Subgroups — C₃³×#101 #11722214

Order 864.

532 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃³×M₁₆	C₂	1	2	yes	maximal
3	C₃²×#101	C₃	1	13	yes	maximal, direct product factor
4	C₃³×Q₈	—	2	2	no	—
5	C₂×C₃³×C₄	C₄	1	2	yes	—
6	C₂×C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₃³×C₈	—	2	2	no	—
8	C₂×C₃²×Q₈	C₂×C₃	1	13	yes	—
9	C₃²×M₁₆	C₂×C₃	1	26	yes	—
10	C₂²×C₃³	C₂×C₄	1	1	yes	characteristic
11	C₃³×C₄	—	2	2	no	—
12	C₃³×C₄	D₄	1	2	yes	—
13	C₃×#101	C₃²	1	13	yes	direct product factor
14	C₃²×Q₈	—	2	26	no	—
15	C₂×C₃²×C₄	C₃×C₄	1	26	yes	—
16	C₂×C₃²×C₄	C₂²×C₃	1	13	yes	—
17	C₃²×C₈	—	2	26	no	—
18	C₂×C₃³	—	2	1	no	—
19	C₂×C₃³	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₃×Q₈	C₂×C₃²	1	13	yes	—
21	C₃×M₁₆	C₂×C₃²	1	26	yes	—
22	C₂²×C₃²	C₂×C₃×C₄	1	13	yes	—
23	C₃²×C₄	—	2	26	no	—
24	C₃²×C₄	C₃×D₄	1	26	yes	—
25	#101	C₃³	1	1	yes	characteristic, direct product factor, Sylow
26	C₃³	#101	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×Q₈	—	2	26	no	—
28	C₂×C₃×C₄	C₃²×C₄	1	26	yes	—
29	C₂×C₃×C₄	C₂²×C₃²	1	13	yes	—
30	C₃×C₈	—	2	26	no	—
31	C₂×C₃²	—	2	13	no	—
32	C₂×C₃²	C₃×C₂²⋊C₄	1	13	yes	—
33	C₂×Q₈	C₂×C₃³	1	1	yes	characteristic
34	M₁₆	C₂×C₃³	1	2	yes	—
35	C₂²×C₃	C₂×C₃²×C₄	1	13	yes	—
36	C₃×C₄	—	2	26	no	—
37	C₃×C₄	C₃²×D₄	1	26	yes	—
38	C₃²	C₃×#101	1	13	yes	direct product factor
39	Q₈	—	2	2	no	—
40	C₂×C₄	C₃³×C₄	1	2	yes	—
41	C₂×C₄	C₂²×C₃³	1	1	yes	characteristic
42	C₈	—	2	2	no	—
43	C₂×C₃	—	2	13	no	—
44	C₂×C₃	C₃²×C₂²⋊C₄	1	13	yes	—
45	C₂²	C₂×C₃³×C₄	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₃³×D₄	1	2	yes	—
48	C₃	C₃²×#101	1	13	yes	direct product factor
49	C₂	—	2	1	no	—
50	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	C₂²×C₃³	C₂×C₄
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
3. C₃²×#101	C₃	direct (N × H)
13. C₃×#101	C₃²	direct (N × H)
25. #101	C₃³	direct (N × H)
26. C₃³	#101	direct (N × H)
38. C₃²	C₃×#101	direct (N × H)
48. C₃	C₃²×#101	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×Q₈	2
C₃³×M₁₆	2
C₃²×#101	3

Subgroups — C33×#101 #11722214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#101 #11722214