Subgroups — C₂×#10624999 #13092448

Order 1472.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₃	C₂	1	2	yes	maximal
3	#10624999	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₃	—	2	2	no	—
6	C₂×C₈×C₂₃	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₃	C₂²	1	2	yes	—
8	C₄⋊Dic₂₃	—	2	2	no	—
9	C₄⋊Dic₂₃	C₂²	1	4	yes	—
10	C₂³×C₂₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	Q₈	1	2	yes	—
14	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	4	no	—
16	C₂×Dic₂₃	—	4	4	no	—
17	C₈×C₂₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
19	C₂²×C₂₃	SD₁₆	1	4	yes	—
20	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
22	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₂₃	—	4	4	no	—
25	C₂×#106	—	23	1	no	maximal, Sylow
26	C₂×C₂₃	#106	1	4	yes	complemented
27	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₂₃	C₂×SD₁₆	1	2	yes	—
29	C₂²×C₈	D₂₃	1	1	yes	characteristic
30	C₂×C₄⋊C₄	—	23	2	no	—
31	#106	—	23	4	no	—
32	C₂₃	C₂×#106	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	—	46	2	no	—
34	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
35	C₂×C₈	Dic₂₃	1	4	yes	complemented
36	C₂×C₈	C₂×D₂₃	1	2	yes	—
37	C₄⋊C₄	—	23	4	no	—
38	C₄⋊C₄	—	46	2	no	—
39	C₂³	D₉₂	1	1	yes	characteristic
40	C₂×C₄	—	46	4	no	—
41	C₂×C₄	—	92	4	no	—
42	C₂×C₄	Dic₄₆	1	2	yes	—
43	C₂×C₄	D₉₂	1	1	yes	characteristic
44	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
45	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
46	C₈	C₂×Dic₂₃	1	4	yes	complemented
47	C₂²	#67263	1	4	yes	—
48	C₂²	C₄⋊Dic₂₃	1	2	yes	—
49	C₂²	C₂×D₉₂	1	1	yes	characteristic
50	C₄	—	92	4	no	—
51	C₄	C₄⋊Dic₂₃	1	2	yes	—
52	C₄	C₂×Dic₄₆	1	1	yes	characteristic
53	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
54	C₂	#10624999	1	4	yes	direct product factor
55	C₂	C₂×#67263	1	2	yes	—
56	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	C₂×#106
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #10624999	C₂	direct (N × H)
6. C₂×C₈×C₂₃	C₄	semidirect
17. C₈×C₂₃	C₂×C₄	semidirect
26. C₂×C₂₃	#106	semidirect
32. C₂₃	C₂×#106	semidirect
35. C₂×C₈	Dic₂₃	semidirect
46. C₈	C₂×Dic₂₃	semidirect
54. C₂	#10624999	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₃	2
C₂×C₄⋊Dic₂₃	2
#10624999	2
C₂×#106	23

Subgroups — C2×#10624999 #13092448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624999 #13092448