Subgroups — C₃×#341 #4588

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	2	yes	maximal
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	#341	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
5	C₃×M₁₆	—	2	2	no	—
6	C₃×M₁₆	C₄	1	4	yes	—
7	C₂×C₃×C₈	—	2	2	no	—
8	C₂×C₃×C₈	—	2	2	no	—
9	C₂×C₃×C₈	C₄	1	2	yes	—
10	C₂×M₁₆	C₂×C₃	1	2	yes	—
11	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
12	C₂³×C₃	Q₈	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
15	C₂×C₃×C₄	D₄	1	2	yes	—
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×C₈	—	2	2	no	—
18	C₃×C₈	—	2	4	no	—
19	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
20	M₁₆	—	2	2	no	—
21	M₁₆	C₃×C₄	1	4	yes	—
22	C₂×C₈	—	2	2	no	—
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	C₃×C₄	1	2	yes	—
25	C₂²×C₃	—	2	2	no	—
26	C₂²×C₃	C₄⋊C₄	1	2	yes	—
27	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
28	C₃×C₄	C₄²	1	1	yes	characteristic
29	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂³	C₃×Q₈	1	1	yes	characteristic
32	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
34	C₂×C₄	C₃×D₄	1	1	yes	characteristic
35	C₂×C₄	C₃×D₄	1	2	yes	—
36	C₈	—	2	2	no	—
37	C₈	—	2	4	no	—
38	C₂×C₃	—	2	2	no	—
39	C₂×C₃	#95	1	1	yes	characteristic
40	C₂×C₃	#108	1	2	yes	—
41	C₂²	—	2	2	no	—
42	C₂²	C₃×C₄⋊C₄	1	2	yes	—
43	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
44	C₄	C₃×C₄²	1	1	yes	characteristic
45	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
46	C₄	C₃×C₂²⋊C₄	1	2	yes	—
47	C₃	#341	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	—	2	2	no	—
49	C₂	C₃×#95	1	1	yes	characteristic
50	C₂	C₃×#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂²×C₃
socle	C₂²×C₃	C₄⋊C₄
prime radical	C₂³×C₃	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. #341	C₃	direct (N × H)
47. C₃	#341	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
C₂²×C₃×C₈	2
#341	3

Subgroups — C3×#341 #4588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#341 #4588