Subgroups — #830

Order 96.

50 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	C₂×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈	—	3	1	no	maximal, Sylow
4	C₂³×C₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄	—	2	2	no	—
6	C₂×C₃×C₄	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₃⋊C₈	—	2	2	no	—
9	C₂²×C₄	D₃	1	1	yes	characteristic
10	C₂×C₈	—	3	2	no	—
11	C₂²×C₃	—	2	1	no	—
12	C₂²×C₃	—	2	1	no	—
13	C₂²×C₃	C₈	1	2	yes	complemented
14	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄	—	2	1	no	—
16	C₃×C₄	D₄	1	2	yes	—
17	C₂³	Dic₃	1	1	yes	characteristic
18	C₂×C₄	—	2	2	no	—
19	C₂×C₄	Dic₃	1	1	yes	characteristic
20	C₂×C₄	C₂×D₃	1	1	yes	characteristic
21	C₈	—	6	2	no	—
22	C₂×C₃	—	2	2	no	—
23	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃	M₁₆	1	1	yes	characteristic
26	C₂²	—	2	1	no	—
27	C₂²	—	2	1	no	—
28	C₂²	C₃⋊C₈	1	2	yes	complemented
29	C₂²	C₂×Dic₃	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	#67	1	2	yes	—
32	C₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	2	2	no	—
34	C₂	C₂×C₃⋊C₈	1	1	yes	characteristic
35	C₂	#208	1	1	yes	characteristic
36	C₂	#217	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.