Subgroups — C₂×C₃×#108 #5303

Order 192.

106 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	C₃×#108	C₂	1	4	yes	maximal, direct product factor
4	C₂×#108	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×M₁₆	—	2	2	no	—
7	C₃×M₁₆	C₂²	1	4	yes	—
8	C₂×C₃×C₈	—	2	2	no	—
9	C₂×C₃×C₈	C₄	1	2	yes	—
10	C₂×C₃×C₈	C₄	1	2	yes	—
11	C₂×C₃×C₈	C₂²	1	2	yes	—
12	C₂×M₁₆	C₂×C₃	1	2	yes	—
13	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
14	#108	C₂×C₃	1	4	yes	direct product factor
15	C₂³×C₃	Q₈	1	1	yes	characteristic
16	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×C₃×C₄	D₄	1	1	yes	characteristic
20	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
22	C₃×C₈	—	2	4	no	—
23	C₃×C₈	C₂×C₄	1	4	yes	—
24	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
25	M₁₆	—	2	2	no	—
26	M₁₆	C₂²×C₃	1	4	yes	—
27	C₂×C₈	—	2	2	no	—
28	C₂×C₈	C₃×C₄	1	2	yes	—
29	C₂×C₈	C₃×C₄	1	2	yes	—
30	C₂×C₈	C₂²×C₃	1	2	yes	—
31	C₂²×C₃	—	2	2	no	—
32	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
35	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
36	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
37	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
38	C₃×C₄	C₂×D₄	1	1	yes	characteristic
39	C₂³	C₃×Q₈	1	1	yes	characteristic
40	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂×C₄	C₃×D₄	1	1	yes	characteristic
43	C₂×C₄	C₃×D₄	1	1	yes	characteristic
44	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
45	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
46	C₈	—	2	4	no	—
47	C₈	C₂×C₃×C₄	1	4	yes	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	#108	1	2	yes	direct product factor
51	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²	—	2	2	no	—
53	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
54	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
55	C₂²	C₂×C₃×Q₈	1	1	yes	characteristic
56	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
57	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
58	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
59	C₄	C₂×C₃×D₄	1	1	yes	characteristic
60	C₃	C₂×#108	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	C₃×#108	1	2	yes	direct product factor
64	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×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. C₃×#108	C₂	direct (N × H)
4. C₂×#108	C₃	direct (N × H)
14. #108	C₂×C₃	direct (N × H)
50. C₂×C₃	#108	direct (N × H)
60. C₃	C₂×#108	direct (N × H)
63. C₂	C₃×#108	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
C₃×#108	2
C₂×#108	3

Subgroups — C2×C3×#108 #5303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#108 #5303