Subgroups — C₂₃×#1712 #15669331

Order 2944.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#493	C₂	1	6	yes	maximal, complemented
2	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×C₂₃	—	2	12	no	—
4	C₂₃×#127	C₂²	1	4	yes	—
5	C₄×C₈×C₂₃	C₂²	1	3	yes	—
6	C₂×D₄×C₂₃	—	2	12	no	—
7	D₈×C₂₃	—	4	24	no	—
8	C₂×C₈×C₂₃	D₄	1	6	yes	—
9	C₄²×C₂₃	C₂³	1	1	yes	characteristic
10	C₂³×C₂₃	—	4	4	no	—
11	D₄×C₂₃	—	4	24	no	—
12	C₂×C₄×C₂₃	C₂×D₄	1	3	yes	—
13	C₈×C₂₃	D₈	1	12	yes	complemented
14	#1712	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₂₃	—	8	12	no	—
16	C₂²×C₂₃	#127	1	1	yes	characteristic
17	C₄×C₂₃	C₂×D₈	1	6	yes	—
18	#493	C₂×C₂₃	1	6	yes	complemented
19	C₈²	C₂×C₂₃	1	1	yes	characteristic, complemented
20	C₂×C₂₃	—	16	4	no	—
21	C₂×C₂₃	#493	1	3	yes	—
22	C₂×D₈	—	2	12	no	—
23	#127	C₂²×C₂₃	1	4	yes	—
24	C₄×C₈	C₂²×C₂₃	1	3	yes	—
25	C₂₃	#1712	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×D₄	—	2	12	no	—
27	D₈	—	4	24	no	—
28	C₂×C₈	D₄×C₂₃	1	6	yes	—
29	C₄²	C₂³×C₂₃	1	1	yes	characteristic
30	C₂³	—	4	4	no	—
31	D₄	—	4	24	no	—
32	C₂×C₄	C₂×D₄×C₂₃	1	3	yes	—
33	C₈	D₈×C₂₃	1	12	yes	complemented
34	C₂²	—	8	12	no	—
35	C₂²	C₂₃×#127	1	1	yes	characteristic
36	C₄	C₂×D₈×C₂₃	1	6	yes	—
37	C₂	—	16	4	no	—
38	C₂	C₂₃×#493	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×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.