Subgroups — C₂×C₃×#100 #5285

Order 192.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×#100	C₂	1	4	yes	maximal, direct product factor
4	C₂×#100	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁴×C₃	C₄	1	2	yes	—
6	C₂×C₃×D₄	—	2	2	no	—
7	C₂×C₃×D₄	—	2	2	no	—
8	C₂×C₃×D₄	C₄	1	2	yes	—
9	C₂×C₃×D₄	C₂²	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	complemented
13	C₂×C₃×C₈	—	2	2	no	—
14	C₂²×D₄	C₂×C₃	1	1	yes	characteristic
15	C₂×M₁₆	C₂×C₃	1	2	yes	complemented
16	#100	C₂×C₃	1	4	yes	direct product factor
17	C₂³×C₃	—	2	2	no	—
18	C₂³×C₃	—	2	2	no	—
19	C₂³×C₃	—	4	4	no	—
20	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₃	C₂×C₄	1	4	yes	—
22	C₃×D₄	—	2	4	no	—
23	C₃×D₄	—	2	4	no	—
24	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	D₄	1	2	yes	—
26	C₂×C₃×C₄	D₄	1	2	yes	—
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₃×C₈	—	2	4	no	—
29	C₂⁴	C₃×C₄	1	2	yes	—
30	C₂×D₄	—	2	2	no	—
31	C₂×D₄	—	2	2	no	—
32	C₂×D₄	C₃×C₄	1	2	yes	—
33	C₂×D₄	C₂²×C₃	1	2	yes	—
34	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
35	M₁₆	—	2	2	no	—
36	M₁₆	C₂²×C₃	1	4	yes	complemented
37	C₂×C₈	—	2	2	no	—
38	C₂²×C₃	—	2	2	no	—
39	C₂²×C₃	—	2	4	no	—
40	C₂²×C₃	—	4	4	no	—
41	C₂²×C₃	—	4	4	no	—
42	C₂²×C₃	—	4	4	no	—
43	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
46	C₃×C₄	C₂²⋊C₄	1	2	yes	—
47	C₃×C₄	C₂×D₄	1	2	yes	—
48	C₂³	—	2	2	no	—
49	C₂³	—	2	2	no	—
50	C₂³	—	4	4	no	—
51	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
52	C₂³	C₂×C₃×C₄	1	4	yes	—
53	D₄	—	2	4	no	—
54	D₄	—	2	4	no	—
55	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
56	C₂×C₄	C₃×D₄	1	2	yes	—
57	C₂×C₄	C₃×D₄	1	2	yes	—
58	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
59	C₈	—	2	4	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	2	1	no	—
62	C₂×C₃	—	4	4	no	—
63	C₂×C₃	#100	1	2	yes	direct product factor
64	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²	—	2	2	no	—
66	C₂²	—	2	4	no	—
67	C₂²	—	4	4	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
72	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
73	C₄	C₃×C₂²⋊C₄	1	2	yes	—
74	C₄	C₂×C₃×D₄	1	2	yes	—
75	C₃	C₂×#100	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	4	4	no	—
79	C₂	C₃×#100	1	2	yes	direct product factor
80	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	C₂²×C₃×D₄	C₂
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
2. C₂×C₃×M₁₆	C₂	semidirect
3. C₃×#100	C₂	direct (N × H)
4. C₂×#100	C₃	direct (N × H)
12. C₃×M₁₆	C₂²	semidirect
15. C₂×M₁₆	C₂×C₃	semidirect
16. #100	C₂×C₃	direct (N × H)
36. M₁₆	C₂²×C₃	semidirect
63. C₂×C₃	#100	direct (N × H)
75. C₃	C₂×#100	direct (N × H)
79. C₂	C₃×#100	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×D₄	2
C₂×C₃×M₁₆	2
C₃×#100	2
C₂×#100	3

Subgroups — C2×C3×#100 #5285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#100 #5285