Subgroups — C₂×#986 #5922

Order 192.

169 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#986	C₂	1	4	yes	maximal, direct product factor
3	C₂×GL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
4	C₂×AGL(1,ℤ/8)	—	3	1	no	maximal, Sylow
5	C₂×D₁₂	—	4	1	no	maximal
6	#41⋊C₃	C₂²	1	2	yes	complemented
7	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
8	GL(2,𝔽₃)	C₂²	1	4	yes	complemented
9	C₂×#41	D₃	1	1	yes	characteristic, complemented
10	C₂²×D₄	—	3	1	no	—
11	AGL(1,ℤ/8)	—	3	4	no	—
12	AGL(1,ℤ/8)	—	3	4	no	—
13	C₂×SD₁₆	—	3	2	no	—
14	C₂×D₈	—	3	2	no	—
15	C₂×M₁₆	—	3	1	no	—
16	C₂²×D₃	—	4	2	no	—
17	C₂×C₃×C₄	—	4	1	no	—
18	D₁₂	—	4	4	no	—
19	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic, complemented
20	C₂⁴	—	6	1	no	—
21	#41	—	3	2	no	—
22	#41	C₂×D₃	1	2	yes	complemented
23	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
24	C₂×D₄	—	3	1	no	—
25	C₂×D₄	—	3	2	no	—
26	C₂×D₄	—	3	4	no	—
27	C₂×D₄	—	6	2	no	—
28	C₂×D₄	—	6	1	no	—
29	C₂²×C₄	—	3	1	no	—
30	SD₁₆	—	3	4	no	—
31	SD₁₆	—	3	4	no	—
32	D₈	—	3	8	no	—
33	M₁₆	—	3	4	no	—
34	C₂×C₈	—	3	2	no	—
35	C₂²×C₃	—	4	1	no	—
36	C₂×D₃	—	4	4	no	—
37	C₂×D₃	—	8	4	no	—
38	C₃×C₄	—	4	2	no	—
39	C₂³	—	3	1	no	—
40	C₂³	—	6	4	no	—
41	C₂³	—	6	2	no	—
42	C₂³	—	12	4	no	—
43	Q₈	—	3	1	no	—
44	Q₈	C₂²×D₃	1	1	yes	characteristic
45	D₄	—	3	2	no	—
46	D₄	—	3	4	no	—
47	D₄	—	6	1	no	—
48	D₄	—	6	2	no	—
49	D₄	—	6	4	no	—
50	C₂×C₄	—	3	1	no	—
51	C₂×C₄	—	3	2	no	—
52	C₂×C₄	—	3	2	no	—
53	C₂×C₄	S₄	1	1	yes	characteristic
54	C₈	—	3	4	no	—
55	C₂×C₃	—	4	2	no	—
56	C₂×C₃	—	4	1	no	—
57	D₃	—	8	4	no	—
58	C₂²	—	3	2	no	—
59	C₂²	—	6	2	no	—
60	C₂²	—	6	4	no	—
61	C₂²	—	12	8	no	—
62	C₂²	—	12	4	no	—
63	C₂²	C₂×S₄	1	1	yes	characteristic
64	C₄	—	3	1	no	—
65	C₄	—	3	1	no	—
66	C₄	C₂×S₄	1	2	yes	—
67	C₃	—	4	1	no	Sylow
68	C₂	—	6	2	no	—
69	C₂	—	12	4	no	—
70	C₂	#986	1	2	yes	direct product factor
71	C₂	C₂²×S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂³
Frattini	C₂	C₂²×S₄
Fitting	C₂×#41	D₃
hypercenter	C₂×C₄	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#41⋊C₃	C₂	semidirect
2. #986	C₂	direct (N × H)
3. C₂×GL(2,𝔽₃)	C₂	semidirect
6. #41⋊C₃	C₂²	semidirect
7. C₂×SL(2,𝔽₃)	C₂²	semidirect
8. GL(2,𝔽₃)	C₂²	semidirect
9. C₂×#41	D₃	semidirect
19. SL(2,𝔽₃)	C₂³	semidirect
22. #41	C₂×D₃	semidirect
70. C₂	#986	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×#41⋊C₃	2
#986	2
C₂×GL(2,𝔽₃)	2
C₂×AGL(1,ℤ/8)	3
C₂×D₁₂	4

Subgroups — C2×#986 #5922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#986 #5922