Subgroups — #4699

Order 192.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂	C₂	1	4	yes	maximal
2	#869	C₂	1	2	yes	maximal
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	#494	—	3	1	no	maximal, Sylow
5	C₂×Dic₆	C₂²	1	4	yes	—
6	C₂×C₃×C₈	C₂²	1	2	yes	—
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃	—	2	4	no	—
9	Dic₁₂	—	2	8	no	—
10	C₂×Q₁₆	—	3	4	no	—
11	C₄⋊Q₈	—	3	2	no	—
12	C₄×C₈	D₃	1	1	yes	characteristic
13	C₂×C₃×C₄	D₄	1	2	yes	—
14	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
15	C₂×Dic₃	—	2	4	no	—
16	Dic₆	—	2	8	no	—
17	C₃×C₈	D₄	1	4	yes	—
18	C₂×Q₈	—	3	4	no	—
19	Q₁₆	—	6	8	no	—
20	C₂×C₈	C₂×D₃	1	2	yes	—
21	C₄⋊C₄	—	6	4	no	—
22	C₄²	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
24	C₃×C₄	Q₁₆	1	4	yes	complemented
25	C₃×C₄	C₂×D₄	1	2	yes	—
26	Dic₃	—	4	4	no	—
27	Q₈	—	6	8	no	—
28	C₂×C₄	—	6	4	no	—
29	C₂×C₄	D₁₂	1	2	yes	—
30	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
31	C₈	D₁₂	1	4	yes	—
32	C₂×C₃	#127	1	1	yes	characteristic
33	C₂×C₃	C₂×Q₁₆	1	2	yes	—
34	C₂²	C₂×D₁₂	1	1	yes	characteristic
35	C₄	—	12	4	no	—
36	C₄	Dic₁₂	1	4	yes	complemented
37	C₄	C₂×D₁₂	1	2	yes	—
38	C₃	#494	1	1	yes	characteristic, complemented, Sylow
39	C₂	#874	1	1	yes	characteristic
40	C₂	C₂×Dic₁₂	1	2	yes	—

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.