Subgroups — #13092445

Order 1472.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625097	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₂₃⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	M₁₆×C₂₃	—	2	2	no	—
7	C₂×C₈×C₂₃	C₂²	1	2	yes	—
8	C₂²⋊Dic₂₃	C₄	1	2	yes	—
9	C₄⋊Dic₂₃	C₄	1	2	yes	—
10	C₄×Dic₂₃	C₂²	1	2	yes	—
11	C₂×C₂₃⋊C₈	—	2	2	no	—
12	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	D₄	1	2	yes	—
16	C₂×C₄×C₂₃	Q₈	1	2	yes	—
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₃	C₂×C₄	1	4	yes	—
19	C₈×C₂₃	—	2	2	no	—
20	C₂₃⋊C₈	—	2	2	no	—
21	C₂²×C₂₃	—	2	2	no	—
22	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
25	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
27	Dic₂₃	—	2	4	no	—
28	#424	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	—	2	2	no	—
30	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₂₃	#131	1	2	yes	—
32	C₂×M₁₆	D₂₃	1	1	yes	characteristic
33	C₂²×C₈	—	23	1	no	—
34	#117	—	23	1	no	—
35	C₄⋊C₈	—	23	4	no	—
36	C₂₃	#424	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
38	M₁₆	—	2	2	no	—
39	C₂×C₈	—	23	2	no	—
40	C₂×C₈	—	46	2	no	—
41	C₂×C₈	C₂×D₂₃	1	2	yes	—
42	C₄⋊C₄	—	23	2	no	—
43	C₂²⋊C₄	—	23	2	no	—
44	C₄²	—	23	2	no	—
45	C₂³	C₄×D₂₃	1	1	yes	characteristic
46	C₂×C₄	—	23	4	no	—
47	C₂×C₄	Dic₄₆	1	2	yes	—
48	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	46	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	Dic₂₃⋊C₄	1	2	yes	—
55	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
56	C₄	—	46	4	no	—
57	C₄	Dic₂₃⋊C₄	1	2	yes	—
58	C₄	C₂×Dic₄₆	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	#10625078	1	2	yes	—
62	C₂	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator, socle	C₂²×C₂₃	C₂²×C₄
Fitting	C₂×M₁₆×C₂₃	C₂
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#424
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. Dic₂₃⋊C₈	C₂	semidirect
36. C₂₃	#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
#10625097	2
C₂²×C₂₃⋊C₈	2
Dic₂₃⋊C₈	2
#424	23