Subgroups — C₃×#343 #4590

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#343	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₄	1	2	yes	—
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×M₁₆	—	2	2	no	—
7	C₃×M₁₆	C₄	1	4	yes	complemented
8	C₂×C₃×C₈	—	2	2	no	—
9	C₃×C₄⋊C₄	—	2	2	no	—
10	C₂×M₁₆	C₂×C₃	1	2	yes	—
11	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
12	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄	—	2	2	no	—
14	C₂×C₃×C₄	—	4	2	no	—
15	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₂×C₃×C₄	D₄	1	2	yes	—
18	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
19	C₃×C₈	—	2	4	no	—
20	C₂²×C₄	C₃×C₄	1	2	yes	—
21	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
22	M₁₆	—	2	2	no	—
23	M₁₆	C₃×C₄	1	4	yes	complemented
24	C₂×C₈	—	2	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₂²×C₃	—	2	1	no	—
27	C₂²×C₃	—	2	1	no	—
28	C₂²×C₃	C₄²	1	1	yes	characteristic
29	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
31	C₃×C₄	—	4	2	no	—
32	C₃×C₄	C₂²⋊C₄	1	2	yes	—
33	C₃×C₄	C₄⋊C₄	1	2	yes	—
34	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	—	4	2	no	—
37	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
38	C₂×C₄	C₃×D₄	1	1	yes	characteristic
39	C₂×C₄	C₃×D₄	1	2	yes	—
40	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
41	C₈	—	2	4	no	—
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	#95	1	1	yes	characteristic
45	C₂×C₃	#100	1	1	yes	characteristic
46	C₂×C₃	#101	1	1	yes	characteristic
47	C₂²	—	2	1	no	—
48	C₂²	—	2	1	no	—
49	C₂²	C₃×C₄²	1	1	yes	characteristic
50	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	C₃×C₂²⋊C₄	1	2	yes	—
54	C₄	C₃×C₄⋊C₄	1	2	yes	—
55	C₃	#343	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	C₃×#95	1	1	yes	characteristic
59	C₂	C₃×#100	1	1	yes	characteristic
60	C₂	C₃×#101	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²⋊C₄
commutator	C₂²	C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂²×C₃
prime radical	C₂³×C₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. #343	C₃	direct (N × H)
7. C₃×M₁₆	C₄	semidirect
23. M₁₆	C₃×C₄	semidirect
55. C₃	#343	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×C₃×M₁₆	2
C₂×C₃×C₄⋊C₄	2
#343	3

Subgroups — C3×#343 #4590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#343 #4590