Subgroups — (C₂×D₃)⋊C₈ #820

Order 96.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₈	—	3	1	no	maximal, Sylow
5	C₂²×D₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×Dic₃	C₄	1	1	yes	characteristic
8	C₄×D₃	—	2	1	no	—
9	C₄×D₃	—	2	1	no	—
10	C₃×C₈	—	2	1	no	—
11	C₃⋊C₈	—	2	1	no	—
12	C₂²×C₄	—	3	1	no	—
13	C₂×C₈	—	3	1	no	—
14	C₂×C₈	D₃	1	1	yes	characteristic, complemented
15	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃	—	2	1	no	—
17	C₂×D₃	—	2	1	no	—
18	C₂×D₃	C₈	1	2	yes	complemented
19	C₃×C₄	D₄	1	1	yes	characteristic
20	C₃×C₄	D₄	1	1	yes	characteristic
21	Dic₃	—	2	1	no	—
22	C₂³	—	3	1	no	—
23	C₂×C₄	—	3	1	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₄	—	6	1	no	—
26	C₂×C₄	C₂×D₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	6	1	no	—
29	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₃	M₁₆	1	1	yes	characteristic
32	D₃	—	2	2	no	—
33	C₂²	—	3	2	no	—
34	C₂²	—	6	1	no	—
35	C₂²	—	6	1	no	—
36	C₂²	C₄×D₃	1	1	yes	characteristic
37	C₄	—	6	1	no	—
38	C₄	D₁₂	1	1	yes	characteristic
39	C₄	#67	1	1	yes	characteristic
40	C₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂	—	6	2	no	—
42	C₂	D₃×C₈	1	1	yes	characteristic
43	C₂	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
44	C₂	(C₂×D₃)⋊C₄	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.