Subgroups — C₂×#13092250 #15675688

Order 2944.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic
2	#13092250	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₂₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₆×D₂₃	C₄	1	2	yes	—
9	C₁₆×D₂₃	C₂²	1	2	yes	—
10	C₂₃×C₃₂	C₂²	1	2	yes	complemented
11	C₂₃⋊C₃₂	C₂²	1	2	yes	complemented
12	C₂×C₄×D₂₃	C₈	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₂₃⋊C₈	C₈	1	1	yes	characteristic
15	C₈×D₂₃	C₈	1	2	yes	—
16	C₈×D₂₃	C₂×C₄	1	2	yes	—
17	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂²×D₂₃	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₂₃	C₁₆	1	1	yes	characteristic
23	C₄×D₂₃	C₁₆	1	2	yes	—
24	C₄×D₂₃	C₂×C₈	1	2	yes	—
25	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
26	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₂₃⋊C₈	C₂×C₈	1	2	yes	—
28	C₂×M₆₄	—	23	1	no	maximal, Sylow
29	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
30	C₂×D₂₃	—	2	2	no	—
31	C₂×D₂₃	C₂×C₁₆	1	2	yes	—
32	C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
34	Dic₂₃	C₂×C₁₆	1	2	yes	—
35	C₂²×C₁₆	—	23	1	no	—
36	M₆₄	—	23	4	no	—
37	C₂×C₃₂	—	23	1	no	—
38	C₂×C₃₂	D₂₃	1	1	yes	characteristic, complemented
39	C₂×C₂₃	M₆₄	1	2	yes	complemented
40	C₂×C₂₃	C₂²×C₁₆	1	1	yes	characteristic
41	D₂₃	—	2	2	no	—
42	C₂²×C₈	—	23	1	no	—
43	C₂×C₁₆	—	23	1	no	—
44	C₂×C₁₆	—	23	2	no	—
45	C₂×C₁₆	—	23	2	no	—
46	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
47	C₃₂	—	23	2	no	—
48	C₃₂	C₂×D₂₃	1	2	yes	complemented
49	C₂₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	23	1	no	—
51	C₂×C₈	—	23	1	no	—
52	C₂×C₈	—	23	2	no	—
53	C₂×C₈	—	23	2	no	—
54	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
55	C₁₆	—	23	2	no	—
56	C₁₆	C₄×D₂₃	1	1	yes	characteristic
57	C₁₆	C₂²×D₂₃	1	1	yes	characteristic
58	C₂³	—	23	1	no	—
59	C₂×C₄	—	23	1	no	—
60	C₂×C₄	—	23	2	no	—
61	C₂×C₄	—	23	2	no	—
62	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
63	C₈	—	23	2	no	—
64	C₈	C₈×D₂₃	1	1	yes	characteristic
65	C₈	C₂×C₄×D₂₃	1	1	yes	characteristic
66	C₂²	—	23	2	no	—
67	C₂²	—	46	2	no	—
68	C₂²	C₁₆×D₂₃	1	1	yes	characteristic
69	C₄	—	23	2	no	—
70	C₄	C₁₆×D₂₃	1	1	yes	characteristic
71	C₄	C₂×C₈×D₂₃	1	1	yes	characteristic
72	C₂	—	46	2	no	—
73	C₂	#13092250	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₂₃
commutator	C₂×C₂₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₂₃
Fitting	C₂×C₂₃×C₃₂	C₂
socle	C₂²×C₂₃	C₂×C₁₆
prime radical	C₂²×D₂₃	C₁₆
cosocle	C₁₆×C₂₃	C₂³
hypercenter	C₂×C₃₂	D₂₃
hypocenter	C₂₃	C₂×M₆₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #13092250	C₂	direct (N × H)
3. C₂×C₂₃⋊C₃₂	C₂	semidirect
4. C₂×C₂₃×C₃₂	C₂	semidirect
10. C₂₃×C₃₂	C₂²	semidirect
11. C₂₃⋊C₃₂	C₂²	semidirect
38. C₂×C₃₂	D₂₃	semidirect
39. C₂×C₂₃	M₆₄	semidirect
48. C₃₂	C₂×D₂₃	semidirect
49. C₂₃	C₂×M₆₄	semidirect
73. C₂	#13092250	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₂₃	2
#13092250	2
C₂×C₂₃⋊C₃₂	2
C₂×C₂₃×C₃₂	2
C₂×M₆₄	23

Subgroups — C2×#13092250 #15675688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092250 #15675688