Subgroups — C₂×#812 #5097

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	#812	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×M₃₂	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
6	C₂×C₃×C₈	C₄	1	1	yes	characteristic
7	C₂×C₃×C₈	C₄	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₃⋊C₁₆	C₂²	1	4	yes	complemented
11	C₂²×C₈	D₃	1	1	yes	characteristic
12	M₃₂	—	3	4	no	—
13	C₂×C₁₆	—	3	2	no	—
14	C₂³×C₃	C₈	1	1	yes	characteristic
15	C₂×C₃×C₄	C₈	1	2	yes	—
16	C₂×C₃×C₄	C₈	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₃×C₈	C₂×C₄	1	2	yes	—
20	C₃×C₈	C₂×C₄	1	1	yes	characteristic
21	C₃×C₈	C₂³	1	1	yes	characteristic
22	C₂²×C₄	Dic₃	1	1	yes	characteristic
23	C₂×C₈	Dic₃	1	1	yes	characteristic
24	C₂×C₈	Dic₃	1	2	yes	—
25	C₂×C₈	C₂×D₃	1	2	yes	—
26	C₂×C₈	C₂×D₃	1	1	yes	characteristic
27	C₁₆	—	3	4	no	—
28	C₂²×C₃	—	2	2	no	—
29	C₂²×C₃	C₂×C₈	1	2	yes	—
30	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
31	C₃×C₄	C₂×C₈	1	2	yes	—
32	C₃×C₄	C₂×C₈	1	1	yes	characteristic
33	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₂³	C₃⋊C₈	1	1	yes	characteristic
35	C₂×C₄	C₃⋊C₈	1	2	yes	—
36	C₂×C₄	C₃⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₃	1	2	yes	—
38	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
39	C₈	C₂×Dic₃	1	2	yes	—
40	C₈	C₂×Dic₃	1	1	yes	characteristic
41	C₈	C₂²×D₃	1	1	yes	characteristic
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	M₃₂	1	2	yes	complemented
44	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
45	C₂²	—	2	2	no	—
46	C₂²	C₂×C₃⋊C₈	1	2	yes	—
47	C₂²	C₂×C₃⋊C₈	1	1	yes	characteristic
48	C₄	C₂×C₃⋊C₈	1	2	yes	—
49	C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
50	C₄	C₂²×Dic₃	1	1	yes	characteristic
51	C₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	2	2	no	—
53	C₂	#812	1	2	yes	direct product factor
54	C₂	C₂²×C₃⋊C₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #812	C₂	direct (N × H)
3. C₂×C₃⋊C₁₆	C₂	semidirect
10. C₃⋊C₁₆	C₂²	semidirect
43. C₂×C₃	M₃₂	semidirect
51. C₃	C₂×M₃₂	semidirect
53. C₂	#812	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×C₈	2
#812	2
C₂×C₃⋊C₁₆	2
C₂×M₃₂	3

Subgroups — C2×#812 #5097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#812 #5097