Subgroups — #4511

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
3	#812	C₂	1	1	yes	maximal, characteristic
4	#364	—	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	—	2	1	no	—
9	C₃⋊C₁₆	—	2	1	no	—
10	M₃₂	—	3	1	no	—
11	M₃₂	D₃	1	1	yes	characteristic
12	C₄×C₈	—	3	1	no	—
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃	—	2	1	no	—
15	C₃×C₈	D₄	1	1	yes	characteristic
16	C₃×C₈	Q₈	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	—	2	1	no	—
22	C₁₆	—	6	1	no	—
23	C₂²×C₃	M₁₆	1	1	yes	characteristic
24	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
25	C₃×C₄	C₂×C₈	1	1	yes	characteristic
26	Dic₃	—	2	2	no	—
27	C₂×C₄	—	6	1	no	—
28	C₂×C₄	C₄×D₃	1	1	yes	characteristic
29	C₈	—	3	2	no	—
30	C₈	Dic₆	1	1	yes	characteristic
31	C₈	#67	1	1	yes	characteristic
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
34	C₂²	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
35	C₄	—	6	2	no	—
36	C₄	D₃×C₈	1	1	yes	characteristic
37	C₄	Dic₃⋊C₄	1	1	yes	characteristic
38	C₃	#364	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	2	1	no	—
40	C₂	Dic₃⋊C₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
38. C₃	#364	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.