Subgroups — #13092444

Order 1472.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₂₃⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₂₃	C₄	1	2	yes	—
7	C₂²⋊C₄×C₂₃	C₄	1	2	yes	—
8	C₄²×C₂₃	C₂²	1	2	yes	—
9	#67267	—	2	2	no	—
10	C₂×C₂₃⋊C₈	—	2	2	no	—
11	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
12	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	D₄	1	2	yes	—
17	C₂×C₄×C₂₃	Q₈	1	2	yes	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₈	—	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	—	2	4	no	—
25	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
26	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
27	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
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	—	23	1	no	—
33	C₂²×C₈	—	23	1	no	—
34	#117	D₂₃	1	1	yes	characteristic
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	—	46	2	no	—
39	C₂×C₈	—	23	2	no	—
40	C₂×C₈	—	23	2	no	—
41	C₂×C₈	—	46	2	no	—
42	C₄⋊C₄	Dic₂₃	1	2	yes	—
43	C₂²⋊C₄	Dic₂₃	1	2	yes	—
44	C₄²	C₂×D₂₃	1	2	yes	—
45	C₂³	C₂×Dic₂₃	1	1	yes	characteristic
46	C₂×C₄	Dic₄₆	1	2	yes	—
47	C₂×C₄	D₉₂	1	2	yes	—
48	C₂×C₄	C₂×Dic₂₃	1	4	yes	—
49	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	46	2	no	—
52	C₈	—	46	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₂₃	1	2	yes	—
55	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
56	C₄	—	2	4	no	—
57	C₄	C₄⋊Dic₂₃	1	2	yes	—
58	C₄	C₂×Dic₄₆	1	1	yes	characteristic
59	C₄	C₂×D₉₂	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
62	C₂	#10625119	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator, socle	C₂²×C₂₃	C₂²×C₄
Fitting	C₂₃×#117	C₂
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#117	D₂₃
hypocenter	C₂₃	#424
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. C₄⋊(C₂₃⋊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
C₂₃×#117	2
C₂×#67267	2
C₂²×C₂₃⋊C₈	2
C₄⋊(C₂₃⋊C₈)	2
#424	23