Subgroups — #4454

Order 192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#322	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	C₄	1	2	yes	—
6	C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₈	C₄	1	2	yes	—
8	C₂×C₃⋊C₈	C₄	1	2	yes	—
9	C₄×C₈	—	3	1	no	—
10	C₄×C₈	—	3	1	no	—
11	C₄×C₈	D₃	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
15	C₃×C₈	—	2	2	no	—
16	C₃⋊C₈	—	2	2	no	—
17	C₃⋊C₈	C₈	1	4	yes	complemented
18	C₂×C₈	—	3	2	no	—
19	C₂×C₈	—	3	2	no	—
20	C₂×C₈	Dic₃	1	2	yes	—
21	C₄²	C₂×D₃	1	1	yes	characteristic
22	C₂²×C₃	C₄²	1	1	yes	characteristic
23	C₃×C₄	C₂×C₈	1	2	yes	—
24	C₃×C₄	M₁₆	1	2	yes	—
25	C₃×C₄	M₁₆	1	2	yes	—
26	C₂×C₄	C₄×D₃	1	1	yes	characteristic
27	C₂×C₄	C₄×D₃	1	1	yes	characteristic
28	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
29	C₈	—	2	2	no	—
30	C₈	—	3	4	no	—
31	C₈	—	6	2	no	—
32	C₂×C₃	C₄×C₈	1	1	yes	characteristic
33	C₂×C₃	#97	1	1	yes	characteristic
34	C₂×C₃	#97	1	1	yes	characteristic
35	C₂²	C₄×Dic₃	1	1	yes	characteristic
36	C₄	D₃×C₈	1	2	yes	—
37	C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
38	C₄	#208	1	2	yes	—
39	C₃	#322	1	1	yes	characteristic, complemented, Sylow
40	C₂	#803	1	1	yes	characteristic
41	C₂	C₈×Dic₃	1	1	yes	characteristic
42	C₂	#815	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₃⋊C₈	C₈	semidirect
39. C₃	#322	semidirect

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