Subgroups — C₂×Dic₂₄ #4905

Order 192.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂	C₂	1	2	yes	maximal
2	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₂₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₃₂	—	3	1	no	maximal, Sylow
5	C₂×Dic₆	—	2	2	no	—
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	Dic₁₂	—	2	2	no	—
8	Dic₁₂	C₂²	1	4	yes	—
9	C₃×C₁₆	C₂²	1	2	yes	—
10	C₂×Q₁₆	—	3	2	no	—
11	Q₃₂	—	3	4	no	—
12	C₂×C₁₆	D₃	1	1	yes	characteristic
13	C₂×C₃×C₄	D₄	1	1	yes	characteristic
14	C₂×Dic₃	—	4	2	no	—
15	Dic₆	—	2	4	no	—
16	Dic₆	—	4	2	no	—
17	C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₈	C₂³	1	1	yes	characteristic
19	C₂×Q₈	—	6	2	no	—
20	Q₁₆	—	3	4	no	—
21	Q₁₆	—	6	2	no	—
22	C₂×C₈	C₂×D₃	1	1	yes	characteristic
23	C₁₆	C₂×D₃	1	2	yes	—
24	C₂²×C₃	D₈	1	1	yes	characteristic
25	C₃×C₄	D₈	1	1	yes	characteristic
26	C₃×C₄	C₂×D₄	1	1	yes	characteristic
27	Dic₃	—	4	4	no	—
28	Q₈	—	6	4	no	—
29	Q₈	—	12	2	no	—
30	C₂×C₄	—	12	2	no	—
31	C₂×C₄	D₁₂	1	1	yes	characteristic
32	C₈	D₁₂	1	1	yes	characteristic
33	C₈	C₂²×D₃	1	1	yes	characteristic
34	C₂×C₃	Q₃₂	1	2	yes	complemented
35	C₂×C₃	C₂×D₈	1	1	yes	characteristic
36	C₂²	D₂₄	1	1	yes	characteristic
37	C₄	—	12	4	no	—
38	C₄	D₂₄	1	1	yes	characteristic
39	C₄	C₂×D₁₂	1	1	yes	characteristic
40	C₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
41	C₂	Dic₂₄	1	2	yes	direct product factor
42	C₂	C₂×D₂₄	1	1	yes	characteristic

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.