Subgroups — C₂×#876 #5478

Order 192.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
3	C₂×Dic₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	#876	C₂	1	8	yes	maximal, direct product factor
5	C₂×#126	—	3	1	no	maximal, Sylow
6	C₂³×D₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	3	yes	—
8	C₂²×Dic₃	C₂²	1	3	yes	—
9	C₃×C₄²	C₂²	1	4	yes	complemented
10	(C₂×D₃)⋊C₄	C₂²	1	12	yes	—
11	Dic₃⋊C₄	C₂²	1	12	yes	complemented
12	#126	—	3	8	no	—
13	C₂×C₄⋊C₄	—	3	3	no	—
14	C₂×C₂²⋊C₄	—	3	3	no	—
15	C₂×C₄²	D₃	1	1	yes	characteristic, complemented
16	C₂³×C₃	C₂³	1	1	yes	characteristic
17	C₂²×D₃	—	2	6	no	—
18	C₂²×D₃	C₂³	1	2	yes	—
19	C₂×C₃×C₄	—	2	6	no	—
20	C₂×C₃×C₄	C₂³	1	6	yes	—
21	C₂×Dic₃	—	2	6	no	—
22	C₂×Dic₃	C₂³	1	6	yes	—
23	C₂⁴	—	3	1	no	—
24	C₂²×C₄	—	3	3	no	—
25	C₂²×C₄	C₂×D₃	1	3	yes	—
26	C₄⋊C₄	—	3	12	no	—
27	C₂²⋊C₄	—	3	12	no	—
28	C₄²	C₂×D₃	1	4	yes	complemented
29	C₂²×C₃	#41	1	6	yes	—
30	C₂²×C₃	C₂⁴	1	1	yes	characteristic
31	C₂×D₃	—	2	6	no	—
32	C₂×D₃	—	4	4	no	—
33	C₃×C₄	—	2	6	no	—
34	Dic₃	—	2	6	no	—
35	C₂³	—	3	2	no	—
36	C₂³	—	6	6	no	—
37	C₂³	C₂²×D₃	1	1	yes	characteristic
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	3	6	no	—
40	C₂×C₄	—	6	6	no	—
41	C₂×C₄	C₂²×D₃	1	6	yes	—
42	C₂×C₃	#126	1	4	yes	complemented
43	C₂×C₃	C₂×#41	1	3	yes	—
44	D₃	—	4	2	no	—
45	C₂²	—	6	6	no	—
46	C₂²	—	12	4	no	—
47	C₂²	#235	1	6	yes	—
48	C₂²	C₂³×D₃	1	1	yes	characteristic
49	C₄	—	2	6	no	—
50	C₄	—	6	6	no	—
51	C₃	C₂×#126	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	12	2	no	—
53	C₂	#876	1	4	yes	direct product factor
54	C₂	C₂×#235	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂³×D₃	C₂²
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₂×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄²	C₂	semidirect
3. C₂×Dic₃⋊C₄	C₂	semidirect
4. #876	C₂	direct (N × H)
9. C₃×C₄²	C₂²	semidirect
11. Dic₃⋊C₄	C₂²	semidirect
15. C₂×C₄²	D₃	semidirect
28. C₄²	C₂×D₃	semidirect
42. C₂×C₃	#126	semidirect
51. C₃	C₂×#126	semidirect
53. C₂	#876	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×C₄²	2
C₂×(C₂×D₃)⋊C₄	2
C₂×Dic₃⋊C₄	2
#876	2
C₂×#126	3

Subgroups — C2×#876 #5478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#876 #5478