Subgroups — C₂×#828 #5178

Order 192.

90 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, complemented
2	C₂×D₂₄	C₂	1	1	yes	maximal, characteristic
3	#828	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×SD₃₂	—	3	1	no	maximal, Sylow
6	C₂×C₃×Q₈	—	2	1	no	—
7	C₂×D₁₂	—	2	1	no	—
8	C₃×Q₁₆	—	2	1	no	—
9	C₃×Q₁₆	C₂²	1	2	yes	complemented
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	D₂₄	—	2	1	no	—
12	D₂₄	C₂²	1	2	yes	—
13	C₃⋊C₁₆	C₂²	1	2	yes	complemented
14	C₂×Q₁₆	D₃	1	1	yes	characteristic, complemented
15	C₂×D₈	—	3	1	no	—
16	SD₃₂	—	3	4	no	—
17	C₂×C₁₆	—	3	1	no	—
18	C₂²×D₃	—	4	1	no	—
19	C₃×Q₈	—	2	2	no	—
20	C₃×Q₈	—	4	1	no	—
21	C₂×C₃×C₄	—	4	1	no	—
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	D₁₂	—	2	2	no	—
24	D₁₂	—	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×D₄	—	6	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	C₂×D₃	1	2	yes	complemented
31	D₈	—	3	2	no	—
32	D₈	—	6	1	no	—
33	C₂×C₈	C₂×D₃	1	1	yes	characteristic
34	C₁₆	—	3	2	no	—
35	C₂²×C₃	D₈	1	1	yes	characteristic
36	C₂×D₃	—	4	2	no	—
37	C₂×D₃	—	8	2	no	—
38	C₃×C₄	—	4	2	no	—
39	C₃×C₄	D₈	1	1	yes	characteristic
40	C₃×C₄	C₂×D₄	1	1	yes	characteristic
41	C₂³	—	12	1	no	—
42	Q₈	—	2	2	no	—
43	Q₈	—	4	1	no	—
44	D₄	—	6	2	no	—
45	D₄	—	12	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	#67	1	1	yes	characteristic
48	C₈	#67	1	1	yes	characteristic
49	C₈	C₂²×D₃	1	1	yes	characteristic
50	C₂×C₃	SD₃₂	1	2	yes	complemented
51	C₂×C₃	C₂×D₈	1	1	yes	characteristic
52	D₃	—	8	2	no	—
53	C₂²	—	12	2	no	—
54	C₂²	—	24	2	no	—
55	C₂²	#213	1	1	yes	characteristic
56	C₄	—	4	2	no	—
57	C₄	#213	1	1	yes	characteristic
58	C₄	C₂×#67	1	1	yes	characteristic
59	C₃	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
60	C₂	—	24	2	no	—
61	C₂	#828	1	2	yes	direct product factor
62	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	C₂²×C₃	D₈
prime radical	C₂×D₂₄	C₂
hypercenter	C₂×Q₁₆	D₃
hypocenter	C₃	C₂×SD₃₂
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
1. C₂×C₃×Q₁₆	C₂	semidirect
3. #828	C₂	direct (N × H)
4. C₂×C₃⋊C₁₆	C₂	semidirect
9. C₃×Q₁₆	C₂²	semidirect
13. C₃⋊C₁₆	C₂²	semidirect
14. C₂×Q₁₆	D₃	semidirect
30. Q₁₆	C₂×D₃	semidirect
50. C₂×C₃	SD₃₂	semidirect
59. C₃	C₂×SD₃₂	semidirect
61. C₂	#828	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×D₂₄	2
#828	2
C₂×C₃⋊C₁₆	2
C₂×SD₃₂	3

Subgroups — C2×#828 #5178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#828 #5178