Subgroups — C₂×#829 #5180

Order 192.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	#829	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₃₂	—	3	1	no	maximal, Sylow
6	C₂×C₃×Q₈	—	2	1	no	—
7	C₂×Dic₆	—	2	1	no	—
8	C₃×Q₁₆	—	2	1	no	—
9	C₃×Q₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	Dic₁₂	—	2	1	no	—
12	Dic₁₂	C₂²	1	2	yes	—
13	C₃⋊C₁₆	C₂²	1	2	yes	—
14	C₂×Q₁₆	—	3	1	no	—
15	C₂×Q₁₆	D₃	1	1	yes	characteristic
16	Q₃₂	—	3	4	no	—
17	C₂×C₁₆	—	3	1	no	—
18	C₃×Q₈	—	2	2	no	—
19	C₃×Q₈	—	4	1	no	—
20	C₂×C₃×C₄	—	4	1	no	—
21	C₂×C₃×C₄	D₄	1	1	yes	characteristic
22	C₂×Dic₃	—	4	1	no	—
23	Dic₆	—	2	2	no	—
24	Dic₆	—	4	1	no	—
25	C₃×C₈	D₄	1	1	yes	characteristic
26	C₃×C₈	C₂³	1	1	yes	characteristic
27	C₂×Q₈	—	2	1	no	—
28	C₂×Q₈	—	6	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	—	3	2	no	—
31	Q₁₆	—	6	1	no	—
32	Q₁₆	C₂×D₃	1	2	yes	—
33	C₂×C₈	C₂×D₃	1	1	yes	characteristic
34	C₁₆	—	3	2	no	—
35	C₂²×C₃	D₈	1	1	yes	characteristic
36	C₃×C₄	—	4	2	no	—
37	C₃×C₄	D₈	1	1	yes	characteristic
38	C₃×C₄	C₂×D₄	1	1	yes	characteristic
39	Dic₃	—	4	2	no	—
40	Q₈	—	2	2	no	—
41	Q₈	—	4	1	no	—
42	Q₈	—	6	2	no	—
43	Q₈	—	12	1	no	—
44	C₂×C₄	—	4	1	no	—
45	C₂×C₄	—	12	1	no	—
46	C₂×C₄	#67	1	1	yes	characteristic
47	C₈	#67	1	1	yes	characteristic
48	C₈	C₂²×D₃	1	1	yes	characteristic
49	C₂×C₃	Q₃₂	1	2	yes	complemented
50	C₂×C₃	C₂×D₈	1	1	yes	characteristic
51	C₂²	#213	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	12	2	no	—
54	C₄	#213	1	1	yes	characteristic
55	C₄	C₂×#67	1	1	yes	characteristic
56	C₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
57	C₂	#829	1	2	yes	direct product factor
58	C₂	C₂×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#213
commutator, cosocle	C₃×C₈	C₂³
Frattini	C₈	C₂²×D₃
Fitting	C₂×C₃×Q₁₆	C₂
socle, prime radical	C₂²×C₃	D₈
hypercenter	C₂×Q₁₆	D₃
hypocenter	C₃	C₂×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #829	C₂	direct (N × H)
49. C₂×C₃	Q₃₂	semidirect
56. C₃	C₂×Q₃₂	semidirect
57. C₂	#829	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×C₃×Q₁₆	2
C₂×Dic₁₂	2
#829	2
C₂×C₃⋊C₁₆	2
C₂×Q₃₂	3

Subgroups — C2×#829 #5180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#829 #5180