Subgroups — C₃×#413 #5287

Order 192.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×#101	C₂	1	2	yes	maximal, complemented
4	C₃×#100	C₂	1	2	yes	maximal, complemented
5	#413	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃×#41	—	2	2	no	—
7	C₃×#41	—	2	2	no	—
8	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×D₄	C₄	1	2	yes	—
10	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₄	1	2	yes	—
12	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₃×M₁₆	—	2	2	no	—
14	C₃×M₁₆	C₂²	1	4	yes	—
15	C₂×C₃×C₈	—	2	2	no	—
16	C₂×#41	C₂×C₃	1	1	yes	characteristic
17	C₂×M₁₆	C₂×C₃	1	2	yes	complemented
18	#101	C₂×C₃	1	2	yes	complemented
19	#100	C₂×C₃	1	2	yes	complemented
20	C₂³×C₃	C₂×C₄	1	2	yes	—
21	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
22	C₃×Q₈	—	2	2	no	—
23	C₃×D₄	—	2	4	no	—
24	C₃×D₄	—	2	2	no	—
25	C₂×C₃×C₄	—	2	2	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
28	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄	D₄	1	2	yes	—
30	C₂×C₃×C₄	D₄	1	2	yes	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₃×C₈	—	2	4	no	—
33	#41	—	2	2	no	—
34	#41	—	2	2	no	—
35	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
36	C₂×D₄	C₃×C₄	1	2	yes	—
37	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
38	C₂²×C₄	C₃×C₄	1	2	yes	—
39	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
40	M₁₆	—	2	2	no	—
41	M₁₆	C₂²×C₃	1	4	yes	—
42	C₂×C₈	—	2	2	no	—
43	C₂²×C₃	—	2	2	no	—
44	C₂²×C₃	—	4	1	no	—
45	C₂²×C₃	—	4	2	no	—
46	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
48	C₃×C₄	—	2	2	no	—
49	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
50	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
51	C₃×C₄	C₂×D₄	1	2	yes	—
52	C₂³	C₂×C₃×C₄	1	2	yes	—
53	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
54	Q₈	—	2	2	no	—
55	D₄	—	2	4	no	—
56	D₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
60	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
61	C₂×C₄	C₃×D₄	1	2	yes	—
62	C₂×C₄	C₃×D₄	1	2	yes	—
63	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
64	C₈	—	2	4	no	—
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	—	4	2	no	—
68	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂²	—	2	2	no	—
70	C₂²	—	4	1	no	—
71	C₂²	—	4	2	no	—
72	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
73	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
76	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
77	C₄	C₂×C₃×D₄	1	2	yes	—
78	C₃	#413	1	1	yes	characteristic, direct product factor, Sylow
79	C₂	—	2	1	no	—
80	C₂	—	2	2	no	—
81	C₂	—	4	2	no	—
82	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²⋊C₄
commutator	C₂²	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂×C₃	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#41	C₂
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
2. C₂×C₃×M₁₆	C₂	semidirect
3. C₃×#101	C₂	semidirect
4. C₃×#100	C₂	semidirect
5. #413	C₃	direct (N × H)
17. C₂×M₁₆	C₂×C₃	semidirect
18. #101	C₂×C₃	semidirect
19. #100	C₂×C₃	semidirect
78. C₃	#413	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×#41	2
C₂×C₃×M₁₆	2
C₃×#101	2
C₃×#100	2
#413	3

Subgroups — C3×#413 #5287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#413 #5287