Subgroups — C₂×#983 #5917

Order 192.

153 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, complemented
2	#983	C₂	1	4	yes	maximal, direct product factor
3	C₂×GL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#226	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#137	—	3	1	no	maximal, Sylow
6	C₂×#67	—	4	1	no	maximal
7	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
8	C₂×SL(2,𝔽₃)	C₂²	1	2	yes	complemented
9	GL(2,𝔽₃)	C₂²	1	2	yes	complemented
10	#226	C₂²	1	2	yes	complemented
11	C₂×#41	—	3	1	no	—
12	C₂²×Q₈	D₃	1	1	yes	characteristic, complemented
13	#137	—	3	4	no	—
14	#137	—	3	4	no	—
15	C₂×Q₁₆	—	3	1	no	—
16	C₂×Q₁₆	—	3	1	no	—
17	C₂×SD₁₆	—	3	1	no	—
18	C₂×SD₁₆	—	3	1	no	—
19	C₂×M₁₆	—	3	1	no	—
20	C₂³×C₃	—	4	1	no	—
21	C₂²×D₃	—	4	1	no	—
22	#67	—	4	4	no	—
23	C₂×Dic₃	—	4	1	no	—
24	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic
25	#41	—	3	4	no	—
26	#41	—	6	2	no	—
27	C₂×Q₈	—	3	1	no	—
28	C₂×Q₈	—	3	2	no	—
29	C₂×Q₈	—	3	1	no	—
30	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
31	C₂×Q₈	C₂×D₃	1	2	yes	complemented
32	C₂×D₄	—	3	1	no	—
33	C₂×D₄	—	6	1	no	—
34	C₂²×C₄	—	3	1	no	—
35	C₂²×C₄	—	6	1	no	—
36	Q₁₆	—	3	2	no	—
37	Q₁₆	—	3	4	no	—
38	Q₁₆	—	3	2	no	—
39	SD₁₆	—	3	2	no	—
40	SD₁₆	—	3	4	no	—
41	SD₁₆	—	3	2	no	—
42	M₁₆	—	3	4	no	—
43	C₂×C₈	—	3	1	no	—
44	C₂×C₈	—	3	1	no	—
45	C₂²×C₃	—	4	2	no	—
46	C₂²×C₃	—	4	1	no	—
47	C₂²×C₃	—	8	2	no	—
48	C₂×D₃	—	4	2	no	—
49	C₂×D₃	—	8	2	no	—
50	Dic₃	—	4	2	no	—
51	C₂³	—	6	1	no	—
52	C₂³	S₄	1	1	yes	characteristic
53	Q₈	—	3	1	no	—
54	Q₈	—	3	2	no	—
55	Q₈	—	3	2	no	—
56	Q₈	—	6	1	no	—
57	Q₈	—	6	1	no	—
58	Q₈	C₂²×D₃	1	1	yes	characteristic
59	D₄	—	3	2	no	—
60	D₄	—	6	1	no	—
61	D₄	—	6	4	no	—
62	C₂×C₄	—	3	2	no	—
63	C₂×C₄	—	3	2	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	6	4	no	—
67	C₂×C₄	—	6	1	no	—
68	C₈	—	3	2	no	—
69	C₈	—	3	2	no	—
70	C₂×C₃	—	4	2	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂×C₃	—	8	2	no	—
73	D₃	—	8	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	6	2	no	—
76	C₂²	—	12	2	no	—
77	C₂²	C₂×S₄	1	2	yes	—
78	C₂²	C₂×S₄	1	1	yes	characteristic
79	C₄	—	3	1	no	—
80	C₄	—	3	2	no	—
81	C₄	—	3	1	no	—
82	C₄	—	6	2	no	—
83	C₃	—	4	1	no	Sylow
84	C₂	—	2	2	no	—
85	C₂	—	12	2	no	—
86	C₂	#983	1	2	yes	direct product factor
87	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	C₂²×Q₈	D₃
hypercenter	C₂³	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂²×SL(2,𝔽₃)	C₂	semidirect
2. #983	C₂	direct (N × H)
3. C₂×GL(2,𝔽₃)	C₂	semidirect
4. C₂×#226	C₂	semidirect
8. C₂×SL(2,𝔽₃)	C₂²	semidirect
9. GL(2,𝔽₃)	C₂²	semidirect
10. #226	C₂²	semidirect
12. C₂²×Q₈	D₃	semidirect
31. C₂×Q₈	C₂×D₃	semidirect
86. C₂	#983	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
#983	2
C₂×GL(2,𝔽₃)	2
C₂×#226	2
C₂×#137	3
C₂×#67	4

Subgroups — C2×#983 #5917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#983 #5917