Finite Group Databasebeta

← #13139857

Subgroups — #13139857

Order 1728.

730 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3×D9C211yesmaximal, characteristic
2C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
3C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic
4#11720572C211yesmaximal, characteristic, complemented
5C9×C3⋊#95C211yesmaximal, characteristic, complemented
6#11720331C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591362—31nomaximal
9#10588344—31nomaximal
10C23×C3×D9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3⋊Dic9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C2×Dic3×D9—22no—
18C2×Dic3×D9—22no—
19C2×Dic3×D9C414yescomplemented
20C3×(C2×D9)⋊C4—22no—
21(C2×D9)⋊Dic3—22no—
22C22×D3×Dic3—31no—
23C2×C3×(C2×D3)⋊C4—31no—
24C2×(C2×D3)⋊Dic3—31no—
25C22×C4×D9—31no—
26#63658—31no—
27C3×C3⋊#95D311yescharacteristic
28#63579—31no—
29#63579—31no—
30C2×(C2×D9)⋊C4—31no—
31C2×(C2×D9)⋊C4D311yescharacteristic
32C9×#95—31no—
33C9⋊#95—31no—
34C9⋊#95—31no—
35C9⋊#95—31no—
36C9⋊#95—61no—
37C23×C3×C9C2311yescharacteristic
38C22×C3×D9—21no—
39C22×C3×D9—21no—
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9C2×C412yes—
43C22×C3×D9D412yes—
44C22×C3×D9D412yes—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3⋊Dic9—21no—
49C2×C3⋊Dic9—21no—
50C2×C3⋊Dic9—21no—
51C2×C3⋊Dic9—21no—
52C2×C3⋊Dic9—21no—
53C2×C3⋊Dic9C2×C412yes—
54C2×C9×Dic3—21no—
55C2×C9×Dic3—21no—
56C2×C9×Dic3—21no—
57C2×C9×Dic3—21no—
58C2×C9×Dic3—21no—
59C2×C9×Dic3C2×C412yes—
60C2×C3×Dic9—21no—
61C2×C3×Dic9—21no—
62C2×C3×Dic9—21no—
63Dic3×D9—28no—
64#4943—91no—
65#4664—91no—
66C23×C3×D3—31no—
67C22×C32×C4C2×D311yescharacteristic
68C22×C3⋊Dic3—31no—
69C22×C3⋊Dic3—31no—
70C22×C3×Dic3—31no—
71C22×C3×Dic3C2×D311yescharacteristic
72C22×C3×Dic3C2×D311yescharacteristic
73C2×D3×Dic3—34no—
74C2×D3×Dic3—62no—
75C2×D3×Dic3—62no—
76C23×D9C2×D311yescharacteristic
77C3×(C2×D3)⋊C4—62no—
78(C2×D3)⋊Dic3—62no—
79C22×C4×C9—21no—
80C22×C4×C9—31no—
81C22×C4×C9—31no—
82C22×C4×C9C2×D311yescharacteristic
83C22×Dic9—31no—
84C22×Dic9—31no—
85C22×Dic9—61no—
86C22×Dic9—61no—
87C22×Dic9C2×D311yescharacteristic
88C2×C4×D9—34no—
89C2×C4×D9—62no—
90C2×C4×D9—62no—
91(C2×D9)⋊C4—22no—
92(C2×D9)⋊C4—62no—
93C22×C3×C9C22×C411yescharacteristic
94C22×C3×C9C2×D411yescharacteristic
95C22×C3×C9C2×D411yescharacteristic
96C22×C3×C9#4111yescharacteristic
97C22×C3×C9#4111yescharacteristic
98C22×C3×C9#4111yescharacteristic
99C22×C3×C9#4111yescharacteristic
100C2×C3×D9—22no—
101C2×C3×D9—22no—
102C2×C3×D9—22no—
103C2×C3×D9—22no—
104C2×C3×D9—22no—
105C2×C3×D9—22no—
106C2×C3×D9C22⋊C414yes—
107C3×C4×C9—41no—
108C3⋊Dic9—22no—
109C3⋊Dic9—41no—
110C9×Dic3—22no—
111C9×Dic3—41no—
112C3×Dic9—41no—
113C23×Dic3—91no—
114C22×C4×D3—91no—
115C2×C3×C22⋊C4—91no—
116C2×#217—91no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—91no—
119C3×#95—31no—
120C3⋊#95—91no—
121C3⋊#95—91no—
122C3⋊#95—91no—
123C3⋊#95—91no—
124C3⋊#95—91no—
125C3⋊#95—91no—
126C3⋊#95—181no—
127C3⋊#95D911yescharacteristic, complemented
128C23×C32C22×D311yescharacteristic
129C22×C3×D3—32no—
130C22×C3×D3—32no—
131C22×C3×D3—32no—
132C22×C3×D3—61no—
133C22×C3×D3—61no—
134C22×C3×D3—61no—
135C22×C3×D3—61no—
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—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—61no—
151C2×C3×Dic3—61no—
152C2×C3×Dic3—61no—
153C2×C3×Dic3C4×D312yes—
154D3×Dic3—68no—
155C23×C9—21no—
156C23×C9C22×D311yescharacteristic
157C22×D9—21no—
158C22×D9—21no—
159C22×D9—21no—
160C22×D9—21no—
161C22×D9C4×D312yes—
162C22×D9D1212yes—
163C22×D9#6712yes—
164C2×C4×C9—22no—
165C2×C4×C9—21no—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—32no—
169C2×C4×C9—41no—
170C2×C4×C9—41no—
171C2×C4×C9—61no—
172C2×C4×C9—61no—
173C2×C4×C9—61no—
174C2×C4×C9—61no—
175C2×C4×C9—61no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—32no—
180C2×Dic9—62no—
181C2×Dic9—61no—
182C2×Dic9—61no—
183C2×Dic9—62no—
184C2×Dic9—61no—
185C2×Dic9—61no—
186C2×Dic9—61no—
187C2×Dic9—121no—
188C2×Dic9—121no—
189C2×Dic9—121no—
190C2×Dic9—121no—
191C4×D9—68no—
192#381—271noSylow
193C2×C3×C9C2×C22⋊C411yescharacteristic
194C2×C3×C9#11711yescharacteristic
195C2×C3×C9#11711yescharacteristic
196C2×C3×C9#12311yescharacteristic
197C2×C3×C9#12311yescharacteristic
198C2×C3×C9#12311yescharacteristic
199C2×C3×C9#12311yescharacteristic
200C3×D9—24no—
201C24×C3—91no—
202C23×D3—31no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—91no—
207C22×C3×C4C2×D911yescharacteristic
208C22×C3×C4D3211yescharacteristic
209C22×Dic3—31no—
210C22×Dic3—91no—
211C22×Dic3—91no—
212C22×Dic3—94no—
213C22×Dic3—91no—
214C22×Dic3—91no—
215C22×Dic3—181no—
216C22×Dic3—181no—
217C22×Dic3—182no—
218C22×Dic3—182no—
219C22×Dic3C2×D911yescharacteristic
220C22×Dic3C2×D911yescharacteristic
221C2×C4×D3—94no—
222C2×C4×D3—182no—
223C2×C4×D3—182no—
224C3×C22⋊C4—182no—
225#217—182no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—182no—
228C22×C32C2×C4×D311yescharacteristic
229C22×C32#23511yescharacteristic
230C22×C32#23511yescharacteristic
231C22×C32D3×D411yescharacteristic
232C22×C32D3×D411yescharacteristic
233C22×C32#23711yescharacteristic
234C22×C32#23911yescharacteristic
235C2×C3×D3—34no—
236C2×C3×D3—62no—
237C2×C3×D3—62no—
238C2×C3×D3—62no—
239C2×C3×D3—62no—
240C2×C3×D3—62no—
241C2×C3×D3—62no—
242C32×C4—41no—
243C3⋊Dic3—62no—
244C3⋊Dic3—121no—
245C3×Dic3—22no—
246C3×Dic3—41no—
247C3×Dic3—121no—
248C22×C9—21no—
249C22×C9—21no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9—21no—
253C22×C9—21no—
254C22×C9—21no—
255C22×C9C2×C4×D311yescharacteristic
256C22×C9C2×D1211yescharacteristic
257C22×C9#23711yescharacteristic
258C22×C9#23711yescharacteristic
259C22×C9#23711yescharacteristic
260C22×C9#23711yescharacteristic
261C22×C9C2×#6711yescharacteristic
262C2×D9—22no—
263C2×D9—22no—
264C2×D9—22no—
265C2×D9—22no—
266C2×D9—22no—
267C2×D9—22no—
268C2×D9(C2×D3)⋊C414yes—
269C4×C9—42no—
270C4×C9—41no—
271C4×C9—62no—
272C4×C9—121no—
273Dic9—41no—
274Dic9—62no—
275Dic9—122no—
276Dic9—122no—
277Dic9—121no—
278C23×C4—271no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—271no—
281#95—31no—
282#95—271no—
283#95—271no—
284#95—271no—
285C3×C9#38111yescharacteristic, complemented, Sylow
286C23×C3—21no—
287C23×C3—92no—
288C23×C3—92no—
289C23×C3—92no—
290C23×C3—181no—
291C23×C3—181no—
292C23×C3—181no—
293C23×C3—181no—
294C23×C3C22×D911yescharacteristic
295C23×C3C2×D3211yescharacteristic
296C22×D3—32no—
297C22×D3—32no—
298C22×D3—32no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—61no—
302C22×D3—61no—
303C2×C3×C4—22no—
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—32no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—181no—
319C2×C3×C4—181no—
320C2×C3×C4—181no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—92no—
330C2×Dic3—92no—
331C2×Dic3—182no—
332C2×Dic3—188no—
333C2×Dic3—181no—
334C2×Dic3—181no—
335C2×Dic3—181no—
336C2×Dic3—181no—
337C2×Dic3—182no—
338C2×Dic3—181no—
339C2×Dic3—181no—
340C2×Dic3—181no—
341C2×Dic3—181no—
342C2×Dic3—181no—
343C2×Dic3—181no—
344C2×Dic3—361no—
345C2×Dic3—361no—
346C2×Dic3—361no—
347C2×Dic3—361no—
348C2×Dic3C4×D912yes—
349C4×D3—188no—
350C2×C32#87211yescharacteristic
351C2×C32D3×C22⋊C411yescharacteristic
352C2×C32#88311yescharacteristic
353C2×C32#88311yescharacteristic
354C2×C32#89211yescharacteristic
355C2×C32#89411yescharacteristic
356C2×C32#89411yescharacteristic
357C3×D3—64no—
358C2×C9—21no—
359C2×C9—21no—
360C2×C9—21no—
361C2×C9—21no—
362C2×C9—21no—
363C2×C9—21no—
364C2×C9—21no—
365C2×C9#87711yescharacteristic
366C2×C9#87711yescharacteristic
367C2×C9#88611yescharacteristic
368C2×C9#88611yescharacteristic
369C2×C9C2×(C2×D3)⋊C411yescharacteristic
370C2×C9#93511yescharacteristic
371C2×C9#93511yescharacteristic
372D9—24no—
373C24—91no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—91no—
377C22×C4—274no—
378C22×C4—271no—
379C22×C4—271no—
380C22×C4—542no—
381C22×C4—542no—
382C22×C4D3×D911yescharacteristic
383C22⋊C4—182no—
384C22⋊C4—542no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—94no—
393C22×C3—182no—
394C22×C3—182no—
395C22×C3—182no—
396C22×C3—182no—
397C22×C3—182no—
398C22×C3—182no—
399C22×C3C2×C4×D911yescharacteristic
400C22×C3#369711yescharacteristic
401C22×C3#369711yescharacteristic
402C22×C3D4×D911yescharacteristic
403C22×C3D4×D911yescharacteristic
404C22×C3#369911yescharacteristic
405C22×C3#370111yescharacteristic
406C22×C3#379511yescharacteristic
407C22×C3#379611yescharacteristic
408C22×C3C4×D3211yescharacteristic
409C22×C3D3×D1211yescharacteristic
410C22×C3#380411yescharacteristic
411C22×C3#380511yescharacteristic
412C22×C3D3×#6711yescharacteristic
413C2×D3—34no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—62no—
420C3×C4—42no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—62no—
424C3×C4—121no—
425C3×C4—361no—
426Dic3—22no—
427Dic3—41no—
428Dic3—121no—
429Dic3—182no—
430Dic3—182no—
431Dic3—362no—
432Dic3—362no—
433Dic3—361no—
434Dic3—361no—
435C32#466411yescharacteristic
436C9—21no—
437C9#494311yescharacteristic, complemented
438C23—92no—
439C23—92no—
440C23—92no—
441C23—181no—
442C23—181no—
443C23—181no—
444C23—181no—
445C23C2×D3×D911yescharacteristic
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—32no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—272no—
459C2×C4—548no—
460C2×C4—541no—
461C2×C4—541no—
462C2×C4—541no—
463C2×C4—541no—
464C2×C4—541no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—184no—
473C2×C3#6343411yescharacteristic
474C2×C3C22⋊C4×D911yescharacteristic
475C2×C3#6344511yescharacteristic
476C2×C3#6344511yescharacteristic
477C2×C3#6345411yescharacteristic
478C2×C3#6345611yescharacteristic
479C2×C3#6345611yescharacteristic
480C2×C3#6387711yescharacteristic
481C2×C3#6387811yescharacteristic
482C2×C3#6388411yescharacteristic
483C2×C3#6389011yescharacteristic
484C2×C3#6389111yescharacteristic
485C2×C3D3×(C2×D3)⋊C411yescharacteristic
486C2×C3#6396911yescharacteristic
487D3—64no—
488C22—94no—
489C22—182no—
490C22—182no—
491C22—182no—
492C22—182no—
493C22—182no—
494C22—182no—
495C22#8863411yescharacteristic
496C22#8864111yescharacteristic
497C22C4×D3×D911yescharacteristic
498C22D9×D1211yescharacteristic
499C22#8865811yescharacteristic
500C22#8866311yescharacteristic
501C22D9×#6711yescharacteristic
502C4—41no—
503C4—62no—
504C4—121no—
505C4—361no—
506C4—542no—
507C4—1081no—
508C3—21no—
509C3#1058834411yescharacteristic, complemented
510C3#1059136211yescharacteristic
511C2—184no—
512C2#1172097411yescharacteristic
513C2#1172097511yescharacteristic
514C2#1172098111yescharacteristic
515C2#1172098811yescharacteristic
516C2#1172098911yescharacteristic
517C2D9×(C2×D3)⋊C411yescharacteristic
518C2#1172126911yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#381
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11720572C2semidirect
5. C9×C3⋊#95C2semidirect
6. #11720331C2semidirect
7. #11720331C2semidirect
19. C2×Dic3×D9C4semidirect
127. C3⋊#95D9semidirect
285. C3×C9#381semidirect
437. C9#4943semidirect
509. C3#10588344semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×D92
C2×C3×(C2×D9)⋊C42
C2×(C2×D9)⋊Dic32
#117205722
C9×C3⋊#952
#117203312
#105913623
#105883443