Subgroups — C₃³×#108 #11722221

Order 864.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×#108	C₃	1	13	yes	maximal, direct product factor
4	C₂×C₃³×C₄	C₂²	1	1	yes	characteristic
5	C₃³×C₈	—	2	2	no	—
6	C₃³×C₈	C₄	1	2	yes	—
7	C₃²×M₁₆	C₂×C₃	1	26	yes	—
8	C₂×C₃²×C₈	C₂×C₃	1	13	yes	—
9	C₂²×C₃³	Q₈	1	1	yes	characteristic
10	C₃³×C₄	C₂×C₄	1	1	yes	characteristic
11	C₃³×C₄	D₄	1	1	yes	characteristic
12	C₃×#108	C₃²	1	13	yes	direct product factor
13	C₂×C₃²×C₄	C₂²×C₃	1	13	yes	—
14	C₃²×C₈	—	2	26	no	—
15	C₃²×C₈	C₃×C₄	1	26	yes	—
16	C₂×C₃³	—	2	1	no	—
17	C₂×C₃³	C₄⋊C₄	1	1	yes	characteristic
18	C₃×M₁₆	C₂×C₃²	1	26	yes	—
19	C₂×C₃×C₈	C₂×C₃²	1	13	yes	—
20	C₂²×C₃²	C₃×Q₈	1	13	yes	—
21	C₃²×C₄	C₂×C₃×C₄	1	13	yes	—
22	C₃²×C₄	C₃×D₄	1	13	yes	—
23	#108	C₃³	1	1	yes	characteristic, direct product factor, Sylow
24	C₃³	#108	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃×C₄	C₂²×C₃²	1	13	yes	—
26	C₃×C₈	—	2	26	no	—
27	C₃×C₈	C₃²×C₄	1	26	yes	—
28	C₂×C₃²	—	2	13	no	—
29	C₂×C₃²	C₃×C₄⋊C₄	1	13	yes	—
30	M₁₆	C₂×C₃³	1	2	yes	—
31	C₂×C₈	C₂×C₃³	1	1	yes	characteristic
32	C₂²×C₃	C₃²×Q₈	1	13	yes	—
33	C₃×C₄	C₂×C₃²×C₄	1	13	yes	—
34	C₃×C₄	C₃²×D₄	1	13	yes	—
35	C₃²	C₃×#108	1	13	yes	direct product factor
36	C₂×C₄	C₂²×C₃³	1	1	yes	characteristic
37	C₈	—	2	2	no	—
38	C₈	C₃³×C₄	1	2	yes	—
39	C₂×C₃	—	2	13	no	—
40	C₂×C₃	C₃²×C₄⋊C₄	1	13	yes	—
41	C₂²	C₃³×Q₈	1	1	yes	characteristic
42	C₄	C₂×C₃³×C₄	1	1	yes	characteristic
43	C₄	C₃³×D₄	1	1	yes	characteristic
44	C₃	C₃²×#108	1	13	yes	direct product factor
45	C₂	—	2	1	no	—
46	C₂	C₃³×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃³×C₄	D₄
commutator	C₄	C₂×C₃³×C₄
Frattini, cosocle	C₂×C₄	C₂²×C₃³
socle	C₂×C₃³	C₄⋊C₄
prime radical	C₂²×C₃³	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃³×C₄ ◁ C₂×C₃³×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃²×#108	C₃	direct (N × H)
12. C₃×#108	C₃²	direct (N × H)
23. #108	C₃³	direct (N × H)
24. C₃³	#108	direct (N × H)
35. C₃²	C₃×#108	direct (N × H)
44. C₃	C₃²×#108	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×M₁₆	2
C₂×C₃³×C₈	2
C₃²×#108	3

Subgroups — C33×#108 #11722221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#108 #11722221