Finite Group Databasebeta

← C3×#66431⋊C3 #72243378

Subgroups — C3×#66431⋊C3 #72243378

Order 2916.

1672 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C3⋊AGL(1,ℤ/9)C212yesmaximal, complemented
2C3×C3⋊D3×3−1+2C211yesmaximal, characteristic, complemented
3C32×#1113—31nomaximal
4#66431⋊C3C313yesmaximal, direct product factor
5C3×#66431C311yesmaximal, characteristic, complemented
6C3×D3×AGL(1,ℤ/9)—32nomaximal
7C33×3−1+2C2211yescharacteristic, complemented, Sylow
8C33×C3⋊D3—32no—
9C33×C3⋊D3D311yescharacteristic
10C3⋊D3×3−1+2—23no—
11C3⋊D3×3−1+2C2×C313yescomplemented
12C3×C3⋊AGL(1,ℤ/9)—26no—
13C3×C3⋊AGL(1,ℤ/9)—22no—
14C3×C3⋊AGL(1,ℤ/9)D312yescomplemented
15C3×C3⋊AGL(1,ℤ/9)C2×C316yescomplemented
16C3×C9×C3⋊D3—21no—
17C3×C9×C3⋊D3C2×C311yescharacteristic, complemented
18C32×C3⋊D9C2×C312yescomplemented
19C3×D3×3−1+2—32no—
20C3×D3×3−1+2—61no—
21C32×AGL(1,ℤ/9)—32no—
22C32×AGL(1,ℤ/9)—62no—
23C3×#1113—31no—
24C3×#1113—33no—
25C32×D32—92no—
26C32×D32—91no—
27C2×C3×AGL(1,ℤ/9)—91no—
28#66431C3211yescharacteristic, complemented
29D3×AGL(1,ℤ/9)—36no—
30C3×D3×D9—32no—
31C35C2×D311yescharacteristic
32C32×3−1+2—21no—
33C32×3−1+2—23no—
34C32×3−1+2—22no—
35C32×3−1+2—26no—
36C32×3−1+2—22no—
37C32×3−1+2—42no—
38C32×3−1+2—42no—
39C32×3−1+2—41no—
40C32×3−1+2—46no—
41C32×3−1+2—43no—
42C32×3−1+2—46no—
43C32×3−1+2—41no—
44C32×3−1+2C2×D312yescomplemented
45C32×3−1+2C22×C313yescomplemented
46C33×C9—21no—
47C33×C9C22×C311yescharacteristic, complemented
48C32×C3⋊D3—32no—
49C32×C3⋊D3—31no—
50C32×C3⋊D3—32no—
51C32×C3⋊D3—36no—
52C32×C3⋊D3—61no—
53C32×C3⋊D3—62no—
54C32×C3⋊D3—66no—
55C32×C3⋊D3C3×D311yescharacteristic
56C32×C3⋊D3C3×D313yes—
57C33×D3—32no—
58C33×D3—61no—
59C33×D3—92no—
60C33×D3—92no—
61C33×D3—182no—
62C2×C3×3−1+2—91no—
63C3⋊AGL(1,ℤ/9)—26no—
64C3⋊AGL(1,ℤ/9)C3×D316yescomplemented
65C9×C3⋊D3—23no—
66C9×C3⋊D3—21no—
67C9×C3⋊D3C2×C3211yescharacteristic, complemented
68C3×C3⋊D9—22no—
69C3×C3⋊D9C3×D312yescomplemented
70C3×C3⋊D9C2×C3212yescomplemented
71D3×3−1+2—36no—
72D3×3−1+2—63no—
73D3×3−1+2—66no—
74D3×3−1+2—66no—
75C3×AGL(1,ℤ/9)—32no—
76C3×AGL(1,ℤ/9)—36no—
77C3×AGL(1,ℤ/9)—62no—
78C3×AGL(1,ℤ/9)—66no—
79C3×AGL(1,ℤ/9)—62no—
80C3×AGL(1,ℤ/9)—66no—
81C3×AGL(1,ℤ/9)—64no—
82C3×AGL(1,ℤ/9)—612no—
83C3×D3×C9—32no—
84C3×D3×C9—61no—
85C3×D3×C9—62no—
86C3×D3×C9—62no—
87C32×D9—32no—
88C32×D9—62no—
89C2×C32×D3—271no—
90C2×C32×D3—272no—
91#1113—31no—
92C3×D32—92no—
93C3×D32—96no—
94C3×D32—93no—
95C3×D32—91no—
96C2×AGL(1,ℤ/9)—93no—
97C2×C3×D9—91no—
98D3×D9—32no—
99C34—26no—
100C34—22no—
101C34—21no—
102C34—31no—
103C34—41no—
104C34—43no—
105C34—61no—
106C34—62no—
107C34—122no—
108C34—121no—
109C34—122no—
110C34D3212yes—
111C34C2×C3×D311yescharacteristic
112C34C2×C3×D313yes—
113C3×3−1+2—26no—
114C3×3−1+2—26no—
115C3×3−1+2—23no—
116C3×3−1+2—212no—
117C3×3−1+2—24no—
118C3×3−1+2—26no—
119C3×3−1+2—22no—
120C3×3−1+2—26no—
121C3×3−1+2—22no—
122C3×3−1+2—26no—
123C3×3−1+2—42no—
124C3×3−1+2—46no—
125C3×3−1+2—46no—
126C3×3−1+2—43no—
127C3×3−1+2—46no—
128C3×3−1+2—412no—
129C3×3−1+2—46no—
130C3×3−1+2—42no—
131C3×3−1+2—412no—
132C3×3−1+2—412no—
133C3×3−1+2—46no—
134C3×3−1+2—44no—
135C3×3−1+2—46no—
136C3×3−1+2—43no—
137C3×3−1+2—46no—
138C3×3−1+2—412no—
139C3×3−1+2—46no—
140C3×3−1+2—424no—
141C3×3−1+2—412no—
142C3×3−1+2—46no—
143C3×3−1+2—412no—
144C3×3−1+2—44no—
145C3×3−1+2—424no—
146C3×3−1+2—412no—
147C3×3−1+2—412no—
148C3×3−1+2—46no—
149C3×3−1+2—42no—
150C3×3−1+2—46no—
151C3×3−1+2—41no—
152C3×3−1+2—43no—
153C3×3−1+2—41no—
154C3×3−1+2D3211yescharacteristic, complemented
155C3×3−1+2C2×C3×D316yescomplemented
156C32×C9—22no—
157C32×C9—22no—
158C32×C9—22no—
159C32×C9—23no—
160C32×C9—21no—
161C32×C9—21no—
162C32×C9—22no—
163C32×C9—42no—
164C32×C9—41no—
165C32×C9—42no—
166C32×C9—41no—
167C32×C9—46no—
168C32×C9—46no—
169C32×C9—42no—
170C32×C9—42no—
171C32×C9C2×C3×D312yescomplemented
172C32×C9C22×C3211yescharacteristic, complemented
173C2×C33—91no—
174C2×C33—272no—
175C3×C3⋊D3—21no—
176C3×C3⋊D3—32no—
177C3×C3⋊D3—36no—
178C3×C3⋊D3—32no—
179C3×C3⋊D3—33no—
180C3×C3⋊D3—62no—
181C3×C3⋊D3—66no—
182C3×C3⋊D3AGL(1,ℤ/9)11yescharacteristic, complemented
183C3×C3⋊D3C32×D311yescharacteristic
184C32×D3—32no—
185C32×D3—36no—
186C32×D3—61no—
187C32×D3—63no—
188C32×D3—92no—
189C32×D3—92no—
190C32×D3—92no—
191C32×D3—96no—
192C32×D3—92no—
193C32×D3—92no—
194C32×D3—96no—
195C32×D3—182no—
196C32×D3—181no—
197C32×D3—182no—
198C32×D3—182no—
199C32×D3—186no—
200C32×D3—186no—
201C32×D3—182no—
202C32×D3—182no—
203C32×D3—182no—
204C32×D3—186no—
205C32×D3—184no—
206C32×D3—1812no—
207C2×3−1+2—93no—
208C2×3−1+2—183no—
209C2×C3×C9—91no—
210C2×C3×C9—181no—
211C3⋊D9C32×D312yescomplemented
212AGL(1,ℤ/9)—36no—
213AGL(1,ℤ/9)—66no—
214AGL(1,ℤ/9)—66no—
215AGL(1,ℤ/9)—612no—
216D3×C9—32no—
217D3×C9—61no—
218D3×C9—62no—
219D3×C9—66no—
220D3×C9—62no—
221D3×C9—66no—
222C3×D9—32no—
223C3×D9—32no—
224C3×D9—62no—
225C3×D9—62no—
226C3×D9—62no—
227C3×D9—64no—
228C22×C32—811no—
229C2×C3×D3—272no—
230C2×C3×D3—271no—
231C2×C3×D3—273no—
232C2×C3×D3—276no—
233D32—92no—
234D32—91no—
235C2×D9—91no—
236C33—22no—
237C33—21no—
238C33—22no—
239C33—21no—
240C33—26no—
241C33—22no—
242C33—26no—
243C33—23no—
244C33—32no—
245C33—33no—
246C33—41no—
247C33—42no—
248C33—42no—
249C33—41no—
250C33—43no—
251C33—46no—
252C33—46no—
253C33—43no—
254C33—41no—
255C33—62no—
256C33—62no—
257C33—66no—
258C33—66no—
259C33—61no—
260C33—62no—
261C33—612no—
262C33—64no—
263C33—62no—
264C33—122no—
265C33—121no—
266C33—122no—
267C33—126no—
268C33—121no—
269C33—122no—
270C33—123no—
271C33—124no—
272C33—1212no—
273C33—123no—
274C33—122no—
275C33—122no—
276C33—1212no—
277C33—126no—
278C33—124no—
279C33—126no—
280C33C2×AGL(1,ℤ/9)11yescharacteristic, complemented
281C33C3×D3212yes—
282C33C3×D3216yes—
283C33#111311yescharacteristic
284C33C2×C32×D311yescharacteristic
2853−1+2—23no—
2863−1+2—212no—
2873−1+2—26no—
2883−1+2—26no—
2893−1+2—46no—
2903−1+2—412no—
2913−1+2—46no—
2923−1+2—412no—
2933−1+2—412no—
2943−1+2—46no—
2953−1+2—46no—
2963−1+2—412no—
2973−1+2—424no—
2983−1+2—412no—
2993−1+2—46no—
3003−1+2—424no—
3013−1+2—412no—
3023−1+2—46no—
3033−1+2—46no—
3043−1+2—43no—
3053−1+2—43no—
3063−1+2C3×D3213yescomplemented
307C3×C9—21no—
308C3×C9—24no—
309C3×C9—26no—
310C3×C9—22no—
311C3×C9—22no—
312C3×C9—26no—
313C3×C9—22no—
314C3×C9—22no—
315C3×C9—22no—
316C3×C9—21no—
317C3×C9—42no—
318C3×C9—41no—
319C3×C9—46no—
320C3×C9—44no—
321C3×C9—46no—
322C3×C9—42no—
323C3×C9—42no—
324C3×C9—44no—
325C3×C9—46no—
326C3×C9—412no—
327C3×C9—42no—
328C3×C9—412no—
329C3×C9—42no—
330C3×C9—46no—
331C3×C9—41no—
332C3×C9—42no—
333C3×C9—42no—
334C3×C9—41no—
335C3×C9C3×D3211yescharacteristic, complemented
336C3×C9C2×C32×D312yescomplemented
337C2×C32—91no—
338C2×C32—93no—
339C2×C32—271no—
340C2×C32—272no—
341C2×C32—276no—
342C2×C32—272no—
343C2×C32—541no—
344C2×C32—546no—
345C2×C32—542no—
346C3⋊D3—32no—
347C3⋊D3C3×AGL(1,ℤ/9)11yescharacteristic, complemented
348C3×D3—32no—
349C3×D3—32no—
350C3×D3—62no—
351C3×D3—61no—
352C3×D3—61no—
353C3×D3—62no—
354C3×D3—96no—
355C3×D3—96no—
356C3×D3—92no—
357C3×D3—92no—
358C3×D3—92no—
359C3×D3—92no—
360C3×D3—96no—
361C3×D3—183no—
362C3×D3—182no—
363C3×D3—186no—
364C3×D3—182no—
365C3×D3—186no—
366C3×D3—182no—
367C3×D3—182no—
368C3×D3—186no—
369C3×D3—184no—
370C3×D3—1812no—
371C2×C9—91no—
372C2×C9—181no—
373C2×C9—183no—
374D9—32no—
375D9—62no—
376C22×C3—811no—
377C22×C3—813no—
378C2×D3—272no—
379C2×D3—271no—
380C32—22no—
381C32—24no—
382C32—21no—
383C32—22no—
384C32—22no—
385C32—22no—
386C32—22no—
387C32—21no—
388C32—22no—
389C32—26no—
390C32—31no—
391C32—36no—
392C32—41no—
393C32—42no—
394C32—41no—
395C32—42no—
396C32—44no—
397C32—42no—
398C32—44no—
399C32—42no—
400C32—41no—
401C32—42no—
402C32—41no—
403C32—43no—
404C32—61no—
405C32—66no—
406C32—66no—
407C32—63no—
408C32—612no—
409C32—62no—
410C32—66no—
411C32—122no—
412C32—123no—
413C32—126no—
414C32—122no—
415C32—126no—
416C32—123no—
417C32—123no—
418C32—126no—
419C32—126no—
420C32—126no—
421C32—1212no—
422C32—1212no—
423C32—121no—
424C32D3×AGL(1,ℤ/9)12yescomplemented
425C32C2×C3×AGL(1,ℤ/9)11yescharacteristic, complemented
426C32C32×D3212yes—
427C32C3×#111311yescharacteristic
428C32C3×#111313yes—
429C9—22no—
430C9—23no—
431C9—21no—
432C9—42no—
433C9—41no—
434C9—42no—
435C9—46no—
436C9—46no—
437C9C32×D3211yescharacteristic, complemented
438C2×C3—91no—
439C2×C3—91no—
440C2×C3—181no—
441C2×C3—273no—
442C2×C3—276no—
443C2×C3—272no—
444C2×C3—272no—
445C2×C3—542no—
446C2×C3—546no—
447D3—32no—
448D3—61no—
449D3—92no—
450D3—92no—
451D3—182no—
452C22—811noSylow
453C3—21no—
454C3—22no—
455C3—21no—
456C3—22no—
457C3—33no—
458C3—42no—
459C3—41no—
460C3—42no—
461C3—41no—
462C3—66no—
463C3—123no—
464C3C3×D3×AGL(1,ℤ/9)12yescomplemented
465C3#66431⋊C311yescharacteristic, direct product factor
466C3C32×#111311yescharacteristic
467C2—91no—
468C2—272no—
subgroupG/H
center, hypercenterC3#66431⋊C3
commutator, cosocle, hypocenterC32×C9C22×C32
FrattiniC3C32×#1113
FittingC33×3−1+2C22
socleC34C2×C3×D3
LCSG ▷ C32×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C3⋊AGL(1,ℤ/9)C2semidirect
2. C3×C3⋊D3×3−1+2C2semidirect
4. #66431⋊C3C3direct (N × H)
5. C3×#66431C3semidirect
7. C33×3−1+2C22semidirect
11. C3⋊D3×3−1+2C2×C3semidirect
14. C3×C3⋊AGL(1,ℤ/9)D3semidirect
15. C3×C3⋊AGL(1,ℤ/9)C2×C3semidirect
17. C3×C9×C3⋊D3C2×C3semidirect
18. C32×C3⋊D9C2×C3semidirect
28. #66431C32semidirect
44. C32×3−1+2C2×D3semidirect
45. C32×3−1+2C22×C3semidirect
47. C33×C9C22×C3semidirect
64. C3⋊AGL(1,ℤ/9)C3×D3semidirect
67. C9×C3⋊D3C2×C32semidirect
69. C3×C3⋊D9C3×D3semidirect
70. C3×C3⋊D9C2×C32semidirect
154. C3×3−1+2D32semidirect
155. C3×3−1+2C2×C3×D3semidirect
171. C32×C9C2×C3×D3semidirect
172. C32×C9C22×C32semidirect
182. C3×C3⋊D3AGL(1,ℤ/9)semidirect
211. C3⋊D9C32×D3semidirect
280. C33C2×AGL(1,ℤ/9)semidirect
306. 3−1+2C3×D32semidirect
335. C3×C9C3×D32semidirect
336. C3×C9C2×C32×D3semidirect
347. C3⋊D3C3×AGL(1,ℤ/9)semidirect
424. C32D3×AGL(1,ℤ/9)semidirect
425. C32C2×C3×AGL(1,ℤ/9)semidirect
437. C9C32×D32semidirect
464. C3C3×D3×AGL(1,ℤ/9)semidirect
465. C3#66431⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C3⋊AGL(1,ℤ/9)2
C3×C3⋊D3×3−1+22
C32×#11133
#66431⋊C33
C3×#664313
C3×D3×AGL(1,ℤ/9)3