Subgroups — #13092263

Order 1472.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₃	C₂	1	2	yes	maximal
3	C₂₃⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₃	C₂²	1	4	yes	—
7	C₄²×C₂₃	C₄	1	4	yes	complemented
8	C₄×Dic₂₃	C₄	1	8	yes	complemented
9	C₂³×C₂₃	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₂₃	—	2	4	no	—
11	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
12	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
13	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
14	C₂×Dic₂₃	—	2	8	no	—
15	C₂×Dic₂₃	C₂×C₄	1	8	yes	—
16	C₂²×C₂₃	C₂²×C₄	1	2	yes	—
17	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₂₃	#41	1	4	yes	—
19	C₄×C₂₃	—	2	4	no	—
20	C₄×C₂₃	C₄²	1	4	yes	—
21	Dic₂₃	—	2	8	no	—
22	#376	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
24	C₂×C₂₃	#117	1	4	yes	—
25	C₂×C₂₃	#117	1	2	yes	—
26	C₂×C₄²	—	23	2	no	—
27	C₂×C₄²	D₂₃	1	1	yes	characteristic
28	#95	—	23	4	no	—
29	C₂₃	#376	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	—	23	4	no	—
31	C₂²×C₄	C₂×D₂₃	1	2	yes	—
32	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
33	C₄²	—	23	8	no	—
34	C₄²	Dic₂₃	1	4	yes	complemented
35	C₂³	C₂²×D₂₃	1	1	yes	characteristic
36	C₂×C₄	—	2	4	no	—
37	C₂×C₄	—	23	8	no	—
38	C₂×C₄	—	46	8	no	—
39	C₂×C₄	C₄×D₂₃	1	4	yes	—
40	C₂×C₄	C₂×Dic₂₃	1	4	yes	—
41	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
42	C₂²	C₂×C₄×D₂₃	1	2	yes	—
43	C₂²	#67288	1	4	yes	—
44	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
45	C₄	—	2	4	no	—
46	C₄	—	46	8	no	—
47	C₄	C₄×Dic₂₃	1	4	yes	—
48	C₂	#10625043	1	4	yes	—
49	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic
50	C₂	#10625097	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Frattini	C₂³	C₂²×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle, prime radical, cosocle	C₂³×C₂₃	C₂³
hypercenter	C₂×C₄²	D₂₃
hypocenter	C₂₃	#376
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄²×C₂₃	C₄	semidirect
8. C₄×Dic₂₃	C₄	semidirect
29. C₂₃	#376	semidirect
34. C₄²	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₂₃	2
C₂×C₄×Dic₂₃	2
C₂₃⋊#95	2
#376	23