Subgroups — C₃³×#100 #11722213

Order 864.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃³×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₃²×#100	C₃	1	13	yes	maximal, direct product factor
4	C₂³×C₃³	C₄	1	2	yes	—
5	C₃³×D₄	—	2	2	no	—
6	C₂×C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₃³×C₈	—	2	2	no	—
8	C₂×C₃²×D₄	C₂×C₃	1	13	yes	—
9	C₃²×M₁₆	C₂×C₃	1	26	yes	complemented
10	C₂²×C₃³	—	2	2	no	—
11	C₂²×C₃³	—	4	2	no	—
12	C₂²×C₃³	C₂×C₄	1	1	yes	characteristic
13	C₃³×C₄	D₄	1	2	yes	—
14	C₃×#100	C₃²	1	13	yes	direct product factor
15	C₂³×C₃²	C₃×C₄	1	26	yes	—
16	C₃²×D₄	—	2	26	no	—
17	C₂×C₃²×C₄	C₂²×C₃	1	13	yes	—
18	C₃²×C₈	—	2	26	no	—
19	C₂×C₃³	—	2	1	no	—
20	C₂×C₃³	—	4	2	no	—
21	C₂×C₃³	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₃×D₄	C₂×C₃²	1	13	yes	—
23	C₃×M₁₆	C₂×C₃²	1	26	yes	complemented
24	C₂²×C₃²	—	2	26	no	—
25	C₂²×C₃²	—	4	26	no	—
26	C₂²×C₃²	C₂×C₃×C₄	1	13	yes	—
27	C₃²×C₄	C₃×D₄	1	26	yes	—
28	#100	C₃³	1	1	yes	characteristic, direct product factor, Sylow
29	C₃³	#100	1	1	yes	characteristic, direct product factor, Sylow
30	C₂³×C₃	C₃²×C₄	1	26	yes	—
31	C₃×D₄	—	2	26	no	—
32	C₂×C₃×C₄	C₂²×C₃²	1	13	yes	—
33	C₃×C₈	—	2	26	no	—
34	C₂×C₃²	—	2	13	no	—
35	C₂×C₃²	—	4	26	no	—
36	C₂×C₃²	C₃×C₂²⋊C₄	1	13	yes	—
37	C₂×D₄	C₂×C₃³	1	1	yes	characteristic
38	M₁₆	C₂×C₃³	1	2	yes	complemented
39	C₂²×C₃	—	2	26	no	—
40	C₂²×C₃	—	4	26	no	—
41	C₂²×C₃	C₂×C₃²×C₄	1	13	yes	—
42	C₃×C₄	C₃²×D₄	1	26	yes	—
43	C₃²	C₃×#100	1	13	yes	direct product factor
44	C₂³	C₃³×C₄	1	2	yes	—
45	D₄	—	2	2	no	—
46	C₂×C₄	C₂²×C₃³	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₂×C₃	—	2	13	no	—
49	C₂×C₃	—	4	26	no	—
50	C₂×C₃	C₃²×C₂²⋊C₄	1	13	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	—	4	2	no	—
53	C₂²	C₂×C₃³×C₄	1	1	yes	characteristic
54	C₄	C₃³×D₄	1	2	yes	—
55	C₃	C₃²×#100	1	13	yes	direct product factor
56	C₂	—	2	1	no	—
57	C₂	—	4	2	no	—
58	C₂	C₃³×C₂²⋊C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃³×M₁₆	C₂	semidirect
3. C₃²×#100	C₃	direct (N × H)
9. C₃²×M₁₆	C₂×C₃	semidirect
14. C₃×#100	C₃²	direct (N × H)
23. C₃×M₁₆	C₂×C₃²	semidirect
28. #100	C₃³	direct (N × H)
29. C₃³	#100	direct (N × H)
38. M₁₆	C₂×C₃³	semidirect
43. C₃²	C₃×#100	direct (N × H)
55. C₃	C₃²×#100	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×D₄	2
C₃³×M₁₆	2
C₃²×#100	3

Subgroups — C33×#100 #11722213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#100 #11722213