Subgroups — #5812

Order 192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₃	C₂	1	8	yes	maximal, complemented
3	#926	C₂	1	6	yes	maximal
4	#519	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	C₄	1	8	yes	complemented
6	C₂×C₃×Q₈	C₂²	1	4	yes	—
7	C₂²×C₃×C₄	C₂²	1	3	yes	—
8	#217	C₂²	1	4	yes	—
9	C₄⋊Dic₃	C₂²	1	12	yes	—
10	C₄×Dic₃	C₂²	1	12	yes	—
11	C₂²×Q₈	D₃	1	1	yes	characteristic
12	C₄×Q₈	—	3	8	no	—
13	#117	—	3	6	no	—
14	C₂³×C₃	C₂³	1	1	yes	characteristic
15	C₃×Q₈	C₂×C₄	1	16	yes	—
16	C₂×C₃×C₄	C₂×C₄	1	12	yes	—
17	C₂×C₃×C₄	C₂³	1	6	yes	—
18	C₂×Dic₃	C₂³	1	8	yes	—
19	C₂×Q₈	Dic₃	1	8	yes	complemented
20	C₂×Q₈	C₂×D₃	1	4	yes	—
21	C₂²×C₄	C₂×D₃	1	3	yes	—
22	C₄⋊C₄	—	3	12	no	—
23	C₂²⋊C₄	—	3	4	no	—
24	C₄²	—	3	12	no	—
25	C₂²×C₃	—	2	2	no	—
26	C₂²×C₃	C₂²×C₄	1	2	yes	—
27	C₂²×C₃	C₂⁴	1	1	yes	characteristic
28	C₃×C₄	C₂²×C₄	1	12	yes	—
29	Dic₃	—	2	8	no	—
30	C₂³	C₂²×D₃	1	1	yes	characteristic
31	Q₈	C₂×Dic₃	1	16	yes	—
32	C₂×C₄	—	3	8	no	—
33	C₂×C₄	C₂×Dic₃	1	12	yes	—
34	C₂×C₄	C₂²×D₃	1	6	yes	—
35	C₂×C₃	—	2	2	no	—
36	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₃	2₋¹⁺⁴	1	2	yes	—
38	C₂²	—	2	2	no	—
39	C₂²	C₂²×Dic₃	1	2	yes	—
40	C₂²	C₂³×D₃	1	1	yes	characteristic
41	C₄	—	6	8	no	—
42	C₄	C₂²×Dic₃	1	12	yes	—
43	C₃	#519	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	2	2	no	—
45	C₂	#1007	1	2	yes	—
46	C₂	C₂³×Dic₃	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.