Subgroups — #13092524

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₂₃	C₂	1	2	yes	maximal
3	#10625017	C₂	1	2	yes	maximal
4	#10624999	C₂	1	1	yes	maximal, characteristic
5	#10624997	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
7	Q₁₆×C₂₃	C₄	1	4	yes	complemented
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₃	—	2	2	no	—
10	C₄⋊Dic₂₃	C₂²	1	2	yes	—
11	C₄×Dic₂₃	—	2	2	no	—
12	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
14	Q₈×C₂₃	—	2	2	no	—
15	Q₈×C₂₃	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₃	—	2	2	no	—
19	C₂×Dic₂₃	D₄	1	2	yes	—
20	C₈×C₂₃	C₂×C₄	1	2	yes	—
21	C₂₃⋊C₈	—	2	1	no	—
22	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₂₃	—	2	4	no	—
24	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₃	#41	1	1	yes	characteristic
26	Dic₂₃	—	2	2	no	—
27	Dic₂₃	—	4	2	no	—
28	#441	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
30	C₂×C₂₃	#137	1	2	yes	—
31	C₂×Q₁₆	D₂₃	1	1	yes	characteristic
32	C₄×Q₈	—	23	2	no	—
33	#106	—	23	1	no	—
34	#103	—	23	2	no	—
35	#97	—	23	1	no	—
36	C₂₃	#441	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	C₂×D₂₃	1	2	yes	—
38	Q₁₆	Dic₂₃	1	4	yes	complemented
39	C₂×C₈	—	23	1	no	—
40	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
41	C₄⋊C₄	—	23	2	no	—
42	C₄⋊C₄	—	46	2	no	—
43	C₄²	—	23	1	no	—
44	C₄²	—	46	2	no	—
45	Q₈	—	2	2	no	—
46	Q₈	C₂×Dic₂₃	1	4	yes	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	23	2	no	—
49	C₂×C₄	—	46	2	no	—
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	46	1	no	—
52	C₈	C₂×Dic₂₃	1	2	yes	—
53	C₂²	D₄×D₂₃	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	46	2	no	—
56	C₄	—	92	2	no	—
57	C₄	#67290	1	1	yes	characteristic
58	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
59	C₂	#10625089	1	2	yes	—
60	C₂	D₄×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#441
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
7. Q₁₆×C₂₃	C₄	semidirect
36. C₂₃	#441	semidirect
38. Q₁₆	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₃	2
Q₈×Dic₂₃	2
#10625017	2
#10624999	2
#10624997	2
#441	23