Subgroups — C₂₃×#2867 #15670486

Order 2944.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#127	C₂	1	14	yes	maximal, complemented
2	C₄³×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄×C₂₃	C₂²	1	28	yes	—
4	C₂₃×#127	—	2	56	no	—
5	C₂×C₄²×C₂₃	C₂²	1	7	yes	—
6	C₂⁴×C₂₃	C₂³	1	8	yes	—
7	C₂×D₄×C₂₃	—	2	168	no	—
8	C₂²×C₄×C₂₃	C₂³	1	7	yes	—
9	C₄²×C₂₃	D₄	1	28	yes	complemented
10	C₂³×C₂₃	—	2	56	no	—
11	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
12	D₄×C₂₃	—	4	112	no	—
13	C₂×C₄×C₂₃	C₂×D₄	1	42	yes	—
14	#2867	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₂₃	—	4	56	no	—
16	C₂²×C₂₃	C₂²×D₄	1	7	yes	—
17	C₄×C₂₃	#127	1	28	yes	complemented
18	C₂×#127	C₂×C₂₃	1	14	yes	complemented
19	C₄³	C₂×C₂₃	1	1	yes	characteristic, complemented
20	C₂×C₂₃	—	8	8	no	—
21	C₂×C₂₃	C₂×#127	1	7	yes	—
22	C₂²×D₄	C₂²×C₂₃	1	28	yes	—
23	#127	—	2	56	no	—
24	C₂×C₄²	C₂²×C₂₃	1	7	yes	—
25	C₂₃	#2867	1	1	yes	characteristic, direct product factor, Sylow
26	C₂⁴	C₂³×C₂₃	1	8	yes	—
27	C₂×D₄	—	2	168	no	—
28	C₂²×C₄	C₂³×C₂₃	1	7	yes	—
29	C₄²	D₄×C₂₃	1	28	yes	complemented
30	C₂³	—	2	56	no	—
31	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
32	D₄	—	4	112	no	—
33	C₂×C₄	C₂×D₄×C₂₃	1	42	yes	—
34	C₂²	—	4	56	no	—
35	C₂²	C₂²×D₄×C₂₃	1	7	yes	—
36	C₄	C₂₃×#127	1	28	yes	complemented
37	C₂	—	8	8	no	—
38	C₂	C₂×C₂₃×#127	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

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.