Subgroups — C₂×#859 #5418

Order 192.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	#859	C₂	1	2	yes	maximal, direct product factor
3	C₂×#103	—	3	1	no	maximal, Sylow
4	C₂²×Dic₃	—	4	1	no	maximal
5	C₂×SL(2,𝔽₃)	C₄	1	2	yes	complemented
6	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₂²×Q₈	D₃	1	1	yes	characteristic
8	C₂²×C₈	—	3	1	no	—
9	C₂×C₄⋊C₄	—	3	1	no	—
10	#103	—	3	2	no	—
11	#103	—	3	2	no	—
12	C₂³×C₃	—	4	1	no	—
13	C₂×Dic₃	—	4	2	no	—
14	C₂×Dic₃	—	4	4	no	—
15	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented
16	C₂×Q₈	—	3	1	no	—
17	C₂×Q₈	—	3	2	no	—
18	C₂×Q₈	Dic₃	1	2	yes	complemented
19	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
20	C₂²×C₄	—	3	1	no	—
21	C₂²×C₄	—	6	1	no	—
22	C₂×C₈	—	3	2	no	—
23	C₂×C₈	—	6	2	no	—
24	C₄⋊C₄	—	3	2	no	—
25	C₄⋊C₄	—	6	1	no	—
26	C₂²×C₃	—	4	2	no	—
27	C₂²×C₃	—	4	2	no	—
28	C₂²×C₃	—	4	2	no	—
29	C₂²×C₃	—	4	1	no	—
30	Dic₃	—	4	4	no	—
31	C₂³	S₄	1	1	yes	characteristic
32	Q₈	—	3	2	no	—
33	Q₈	—	3	1	no	—
34	Q₈	—	6	1	no	—
35	Q₈	C₂×Dic₃	1	1	yes	characteristic, complemented
36	C₂×C₄	—	3	2	no	—
37	C₂×C₄	—	3	2	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	6	2	no	—
41	C₂×C₄	—	12	2	no	—
42	C₈	—	6	2	no	—
43	C₂×C₃	—	4	4	no	—
44	C₂×C₃	—	4	1	no	—
45	C₂×C₃	—	4	1	no	—
46	C₂×C₃	—	4	1	no	—
47	C₂²	#226	1	2	yes	—
48	C₂²	GL(2,𝔽₃)	1	2	yes	—
49	C₂²	SL(2,ℤ/4)	1	2	yes	—
50	C₂²	C₂×S₄	1	1	yes	characteristic
51	C₄	—	3	1	no	—
52	C₄	—	3	1	no	—
53	C₄	—	3	2	no	—
54	C₄	—	12	2	no	—
55	C₃	—	4	1	no	Sylow
56	C₂	#859	1	4	yes	direct product factor
57	C₂	C₂×#226	1	1	yes	characteristic
58	C₂	C₂×GL(2,𝔽₃)	1	1	yes	characteristic
59	C₂	C₂×SL(2,ℤ/4)	1	1	yes	characteristic

	subgroup	G/H
center, socle, hypercenter	C₂³	S₄
commutator, hypocenter	SL(2,𝔽₃)	C₂×C₄
Frattini	C₂²	C₂×S₄
Fitting	C₂²×Q₈	D₃
prime radical	C₂²×SL(2,𝔽₃)	C₂
cosocle	C₂×SL(2,𝔽₃)	C₂²
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. #859	C₂	direct (N × H)
5. C₂×SL(2,𝔽₃)	C₄	semidirect
15. SL(2,𝔽₃)	C₂×C₄	semidirect
18. C₂×Q₈	Dic₃	semidirect
35. Q₈	C₂×Dic₃	semidirect
56. C₂	#859	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×SL(2,𝔽₃)	2
#859	2
C₂×#103	3
C₂²×Dic₃	4

Subgroups — C2×#859 #5418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#859 #5418