Subgroups — #4695

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄	C₂	1	4	yes	maximal, complemented
2	#874	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#493	—	3	1	no	maximal, Sylow
5	C₂×D₁₂	—	2	4	no	—
6	C₂×D₁₂	C₂²	1	4	yes	—
7	C₂×C₃×C₈	C₂²	1	2	yes	—
8	C₃×C₄²	C₂²	1	1	yes	characteristic
9	D₂₄	—	2	8	no	—
10	C₂×D₈	—	3	4	no	—
11	#127	—	3	2	no	—
12	C₄×C₈	D₃	1	1	yes	characteristic, complemented
13	C₂²×D₃	—	2	4	no	—
14	C₂×C₃×C₄	D₄	1	2	yes	—
15	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
16	D₁₂	—	2	8	no	—
17	D₁₂	—	4	8	no	—
18	C₃×C₈	D₄	1	4	yes	complemented
19	C₂×D₄	—	3	4	no	—
20	C₂×D₄	—	6	4	no	—
21	D₈	—	6	8	no	—
22	C₂×C₈	C₂×D₃	1	2	yes	—
23	C₄²	C₂×D₃	1	1	yes	characteristic
24	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₃	—	4	4	no	—
26	C₂×D₃	—	4	8	no	—
27	C₃×C₄	D₈	1	4	yes	complemented
28	C₃×C₄	C₂×D₄	1	2	yes	—
29	C₂³	—	6	4	no	—
30	D₄	—	6	8	no	—
31	D₄	—	12	8	no	—
32	C₂×C₄	D₁₂	1	2	yes	—
33	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
34	C₈	D₁₂	1	4	yes	complemented
35	C₂×C₃	#127	1	1	yes	characteristic
36	C₂×C₃	C₂×D₈	1	2	yes	—
37	D₃	—	8	4	no	—
38	C₂²	—	12	4	no	—
39	C₂²	—	12	8	no	—
40	C₂²	C₂×D₁₂	1	1	yes	characteristic
41	C₄	D₂₄	1	4	yes	complemented
42	C₄	C₂×D₁₂	1	2	yes	—
43	C₃	#493	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	24	4	no	—
45	C₂	#874	1	1	yes	characteristic
46	C₂	C₂×D₂₄	1	2	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.