Subgroups — C₂×#984 #5920

Order 192.

141 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
2	#984	C₂	1	4	yes	maximal, direct product factor
3	C₂×#226	C₂	1	2	yes	maximal, complemented
4	C₂×#137	—	3	1	no	maximal, Sylow
5	C₂×Dic₆	—	4	1	no	maximal
6	#41⋊C₃	C₂²	1	2	yes	—
7	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
8	#226	C₂²	1	4	yes	complemented
9	C₂×#41	D₃	1	1	yes	characteristic
10	C₂²×Q₈	—	3	1	no	—
11	#137	—	3	4	no	—
12	#137	—	3	4	no	—
13	C₂×Q₁₆	—	3	2	no	—
14	C₂×SD₁₆	—	3	2	no	—
15	C₂×M₁₆	—	3	1	no	—
16	C₂×C₃×C₄	—	4	1	no	—
17	C₂×Dic₃	—	4	2	no	—
18	Dic₆	—	4	4	no	—
19	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic
20	#41	—	3	2	no	—
21	#41	C₂×D₃	1	2	yes	—
22	C₂×Q₈	—	3	2	no	—
23	C₂×Q₈	—	3	4	no	—
24	C₂×Q₈	—	6	2	no	—
25	C₂×Q₈	—	6	1	no	—
26	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
27	C₂×D₄	—	3	1	no	—
28	C₂²×C₄	—	3	1	no	—
29	C₂²×C₄	—	6	1	no	—
30	Q₁₆	—	3	4	no	—
31	Q₁₆	—	3	4	no	—
32	SD₁₆	—	3	8	no	—
33	M₁₆	—	3	4	no	—
34	C₂×C₈	—	3	2	no	—
35	C₂²×C₃	—	4	1	no	—
36	C₃×C₄	—	4	2	no	—
37	Dic₃	—	4	4	no	—
38	C₂³	—	3	1	no	—
39	Q₈	—	3	1	no	—
40	Q₈	—	3	4	no	—
41	Q₈	—	6	2	no	—
42	Q₈	—	6	4	no	—
43	Q₈	C₂²×D₃	1	1	yes	characteristic
44	D₄	—	3	2	no	—
45	D₄	—	6	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	—	3	2	no	—
48	C₂×C₄	—	3	2	no	—
49	C₂×C₄	—	6	4	no	—
50	C₂×C₄	—	6	2	no	—
51	C₂×C₄	S₄	1	1	yes	characteristic
52	C₈	—	3	4	no	—
53	C₂×C₃	—	4	2	no	—
54	C₂×C₃	—	4	1	no	—
55	C₂²	—	3	2	no	—
56	C₂²	—	6	2	no	—
57	C₂²	C₂×S₄	1	1	yes	characteristic
58	C₄	—	3	1	no	—
59	C₄	—	3	1	no	—
60	C₄	—	6	4	no	—
61	C₄	C₂×S₄	1	2	yes	—
62	C₃	—	4	1	no	Sylow
63	C₂	—	6	2	no	—
64	C₂	#984	1	2	yes	direct product factor
65	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
prime radical	C₂×#41⋊C₃	C₂
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
2. #984	C₂	direct (N × H)
3. C₂×#226	C₂	semidirect
8. #226	C₂²	semidirect
64. C₂	#984	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
#984	2
C₂×#226	2
C₂×#137	3
C₂×Dic₆	4

Subgroups — C2×#984 #5920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#984 #5920