Subgroups — C₂×#208 #921

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	#208	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×M₁₆	—	3	1	no	maximal, Sylow
5	C₂³×C₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄	C₄	1	2	yes	—
7	C₂×C₃×C₄	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄	C₂²	1	2	yes	—
9	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₃⋊C₈	C₂²	1	4	yes	complemented
11	C₂²×C₄	D₃	1	1	yes	characteristic
12	M₁₆	—	3	4	no	—
13	C₂×C₈	—	3	2	no	—
14	C₂²×C₃	—	2	2	no	—
15	C₂²×C₃	C₂×C₄	1	2	yes	—
16	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
17	C₃×C₄	C₂×C₄	1	2	yes	—
18	C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄	C₂³	1	1	yes	characteristic
20	C₂³	Dic₃	1	1	yes	characteristic
21	C₂×C₄	Dic₃	1	1	yes	characteristic
22	C₂×C₄	Dic₃	1	2	yes	—
23	C₂×C₄	C₂×D₃	1	2	yes	—
24	C₂×C₄	C₂×D₃	1	1	yes	characteristic
25	C₈	—	3	4	no	—
26	C₂×C₃	—	2	2	no	—
27	C₂×C₃	M₁₆	1	2	yes	complemented
28	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²	—	2	2	no	—
30	C₂²	C₂×Dic₃	1	2	yes	—
31	C₂²	C₂×Dic₃	1	1	yes	characteristic
32	C₄	C₂×Dic₃	1	2	yes	—
33	C₄	C₂×Dic₃	1	1	yes	characteristic
34	C₄	C₂²×D₃	1	1	yes	characteristic
35	C₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	2	2	no	—
37	C₂	#208	1	2	yes	direct product factor
38	C₂	C₂²×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.