Subgroups — #809

Order 96.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#102	—	3	1	no	maximal, Sylow
5	C₂²×D₃	—	2	1	no	—
6	C₂×C₃×C₄	—	2	1	no	—
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	D₁₂	—	2	1	no	—
9	D₁₂	C₄	1	2	yes	complemented
10	C₃⋊C₈	—	2	1	no	—
11	C₂×D₄	—	3	1	no	—
12	C₂×C₈	—	3	1	no	—
13	C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
14	C₂²×C₃	D₄	1	1	yes	characteristic
15	C₂×D₃	—	2	2	no	—
16	C₂×D₃	—	4	1	no	—
17	C₂×D₃	—	4	1	no	—
18	C₃×C₄	—	4	1	no	—
19	C₃×C₄	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄	D₄	1	1	yes	characteristic
21	C₂³	—	6	1	no	—
22	D₄	—	3	2	no	—
23	D₄	—	6	1	no	—
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	C₂×D₃	1	1	yes	characteristic
26	C₈	—	6	1	no	—
27	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₃	D₈	1	1	yes	characteristic
29	C₂×C₃	SD₁₆	1	1	yes	characteristic
30	D₃	—	4	2	no	—
31	C₂²	—	6	2	no	—
32	C₂²	—	12	1	no	—
33	C₂²	—	12	1	no	—
34	C₂²	#67	1	1	yes	characteristic
35	C₄	—	4	1	no	—
36	C₄	C₄×D₃	1	1	yes	characteristic
37	C₄	D₁₂	1	1	yes	characteristic
38	C₃	#102	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	12	2	no	—
40	C₂	(C₂×D₃)⋊C₄	1	1	yes	characteristic
41	C₂	#213	1	1	yes	characteristic
42	C₂	#215	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.