Subgroups — C₃×#344 #4591

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#117	C₂	1	1	yes	maximal, characteristic
4	#344	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×M₁₆	—	2	1	no	—
7	C₃×M₁₆	—	2	1	no	—
8	C₃×M₁₆	—	2	1	no	—
9	C₃×M₁₆	C₄	1	2	yes	complemented
10	C₂×C₃×C₈	—	2	1	no	—
11	C₂×C₃×C₈	C₄	1	2	yes	complemented
12	C₃×C₄⋊C₄	—	2	1	no	—
13	C₃×C₂²⋊C₄	C₄	1	2	yes	—
14	C₃×C₄²	—	2	1	no	—
15	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
16	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
17	#117	C₂×C₃	1	1	yes	characteristic
18	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	D₄	1	1	yes	characteristic
24	C₂×C₃×C₄	D₄	1	1	yes	characteristic
25	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
26	C₃×C₈	—	2	2	no	—
27	C₃×C₈	—	2	2	no	—
28	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
29	M₁₆	—	2	1	no	—
30	M₁₆	—	2	1	no	—
31	M₁₆	—	2	1	no	—
32	M₁₆	C₃×C₄	1	2	yes	complemented
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	C₃×C₄	1	2	yes	complemented
35	C₄⋊C₄	—	2	1	no	—
36	C₂²⋊C₄	C₃×C₄	1	2	yes	—
37	C₄²	—	2	1	no	—
38	C₂²×C₃	—	4	1	no	—
39	C₂²×C₃	C₄²	1	1	yes	characteristic
40	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
42	C₃×C₄	—	4	2	no	—
43	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
44	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
45	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
46	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
47	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
50	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₄	C₃×D₄	1	1	yes	characteristic
52	C₂×C₄	C₃×D₄	1	1	yes	characteristic
53	C₂×C₄	C₃×D₄	1	1	yes	characteristic
54	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
55	C₈	—	2	2	no	—
56	C₈	—	2	2	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	#95	1	1	yes	characteristic
61	C₂²	—	4	1	no	—
62	C₂²	C₃×C₄²	1	1	yes	characteristic
63	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
64	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
65	C₄	—	4	2	no	—
66	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
67	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
68	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
69	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
70	C₃	#344	1	1	yes	characteristic, direct product factor, Sylow
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	C₃×#95	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²⋊C₄
commutator	C₂²	C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂²×C₃
socle	C₂×C₃	#95
prime radical	C₂³×C₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. #344	C₃	direct (N × H)
9. C₃×M₁₆	C₄	semidirect
11. C₂×C₃×C₈	C₄	semidirect
32. M₁₆	C₃×C₄	semidirect
34. C₂×C₈	C₃×C₄	semidirect
70. C₃	#344	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
C₃×#117	2
#344	3

Subgroups — C3×#344 #4591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#344 #4591