Subgroups — C₂×#874 #5475

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂	C₂	1	6	yes	maximal, complemented
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	#874	C₂	1	8	yes	maximal, direct product factor
4	C₂×#127	—	3	1	no	maximal, Sylow
5	C₂³×D₃	C₂²	1	4	yes	—
6	C₂²×C₃×C₄	C₂²	1	3	yes	—
7	C₂×D₁₂	—	2	24	no	—
8	C₂×D₁₂	C₂²	1	24	yes	complemented
9	C₃×C₄²	C₂²	1	4	yes	complemented
10	C₂²×D₄	—	3	6	no	—
11	#127	—	3	8	no	—
12	C₂×C₄²	D₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₂²×D₃	—	2	24	no	—
15	C₂²×D₃	C₂³	1	8	yes	—
16	C₂×C₃×C₄	D₄	1	12	yes	complemented
17	C₂×C₃×C₄	C₂³	1	6	yes	—
18	D₁₂	—	2	48	no	—
19	C₂⁴	—	3	4	no	—
20	C₂×D₄	—	3	24	no	—
21	C₂×D₄	—	6	24	no	—
22	C₂²×C₄	C₂×D₃	1	3	yes	—
23	C₄²	C₂×D₃	1	4	yes	complemented
24	C₂²×C₃	C₂×D₄	1	6	yes	—
25	C₂²×C₃	C₂⁴	1	1	yes	characteristic
26	C₂×D₃	—	2	24	no	—
27	C₂×D₃	—	4	16	no	—
28	C₃×C₄	C₂×D₄	1	12	yes	complemented
29	C₂³	—	3	8	no	—
30	C₂³	—	6	24	no	—
31	C₂³	C₂²×D₃	1	1	yes	characteristic
32	D₄	—	6	48	no	—
33	C₂×C₄	D₁₂	1	12	yes	complemented
34	C₂×C₄	C₂²×D₃	1	6	yes	—
35	C₂×C₃	#127	1	4	yes	complemented
36	C₂×C₃	C₂²×D₄	1	3	yes	—
37	D₃	—	4	8	no	—
38	C₂²	—	6	24	no	—
39	C₂²	—	12	16	no	—
40	C₂²	C₂×D₁₂	1	6	yes	—
41	C₂²	C₂³×D₃	1	1	yes	characteristic
42	C₄	C₂×D₁₂	1	12	yes	complemented
43	C₃	C₂×#127	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	12	8	no	—
45	C₂	#874	1	4	yes	direct product factor
46	C₂	C₂²×D₁₂	1	3	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.