Finite Group Databasebeta

← #13139729

Subgroups — #13139729

Order 1728.

634 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
1C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
2C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic
4C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic
5C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
6C2×Dic9⋊Dic3C211yesmaximal, characteristic, complemented
7#11720572C211yesmaximal, characteristic, complemented
8#10591306—31nomaximal
9#10588674—31nomaximal
10C23×C3×D9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3⋊Dic9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C3×(C2×D9)⋊C4—22no—
18C9×Dic3⋊C4—22no—
19(C2×D9)⋊Dic3—22no—
20(C2×D9)⋊Dic3—22no—
21Dic3⋊Dic9—22no—
22Dic9⋊Dic3—22no—
23C2×C3×(C2×D3)⋊C4—31no—
24C2×C3×Dic3⋊C4D311yescharacteristic
25C2×Dic3⋊Dic3—31no—
26C2×Dic3⋊Dic3—31no—
27C2×(C2×D3)⋊Dic3—31no—
28C2×(C2×D3)⋊Dic3—31no—
29#63658—31no—
30C2×C9×C4⋊C4—31no—
31C2×(C2×D9)⋊C4—31no—
32C2×(C2×D9)⋊C4—31no—
33C2×(C2×D9)⋊C4D311yescharacteristic
34C2×C4⋊Dic9—31no—
35C2×Dic9⋊C4—31no—
36C9⋊#95—31no—
37C9⋊#95—61no—
38C23×C3×C9C2311yescharacteristic
39C22×C3×D9—21no—
40C22×C3×D9—21no—
41C22×C3×D9—21no—
42C22×C3×D9—21no—
43C22×C3×D9—21no—
44C22×C3×D9—21no—
45C22×C3×D9Q812yes—
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9—21no—
49C2×C3⋊Dic9—21no—
50C2×C3⋊Dic9—21no—
51C2×C3⋊Dic9—21no—
52C2×C3⋊Dic9—21no—
53C2×C3⋊Dic9—21no—
54C2×C3⋊Dic9—21no—
55C2×C9×Dic3—21no—
56C2×C9×Dic3—21no—
57C2×C9×Dic3—21no—
58C2×C9×Dic3—21no—
59C2×C9×Dic3D412yes—
60C2×C9×Dic3D412yes—
61C2×C3×Dic9—21no—
62C2×C3×Dic9—21no—
63C2×C3×Dic9D412yes—
64#4994—91no—
65#4948—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
73C23×D9C2×D311yescharacteristic
74C3×(C2×D3)⋊C4—62no—
75C3×Dic3⋊C4—22no—
76Dic3⋊Dic3—62no—
77Dic3⋊Dic3—62no—
78(C2×D3)⋊Dic3—62no—
79(C2×D3)⋊Dic3—62no—
80C22×C4×C9—21no—
81C22×C4×C9—31no—
82C22×C4×C9—31no—
83C22×C4×C9C2×D311yescharacteristic
84C22×Dic9—31no—
85C22×Dic9—31no—
86C22×Dic9—61no—
87C22×Dic9—61no—
88C22×Dic9C2×D311yescharacteristic
89C9×C4⋊C4—62no—
90(C2×D9)⋊C4—22no—
91(C2×D9)⋊C4—62no—
92(C2×D9)⋊C4—62no—
93C4⋊Dic9—62no—
94Dic9⋊C4—62no—
95C22×C3×C9C2×D411yescharacteristic
96C22×C3×C9C2×D411yescharacteristic
97C22×C3×C9C2×D411yescharacteristic
98C22×C3×C9C2×Q811yescharacteristic
99C22×C3×C9#4111yescharacteristic
100C22×C3×C9#4111yescharacteristic
101C22×C3×C9#4111yescharacteristic
102C2×C3×D9—22no—
103C2×C3×D9—22no—
104C2×C3×D9—22no—
105C2×C3×D9—41no—
106C2×C3×D9—41no—
107C2×C3×D9—41no—
108C2×C3×D9—41no—
109C3×C4×C9—41no—
110C3⋊Dic9—41no—
111C3⋊Dic9—41no—
112C9×Dic3—22no—
113C9×Dic3—22no—
114C3×Dic9—22no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C22⋊C4—91no—
117C2×#217—91no—
118C2×#217—91no—
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—91no—
121C2×(C2×D3)⋊C4—91no—
122C2×C4⋊Dic3—91no—
123C2×C4⋊Dic3—91no—
124C2×Dic3⋊C4—91no—
125C2×Dic3⋊C4—91no—
126C2×Dic3⋊C4D911yescharacteristic, complemented
127C3⋊#95—91no—
128C3⋊#95—91no—
129C3⋊#95—181no—
130C23×C32C22×D311yescharacteristic
131C22×C3×D3—32no—
132C22×C3×D3—61no—
133C22×C3×D3—61no—
134C22×C3×D3—61no—
135C22×C3×D3—61no—
136C22×C3×D3—61no—
137C22×C3×D3—61no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C3⋊Dic3—61no—
142C2×C3⋊Dic3—61no—
143C2×C3⋊Dic3—61no—
144C2×C3⋊Dic3—61no—
145C2×C3⋊Dic3—61no—
146C2×C3⋊Dic3—61no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—32no—
152C2×C3×Dic3—61no—
153C2×C3×Dic3—61no—
154C2×C3×Dic3D1212yes—
155C2×C3×Dic3#6712yes—
156C23×C9—21no—
157C23×C9C22×D311yescharacteristic
158C22×D9—21no—
159C22×D9—21no—
160C22×D9—21no—
161C22×D9—21no—
162C22×D9—21no—
163C22×D9—21no—
164C22×D9Dic612yes—
165C2×C4×C9—22no—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—32no—
170C2×C4×C9—32no—
171C2×C4×C9—41no—
172C2×C4×C9—41no—
173C2×C4×C9—61no—
174C2×C4×C9—61no—
175C2×C4×C9—61no—
176C2×C4×C9—61no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—62no—
180C2×Dic9—62no—
181C2×Dic9—61no—
182C2×Dic9—61no—
183C2×Dic9—61no—
184C2×Dic9—61no—
185C2×Dic9—61no—
186C2×Dic9—61no—
187C2×Dic9—121no—
188C2×Dic9—121no—
189C2×Dic9—121no—
190C2×Dic9—121no—
191C2×Dic9#6712yes—
192#396—271noSylow
193C2×C3×C9#12111yescharacteristic
194C2×C3×C9#12111yescharacteristic
195C2×C3×C9#12111yescharacteristic
196C2×C3×C9C22⋊Q811yescharacteristic
197C2×C3×C9C22⋊Q811yescharacteristic
198C2×C3×C9C22⋊Q811yescharacteristic
199C2×C3×C9#12611yescharacteristic
200C3×D9—42no—
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—91no—
213C22×Dic3—91no—
214C22×Dic3—181no—
215C22×Dic3—181no—
216C22×Dic3C2×D911yescharacteristic
217C22×Dic3C2×D911yescharacteristic
218C3×C4⋊C4—62no—
219C3×C22⋊C4—182no—
220#217—182no—
221#217—182no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—182no—
224(C2×D3)⋊C4—182no—
225C4⋊Dic3—182no—
226C4⋊Dic3—182no—
227Dic3⋊C4—22no—
228Dic3⋊C4—182no—
229Dic3⋊C4—182no—
230C22×C32C2×D1211yescharacteristic
231C22×C32#23511yescharacteristic
232C22×C32D3×D411yescharacteristic
233C22×C32#23711yescharacteristic
234C22×C32D3×Q811yescharacteristic
235C22×C32#23911yescharacteristic
236C22×C32C2×#6711yescharacteristic
237C2×C3×D3—62no—
238C2×C3×D3—62no—
239C2×C3×D3—62no—
240C2×C3×D3—121no—
241C2×C3×D3—121no—
242C2×C3×D3—121no—
243C2×C3×D3—121no—
244C32×C4—41no—
245C3⋊Dic3—121no—
246C3⋊Dic3—121no—
247C3×Dic3—22no—
248C3×Dic3—22no—
249C3×Dic3—62no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9—21no—
253C22×C9—21no—
254C22×C9—21no—
255C22×C9—21no—
256C22×C9—21no—
257C22×C9C2×Dic611yescharacteristic
258C22×C9#23511yescharacteristic
259C22×C9D3×D411yescharacteristic
260C22×C9D3×D411yescharacteristic
261C22×C9#23711yescharacteristic
262C22×C9#23711yescharacteristic
263C22×C9C2×#6711yescharacteristic
264C2×D9—22no—
265C2×D9—22no—
266C2×D9—22no—
267C2×D9—41no—
268C2×D9—41no—
269C2×D9—41no—
270C2×D9—41no—
271C4×C9—42no—
272C4×C9—41no—
273C4×C9—62no—
274C4×C9—62no—
275Dic9—22no—
276Dic9—122no—
277Dic9—122no—
278Dic9—121no—
279Dic9—121no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—271no—
282C2×C4⋊C4—271no—
283C2×C22⋊C4—91no—
284C2×C22⋊C4—271no—
285C2×C22⋊C4—271no—
286#95—271no—
287C3×C9#39611yescharacteristic, complemented, Sylow
288C23×C3—21no—
289C23×C3—92no—
290C23×C3—181no—
291C23×C3—181no—
292C23×C3—181no—
293C23×C3—181no—
294C23×C3—181no—
295C23×C3—181no—
296C23×C3C22×D911yescharacteristic
297C23×C3C2×D3211yescharacteristic
298C22×D3—32no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—61no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—92no—
321C2×C3×C4—181no—
322C2×C3×C4—181no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—32no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—182no—
331C2×Dic3—182no—
332C2×Dic3—181no—
333C2×Dic3—181no—
334C2×Dic3—181no—
335C2×Dic3—181no—
336C2×Dic3—181no—
337C2×Dic3—181no—
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×Dic3D3612yes—
349C2×Dic3#61112yes—
350C2×C32#89511yescharacteristic
351C2×C32#89611yescharacteristic
352C2×C32#89711yescharacteristic
353C2×C32#89811yescharacteristic
354C2×C32#93011yescharacteristic
355C2×C32#93911yescharacteristic
356C2×C32#94611yescharacteristic
357C3×D3—122no—
358C2×C9—21no—
359C2×C9—21no—
360C2×C9—21no—
361C2×C9—21no—
362C2×C9—21no—
363C2×C9—21no—
364C2×C9—21no—
365C2×C9#87811yescharacteristic
366C2×C9#87811yescharacteristic
367C2×C9#87911yescharacteristic
368C2×C9#88411yescharacteristic
369C2×C9#92411yescharacteristic
370C2×C9#93811yescharacteristic
371C2×C9#93911yescharacteristic
372D9—42no—
373C24—91no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—91no—
377C22×C4—271no—
378C22×C4—271no—
379C22×C4D3×D911yescharacteristic
380C4⋊C4—62no—
381C4⋊C4—542no—
382C4⋊C4—542no—
383C22⋊C4—182no—
384C22⋊C4—542no—
385C22⋊C4—542no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—182no—
394C22×C3—182no—
395C22×C3—182no—
396C22×C3—361no—
397C22×C3—361no—
398C22×C3—361no—
399C22×C3—361no—
400C22×C3C2×D3611yescharacteristic
401C22×C3#369711yescharacteristic
402C22×C3D4×D911yescharacteristic
403C22×C3#369911yescharacteristic
404C22×C3Q8×D911yescharacteristic
405C22×C3#370111yescharacteristic
406C22×C3C2×#61111yescharacteristic
407C22×C3D3×Dic611yescharacteristic
408C22×C3#379611yescharacteristic
409C22×C3#379811yescharacteristic
410C22×C3D3×D1211yescharacteristic
411C22×C3#380511yescharacteristic
412C22×C3D3×#6711yescharacteristic
413C22×C3D3×#6711yescharacteristic
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—121no—
420C2×D3—121no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4—182no—
427Dic3—22no—
428Dic3—22no—
429Dic3—62no—
430Dic3—362no—
431Dic3—362no—
432Dic3—361no—
433Dic3—361no—
434Dic3—361no—
435Dic3—361no—
436C32#499411yescharacteristic
437C9—21no—
438C9#494811yescharacteristic, complemented
439C23—92no—
440C23—181no—
441C23—181no—
442C23—181no—
443C23—181no—
444C23—181no—
445C23—181no—
446C23C2×D3×D911yescharacteristic
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—92no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—541no—
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—362no—
473C2×C3#6345711yescharacteristic
474C2×C3#6345811yescharacteristic
475C2×C3#6345911yescharacteristic
476C2×C3#6346011yescharacteristic
477C2×C3#6349211yescharacteristic
478C2×C3#6350111yescharacteristic
479C2×C3#6350811yescharacteristic
480C2×C3#6385111yescharacteristic
481C2×C3#6386211yescharacteristic
482C2×C3#6388611yescharacteristic
483C2×C3#6388711yescharacteristic
484C2×C3#6389311yescharacteristic
485C2×C3#6390611yescharacteristic
486C2×C3#6397011yescharacteristic
487D3—122no—
488C22—182no—
489C22—182no—
490C22—182no—
491C22—361no—
492C22—361no—
493C22—361no—
494C22—361no—
495C22D9×Dic611yescharacteristic
496C22#8863411yescharacteristic
497C22#8864011yescharacteristic
498C22D3×D3611yescharacteristic
499C22#8866311yescharacteristic
500C22D3×#61111yescharacteristic
501C22D9×#6711yescharacteristic
502C4—41no—
503C4—62no—
504C4—62no—
505C4—182no—
506C4—1081no—
507C4—1081no—
508C3—21no—
509C3#1058867411yescharacteristic, complemented
510C3#1059130611yescharacteristic
511C2—362no—
512C2#1172093911yescharacteristic
513C2#1172095011yescharacteristic
514C2#1172098311yescharacteristic
515C2#1172098411yescharacteristic
516C2#1172099111yescharacteristic
517C2#1172103411yescharacteristic
518C2#1172128111yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutator, cosocleC23×C3×C9C23
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
hypercenterC22×C4D3×D9
hypocenterC3×C9#396
LCSG ▷ C23×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C9×Dic3⋊C4C2semidirect
5. C2×Dic3⋊Dic9C2semidirect
6. C2×Dic9⋊Dic3C2semidirect
7. #11720572C2semidirect
126. C2×Dic3⋊C4D9semidirect
287. C3×C9#396semidirect
438. C9#4948semidirect
509. C3#10588674semidirect

Maximal subgroups

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

subgroupindex
C2×C3×(C2×D9)⋊C42
C2×C9×Dic3⋊C42
C2×(C2×D9)⋊Dic32
C2×Dic3⋊Dic92
C2×Dic9⋊Dic32
#117205722
#105913063
#105886743