Subgroups — C₂×#204 #902

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#204	C₂	1	4	yes	maximal, direct product factor
5	C₂×SD₁₆	—	3	1	no	maximal, Sylow
6	C₂²×D₃	—	2	1	no	—
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂×Dic₃	—	2	1	no	—
9	D₁₂	—	2	1	no	—
10	D₁₂	C₂²	1	2	yes	—
11	Dic₆	—	2	1	no	—
12	Dic₆	C₂²	1	2	yes	complemented
13	C₃×C₈	C₂²	1	2	yes	complemented
14	C₂×Q₈	—	3	1	no	—
15	C₂×D₄	—	3	1	no	—
16	SD₁₆	—	3	4	no	—
17	C₂×C₈	D₃	1	1	yes	characteristic, complemented
18	C₂²×C₃	D₄	1	1	yes	characteristic
19	C₂×D₃	—	2	2	no	—
20	C₂×D₃	—	4	2	no	—
21	C₃×C₄	D₄	1	1	yes	characteristic
22	C₃×C₄	C₂³	1	1	yes	characteristic
23	Dic₃	—	2	2	no	—
24	C₂³	—	6	1	no	—
25	Q₈	—	3	2	no	—
26	Q₈	—	6	1	no	—
27	D₄	—	3	2	no	—
28	D₄	—	6	1	no	—
29	C₂×C₄	—	6	1	no	—
30	C₂×C₄	C₂×D₃	1	1	yes	characteristic
31	C₈	C₂×D₃	1	2	yes	complemented
32	C₂×C₃	SD₁₆	1	2	yes	complemented
33	C₂×C₃	C₂×D₄	1	1	yes	characteristic
34	D₃	—	4	2	no	—
35	C₂²	—	6	2	no	—
36	C₂²	—	12	2	no	—
37	C₂²	D₁₂	1	1	yes	characteristic
38	C₄	—	6	2	no	—
39	C₄	D₁₂	1	1	yes	characteristic
40	C₄	C₂²×D₃	1	1	yes	characteristic
41	C₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	12	2	no	—
43	C₂	#204	1	2	yes	direct product factor
44	C₂	C₂×D₁₂	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.