Subgroups — C₂×#1007 #5960

Order 192.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#1007	C₂	1	16	yes	maximal, direct product factor
3	C₂×#239	C₂	1	4	yes	maximal, complemented
4	C₂×D₃×Q₈	C₂	1	4	yes	maximal, complemented
5	C₂×#235	C₂	1	6	yes	maximal, complemented
6	C₂×2₋¹⁺⁴	—	3	1	no	maximal, Sylow
7	C₂×C₃×Q₈	C₂²	1	4	yes	—
8	C₂×C₃×Q₈	C₂²	1	8	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	3	yes	—
10	C₂×#67	C₂²	1	4	yes	—
11	#239	C₂²	1	32	yes	complemented
12	D₃×Q₈	C₂²	1	32	yes	complemented
13	#235	C₂²	1	48	yes	complemented
14	C₂×D₁₂	C₂²	1	6	yes	—
15	C₂×C₄×D₃	C₂²	1	12	yes	—
16	C₂×Dic₆	C₂²	1	6	yes	—
17	2₋¹⁺⁴	—	3	16	no	—
18	C₂×#41	—	3	4	no	—
19	C₂×#41	—	3	6	no	—
20	C₂²×Q₈	—	3	4	no	—
21	C₂²×Q₈	D₃	1	1	yes	characteristic, complemented
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₂²×D₃	C₂³	1	4	yes	—
24	C₃×Q₈	C₂³	1	16	yes	—
25	C₂×C₃×C₄	C₂³	1	6	yes	—
26	C₂×C₃×C₄	C₂³	1	12	yes	—
27	#67	C₂³	1	16	yes	—
28	C₂×Dic₃	C₂³	1	4	yes	—
29	D₁₂	C₂³	1	24	yes	—
30	C₄×D₃	C₂³	1	48	yes	—
31	Dic₆	C₂³	1	24	yes	—
32	#41	—	3	32	no	—
33	#41	—	3	48	no	—
34	C₂×Q₈	—	3	32	no	—
35	C₂×Q₈	—	3	6	no	—
36	C₂×Q₈	C₂×D₃	1	4	yes	—
37	C₂×Q₈	C₂×D₃	1	8	yes	complemented
38	C₂×D₄	—	3	4	no	—
39	C₂×D₄	—	3	6	no	—
40	C₂²×C₄	—	3	12	no	—
41	C₂²×C₄	C₂×D₃	1	3	yes	—
42	C₂²×C₃	—	2	2	no	—
43	C₂²×C₃	C₂⁴	1	2	yes	—
44	C₂²×C₃	C₂⁴	1	1	yes	characteristic
45	C₂×D₃	—	2	8	no	—
46	C₂×D₃	C₂⁴	1	8	yes	—
47	C₃×C₄	C₂⁴	1	12	yes	—
48	Dic₃	C₂⁴	1	8	yes	—
49	C₂³	—	3	4	no	—
50	C₂³	C₂²×D₃	1	1	yes	characteristic
51	Q₈	—	3	24	no	—
52	Q₈	C₂²×D₃	1	16	yes	—
53	D₄	—	3	16	no	—
54	D₄	—	3	24	no	—
55	C₂×C₄	—	3	4	no	—
56	C₂×C₄	—	3	48	no	—
57	C₂×C₄	C₂²×D₃	1	12	yes	—
58	C₂×C₄	C₂²×D₃	1	6	yes	—
59	C₂×C₃	—	2	2	no	—
60	C₂×C₃	2₋¹⁺⁴	1	2	yes	complemented
61	C₂×C₃	C₂⁵	1	1	yes	characteristic
62	D₃	—	2	8	no	—
63	C₂²	—	2	2	no	—
64	C₂²	—	3	8	no	—
65	C₂²	—	6	8	no	—
66	C₂²	C₂³×D₃	1	2	yes	—
67	C₂²	C₂³×D₃	1	1	yes	characteristic
68	C₄	—	3	8	no	—
69	C₄	C₂³×D₃	1	12	yes	—
70	C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	2	2	no	—
72	C₂	—	6	8	no	—
73	C₂	#1007	1	2	yes	direct product factor
74	C₂	C₂⁴×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₃
commutator, cosocle	C₂×C₃	C₂⁵
Frattini	C₂	C₂⁴×D₃
Fitting	C₂²×C₃×Q₈	C₂
socle	C₂²×C₃	C₂⁴
hypercenter	C₂²×Q₈	D₃
hypocenter	C₃	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈	C₂	semidirect
2. #1007	C₂	direct (N × H)
3. C₂×#239	C₂	semidirect
4. C₂×D₃×Q₈	C₂	semidirect
5. C₂×#235	C₂	semidirect
8. C₂×C₃×Q₈	C₂²	semidirect
11. #239	C₂²	semidirect
12. D₃×Q₈	C₂²	semidirect
13. #235	C₂²	semidirect
21. C₂²×Q₈	D₃	semidirect
37. C₂×Q₈	C₂×D₃	semidirect
60. C₂×C₃	2₋¹⁺⁴	semidirect
70. C₃	C₂×2₋¹⁺⁴	semidirect
73. C₂	#1007	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×C₃×Q₈	2
#1007	2
C₂×#239	2
C₂×D₃×Q₈	2
C₂×#235	2
C₂×2₋¹⁺⁴	3

Subgroups — C2×#1007 #5960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1007 #5960