Subgroups — #13092182

Order 1472.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	2	yes	maximal
3	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
4	C₂×C₈×C₂₃	—	2	2	no	—
5	C₂×C₈×C₂₃	C₄	1	2	yes	—
6	#67267	—	2	2	no	—
7	#67267	C₄	1	4	yes	—
8	C₂×C₂₃⋊C₈	—	2	2	no	—
9	C₂³×C₂₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	D₄	1	2	yes	—
14	C₈×C₂₃	—	2	2	no	—
15	C₂₃⋊C₈	—	2	4	no	—
16	C₂²×C₂₃	—	2	2	no	—
17	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
18	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₂₃	C₄²	1	1	yes	characteristic
20	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
21	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	#341	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	—	2	2	no	—
24	C₂×C₂₃	#95	1	1	yes	characteristic
25	C₂×C₂₃	#108	1	2	yes	—
26	C₂×M₁₆	—	23	2	no	—
27	C₂²×C₈	D₂₃	1	1	yes	characteristic
28	C₂₃	#341	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
30	M₁₆	—	23	4	no	—
31	M₁₆	—	46	2	no	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	46	2	no	—
34	C₂×C₈	Dic₂₃	1	2	yes	—
35	C₂³	Dic₄₆	1	1	yes	characteristic
36	C₂×C₄	C₄×D₂₃	1	2	yes	—
37	C₂×C₄	D₉₂	1	1	yes	characteristic
38	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
39	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
40	C₈	—	2	2	no	—
41	C₈	—	46	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	Dic₂₃⋊C₄	1	2	yes	—
44	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
45	C₄	C₄×Dic₂₃	1	1	yes	characteristic
46	C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
47	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
48	C₂	—	2	2	no	—
49	C₂	#10625001	1	2	yes	—
50	C₂	C₂₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₄²
Frattini	C₂²×C₄	C₂×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₄⋊C₄
prime radical	C₂³×C₂₃	Q₈
cosocle	C₂²×C₄×C₂₃	C₂²
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	#341
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
28. C₂₃	#341	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₃	2
C₂×#67267	2
#341	23