Finite Group Databasebeta

← C3×#92264⋊C2 #72243330

Subgroups — C3×#92264⋊C2 #72243330

Order 2916.

496 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C3×#92309C211yesmaximal, characteristic, complemented
2C3×#92264C211yesmaximal, characteristic, complemented
3C3×#92264C211yesmaximal, characteristic, complemented
4C3×D3×AGL(1,ℤ/9)—31nomaximal
5C3×D3×AGL(1,ℤ/9)—31nomaximal
6#92264⋊C2C311yesmaximal, characteristic, direct product factor
7#92264⋊C2C311yesmaximal, characteristic, direct product factor
8#92264⋊C2C311yesmaximal, characteristic, direct product factor
9C3×D92C311yesmaximal, characteristic, complemented
10C3×#6896C2211yescharacteristic, complemented, Sylow
11C3×C3⋊AGL(1,ℤ/9)—31no—
12C3×C3⋊AGL(1,ℤ/9)—31no—
13C3×D3×3−1+2—31no—
14C3×D3×3−1+2—31no—
15C32×AGL(1,ℤ/9)D311yescharacteristic
16C32×AGL(1,ℤ/9)D311yescharacteristic
17#92309C2×C311yescharacteristic, complemented
18#92309C2×C311yescharacteristic, complemented
19#92309C2×C311yescharacteristic, complemented
20C3×C9⋊D9C2×C311yescharacteristic, complemented
21#92264—21no—
22#92264—21no—
23#92264—21no—
24#92264—21no—
25#92264—21no—
26#92264—21no—
27#92264C2×C311yescharacteristic, complemented
28#92264C2×C311yescharacteristic, complemented
29#92264C2×C311yescharacteristic, complemented
30#92264C2×C311yescharacteristic, complemented
31#92264C2×C311yescharacteristic, complemented
32#92264C2×C311yescharacteristic, complemented
33C3×D9⋊C9—21no—
34C3×D9⋊C9—21no—
35C3×#4169—61no—
36C3×C9×D9C2×C311yescharacteristic, complemented
37C3×C9×D9C2×C311yescharacteristic, complemented
38C32×D32—91no—
39C2×C3×AGL(1,ℤ/9)—91no—
40C2×C3×AGL(1,ℤ/9)—91no—
41D3×AGL(1,ℤ/9)—31no—
42D3×AGL(1,ℤ/9)—31no—
43D3×AGL(1,ℤ/9)—31no—
44D3×AGL(1,ℤ/9)—31no—
45D3×AGL(1,ℤ/9)—31no—
46D3×AGL(1,ℤ/9)—31no—
47C3×D3×D9—31no—
48C3×D3×D9—31no—
49D92C3211yescharacteristic, complemented
50C32×3−1+2C2×D311yescharacteristic
51C32×3−1+2C2×D311yescharacteristic
52#6896—21no—
53#6896—21no—
54#6896—21no—
55#6896—21no—
56#6896—21no—
57#6896—21no—
58#6896—41no—
59#6896—41no—
60#6896—41no—
61#6896C22×C311yescharacteristic, complemented
62#6896C22×C311yescharacteristic, complemented
63#6896C22×C311yescharacteristic, complemented
64C3×C9⋊C9—21no—
65C3×C9⋊C9—21no—
66C3×C9⋊C9—41no—
67C3×C32⋊C9—21no—
68C3×C92C22×C311yescharacteristic, complemented
69C32×C3⋊D3—91no—
70C33×D3—31no—
71C33×D3—31no—
72C2×C3×3−1+2—91no—
73C2×C3×3−1+2—91no—
74C3⋊AGL(1,ℤ/9)—31no—
75C3⋊AGL(1,ℤ/9)—31no—
76C3⋊AGL(1,ℤ/9)—31no—
77C3⋊AGL(1,ℤ/9)—31no—
78C3⋊AGL(1,ℤ/9)—31no—
79C3⋊AGL(1,ℤ/9)—31no—
80C3×C3⋊D9—31no—
81C3×C3⋊D9—31no—
82C3×C3⋊D9—61no—
83D3×3−1+2—31no—
84D3×3−1+2—31no—
85D3×3−1+2—31no—
86D3×3−1+2—31no—
87D3×3−1+2—31no—
88D3×3−1+2—31no—
89D3×3−1+2—61no—
90D3×3−1+2—61no—
91D3×3−1+2—61no—
92D3×3−1+2—61no—
93D3×3−1+2—61no—
94D3×3−1+2—61no—
95C3×AGL(1,ℤ/9)—61no—
96C3×AGL(1,ℤ/9)—61no—
97C3×AGL(1,ℤ/9)—61no—
98C3×AGL(1,ℤ/9)—61no—
99C3×AGL(1,ℤ/9)—91no—
100C3×AGL(1,ℤ/9)—91no—
101C3×AGL(1,ℤ/9)—181no—
102C3×AGL(1,ℤ/9)—181no—
103C3×AGL(1,ℤ/9)C3×D311yescharacteristic
104C3×AGL(1,ℤ/9)C3×D311yescharacteristic
105C3×AGL(1,ℤ/9)C3×D311yescharacteristic
106C3×AGL(1,ℤ/9)C3×D311yescharacteristic
107C3×AGL(1,ℤ/9)C3×D311yescharacteristic
108C3×AGL(1,ℤ/9)C3×D311yescharacteristic
109C3×D3×C9—31no—
110C3×D3×C9—31no—
111C3×D3×C9—61no—
112C3×D3×C9—61no—
113C32×D9C3×D311yescharacteristic
114C32×D9C3×D311yescharacteristic
115C9⋊D9C2×C3211yescharacteristic, complemented
116D9⋊C9—21no—
117D9⋊C9—21no—
118D9⋊C9—21no—
119D9⋊C9—21no—
120D9⋊C9—21no—
121D9⋊C9—21no—
122#4169—61no—
123#4169—61no—
124#4169—61no—
125C9×D9—21no—
126C9×D9—21no—
127C9×D9C2×C3211yescharacteristic, complemented
128C9×D9C2×C3211yescharacteristic, complemented
129C2×C32×D3—271no—
130C2×C32×D3—271no—
131C3×D32—91no—
132C3×D32—91no—
133C3×D32—91no—
134C3×D32—91no—
135C2×AGL(1,ℤ/9)—91no—
136C2×AGL(1,ℤ/9)—91no—
137C2×AGL(1,ℤ/9)—91no—
138C2×AGL(1,ℤ/9)—91no—
139C2×AGL(1,ℤ/9)—91no—
140C2×AGL(1,ℤ/9)—91no—
141C2×C3×D9—91no—
142C2×C3×D9—91no—
143D3×D9—31no—
144D3×D9—31no—
145C34D3211yescharacteristic
146C3×3−1+2—21no—
147C3×3−1+2—21no—
148C3×3−1+2—21no—
149C3×3−1+2—21no—
150C3×3−1+2—21no—
151C3×3−1+2—21no—
152C3×3−1+2—61no—
153C3×3−1+2—61no—
154C3×3−1+2—61no—
155C3×3−1+2—61no—
156C3×3−1+2—121no—
157C3×3−1+2—121no—
158C3×3−1+2—121no—
159C3×3−1+2—121no—
160C3×3−1+2C2×C3×D311yescharacteristic
161C3×3−1+2C2×C3×D311yescharacteristic
162C3×3−1+2C2×C3×D311yescharacteristic
163C3×3−1+2C2×C3×D311yescharacteristic
164C3×3−1+2C2×C3×D311yescharacteristic
165C3×3−1+2C2×C3×D311yescharacteristic
166C32×C9—21no—
167C32×C9—21no—
168C32×C9—21no—
169C32×C9—41no—
170C32×C9C2×C3×D311yescharacteristic
171C32×C9C2×C3×D311yescharacteristic
172C9⋊C9—21no—
173C9⋊C9—21no—
174C9⋊C9—21no—
175C9⋊C9—21no—
176C9⋊C9—21no—
177C9⋊C9—21no—
178C9⋊C9—41no—
179C9⋊C9—41no—
180C9⋊C9—41no—
181C9⋊C9—41no—
182C9⋊C9—41no—
183C9⋊C9—41no—
184C9⋊C9—41no—
185C9⋊C9—41no—
186C9⋊C9—41no—
187C9⋊C9—41no—
188C9⋊C9—41no—
189C9⋊C9—41no—
190C9⋊C9—41no—
191C9⋊C9—41no—
192C9⋊C9—41no—
193C32⋊C9—21no—
194C32⋊C9—21no—
195C32⋊C9—21no—
196C32⋊C9—41no—
197C32⋊C9—41no—
198C32⋊C9—41no—
199C92—21no—
200C92—21no—
201C92—41no—
202C92C22×C3211yescharacteristic, complemented
203C2×C33—91no—
204C2×C33—91no—
205C3×C3⋊D3—91no—
206C3×C3⋊D3—91no—
207C3×C3⋊D3—91no—
208C3×C3⋊D3—91no—
209C32×D3—31no—
210C32×D3—31no—
211C32×D3—31no—
212C32×D3—31no—
213C32×D3—31no—
214C32×D3—31no—
215C32×D3—31no—
216C32×D3—31no—
217C32×D3—181no—
218C32×D3—181no—
219C32×D3—181no—
220C32×D3—181no—
221C32×D3—271no—
222C32×D3—271no—
223C32×D3—541no—
224C2×3−1+2—91no—
225C2×3−1+2—91no—
226C2×3−1+2—91no—
227C2×3−1+2—91no—
228C2×3−1+2—91no—
229C2×3−1+2—91no—
230C2×3−1+2—181no—
231C2×3−1+2—181no—
232C2×3−1+2—181no—
233C2×3−1+2—181no—
234C2×3−1+2—181no—
235C2×3−1+2—181no—
236C2×C3×C9—91no—
237C2×C3×C9—91no—
238C2×C3×C9—181no—
239C2×C3×C9—181no—
240C3⋊D9—31no—
241C3⋊D9—31no—
242C3⋊D9—61no—
243AGL(1,ℤ/9)—31no—
244AGL(1,ℤ/9)—31no—
245AGL(1,ℤ/9)—31no—
246AGL(1,ℤ/9)—31no—
247AGL(1,ℤ/9)—61no—
248AGL(1,ℤ/9)—61no—
249AGL(1,ℤ/9)—91no—
250AGL(1,ℤ/9)—91no—
251AGL(1,ℤ/9)—91no—
252AGL(1,ℤ/9)—91no—
253AGL(1,ℤ/9)—91no—
254AGL(1,ℤ/9)—91no—
255AGL(1,ℤ/9)—181no—
256AGL(1,ℤ/9)—181no—
257AGL(1,ℤ/9)—181no—
258AGL(1,ℤ/9)—181no—
259AGL(1,ℤ/9)—181no—
260AGL(1,ℤ/9)—181no—
261D3×C9—31no—
262D3×C9—31no—
263D3×C9—61no—
264D3×C9—61no—
265D3×C9—61no—
266D3×C9—61no—
267D3×C9—61no—
268D3×C9—61no—
269D3×C9—61no—
270D3×C9—61no—
271C3×D9—21no—
272C3×D9—21no—
273C3×D9—91no—
274C3×D9—91no—
275C3×D9—181no—
276C3×D9—181no—
277C3×D9—541no—
278C3×D9AGL(1,ℤ/9)11yescharacteristic, complemented
279C3×D9AGL(1,ℤ/9)11yescharacteristic, complemented
280C3×D9C32×D311yescharacteristic
281C3×D9C32×D311yescharacteristic
282C22×C32—811no—
283C2×C3×D3—271no—
284C2×C3×D3—271no—
285C2×C3×D3—271no—
286C2×C3×D3—271no—
287C2×C3×D3—271no—
288C2×C3×D3—271no—
289C2×C3×D3—271no—
290C2×C3×D3—271no—
291D32—91no—
292C2×D9—91no—
293C2×D9—91no—
294C33—61no—
295C33—61no—
296C33—61no—
297C33—61no—
298C33—121no—
299C33—121no—
300C33C3×D3211yescharacteristic
301C33C3×D3211yescharacteristic
302C33C3×D3211yescharacteristic
303C33C3×D3211yescharacteristic
3043−1+2—31no—
3053−1+2—31no—
3063−1+2—31no—
3073−1+2—31no—
3083−1+2—61no—
3093−1+2—61no—
3103−1+2—61no—
3113−1+2—61no—
3123−1+2—61no—
3133−1+2—61no—
3143−1+2—61no—
3153−1+2—61no—
3163−1+2—61no—
3173−1+2—121no—
3183−1+2—121no—
3193−1+2—121no—
3203−1+2—121no—
3213−1+2—121no—
3223−1+2—121no—
3233−1+2—121no—
3243−1+2—121no—
3253−1+2—121no—
3263−1+2—121no—
3273−1+2—121no—
328C3×C9—21no—
329C3×C9—21no—
330C3×C9—21no—
331C3×C9—21no—
332C3×C9—21no—
333C3×C9—21no—
334C3×C9—21no—
335C3×C9—21no—
336C3×C9—21no—
337C3×C9—21no—
338C3×C9—21no—
339C3×C9—21no—
340C3×C9—21no—
341C3×C9—41no—
342C3×C9—41no—
343C3×C9—41no—
344C3×C9—41no—
345C3×C9—41no—
346C3×C9—41no—
347C3×C9—61no—
348C3×C9—121no—
349C3×C9—121no—
350C3×C9—121no—
351C3×C9—121no—
352C3×C9—121no—
353C3×C9—121no—
354C3×C9—122no—
355C3×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
356C3×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
357C3×C9C2×C32×D311yescharacteristic
358C3×C9C2×C32×D311yescharacteristic
359C2×C32—91no—
360C2×C32—91no—
361C2×C32—91no—
362C2×C32—91no—
363C2×C32—91no—
364C2×C32—91no—
365C2×C32—91no—
366C2×C32—91no—
367C2×C32—541no—
368C2×C32—541no—
369C2×C32—541no—
370C2×C32—541no—
371C2×C32—811no—
372C3⋊D3—91no—
373C3×D3—31no—
374C3×D3—31no—
375C3×D3—31no—
376C3×D3—31no—
377C3×D3—61no—
378C3×D3—61no—
379C3×D3—91no—
380C3×D3—181no—
381C3×D3—181no—
382C3×D3—181no—
383C3×D3—181no—
384C3×D3—181no—
385C3×D3—271no—
386C3×D3—271no—
387C3×D3—271no—
388C3×D3—271no—
389C3×D3—271no—
390C3×D3—271no—
391C3×D3—271no—
392C3×D3—271no—
393C3×D3—541no—
394C3×D3—541no—
395C3×D3—541no—
396C3×D3—541no—
397C2×C9—91no—
398C2×C9—91no—
399C2×C9—181no—
400C2×C9—181no—
401C2×C9—181no—
402C2×C9—181no—
403C2×C9—181no—
404C2×C9—181no—
405C2×C9—181no—
406C2×C9—181no—
407D9—91no—
408D9—91no—
409D9—181no—
410D9—181no—
411D9—541no—
412D9C3×AGL(1,ℤ/9)11yescharacteristic, complemented
413D9C3×AGL(1,ℤ/9)11yescharacteristic, complemented
414C22×C3—811no—
415C22×C3—811no—
416C22×C3—811no—
417C22×C3—811no—
418C2×D3—271no—
419C2×D3—271no—
420C32—21no—
421C32—21no—
422C32—21no—
423C32—31no—
424C32—41no—
425C32—61no—
426C32—61no—
427C32—61no—
428C32—61no—
429C32—61no—
430C32—61no—
431C32—61no—
432C32—121no—
433C32—181no—
434C32—181no—
435C32—361no—
436C32—361no—
437C32D3×AGL(1,ℤ/9)11yescharacteristic
438C32D3×AGL(1,ℤ/9)11yescharacteristic
439C32C32×D3211yescharacteristic
440C9—21no—
441C9—21no—
442C9—21no—
443C9—21no—
444C9—41no—
445C9—41no—
446C9—61no—
447C9—61no—
448C9—61no—
449C9—61no—
450C9—61no—
451C9—121no—
452C9—121no—
453C9—121no—
454C9—121no—
455C9—121no—
456C9—121no—
457C9C2×C3×AGL(1,ℤ/9)11yescharacteristic, complemented
458C9C2×C3×AGL(1,ℤ/9)11yescharacteristic, complemented
459C2×C3—91no—
460C2×C3—91no—
461C2×C3—91no—
462C2×C3—91no—
463C2×C3—181no—
464C2×C3—181no—
465C2×C3—271no—
466C2×C3—271no—
467C2×C3—271no—
468C2×C3—541no—
469C2×C3—541no—
470C2×C3—541no—
471C2×C3—811no—
472C2×C3—811no—
473C2×C3—811no—
474C2×C3—811no—
475D3—31no—
476D3—31no—
477D3—271no—
478D3—271no—
479D3—541no—
480C22—811noSylow
481C3—21no—
482C3—21no—
483C3—21no—
484C3—41no—
485C3—181no—
486C3—181no—
487C3—361no—
488C3#92264⋊C211yescharacteristic, direct product factor
489C3C3×D3×AGL(1,ℤ/9)11yescharacteristic
490C3C3×D3×AGL(1,ℤ/9)11yescharacteristic
491C2—91no—
492C2—91no—
493C2—811no—
subgroupG/H
center, hypercenterC3#92264⋊C2
commutator, cosocle, hypocenterC92C22×C32
FrattiniC32C32×D32
FittingC3×#6896C22
socleC33C3×D32
LCSG ▷ C92
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#92309C2semidirect
2. C3×#92264C2semidirect
3. C3×#92264C2semidirect
6. #92264⋊C2C3direct (N × H)
7. #92264⋊C2C3direct (N × H)
8. #92264⋊C2C3direct (N × H)
9. C3×D92C3semidirect
10. C3×#6896C22semidirect
17. #92309C2×C3semidirect
18. #92309C2×C3semidirect
19. #92309C2×C3semidirect
20. C3×C9⋊D9C2×C3semidirect
27. #92264C2×C3semidirect
28. #92264C2×C3semidirect
29. #92264C2×C3semidirect
30. #92264C2×C3semidirect
31. #92264C2×C3semidirect
32. #92264C2×C3semidirect
36. C3×C9×D9C2×C3semidirect
37. C3×C9×D9C2×C3semidirect
49. D92C32semidirect
61. #6896C22×C3semidirect
62. #6896C22×C3semidirect
63. #6896C22×C3semidirect
68. C3×C92C22×C3semidirect
115. C9⋊D9C2×C32semidirect
127. C9×D9C2×C32semidirect
128. C9×D9C2×C32semidirect
202. C92C22×C32semidirect
278. C3×D9AGL(1,ℤ/9)semidirect
279. C3×D9AGL(1,ℤ/9)semidirect
355. C3×C9C2×AGL(1,ℤ/9)semidirect
356. C3×C9C2×AGL(1,ℤ/9)semidirect
412. D9C3×AGL(1,ℤ/9)semidirect
413. D9C3×AGL(1,ℤ/9)semidirect
457. C9C2×C3×AGL(1,ℤ/9)semidirect
458. C9C2×C3×AGL(1,ℤ/9)semidirect
488. C3#92264⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#923092
C3×#922642
C3×D3×AGL(1,ℤ/9)3
#92264⋊C23
C3×D923