Subgroups — #15671436

Order 2944.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092238	C₂	1	2	yes	maximal
2	C₂₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₂₃	—	2	2	no	—
4	C₂₃×C₄⋊Q₈	C₄	1	2	yes	—
5	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	#10624994	—	2	2	no	—
7	C₂×Q₈×C₂₃	—	2	2	no	—
8	Q₁₆×C₂₃	—	4	2	no	—
9	Q₁₆×C₂₃	—	4	2	no	—
10	C₂×C₈×C₂₃	D₄	1	2	yes	—
11	C₄⋊C₄×C₂₃	—	4	2	no	—
12	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂₃⋊C₁₆	—	4	2	no	—
14	Q₈×C₂₃	—	4	4	no	—
15	C₂×C₄×C₂₃	—	2	1	no	—
16	C₂×C₄×C₂₃	—	4	2	no	—
17	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₂₃	D₈	1	2	yes	—
19	C₈×C₂₃	SD₁₆	1	2	yes	—
20	#1358	—	23	1	no	maximal, Sylow
21	C₂²×C₂₃	#100	1	1	yes	characteristic
22	C₄×C₂₃	—	2	2	no	—
23	C₄×C₂₃	—	8	2	no	—
24	C₄×C₂₃	#102	1	2	yes	—
25	#494	D₂₃	1	1	yes	characteristic
26	#364	—	23	2	no	—
27	C₂×C₂₃	—	2	1	no	—
28	C₂×C₂₃	#331	1	1	yes	characteristic
29	C₂×Q₁₆	—	2	2	no	—
30	C₄⋊Q₈	Dic₂₃	1	2	yes	—
31	M₃₂	—	46	2	no	—
32	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
33	C₂₃	#1358	1	1	yes	characteristic, complemented, Sylow
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
40	C₁₆	—	92	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
45	C₈	#67272	1	2	yes	—
46	C₈	#67273	1	2	yes	—
47	C₂²	#10625015	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#10625014	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#13092161	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092161
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#494	C₂
socle	C₂×C₂₃	#331
prime radical	C₂²×C₂₃	#100
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#494	D₂₃
hypocenter	C₂₃	#1358
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
33. C₂₃	#1358	semidirect

Maximal subgroups

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

subgroup	index
#13092238	2
C₂₃×#494	2
#1358	23