Subgroups — C₃×#432 #5306

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊C₈	C₂	1	2	yes	maximal
4	C₃×#97	C₂	1	2	yes	maximal, complemented
5	#432	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₈	C₂²	1	4	yes	—
10	C₃×C₄²	C₄	1	1	yes	characteristic
11	C₃×C₄²	C₄	1	1	yes	characteristic
12	C₃×C₄²	C₂²	1	1	yes	characteristic
13	C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
15	C₄⋊C₈	C₂×C₃	1	2	yes	complemented
16	C₂²⋊C₈	C₂×C₃	1	2	yes	—
17	#97	C₂×C₃	1	2	yes	complemented
18	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₃×C₈	—	2	4	no	—
29	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
30	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
31	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
32	C₂×C₈	C₂²×C₃	1	4	yes	—
33	C₄²	C₃×C₄	1	1	yes	characteristic
34	C₄²	C₃×C₄	1	1	yes	characteristic
35	C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₄²	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₃	—	2	1	no	—
38	C₂²×C₃	—	2	1	no	—
39	C₂²×C₃	M₁₆	1	2	yes	—
40	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
41	C₃×C₄	—	2	1	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	M₁₆	1	2	yes	—
46	C₃×C₄	#41	1	2	yes	—
47	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
52	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
53	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
54	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
56	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
57	C₈	—	2	4	no	—
58	C₂×C₃	—	2	2	no	—
59	C₂×C₃	#117	1	1	yes	characteristic
60	C₂×C₃	C₂×M₁₆	1	1	yes	characteristic
61	C₂×C₃	C₂×M₁₆	1	1	yes	characteristic
62	C₂²	—	2	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	C₃×M₁₆	1	2	yes	—
65	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	C₃×M₁₆	1	2	yes	—
71	C₄	C₃×#41	1	2	yes	—
72	C₃	#432	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	2	2	no	—
74	C₂	C₃×#117	1	1	yes	characteristic
75	C₂	C₂×C₃×M₁₆	1	1	yes	characteristic
76	C₂	C₂×C₃×M₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄⋊C₈	C₂	semidirect
4. C₃×#97	C₂	semidirect
5. #432	C₃	direct (N × H)
15. C₄⋊C₈	C₂×C₃	semidirect
17. #97	C₂×C₃	semidirect
72. C₃	#432	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×C₄²	2
C₃×C₄⋊C₈	2
C₃×C₂²⋊C₈	2
C₃×#97	2
#432	3

Subgroups — C3×#432 #5306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#432 #5306