Subgroups — #4512

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	#815	C₂	1	1	yes	maximal, characteristic
3	#812	C₂	1	1	yes	maximal, characteristic
4	#347	—	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	M₃₂	—	3	1	no	—
11	M₃₂	D₃	1	1	yes	characteristic
12	#97	—	3	1	no	—
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃	—	2	1	no	—
15	C₃×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₈	C₂×C₄	1	1	yes	characteristic
17	C₃⋊C₈	—	2	1	no	—
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	M₁₆	1	1	yes	characteristic
24	C₃×C₄	C₄²	1	1	yes	characteristic
25	C₃×C₄	M₁₆	1	1	yes	characteristic
26	Dic₃	—	4	1	no	—
27	C₂×C₄	—	6	1	no	—
28	C₂×C₄	C₄×D₃	1	1	yes	characteristic
29	C₈	—	6	1	no	—
30	C₈	C₄×D₃	1	1	yes	characteristic
31	C₈	C₂×Dic₃	1	1	yes	characteristic
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	#97	1	1	yes	characteristic
34	C₂²	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
35	C₄	—	12	1	no	—
36	C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
37	C₄	C₄×Dic₃	1	1	yes	characteristic
38	C₃	#347	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	2	1	no	—
40	C₂	#815	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.