Subgroups — C₂×#869 #5468

Order 192.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₃	C₂	1	4	yes	maximal
4	#869	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊Q₈	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	2	yes	—
8	C₂²×Dic₃	C₂²	1	4	yes	—
9	C₂×Dic₆	—	2	8	no	—
10	C₂×Dic₆	C₂²	1	8	yes	—
11	C₃×C₄²	C₂²	1	4	yes	—
12	C₄⋊Dic₃	C₂²	1	16	yes	—
13	C₂²×Q₈	—	3	2	no	—
14	C₄⋊Q₈	—	3	8	no	—
15	C₂×C₄⋊C₄	—	3	4	no	—
16	C₂×C₄²	D₃	1	1	yes	characteristic
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	4	yes	—
19	C₂×C₃×C₄	Q₈	1	8	yes	complemented
20	C₂×C₃×C₄	C₂³	1	2	yes	—
21	C₂×C₃×C₄	C₂³	1	4	yes	—
22	C₂×Dic₃	—	2	8	no	—
23	C₂×Dic₃	C₂³	1	8	yes	—
24	Dic₆	—	2	16	no	—
25	C₂×Q₈	—	3	8	no	—
26	C₂×Q₈	—	6	8	no	—
27	C₂²×C₄	—	3	4	no	—
28	C₂²×C₄	C₂×D₃	1	2	yes	—
29	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
30	C₄⋊C₄	—	3	16	no	—
31	C₄²	C₂×D₃	1	4	yes	—
32	C₂²×C₃	C₂×D₄	1	2	yes	—
33	C₂²×C₃	C₂×Q₈	1	4	yes	—
34	C₂²×C₃	C₂⁴	1	1	yes	characteristic
35	C₃×C₄	C₂×D₄	1	4	yes	—
36	C₃×C₄	C₂×Q₈	1	8	yes	complemented
37	Dic₃	—	2	8	no	—
38	C₂³	C₂²×D₃	1	1	yes	characteristic
39	Q₈	—	6	16	no	—
40	C₂×C₄	—	3	8	no	—
41	C₂×C₄	—	6	8	no	—
42	C₂×C₄	Dic₆	1	8	yes	complemented
43	C₂×C₄	D₁₂	1	4	yes	—
44	C₂×C₄	C₂²×D₃	1	4	yes	—
45	C₂×C₄	C₂²×D₃	1	2	yes	—
46	C₂×C₃	C₄⋊Q₈	1	4	yes	complemented
47	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
48	C₂×C₃	C₂²×Q₈	1	2	yes	—
49	C₂²	C₂×Dic₆	1	4	yes	—
50	C₂²	C₂×D₁₂	1	2	yes	—
51	C₂²	C₂³×D₃	1	1	yes	characteristic
52	C₄	—	6	8	no	—
53	C₄	C₂×Dic₆	1	8	yes	complemented
54	C₄	C₂×D₁₂	1	4	yes	—
55	C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
56	C₂	#869	1	4	yes	direct product factor
57	C₂	C₂²×Dic₆	1	2	yes	—
58	C₂	C₂²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical	C₂³×C₃	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #869	C₂	direct (N × H)
19. C₂×C₃×C₄	Q₈	semidirect
36. C₃×C₄	C₂×Q₈	semidirect
42. C₂×C₄	Dic₆	semidirect
46. C₂×C₃	C₄⋊Q₈	semidirect
53. C₄	C₂×Dic₆	semidirect
55. C₃	C₂×C₄⋊Q₈	semidirect
56. C₂	#869	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×Dic₆	2
C₂×C₃×C₄²	2
C₂×C₄⋊Dic₃	2
#869	2
C₂×C₄⋊Q₈	3

Subgroups — C2×#869 #5468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#869 #5468