Subgroups — #106×D₂₃ #13092446

Order 1472.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₂₃	C₂	1	2	yes	maximal
3	C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#10624999	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624990	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₃	—	2	2	no	—
7	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
10	C₄⋊Dic₂₃	C₂²	1	2	yes	—
11	Dic₂₃⋊C₄	—	2	2	no	—
12	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×D₂₃	C₄	1	4	yes	complemented
14	C₂²×D₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₃	—	2	2	no	—
18	C₂×Dic₂₃	D₄	1	1	yes	characteristic
19	C₄×D₂₃	—	4	4	no	—
20	C₄×D₂₃	C₂×C₄	1	2	yes	—
21	C₄×D₂₃	Q₈	1	2	yes	—
22	C₈×C₂₃	C₂×C₄	1	2	yes	complemented
23	C₂₃⋊C₈	C₂×C₄	1	2	yes	complemented
24	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₂₃	C₄⋊C₄	1	2	yes	—
26	C₂×D₂₃	SD₁₆	1	4	yes	—
27	C₄×C₂₃	—	4	2	no	—
28	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
30	Dic₂₃	—	4	2	no	—
31	Dic₂₃	C₄⋊C₄	1	2	yes	—
32	C₂×#106	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₂₃	C₂×SD₁₆	1	2	yes	—
35	D₂₃	#106	1	4	yes	direct product factor
36	C₂²×C₈	—	23	1	no	—
37	C₂×C₄⋊C₄	—	23	2	no	—
38	#106	—	23	1	no	—
39	#106	—	23	2	no	—
40	#106	D₂₃	1	1	yes	characteristic, direct product factor
41	C₂₃	C₂×#106	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	—	23	1	no	—
43	C₂²×C₄	—	46	2	no	—
44	C₂×C₈	—	23	1	no	—
45	C₂×C₈	—	23	4	no	—
46	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₄⋊C₄	—	23	2	no	—
48	C₄⋊C₄	—	46	2	no	—
49	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
50	C₂³	—	23	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	23	1	no	—
53	C₂×C₄	—	23	2	no	—
54	C₂×C₄	—	23	2	no	—
55	C₂×C₄	—	46	2	no	—
56	C₂×C₄	—	92	4	no	—
57	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
58	C₈	—	23	2	no	—
59	C₈	C₄×D₂₃	1	2	yes	complemented
60	C₂²	—	23	2	no	—
61	C₂²	—	23	4	no	—
62	C₂²	D₄×D₂₃	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	—	23	2	no	—
65	C₄	—	92	2	no	—
66	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
67	C₄	Q₈×D₂₃	1	1	yes	characteristic
68	C₂	—	23	4	no	—
69	C₂	C₄⋊C₄×D₂₃	1	1	yes	characteristic
70	C₂	SD₁₆×D₂₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#106	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂²×D₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#106	D₂₃
hypocenter	C₂₃	C₂×#106
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. C₂₃×#106	C₂	semidirect
4. #10624999	C₂	semidirect
5. #10624990	C₂	semidirect
13. C₈×D₂₃	C₄	semidirect
22. C₈×C₂₃	C₂×C₄	semidirect
23. C₂₃⋊C₈	C₂×C₄	semidirect
35. D₂₃	#106	direct (N × H)
40. #106	D₂₃	direct (N × H)
41. C₂₃	C₂×#106	semidirect
59. C₈	C₄×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₂₃	2
C₄⋊C₄×D₂₃	2
C₂₃×#106	2
#10624999	2
#10624990	2
C₂×#106	23

Subgroups — #106×D23 #13092446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #106×D₂₃ #13092446