Subgroups — C₂×#798 #4900

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#798	C₂	1	4	yes	maximal, direct product factor
5	C₂×M₃₂	—	3	1	no	maximal, Sylow
6	C₂×C₄×D₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊C₈	C₄	1	1	yes	characteristic
9	D₃×C₈	C₄	1	2	yes	—
10	D₃×C₈	C₂²	1	2	yes	—
11	C₃×C₁₆	C₂²	1	2	yes	complemented
12	C₃⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂²×C₈	—	3	1	no	—
14	M₃₂	—	3	4	no	—
15	C₂×C₁₆	—	3	1	no	—
16	C₂×C₁₆	D₃	1	1	yes	characteristic, complemented
17	C₂²×D₃	C₈	1	1	yes	characteristic
18	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃	C₈	1	1	yes	characteristic
20	C₄×D₃	C₈	1	2	yes	—
21	C₄×D₃	C₂×C₄	1	2	yes	—
22	C₃×C₈	C₂×C₄	1	1	yes	characteristic
23	C₃×C₈	C₂³	1	1	yes	characteristic
24	C₃⋊C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₄	—	3	1	no	—
26	C₂×C₈	—	3	1	no	—
27	C₂×C₈	—	3	2	no	—
28	C₂×C₈	—	3	2	no	—
29	C₂×C₈	C₂×D₃	1	1	yes	characteristic
30	C₁₆	—	3	2	no	—
31	C₁₆	C₂×D₃	1	2	yes	complemented
32	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
33	C₂×D₃	—	2	2	no	—
34	C₂×D₃	C₂×C₈	1	2	yes	—
35	C₃×C₄	C₂×C₈	1	1	yes	characteristic
36	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
37	Dic₃	C₂×C₈	1	2	yes	—
38	C₂³	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	3	2	no	—
41	C₂×C₄	—	3	2	no	—
42	C₂×C₄	C₄×D₃	1	1	yes	characteristic
43	C₈	—	3	2	no	—
44	C₈	C₄×D₃	1	1	yes	characteristic
45	C₈	C₂²×D₃	1	1	yes	characteristic
46	C₂×C₃	M₃₂	1	2	yes	complemented
47	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
48	D₃	—	2	2	no	—
49	C₂²	—	3	2	no	—
50	C₂²	—	6	2	no	—
51	C₂²	D₃×C₈	1	1	yes	characteristic
52	C₄	—	3	2	no	—
53	C₄	D₃×C₈	1	1	yes	characteristic
54	C₄	C₂×C₄×D₃	1	1	yes	characteristic
55	C₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	6	2	no	—
57	C₂	#798	1	2	yes	direct product factor
58	C₂	C₂×D₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃
commutator	C₂×C₃	C₂²×C₈
Frattini	C₈	C₂²×D₃
Fitting	C₂×C₃×C₁₆	C₂
socle	C₂²×C₃	C₂×C₈
prime radical	C₂²×D₃	C₈
cosocle	C₃×C₈	C₂³
hypercenter	C₂×C₁₆	D₃
hypocenter	C₃	C₂×M₃₂
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₁₆	C₂	semidirect
3. C₂×C₃⋊C₁₆	C₂	semidirect
4. #798	C₂	direct (N × H)
11. C₃×C₁₆	C₂²	semidirect
12. C₃⋊C₁₆	C₂²	semidirect
16. C₂×C₁₆	D₃	semidirect
31. C₁₆	C₂×D₃	semidirect
46. C₂×C₃	M₃₂	semidirect
55. C₃	C₂×M₃₂	semidirect
57. C₂	#798	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×D₃×C₈	2
C₂×C₃×C₁₆	2
C₂×C₃⋊C₁₆	2
#798	2
C₂×M₃₂	3

Subgroups — C2×#798 #4900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#798 #4900