Finite Group Databasebeta

← #13139666

Subgroups — #13139666

Order 1728.

586 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic
3C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic
4C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
5#11720572C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591297—31nomaximal
9#10588633—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3⋊Dic9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C9×(C2×D3)⋊C4—22no—
18(C2×D3)⋊Dic9—22no—
19(C2×D3)⋊Dic9—22no—
20Dic3⋊Dic9—22no—
21C2×C3×(C2×D3)⋊C4D311yescharacteristic
22C2×Dic3⋊Dic3—31no—
23C2×(C2×D3)⋊Dic3—31no—
24C2×(C2×D3)⋊Dic3—31no—
25#63658—31no—
26C3×C3⋊#95—31no—
27#63579—31no—
28C2×C9×C22⋊C4—31no—
29C2×#3676—31no—
30C2×#3676—31no—
31C2×C4⋊Dic9—31no—
32C9⋊#95—31no—
33C9⋊#95—31no—
34C9⋊#95—61no—
35C9⋊#95D311yescharacteristic, complemented
36C23×C3×C9C2311yescharacteristic
37C22×D3×C9—21no—
38C22×D3×C9—21no—
39C22×D3×C9—21no—
40C22×D3×C9—21no—
41C22×D3×C9—21no—
42C22×D3×C9—21no—
43C22×D3×C9D412yes—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9—21no—
47C2×C3⋊Dic9—21no—
48C2×C3⋊Dic9—21no—
49C2×C3⋊Dic9—21no—
50C2×C3⋊Dic9—21no—
51C2×C3⋊Dic9—21no—
52C2×C3⋊Dic9—21no—
53C2×C9×Dic3—21no—
54C2×C9×Dic3—21no—
55C2×C9×Dic3D412yes—
56C2×C3×Dic9—21no—
57C2×C3×Dic9—21no—
58C2×C3×Dic9—21no—
59C2×C3×Dic9—21no—
60C2×C3×Dic9—21no—
61C2×C3×Dic9—21no—
62#4953—91no—
63#4675—91no—
64C23×C3×D3C2×D311yescharacteristic
65C22×C32×C4C2×D311yescharacteristic
66C22×C3⋊Dic3—31no—
67C22×C3⋊Dic3—31no—
68C22×C3×Dic3—31no—
69C22×C3×Dic3—31no—
70C22×C3×Dic3C2×D311yescharacteristic
71C24×C9—31no—
72C3×(C2×D3)⋊C4—22no—
73Dic3⋊Dic3—62no—
74(C2×D3)⋊Dic3—62no—
75(C2×D3)⋊Dic3—62no—
76C22×C4×C9—21no—
77C22×C4×C9—31no—
78C22×C4×C9C2×D311yescharacteristic
79C22×Dic9—31no—
80C22×Dic9—31no—
81C22×Dic9—61no—
82C22×Dic9—61no—
83C22×Dic9C2×D311yescharacteristic
84C22×Dic9C2×D311yescharacteristic
85C9×C22⋊C4—62no—
86#3676—62no—
87#3676—62no—
88C4⋊Dic9—62no—
89C22×C3×C9C2×D411yescharacteristic
90C22×C3×C9C2×D411yescharacteristic
91C22×C3×C9#4111yescharacteristic
92C22×C3×C9#4111yescharacteristic
93C22×C3×C9#4111yescharacteristic
94C22×C3×C9#4111yescharacteristic
95C22×C3×C9#4111yescharacteristic
96C2×D3×C9—22no—
97C2×D3×C9—22no—
98C2×D3×C9—22no—
99C2×D3×C9—41no—
100C2×D3×C9—41no—
101C2×D3×C9—41no—
102C2×D3×C9—41no—
103C3×C4×C9—41no—
104C3⋊Dic9—41no—
105C3⋊Dic9—41no—
106C9×Dic3—22no—
107C3×Dic9—41no—
108C3×Dic9—41no—
109C2×C3×C22⋊C4—31no—
110C2×#217—91no—
111C2×#217—91no—
112C2×(C2×D3)⋊C4—91no—
113C2×(C2×D3)⋊C4—91no—
114C2×(C2×D3)⋊C4D911yescharacteristic
115C2×C4⋊Dic3—91no—
116C2×Dic3⋊C4—91no—
117C3×#95—91no—
118C3⋊#95—31no—
119C3⋊#95—91no—
120C3⋊#95—91no—
121C3⋊#95—91no—
122C3⋊#95—91no—
123C3⋊#95—181no—
124C23×C32C22×D311yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3D1212yes—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C3⋊Dic3—61no—
136C2×C3⋊Dic3—61no—
137C2×C3⋊Dic3—61no—
138C2×C3⋊Dic3—61no—
139C2×C3⋊Dic3—61no—
140C2×C3⋊Dic3—61no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
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#6712yes—
150C23×C9—21no—
151C23×C9—32no—
152C23×C9—61no—
153C23×C9—61no—
154C23×C9—61no—
155C23×C9—61no—
156C23×C9—61no—
157C23×C9—61no—
158C23×C9C22×D311yescharacteristic
159C2×C4×C9—22no—
160C2×C4×C9—21no—
161C2×C4×C9—21no—
162C2×C4×C9—21no—
163C2×C4×C9—32no—
164C2×C4×C9—41no—
165C2×C4×C9—41no—
166C2×C4×C9—61no—
167C2×C4×C9—61no—
168C2×Dic9—21no—
169C2×Dic9—21no—
170C2×Dic9—21no—
171C2×Dic9—21no—
172C2×Dic9—21no—
173C2×Dic9—21no—
174C2×Dic9—62no—
175C2×Dic9—62no—
176C2×Dic9—61no—
177C2×Dic9—61no—
178C2×Dic9—61no—
179C2×Dic9—61no—
180C2×Dic9—61no—
181C2×Dic9—61no—
182C2×Dic9—121no—
183C2×Dic9—121no—
184C2×Dic9—121no—
185C2×Dic9—121no—
186#397—271noSylow
187C2×C3×C9#12111yescharacteristic
188C2×C3×C9#12311yescharacteristic
189C2×C3×C9#12311yescharacteristic
190C2×C3×C9#12311yescharacteristic
191C2×C3×C9#12411yescharacteristic
192C2×C3×C9#12611yescharacteristic
193C2×C3×C9#12611yescharacteristic
194D3×C9—42no—
195C24×C3—31no—
196C23×D3C2×D911yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—91no—
200C22×C3×C4—91no—
201C22×C3×C4C2×D911yescharacteristic
202C22×C3×C4D3211yescharacteristic
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—91no—
206C22×Dic3—91no—
207C22×Dic3—91no—
208C22×Dic3—91no—
209C22×Dic3—181no—
210C22×Dic3—181no—
211C22×Dic3C2×D911yescharacteristic
212C3×C22⋊C4—62no—
213#217—182no—
214#217—182no—
215(C2×D3)⋊C4—22no—
216(C2×D3)⋊C4—182no—
217(C2×D3)⋊C4—182no—
218C4⋊Dic3—182no—
219Dic3⋊C4—182no—
220C22×C32C2×D1211yescharacteristic
221C22×C32#23511yescharacteristic
222C22×C32#23711yescharacteristic
223C22×C32#23711yescharacteristic
224C22×C32#23711yescharacteristic
225C22×C32#23711yescharacteristic
226C22×C32C2×#6711yescharacteristic
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—41no—
235C3⋊Dic3—121no—
236C3⋊Dic3—121no—
237C3×Dic3—22no—
238C3×Dic3—121no—
239C3×Dic3—121no—
240C22×C9—21no—
241C22×C9—21no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—21no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9—62no—
248C22×C9—62no—
249C22×C9—62no—
250C22×C9—121no—
251C22×C9—121no—
252C22×C9—121no—
253C22×C9—121no—
254C22×C9#23511yescharacteristic
255C22×C9#23511yescharacteristic
256C22×C9#23511yescharacteristic
257C22×C9D3×D411yescharacteristic
258C22×C9D3×D411yescharacteristic
259C22×C9#23711yescharacteristic
260C22×C9#23911yescharacteristic
261C4×C9—42no—
262C4×C9—41no—
263C4×C9—62no—
264Dic9—41no—
265Dic9—41no—
266Dic9—122no—
267Dic9—122no—
268Dic9—121no—
269Dic9—121no—
270C2×C4⋊C4—271no—
271C2×C22⋊C4—31no—
272C2×C22⋊C4—271no—
273C2×C22⋊C4—271no—
274#95—91no—
275#95—271no—
276#95—271no—
277C3×C9#39711yescharacteristic, complemented, Sylow
278C23×C3—21no—
279C23×C3—32no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3—61no—
283C23×C3—61no—
284C23×C3—61no—
285C23×C3—61no—
286C23×C3C22×D911yescharacteristic
287C23×C3C2×D3211yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—21no—
293C22×D3—21no—
294C22×D3D3612yes—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—32no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—181no—
308C2×C3×C4—181no—
309C2×C3×C4—181no—
310C2×C3×C4—181no—
311C2×C3×C4—181no—
312C2×C3×C4—181no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—182no—
322C2×Dic3—182no—
323C2×Dic3—181no—
324C2×Dic3—181no—
325C2×Dic3—181no—
326C2×Dic3—181no—
327C2×Dic3—181no—
328C2×Dic3—181no—
329C2×Dic3—181no—
330C2×Dic3—181no—
331C2×Dic3—181no—
332C2×Dic3—181no—
333C2×Dic3—181no—
334C2×Dic3—181no—
335C2×Dic3—361no—
336C2×Dic3—361no—
337C2×Dic3—361no—
338C2×Dic3—361no—
339C2×Dic3#61112yes—
340C2×C32#87911yescharacteristic
341C2×C32#87911yescharacteristic
342C2×C32#88611yescharacteristic
343C2×C32#88611yescharacteristic
344C2×C32#93011yescharacteristic
345C2×C32#93511yescharacteristic
346C2×C32#93611yescharacteristic
347C3×D3—42no—
348C2×C9—21no—
349C2×C9—21no—
350C2×C9—21no—
351C2×C9—21no—
352C2×C9—21no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9—122no—
356C2×C9#87611yescharacteristic
357C2×C9#88311yescharacteristic
358C2×C9#88411yescharacteristic
359C2×C9#88511yescharacteristic
360C2×C9#89411yescharacteristic
361C2×C9#89411yescharacteristic
362C2×C9#89811yescharacteristic
363C24—31no—
364C22×C4—31no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—271no—
368C22×C4—271no—
369C22×C4D3×D911yescharacteristic
370C4⋊C4—542no—
371C22⋊C4—62no—
372C22⋊C4—542no—
373C22⋊C4—542no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—62no—
383C22×C3—62no—
384C22×C3—121no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3C2×D3611yescharacteristic
389C22×C3#369711yescharacteristic
390C22×C3#369911yescharacteristic
391C22×C3#369911yescharacteristic
392C22×C3#369911yescharacteristic
393C22×C3#369911yescharacteristic
394C22×C3C2×#61111yescharacteristic
395C22×C3#379511yescharacteristic
396C22×C3#379611yescharacteristic
397C22×C3#379811yescharacteristic
398C22×C3D3×D1211yescharacteristic
399C22×C3#380411yescharacteristic
400C22×C3#380511yescharacteristic
401C22×C3D3×#6711yescharacteristic
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—22no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—41no—
409C3×C4—42no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—62no—
413C3×C4—361no—
414C3×C4—361no—
415Dic3—22no—
416Dic3—121no—
417Dic3—121no—
418Dic3—362no—
419Dic3—362no—
420Dic3—361no—
421Dic3—361no—
422Dic3—361no—
423Dic3—361no—
424C32#495311yescharacteristic
425C9—21no—
426C9#467511yescharacteristic, complemented
427C23—32no—
428C23—61no—
429C23—61no—
430C23—61no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23C2×D3×D911yescharacteristic
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—32no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—541no—
448C2×C4—541no—
449C2×C4—541no—
450C2×C4—541no—
451C2×C4—541no—
452C2×C4—541no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—122no—
461C2×C3#6344111yescharacteristic
462C2×C3#6344111yescharacteristic
463C2×C3#6344811yescharacteristic
464C2×C3#6344811yescharacteristic
465C2×C3#6349211yescharacteristic
466C2×C3#6349711yescharacteristic
467C2×C3#6349811yescharacteristic
468C2×C3#6385911yescharacteristic
469C2×C3#6386211yescharacteristic
470C2×C3#6388411yescharacteristic
471C2×C3#6389011yescharacteristic
472C2×C3#6389111yescharacteristic
473C2×C3#6390611yescharacteristic
474C2×C3#6395911yescharacteristic
475D3—42no—
476C22—62no—
477C22—62no—
478C22—62no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22#8863811yescharacteristic
484C22#8863911yescharacteristic
485C22#8864011yescharacteristic
486C22D3×D3611yescharacteristic
487C22#8866211yescharacteristic
488C22#8866311yescharacteristic
489C22D3×#61111yescharacteristic
490C4—41no—
491C4—62no—
492C4—361no—
493C4—361no—
494C4—1081no—
495C4—1081no—
496C3—21no—
497C3#1058863311yescharacteristic, complemented
498C3#1059129711yescharacteristic
499C2—122no—
500C2#1172096311yescharacteristic
501C2#1172096611yescharacteristic
502C2#1172101511yescharacteristic
503C2#1172102011yescharacteristic
504C2#1172102111yescharacteristic
505C2#1172103411yescharacteristic
506C2#1172126311yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutator, cosocleC23×C3×C9C23
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D3C2×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#397
LCSG ▷ C23×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×Dic3⋊Dic9C2semidirect
5. #11720572C2semidirect
6. C3×C9⋊#95C2semidirect
7. #11720331C2semidirect
35. C9⋊#95D3semidirect
277. C3×C9#397semidirect
426. C9#4675semidirect
497. C3#10588633semidirect

Maximal subgroups

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

subgroupindex
C2×C9×(C2×D3)⋊C42
C2×(C2×D3)⋊Dic92
C2×Dic3⋊Dic92
#117205722
C3×C9⋊#952
#117203312
#105912973
#105886333