Subgroups — #88862

Order 432.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
4	#3755	—	3	13	no	maximal
5	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
6	C₃³×C₄	—	2	1	no	—
7	C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₃²×Q₈	D₃	1	13	yes	complemented
9	C₄⋊(C₃⋊D₃)	—	3	13	no	—
10	C₃⋊(C₃⋊C₈)	—	3	13	no	—
11	C₂×C₃³	D₄	1	1	yes	characteristic
12	C₃⋊(C₃⋊D₃)	—	4	1	no	—
13	#215	—	9	13	no	—
14	C₂×C₃⋊D₃	—	6	13	no	—
15	C₃²×C₄	—	2	13	no	—
16	C₃²×C₄	C₂×D₃	1	13	yes	—
17	C₃³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₃×Q₈	C₃⋊D₃	1	13	yes	complemented
19	D₁₂	—	9	13	no	—
20	C₃⋊C₈	—	9	13	no	—
21	C₂×C₃²	#67	1	13	yes	—
22	C₃⋊D₃	—	12	13	no	—
23	SD₁₆	—	27	1	no	Sylow
24	C₂×D₃	—	18	13	no	—
25	C₃×C₄	—	2	13	no	—
26	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
27	C₃²	#215	1	13	yes	complemented
28	Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
29	D₄	—	27	1	no	—
30	C₈	—	27	1	no	—
31	C₂×C₃	#638	1	13	yes	—
32	D₃	—	36	13	no	—
33	C₂²	—	54	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
36	C₃	#3755	1	13	yes	complemented
37	C₂	—	108	1	no	—
38	C₂	#6312	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.