Finite Group Databasebeta

← #13139840

Subgroups — #13139840

Order 1728.

662 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88534C211yesmaximal, characteristic, complemented
2C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×C4×Dic9C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic
5C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic
6#11720331C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591280—31nomaximal
9#10588625—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3⋊Dic9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17#88534—22no—
18C9×(C2×D3)⋊C4—22no—
19C3×C4×Dic9—22no—
20(C2×D3)⋊Dic9—22no—
21(C2×D3)⋊Dic9C414yescomplemented
22C2×#3750—31no—
23C2×C3×(C2×D3)⋊C4D311yescharacteristic
24C2×C3×C4×Dic3—31no—
25C2×(C2×D3)⋊Dic3—31no—
26C2×(C2×D3)⋊Dic3—31no—
27#63579—31no—
28#63579—31no—
29C2×C9×C22⋊C4—31no—
30C2×#3676—31no—
31C2×#3676—31no—
32C2×Dic9⋊C4—31no—
33C2×Dic9⋊C4—61no—
34C2×C4×Dic9D311yescharacteristic, complemented
35C9⋊#95—31no—
36C9⋊#95—31no—
37C23×C3×C9C2311yescharacteristic
38C22×D3×C9—21no—
39C22×D3×C9—21no—
40C22×D3×C9—21no—
41C22×D3×C9—21no—
42C22×D3×C9—21no—
43C22×D3×C9—21no—
44C22×D3×C9C2×C412yes—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9D412yes—
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×C3×Dic9—21no—
58C2×C3×Dic9—21no—
59C2×C3×Dic9—21no—
60C2×C3×Dic9—21no—
61C2×C3×Dic9C2×C412yes—
62C2×C3×Dic9D412yes—
63#4945—91no—
64#4940—91no—
65C23×C3×D3C2×D311yescharacteristic
66C22×C32×C4C2×D311yescharacteristic
67C22×C3⋊Dic3—31no—
68C22×C3⋊Dic3—31no—
69C22×C3×Dic3—31no—
70C22×C3×Dic3—31no—
71C22×C3×Dic3C2×D311yescharacteristic
72C24×C9—31no—
73#3750—62no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4×Dic3—62no—
76(C2×D3)⋊Dic3—34no—
77(C2×D3)⋊Dic3—62no—
78C22×C4×C9—21no—
79C22×C4×C9—31no—
80C22×C4×C9C2×D311yescharacteristic
81C22×Dic9—31no—
82C22×Dic9—31no—
83C22×Dic9—61no—
84C22×Dic9—61no—
85C22×Dic9C2×D311yescharacteristic
86C22×Dic9C2×D311yescharacteristic
87C9×C22⋊C4—62no—
88#3676—34no—
89#3676—62no—
90Dic9⋊C4—64no—
91Dic9⋊C4—62no—
92C4×Dic9—22no—
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×D3×C9—22no—
101C2×D3×C9—22no—
102C2×D3×C9—22no—
103C2×D3×C9—41no—
104C2×D3×C9—41no—
105C2×D3×C9—41no—
106C2×D3×C9—41no—
107C3×C4×C9—22no—
108C3⋊Dic9—22no—
109C3⋊Dic9—41no—
110C9×Dic3—41no—
111C3×Dic9—22no—
112C3×Dic9—22no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C42—91no—
115C2×#217—91no—
116C2×#217—91no—
117C2×(C2×D3)⋊C4—91no—
118C2×(C2×D3)⋊C4—91no—
119C2×(C2×D3)⋊C4D911yescharacteristic
120C2×Dic3⋊C4—91no—
121C2×Dic3⋊C4—91no—
122C2×Dic3⋊C4—181no—
123C2×C4×Dic3—31no—
124C3⋊#95—91no—
125C3⋊#95—91no—
126C3⋊#95—91no—
127C3⋊#95—91no—
128C23×C32C22×D311yescharacteristic
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3C4×D312yes—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4#6712yes—
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—32no—
149C2×C3×Dic3—32no—
150C2×C3×Dic3—61no—
151C2×C3×Dic3—61no—
152C2×C3×Dic3—61no—
153C2×C3×Dic3—61no—
154C23×C9—21no—
155C23×C9—32no—
156C23×C9—61no—
157C23×C9—61no—
158C23×C9—61no—
159C23×C9—61no—
160C23×C9—61no—
161C23×C9—61no—
162C23×C9C22×D311yescharacteristic
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—22no—
166C2×C4×C9—41no—
167C2×C4×C9—41no—
168C2×C4×C9—61no—
169C2×C4×C9—61no—
170C2×C4×C9—61no—
171C2×C4×C9D1212yes—
172C2×Dic9—21no—
173C2×Dic9—21no—
174C2×Dic9—21no—
175C2×Dic9—21no—
176C2×Dic9—32no—
177C2×Dic9—62no—
178C2×Dic9—62no—
179C2×Dic9—62no—
180C2×Dic9—61no—
181C2×Dic9—61no—
182C2×Dic9—62no—
183C2×Dic9—61no—
184C2×Dic9—61no—
185C2×Dic9—61no—
186C2×Dic9—121no—
187C2×Dic9—121no—
188C2×Dic9C4×D312yes—
189C2×Dic9#6712yes—
190#388—271noSylow
191C2×C3×C9#11711yescharacteristic
192C2×C3×C9C4×D411yescharacteristic
193C2×C3×C9C4×D411yescharacteristic
194C2×C3×C9#12111yescharacteristic
195C2×C3×C9#12311yescharacteristic
196C2×C3×C9#12411yescharacteristic
197C2×C3×C9#12611yescharacteristic
198D3×C9—42no—
199C24×C3—31no—
200C23×D3C2×D911yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—91no—
204C22×C3×C4—91no—
205C22×C3×C4C2×D911yescharacteristic
206C22×C3×C4D3211yescharacteristic
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—91no—
210C22×Dic3—91no—
211C22×Dic3—91no—
212C22×Dic3—91no—
213C22×Dic3—181no—
214C22×Dic3—181no—
215C22×Dic3C2×D911yescharacteristic
216C3×C22⋊C4—62no—
217C3×C42—182no—
218#217—94no—
219#217—182no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4—94no—
222(C2×D3)⋊C4—182no—
223Dic3⋊C4—184no—
224Dic3⋊C4—182no—
225Dic3⋊C4—182no—
226C4×Dic3—62no—
227C22×C32C2×C4×D311yescharacteristic
228C22×C32#23511yescharacteristic
229C22×C32D3×D411yescharacteristic
230C22×C32#23711yescharacteristic
231C22×C32#23711yescharacteristic
232C22×C32#23711yescharacteristic
233C22×C32C2×#6711yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—22no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C32×C4—22no—
242C3⋊Dic3—62no—
243C3⋊Dic3—121no—
244C3×Dic3—41no—
245C3×Dic3—62no—
246C3×Dic3—62no—
247C22×C9—21no—
248C22×C9—21no—
249C22×C9—21no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9—21no—
253C22×C9—21no—
254C22×C9—62no—
255C22×C9—62no—
256C22×C9—62no—
257C22×C9—121no—
258C22×C9—121no—
259C22×C9—121no—
260C22×C9—121no—
261C22×C9C2×C4×D311yescharacteristic
262C22×C9C2×D1211yescharacteristic
263C22×C9#23511yescharacteristic
264C22×C9#23511yescharacteristic
265C22×C9#23511yescharacteristic
266C22×C9#23511yescharacteristic
267C22×C9C2×#6711yescharacteristic
268C4×C9—22no—
269C4×C9—42no—
270C4×C9—121no—
271Dic9—22no—
272Dic9—22no—
273Dic9—64no—
274Dic9—62no—
275Dic9—122no—
276Dic9—121no—
277C2×C4⋊C4—271no—
278C2×C22⋊C4—31no—
279C2×C22⋊C4—271no—
280C2×C22⋊C4—271no—
281C2×C42—91no—
282#95—271no—
283#95—271no—
284C3×C9#38811yescharacteristic, complemented, Sylow
285C23×C3—21no—
286C23×C3—32no—
287C23×C3—61no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3—61no—
291C23×C3—61no—
292C23×C3—61no—
293C23×C3C22×D911yescharacteristic
294C23×C3C2×D3211yescharacteristic
295C22×D3—21no—
296C22×D3—21no—
297C22×D3—21no—
298C22×D3—21no—
299C22×D3—21no—
300C22×D3—21no—
301C22×D3C4×D912yes—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—92no—
313C2×C3×C4—92no—
314C2×C3×C4—181no—
315C2×C3×C4—181no—
316C2×C3×C4—181no—
317C2×C3×C4—181no—
318C2×C3×C4#61112yes—
319C2×C3×C4#62612yes—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—92no—
330C2×Dic3—92no—
331C2×Dic3—182no—
332C2×Dic3—182no—
333C2×Dic3—182no—
334C2×Dic3—181no—
335C2×Dic3—181no—
336C2×Dic3—181no—
337C2×Dic3—181no—
338C2×Dic3—182no—
339C2×Dic3—181no—
340C2×Dic3—181no—
341C2×Dic3—181no—
342C2×Dic3—181no—
343C2×Dic3—181no—
344C2×Dic3—181no—
345C2×Dic3—361no—
346C2×Dic3—361no—
347C2×C32#87711yescharacteristic
348C2×C32#87911yescharacteristic
349C2×C32#67⋊C411yescharacteristic
350C2×C32#88311yescharacteristic
351C2×C32C4×#6711yescharacteristic
352C2×C32#93611yescharacteristic
353C2×C32#93911yescharacteristic
354C3×D3—42no—
355C2×C9—21no—
356C2×C9—21no—
357C2×C9—21no—
358C2×C9—21no—
359C2×C9—21no—
360C2×C9—21no—
361C2×C9—21no—
362C2×C9—122no—
363C2×C9#87211yescharacteristic
364C2×C9C4×D1211yescharacteristic
365C2×C9#87511yescharacteristic
366C2×C9#87611yescharacteristic
367C2×C9C4×#6711yescharacteristic
368C2×C9#92911yescharacteristic
369C2×C9#93011yescharacteristic
370C24—31no—
371C22×C4—31no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—271no—
375C22×C4—271no—
376C22×C4D3×D911yescharacteristic
377C4⋊C4—542no—
378C22⋊C4—62no—
379C22⋊C4—274no—
380C22⋊C4—542no—
381C42—182no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—62no—
392C22×C3—121no—
393C22×C3—121no—
394C22×C3—121no—
395C22×C3—121no—
396C22×C3C2×C4×D911yescharacteristic
397C22×C3#369711yescharacteristic
398C22×C3D4×D911yescharacteristic
399C22×C3#369911yescharacteristic
400C22×C3#369911yescharacteristic
401C22×C3#369911yescharacteristic
402C22×C3C2×#61111yescharacteristic
403C22×C3#379511yescharacteristic
404C22×C3#379511yescharacteristic
405C22×C3#379811yescharacteristic
406C22×C3C4×D3211yescharacteristic
407C22×C3#380411yescharacteristic
408C22×C3C2×#62611yescharacteristic
409C22×C3D3×#6711yescharacteristic
410C2×D3—22no—
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—41no—
414C2×D3—41no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—121no—
421C3×C4—182no—
422C3×C4—182no—
423Dic3—41no—
424Dic3—62no—
425Dic3—62no—
426Dic3—184no—
427Dic3—182no—
428Dic3—182no—
429Dic3—362no—
430Dic3—361no—
431Dic3—361no—
432C32#494511yescharacteristic
433C9—21no—
434C9#494011yescharacteristic, complemented
435C23—32no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—61no—
442C23C2×D3×D911yescharacteristic
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—92no—
449C2×C4—92no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—272no—
455C2×C4—541no—
456C2×C4—541no—
457C2×C4—541no—
458C2×C4—541no—
459C2×C4—541no—
460C2×C4#619512yes—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—122no—
469C2×C3#6343911yescharacteristic
470C2×C3#6344111yescharacteristic
471C2×C3#611⋊C411yescharacteristic
472C2×C3#6344511yescharacteristic
473C2×C3C4×#61111yescharacteristic
474C2×C3#6349811yescharacteristic
475C2×C3#6350111yescharacteristic
476C2×C3#6385911yescharacteristic
477C2×C3#6386011yescharacteristic
478C2×C3#6387711yescharacteristic
479C2×C3#6387911yescharacteristic
480C2×C3C4×#62611yescharacteristic
481C2×C3#6390511yescharacteristic
482C2×C3#6397811yescharacteristic
483D3—42no—
484C22—62no—
485C22—62no—
486C22—62no—
487C22—121no—
488C22—121no—
489C22—121no—
490C22—121no—
491C22#8863811yescharacteristic
492C22#8863811yescharacteristic
493C22#8864011yescharacteristic
494C22C4×D3×D911yescharacteristic
495C22#8866211yescharacteristic
496C22C2×#619511yescharacteristic
497C22D9×#6711yescharacteristic
498C4—22no—
499C4—121no—
500C4—182no—
501C4—182no—
502C4—542no—
503C4—1081no—
504C3—21no—
505C3#1058862511yescharacteristic, complemented
506C3#1059128011yescharacteristic
507C2—122no—
508C2#1172096311yescharacteristic
509C2#1172096411yescharacteristic
510C2#1172101011yescharacteristic
511C2#1172101211yescharacteristic
512C2C4×#619511yescharacteristic
513C2#1172103111yescharacteristic
514C2#1172128811yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D3C2×D3
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#388
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88534C2semidirect
3. C2×C3×C4×Dic9C2semidirect
6. #11720331C2semidirect
7. #11720331C2semidirect
21. (C2×D3)⋊Dic9C4semidirect
34. C2×C4×Dic9D3semidirect
284. C3×C9#388semidirect
434. C9#4940semidirect
505. C3#10588625semidirect

Maximal subgroups

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

subgroupindex
C2×#885342
C2×C9×(C2×D3)⋊C42
C2×C3×C4×Dic92
C2×(C2×D3)⋊Dic92
#117203312
#105912803
#105886253