Subgroups — C₃²×#430 #10593003

Order 576.

306 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃²×#108	C₂	1	4	yes	maximal, complemented
4	C₃×#430	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃²×M₁₆	—	2	2	no	—
7	C₃²×M₁₆	C₄	1	4	yes	—
8	C₃²×M₁₆	C₂²	1	4	yes	—
9	C₂×C₃²×C₈	—	2	2	no	—
10	C₂×C₃²×C₈	C₂²	1	2	yes	—
11	C₂×C₃×M₁₆	C₂×C₃	1	8	yes	—
12	C₂×C₃×M₁₆	C₂×C₃	1	4	yes	—
13	C₃×#108	C₂×C₃	1	16	yes	complemented
14	C₂³×C₃²	Q₈	1	1	yes	characteristic
15	C₂×C₃²×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₃²×C₄	D₄	1	2	yes	—
17	C₂×C₃²×C₄	Q₈	1	1	yes	characteristic
18	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
19	C₃²×C₈	—	2	4	no	—
20	C₃²×C₈	C₂×C₄	1	4	yes	—
21	#430	C₃²	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃×C₄	C₂²×C₃	1	4	yes	—
23	C₃×M₁₆	—	2	8	no	—
24	C₃×M₁₆	C₃×C₄	1	16	yes	—
25	C₃×M₁₆	C₂²×C₃	1	16	yes	—
26	C₂×C₃×C₈	—	2	8	no	—
27	C₂×C₃×C₈	C₂²×C₃	1	8	yes	—
28	C₂²×C₃²	—	4	1	no	—
29	C₂²×C₃²	C₄⋊C₄	1	2	yes	—
30	C₂²×C₃²	C₂×Q₈	1	1	yes	characteristic
31	C₃²×C₄	C₄⋊C₄	1	2	yes	—
32	C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₃²×C₄	C₂×D₄	1	1	yes	characteristic
34	C₂×M₁₆	C₂×C₃²	1	2	yes	—
35	C₂×M₁₆	C₂×C₃²	1	1	yes	characteristic
36	#108	C₂×C₃²	1	4	yes	complemented
37	C₂³×C₃	C₃×Q₈	1	4	yes	—
38	C₂×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
39	C₂×C₃×C₄	C₃×D₄	1	8	yes	—
40	C₂×C₃×C₄	C₃×Q₈	1	4	yes	—
41	C₂×C₃×C₄	C₂³×C₃	1	4	yes	—
42	C₃×C₈	—	2	16	no	—
43	C₃×C₈	C₂×C₃×C₄	1	16	yes	—
44	C₂×C₃²	—	2	2	no	—
45	C₂×C₃²	—	2	1	no	—
46	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₄	C₂²×C₃²	1	1	yes	characteristic
48	M₁₆	—	2	2	no	—
49	M₁₆	C₃²×C₄	1	4	yes	—
50	M₁₆	C₂²×C₃²	1	4	yes	—
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	C₂²×C₃²	1	2	yes	—
53	C₂²×C₃	—	4	4	no	—
54	C₂²×C₃	C₃×C₄⋊C₄	1	8	yes	—
55	C₂²×C₃	C₂×C₃×Q₈	1	4	yes	—
56	C₃×C₄	C₃×C₄⋊C₄	1	8	yes	—
57	C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
58	C₃×C₄	C₂×C₃×D₄	1	4	yes	—
59	C₃²	#430	1	1	yes	characteristic, direct product factor, Sylow
60	C₂³	C₃²×Q₈	1	1	yes	characteristic
61	C₂×C₄	C₂×C₃²×C₄	1	2	yes	—
62	C₂×C₄	C₃²×D₄	1	2	yes	—
63	C₂×C₄	C₃²×Q₈	1	1	yes	characteristic
64	C₂×C₄	C₂³×C₃²	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	C₂×C₃²×C₄	1	4	yes	—
67	C₂×C₃	—	2	8	no	—
68	C₂×C₃	—	2	4	no	—
69	C₂×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
70	C₂²	—	4	1	no	—
71	C₂²	C₃²×C₄⋊C₄	1	2	yes	—
72	C₂²	C₂×C₃²×Q₈	1	1	yes	characteristic
73	C₄	C₃²×C₄⋊C₄	1	2	yes	—
74	C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
75	C₄	C₂×C₃²×D₄	1	1	yes	characteristic
76	C₃	C₃×#430	1	4	yes	direct product factor
77	C₂	—	2	2	no	—
78	C₂	—	2	1	no	—
79	C₂	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	C₂×D₄
commutator	C₄	C₂²×C₃²×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃²
socle	C₂×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃²	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃²×#108	C₂	semidirect
4. C₃×#430	C₃	direct (N × H)
13. C₃×#108	C₂×C₃	semidirect
21. #430	C₃²	direct (N × H)
36. #108	C₂×C₃²	semidirect
59. C₃²	#430	direct (N × H)
76. C₃	C₃×#430	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×C₃²×M₁₆	2
C₃²×#108	2
C₃×#430	3

Subgroups — C32×#430 #10593003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#430 #10593003