic
30C32×#95D311yescharacteristic
31C3×C3⋊#95—31no—
32C2×(C2×D9)⋊C4C2×C311yescharacteristic
33C2×(C2×D9)⋊C4C2×C311yescharacteristic
34C2×C4⋊Dic9C2×C311yescharacteristic, complemented
35C2×Dic9⋊C4C2×C311yescharacteristic, complemented
36C9×#95—21no—
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#4668—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
79C3×(C2×D3)⋊C4—34no—
80C3×(C2×D3)⋊C4—62no—
81C3×C4⋊Dic3—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—
95(C2×D9)⋊C4—22no—
96(C2×D9)⋊C4C3×C414yescomplemented
97C4⋊Dic9—22no—
98Dic9⋊C4—22no—
99C22×C3×C9C22×C411yescharacteristic
100C22×C3×C9C2×D411yescharacteristic
101C22×C3×C9C2×D411yescharacteristic
102C22×C3×C9C2×D411yescharacteristic
103C22×C3×C9C2×Q811yescharacteristic
104C22×C3×C9#4111yescharacteristic
105C22×C3×C9#4111yescharacteristic
106C2×C3×D9—22no—
107C2×C3×D9—22no—
108C2×C3×D9—22no—
109C2×C3×D9—22no—
110C2×C3×D9—22no—
111C2×C3×D9—22no—
112C2×C3×D9C4⋊C414yescomplemented
113C3×C4×C9—22no—
114C3×C4×C9—22no—
115C3×C4×C9—41no—
116C3×Dic9—22no—
117C3×Dic9—22no—
118C3×Dic9—41no—
119C23×C3×C4—91no—
120C22×C4×D3—31no—
121C2×C3×C4⋊C4—91no—
122C2×C3×C4⋊C4—91no—
123C2×C3×C22⋊C4—91no—
124C2×C3×C22⋊C4—91no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×C4⋊Dic3—31no—
128C2×Dic3⋊C4—31no—
129C3×#95—21no—
130C3×#95—91no—
131C3×#95D911yescharacteristic, complemented
132C3×#95C3×D311yescharacteristic
133C3⋊#95—31no—
134C23×C32C22×D311yescharacteristic
135C22×C3×D3—32no—
136C22×C3×D3—32no—
137C22×C3×D3—32no—
138C22×C3×D3—61no—
139C22×C3×D3—61no—
140C22×C3×D3—61no—
141C22×C3×D3—61no—
142C2×C32×C4—21no—
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×C4C4×D312yes—
150C2×C32×C4D1212yes—
151C2×C3×Dic3—32no—
152C2×C3×Dic3—32no—
153C2×C3×Dic3—61no—
154C2×C3×Dic3—61no—
155C2×C3×Dic3—61no—
156C2×C3×Dic3—61no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3—61no—
159C2×C3×Dic3—61no—
160C3×C4×D3—68no—
161C23×C9—21no—
162C23×C9C23×C311yescharacteristic
163C22×D9—21no—
164C22×D9—21no—
165C22×D9—21no—
166C22×D9—21no—
167C22×D9C2×C3×C412yes—
168C22×D9C3×D412yes—
169C22×D9C3×Q812yes—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—22no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—22no—
179C2×C4×C9—22no—
180C2×C4×C9—41no—
181C2×C4×C9—41no—
182C2×C4×C9—41no—
183C2×C4×C9—41no—
184C2×C4×C9—41no—
185C2×C4×C9—41no—
186C2×C4×C9C2×C3×C412yescomplemented
187C2×C4×C9C3×D412yes—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9C2×C3×C412yescomplemented
196C2×Dic9C3×D412yes—
197C4×D9—28no—
198#385—91noSylow
199C2×C3×C9C2×C4⋊C411yescharacteristic
200C2×C3×C9C4×D411yescharacteristic
201C2×C3×C9C4×D411yescharacteristic
202C2×C3×C9#12011yescharacteristic
203C2×C3×C9C22⋊Q811yescharacteristic
204C2×C3×C9C22⋊Q811yescharacteristic
205C2×C3×C9#12311yescharacteristic
206C3×D9—24no—
207C24×C3—91no—
208C23×D3—31no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—91no—
213C22×C3×C4—91no—
214C22×C3×C4—91no—
215C22×C3×C4—182no—
216C22×C3×C4—182no—
217C22×C3×C4—182no—
218C22×C3×C4C2×D911yescharacteristic
219C22×C3×C4C2×D911yescharacteristic
220C22×C3×C4C2×D911yescharacteristic
221C22×C3×C4C2×C3×D311yescharacteristic
222C22×C3×C4C2×C3×D311yescharacteristic
223C22×C3×C4C2×C3×D311yescharacteristic
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C3×C4⋊C4—182no—
231C3×C4⋊C4—182no—
232C3×C22⋊C4—94no—
233C3×C22⋊C4—182no—
234(C2×D3)⋊C4—34no—
235(C2×D3)⋊C4—62no—
236C4⋊Dic3—62no—
237Dic3⋊C4—62no—
238C22×C32C2×C4×D311yescharacteristic
239C22×C32C2×D1211yescharacteristic
240C22×C32#23511yescharacteristic
241C22×C32D3×D411yescharacteristic
242C22×C32D3×D411yescharacteristic
243C22×C32#23711yescharacteristic
244C22×C32D3×Q811yescharacteristic
245C2×C3×D3—34no—
246C2×C3×D3—62no—
247C2×C3×D3—62no—
248C2×C3×D3—62no—
249C2×C3×D3—62no—
250C2×C3×D3—62no—
251C2×C3×D3—62no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4—41no—
255C3×Dic3—62no—
256C3×Dic3—62no—
257C3×Dic3—121no—
258C22×C9—21no—
259C22×C9—21no—
260C22×C9—21no—
261C22×C9—21no—
262C22×C9—21no—
263C22×C9—21no—
264C22×C9—21no—
265C22×C9C22×C3×C411yescharacteristic
266C22×C9C2×C3×D411yescharacteristic
267C22×C9C2×C3×D411yescharacteristic
268C22×C9C2×C3×D411yescharacteristic
269C22×C9C2×C3×Q811yescharacteristic
270C22×C9C3×#4111yescharacteristic
271C22×C9C3×#4111yescharacteristic
272C2×D9—22no—
273C2×D9—22no—
274C2×D9—22no—
275C2×D9—22no—
276C2×D9—22no—
277C2×D9—22no—
278C2×D9C3×C4⋊C414yescomplemented
279C4×C9—22no—
280C4×C9—22no—
281C4×C9—42no—
282C4×C9—42no—
283C4×C9—42no—
284C4×C9—41no—
285Dic9—22no—
286Dic9—22no—
287Dic9—41no—
288C23×C4—91no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293#95—91no—
294#95C3×D911yescharacteristic, complemented
295C3×C9#38511yescharacteristic, complemented, Sylow
296C23×C3—21no—
297C23×C3—92no—
298C23×C3—92no—
299C23×C3—92no—
300C23×C3—181no—
301C23×C3—181no—
302C23×C3—181no—
303C23×C3—181no—
304C23×C3C22×D911yescharacteristic
305C23×C3C22×C3×D311yescharacteristic
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—61no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—61no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
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—22no—
329C2×C3×C4—22no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—92no—
337C2×C3×C4—92no—
338C2×C3×C4—188no—
339C2×C3×C4—181no—
340C2×C3×C4—181no—
341C2×C3×C4—181no—
342C2×C3×C4—181no—
343C2×C3×C4—181no—
344C2×C3×C4—181no—
345C2×C3×C4—181no—
346C2×C3×C4C4×D912yescomplemented
347C2×C3×C4D3612yes—
348C2×C3×C4C3×C4×D312yes—
349C2×C3×C4C3×D1212yes—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C4×D3—68no—
360C2×C32C4×D1211yescharacteristic
361C2×C32#67⋊C411yescharacteristic
362C2×C32#88211yescharacteristic
363C2×C32#88311yescharacteristic
364C2×C32D3×C4⋊C411yescharacteristic
365C2×C32#89611yescharacteristic
366C2×C32#89711yescharacteristic
367C3×D3—64no—
368C2×C9—21no—
369C2×C9—21no—
370C2×C9—21no—
371C2×C9—21no—
372C2×C9—21no—
373C2×C9—21no—
374C2×C9—21no—
375C2×C9C2×C3×C4⋊C411yescharacteristic
376C2×C9C3×C4×D411yescharacteristic
377C2×C9C3×C4×D411yescharacteristic
378C2×C9C3×#12011yescharacteristic
379C2×C9C3×C22⋊Q811yescharacteristic
380C2×C9C3×C22⋊Q811yescharacteristic
381C2×C9C3×#12311yescharacteristic
382D9—24no—
383C24—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4—182no—
390C22×C4C2×C3×D911yescharacteristic
391C22×C4C2×C3×D911yescharacteristic
392C22×C4C2×C3×D911yescharacteristic
393C4⋊C4—182no—
394C4⋊C4—182no—
395C22⋊C4—94no—
396C22⋊C4—182no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—94no—
405C22×C3—182no—
406C22×C3—182no—
407C22×C3—182no—
408C22×C3—182no—
409C22×C3—182no—
410C22×C3—182no—
411C22×C3C2×C4×D911yescharacteristic
412C22×C3C2×D3611yescharacteristic
413C22×C3#369711yescharacteristic
414C22×C3D4×D911yescharacteristic
415C22×C3D4×D911yescharacteristic
416C22×C3#369911yescharacteristic
417C22×C3Q8×D911yescharacteristic
418C22×C3C2×C3×C4×D311yescharacteristic
419C22×C3C2×C3×D1211yescharacteristic
420C22×C3C3×#23511yescharacteristic
421C22×C3C3×D3×D411yescharacteristic
422C22×C3C3×D3×D411yescharacteristic
423C22×C3C3×#23711yescharacteristic
424C22×C3C3×D3×Q811yescharacteristic
425C2×D3—34no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—62no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—182no—
442C3×C4—182no—
443C3×C4—361no—
444Dic3—62no—
445Dic3—62no—
446Dic3—121no—
447C32#466811yescharacteristic
448C9—21no—
449C9C3×#38511yescharacteristic, complemented
450C23—92no—
451C23—92no—
452C23—92no—
453C23—181no—
454C23—181no—
455C23—181no—
456C23—181no—
457C23C22×C3×D911yescharacteristic
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—92no—
466C2×C4—92no—
467C2×C4—188no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4C3×C4×D912yescomplemented
476C2×C4C3×D3612yes—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—184no—
485C2×C3C4×D3611yescharacteristic
486C2×C3#611⋊C411yescharacteristic
487C2×C3#6344411yescharacteristic
488C2×C3#6344511yescharacteristic
489C2×C3C4⋊C4×D911yescharacteristic
490C2×C3#6345811yescharacteristic
491C2×C3#6345911yescharacteristic
492C2×C3C3×C4×D1211yescharacteristic
493C2×C3C3×#67⋊C411yescharacteristic
494C2×C3C3×#88211yescharacteristic
495C2×C3C3×#88311yescharacteristic
496C2×C3C3×D3×C4⋊C411yescharacteristic
497C2×C3C3×#89611yescharacteristic
498C2×C3C3×#89711yescharacteristic
499D3—64no—
500C22—94no—
501C22—182no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22—182no—
506C22—182no—
507C22C2×C3×C4×D911yescharacteristic
508C22C2×C3×D3611yescharacteristic
509C22C3×#369711yescharacteristic
510C22C3×D4×D911yescharacteristic
511C22C3×D4×D911yescharacteristic
512C22C3×#369911yescharacteristic
513C22C3×Q8×D911yescharacteristic
514C4—22no—
515C4—22no—
516C4—41no—
517C4—182no—
518C4—182no—
519C4—361no—
520C3—21no—
521C3#1058834811yescharacteristic, direct product factor
522C3C3×#466811yescharacteristic
523C2—184no—
524C2C3×C4×D3611yescharacteristic
525C2C3×#611⋊C411yescharacteristic
526C2C3×#6344411yescharacteristic
527C2C3×#6344511yescharacteristic
528C2C3×C4⋊C4×D911yescharacteristic
529C2C3×#6345811yescharacteristic
530C2C3×#6345911yescharacteristic
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×#385
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×Dic9⋊C4C2semidirect
6. C3×C9×#95C2semidirect
7. C3×C9⋊#95C2semidirect
9. #10588348C3direct (N × H)
21. C3×(C2×D9)⋊C4C4semidirect
34. C2×C4⋊Dic9C2×C3semidirect
35. C2×Dic9⋊C4C2×C3semidirect
37. C9×#95C2×C3semidirect
38. C9⋊#95C2×C3semidirect
54. C2×C3×C4×C9C2×C4semidirect
63. C2×C3×Dic9C2×C4semidirect
96. (C2×D9)⋊C4C3×C4semidirect
112. C2×C3×D9C4⋊C4semidirect
131. C3×#95D9semidirect
186. C2×C4×C9C2×C3×C4semidirect
195. C2×Dic9C2×C3×C4semidirect
278. C2×D9C3×C4⋊C4semidirect
294. #95C3×D9semidirect
295. C3×C9#385semidirect
346. C2×C3×C4C4×D9semidirect
449. C9C3×#385semidirect
475. C2×C4C3×C4×D9semidirect
521. C3#10588348direct (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×(C2×D9)⋊C42
C2×C3×C4⋊Dic92
C2×C3×Dic9⋊C42
C3×C9×#952
C3×C9⋊#952
C3×#46683
#105883483