Subgroups — #4682

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#869	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#818	C₂	1	4	yes	maximal
4	#500	—	3	1	no	maximal, Sylow
5	C₂×Dic₆	—	2	2	no	—
6	C₂×C₃×C₈	C₂²	1	2	yes	—
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃	—	2	2	no	—
9	C₄⋊Dic₃	C₂²	1	4	yes	—
10	C₄⋊Q₈	—	3	2	no	—
11	#107	—	3	4	no	—
12	C₄×C₈	D₃	1	1	yes	characteristic
13	C₂×C₃×C₄	D₄	1	1	yes	characteristic
14	C₂×C₃×C₄	D₄	1	1	yes	characteristic
15	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
16	C₂×Dic₃	—	2	4	no	—
17	Dic₆	—	4	4	no	—
18	C₃×C₈	Q₈	1	4	yes	complemented
19	C₂×Q₈	—	6	2	no	—
20	C₂×C₈	C₂×D₃	1	2	yes	—
21	C₄⋊C₄	—	3	4	no	—
22	C₄⋊C₄	—	6	2	no	—
23	C₄²	C₂×D₃	1	1	yes	characteristic
24	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
25	C₃×C₄	D₈	1	2	yes	—
26	C₃×C₄	Q₁₆	1	2	yes	—
27	C₃×C₄	C₂×Q₈	1	2	yes	—
28	Dic₃	—	4	4	no	—
29	Q₈	—	12	4	no	—
30	C₂×C₄	—	6	4	no	—
31	C₂×C₄	D₁₂	1	1	yes	characteristic
32	C₂×C₄	D₁₂	1	1	yes	characteristic
33	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
34	C₈	Dic₆	1	4	yes	complemented
35	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
36	C₂×C₃	C₂×D₈	1	1	yes	characteristic
37	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₂²	C₂×D₁₂	1	1	yes	characteristic
39	C₄	—	12	4	no	—
40	C₄	D₂₄	1	2	yes	—
41	C₄	Dic₁₂	1	2	yes	—
42	C₄	C₂×Dic₆	1	2	yes	—
43	C₃	#500	1	1	yes	characteristic, complemented, Sylow
44	C₂	#869	1	1	yes	characteristic
45	C₂	C₂×D₂₄	1	1	yes	characteristic
46	C₂	C₂×Dic₁₂	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.