Subgroups — #823

Order 96.

46 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	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#208	C₂	1	1	yes	maximal, characteristic, complemented
4	#100	—	3	1	no	maximal, Sylow
5	C₂²×D₃	C₄	1	2	yes	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	D₁₂	—	2	1	no	—
8	D₁₂	—	2	1	no	—
9	C₃×C₈	—	2	1	no	—
10	C₃⋊C₈	—	2	1	no	—
11	C₂×D₄	—	3	1	no	—
12	M₁₆	—	3	1	no	—
13	M₁₆	D₃	1	1	yes	characteristic, complemented
14	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃	—	2	2	no	—
16	C₂×D₃	—	4	2	no	—
17	C₃×C₄	D₄	1	1	yes	characteristic
18	C₃×C₄	D₄	1	1	yes	characteristic
19	C₂³	—	3	2	no	—
20	D₄	—	6	1	no	—
21	D₄	—	6	1	no	—
22	C₂×C₄	C₂×D₃	1	1	yes	characteristic
23	C₈	—	2	1	no	—
24	C₈	—	6	1	no	—
25	C₂×C₃	—	2	1	no	—
26	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
27	D₃	—	4	2	no	—
28	C₂²	—	6	2	no	—
29	C₂²	—	12	2	no	—
30	C₂²	C₄×D₃	1	1	yes	characteristic
31	C₄	D₁₂	1	1	yes	characteristic
32	C₄	#67	1	1	yes	characteristic
33	C₃	#100	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	2	1	no	—
35	C₂	—	12	2	no	—
36	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.