Subgroups — C₃×#495 #5369

Order 192.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#495	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₂×C₃×D₄	C₂²	1	2	yes	—
9	C₃×Q₁₆	—	2	2	no	—
10	C₃×SD₁₆	—	2	4	no	—
11	C₃×D₈	—	2	2	no	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₂²⋊C₄	—	2	4	no	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×SD₁₆	C₂×C₃	1	2	yes	complemented
18	C₂×D₈	C₂×C₃	1	1	yes	characteristic
19	#124	C₂×C₃	1	2	yes	complemented
20	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂³×C₃	—	2	2	no	—
22	C₃×Q₈	—	2	2	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₃×D₄	—	2	2	no	—
25	C₃×D₄	—	2	2	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	D₄	1	2	yes	—
28	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
29	C₃×C₈	D₄	1	2	yes	—
30	C₃×C₈	D₄	1	2	yes	—
31	C₂×Q₈	C₂²×C₃	1	2	yes	—
32	C₂×D₄	C₂²×C₃	1	2	yes	—
33	Q₁₆	—	2	2	no	—
34	SD₁₆	—	2	4	no	—
35	D₈	—	2	2	no	—
36	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₂²⋊C₄	—	2	4	no	—
39	C₄²	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₃	—	4	2	no	—
41	C₂²×C₃	—	4	4	no	—
42	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
43	C₃×C₄	—	2	2	no	—
44	C₃×C₄	—	4	2	no	—
45	C₃×C₄	C₂×D₄	1	1	yes	characteristic
46	C₃×C₄	C₂×D₄	1	1	yes	characteristic
47	C₂³	—	2	2	no	—
48	Q₈	—	2	2	no	—
49	Q₈	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	—	2	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	C₃×D₄	1	2	yes	—
54	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
55	C₈	C₃×D₄	1	2	yes	—
56	C₈	C₃×D₄	1	2	yes	—
57	C₂×C₃	—	8	2	no	—
58	C₂×C₃	#127	1	1	yes	characteristic
59	C₂×C₃	#135	1	2	yes	—
60	C₂²	—	4	2	no	—
61	C₂²	—	4	4	no	—
62	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	4	2	no	—
65	C₄	C₂×C₃×D₄	1	1	yes	characteristic
66	C₄	C₂×C₃×D₄	1	1	yes	characteristic
67	C₃	#495	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	8	2	no	—
69	C₂	C₃×#127	1	1	yes	characteristic
70	C₂	C₃×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₈	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₁₆	C₂	semidirect
2. C₂×C₃×SD₁₆	C₂	semidirect
4. C₃×#124	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. #495	C₃	direct (N × H)
16. C₂×Q₁₆	C₂×C₃	semidirect
17. C₂×SD₁₆	C₂×C₃	semidirect
19. #124	C₂×C₃	semidirect
20. C₄×C₈	C₂×C₃	semidirect
67. C₃	#495	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×Q₁₆	2
C₂×C₃×SD₁₆	2
C₂×C₃×D₈	2
C₃×#124	2
C₃×C₄×C₈	2
#495	3

Subgroups — C3×#495 #5369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#495 #5369