Subgroups — #4502

Order 192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#346	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₄×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₃⋊C₈	C₄	1	1	yes	characteristic
8	C₃×C₁₆	C₄	1	2	yes	complemented
9	C₃⋊C₁₆	C₄	1	2	yes	complemented
10	C₂×C₁₆	—	3	1	no	—
11	C₂×C₁₆	D₃	1	1	yes	characteristic
12	C₄×C₈	—	3	1	no	—
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃	C₈	1	2	yes	—
15	C₃×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₈	C₂×C₄	1	1	yes	characteristic
17	C₃⋊C₈	C₈	1	2	yes	—
18	C₂×C₈	—	3	1	no	—
19	C₂×C₈	C₂×D₃	1	1	yes	characteristic
20	C₄²	—	3	1	no	—
21	C₁₆	—	3	2	no	—
22	C₁₆	Dic₃	1	2	yes	complemented
23	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
24	C₃×C₄	C₄²	1	1	yes	characteristic
25	C₃×C₄	C₂×C₈	1	1	yes	characteristic
26	Dic₃	—	2	2	no	—
27	C₂×C₄	—	3	2	no	—
28	C₂×C₄	C₄×D₃	1	1	yes	characteristic
29	C₈	—	3	2	no	—
30	C₈	C₄×D₃	1	1	yes	characteristic
31	C₈	C₂×Dic₃	1	1	yes	characteristic
32	C₂×C₃	C₄×C₈	1	1	yes	characteristic
33	C₂×C₃	M₃₂	1	2	yes	—
34	C₂²	D₃×C₈	1	1	yes	characteristic
35	C₄	—	6	2	no	—
36	C₄	D₃×C₈	1	1	yes	characteristic
37	C₄	C₄×Dic₃	1	1	yes	characteristic
38	C₃	#346	1	1	yes	characteristic, complemented, Sylow
39	C₂	#798	1	2	yes	—
40	C₂	C₈×Dic₃	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.