Subgroups — C₂×C₃×#101 #5286

Order 192.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₃×#101	C₂	direct (N × H)
4. C₂×#101	C₃	direct (N × H)
16. #101	C₂×C₃	direct (N × H)
57. C₂×C₃	#101	direct (N × H)
66. C₃	C₂×#101	direct (N × H)
69. C₂	C₃×#101	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×Q₈	2
C₂×C₃×M₁₆	2
C₃×#101	2
C₂×#101	3

Subgroups — C2×C3×#101 #5286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#101 #5286