Subgroups — #1454⋊C₃ #68013

Order 384.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#1454	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂×C₄²⋊C₃	—	4	1	no	maximal
4	#431	—	3	1	no	—
5	#322	—	3	1	no	—
6	C₈²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄²⋊C₃	—	4	1	no	—
8	C₂×C₄²	A₄	1	1	yes	characteristic
9	C₄⋊C₈	—	3	2	no	—
10	C₂²⋊C₈	—	3	2	no	—
11	C₄×C₈	—	3	1	no	—
12	C₄×C₈	—	3	1	no	—
13	C₂×A₄	—	16	1	no	—
14	C₂²×C₄	—	3	1	no	—
15	C₂×C₈	—	3	2	no	—
16	C₂×C₈	—	3	2	no	—
17	C₄²	—	3	1	no	—
18	C₄²	C₂×A₄	1	1	yes	characteristic
19	A₄	—	16	1	no	—
20	C₂³	C₄²⋊C₃	1	1	yes	characteristic
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	—	6	2	no	—
24	C₈	—	6	2	no	—
25	C₈	—	6	2	no	—
26	C₂×C₃	—	64	1	no	—
27	C₂²	—	6	1	no	—
28	C₂²	C₂×C₄²⋊C₃	1	1	yes	characteristic
29	C₄	—	3	2	no	—
30	C₄	—	6	1	no	—
31	C₃	—	64	1	no	Sylow
32	C₂	—	3	1	no	—
33	C₂	—	4	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₈²	C₂×C₃
Frattini	C₄²	C₂×A₄
Fitting	#1454	C₃
socle	C₂²	C₂×C₄²⋊C₃
LCS	G ▷ C₈²
UCS	C₁

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.