Subgroups — C₃×#362 #4609

Order 192.

54 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
2	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₃×#108	C₂	1	1	yes	maximal, characteristic
4	#362	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₈	—	2	1	no	—
6	C₃×Q₁₆	—	2	1	no	—
7	C₃×Q₁₆	C₄	1	2	yes	—
8	C₃×M₁₆	—	2	1	no	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₁₆	—	2	1	no	—
11	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic
12	M₃₂	C₂×C₃	1	1	yes	characteristic
13	#108	C₂×C₃	1	1	yes	characteristic
14	C₃×Q₈	—	2	2	no	—
15	C₃×Q₈	—	4	1	no	—
16	C₂×C₃×C₄	—	4	1	no	—
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₃×C₈	—	4	1	no	—
19	C₃×C₈	C₂×C₄	1	1	yes	characteristic
20	C₃×C₈	D₄	1	1	yes	characteristic
21	C₂×Q₈	—	2	1	no	—
22	Q₁₆	—	2	1	no	—
23	Q₁₆	C₃×C₄	1	2	yes	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
26	C₁₆	—	2	1	no	—
27	C₂²×C₃	SD₁₆	1	1	yes	characteristic
28	C₃×C₄	—	4	2	no	—
29	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₄	D₈	1	1	yes	characteristic
31	Q₈	—	2	2	no	—
32	Q₈	—	4	1	no	—
33	C₂×C₄	—	4	1	no	—
34	C₂×C₄	C₃×D₄	1	1	yes	characteristic
35	C₈	—	4	1	no	—
36	C₈	C₂×C₃×C₄	1	1	yes	characteristic
37	C₈	C₃×D₄	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	#102	1	1	yes	characteristic
40	C₂²	C₃×SD₁₆	1	1	yes	characteristic
41	C₄	—	4	2	no	—
42	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
43	C₄	C₃×D₈	1	1	yes	characteristic
44	C₃	#362	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₃×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#102
commutator	C₈	C₂×C₃×C₄
Frattini, cosocle	C₂×C₈	C₂²×C₃
prime radical	C₂²×C₃	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. #362	C₃	direct (N × H)
44. C₃	#362	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
C₃×M₃₂	2
C₃×#108	2
#362	3

Subgroups — C3×#362 #4609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#362 #4609