Subgroups — #63732

Order 288.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#157	C₂	1	1	yes	maximal, characteristic
2	#3710	C₂	1	2	yes	maximal
3	C₂×#157	C₄	1	1	yes	characteristic
4	C₂×#157	C₄	1	1	yes	characteristic
5	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃×C₃⋊C₈	—	2	2	no	—
7	D₃×C₈	—	6	2	no	—
8	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
9	#157	—	2	1	no	—
10	#157	C₈	1	2	yes	complemented
11	C₃²×C₄	D₄	1	1	yes	characteristic
12	C₃⋊Dic₃	Q₈	1	1	yes	characteristic
13	C₄⋊C₈	—	9	1	no	maximal, Sylow
14	C₄×D₃	—	6	2	no	—
15	C₃×C₈	—	6	2	no	—
16	C₃⋊C₈	—	2	2	no	—
17	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
18	C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
19	C₃⋊D₃	M₁₆	1	1	yes	characteristic
20	C₂×C₈	—	9	2	no	—
21	C₄²	—	9	1	no	—
22	C₂×D₃	—	6	2	no	—
23	C₃×C₄	—	2	2	no	—
24	Dic₃	—	6	2	no	—
25	C₃²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	9	1	no	—
27	C₂×C₄	—	9	1	no	—
28	C₂×C₄	—	9	1	no	—
29	C₈	—	6	2	no	—
30	C₂×C₃	—	2	2	no	—
31	D₃	—	6	2	no	—
32	D₃	—	6	2	no	—
33	C₂²	—	9	1	no	—
34	C₄	—	9	2	no	—
35	C₄	—	9	1	no	—
36	C₄	—	18	1	no	—
37	C₄	GO⁺(4,𝔽₂)	1	1	yes	characteristic
38	C₃	—	2	2	no	—
39	C₂	—	9	1	no	—
40	C₂	—	9	1	no	—
41	C₂	#3773	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	GO⁺(4,𝔽₂)
commutator	C₃⋊D₃	C₂×C₈
Fitting	C₃²×C₄	D₄
socle	C₂×C₃²	C₄⋊C₄
prime radical	C₂×C₃⋊D₃	C₂×C₄
cosocle	C₄×C₃⋊D₃	C₂²
hypocenter	C₃²	C₄⋊C₈
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. #157	C₈	semidirect
25. C₃²	C₄⋊C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.