Subgroups — C₂₃×#1400 #15669019

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₃×M₆₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂₃×M₃₂	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃×C₃₂	—	2	2	no	—
8	C₂²×C₄×C₂₃	C₈	1	1	yes	characteristic
9	C₂×C₈×C₂₃	—	2	1	no	—
10	C₂×C₈×C₂₃	—	2	1	no	—
11	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₃	—	2	1	no	—
14	C₁₆×C₂₃	D₄	1	2	yes	—
15	C₂³×C₂₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₂₃	—	2	1	no	—
21	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₃	M₁₆	1	1	yes	characteristic
23	#1400	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₂₃	—	2	1	no	—
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₂₃	—	2	1	no	—
28	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₂₃	M₃₂	1	1	yes	characteristic
30	C₂×M₃₂	C₂×C₂₃	1	1	yes	characteristic
31	M₆₄	C₂×C₂₃	1	2	yes	complemented
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	—	4	1	no	—
34	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₂²×C₈	C₄×C₂₃	1	1	yes	characteristic
36	M₃₂	—	2	2	no	—
37	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
38	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
39	C₃₂	—	2	2	no	—
40	C₂₃	#1400	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₄	C₈×C₂₃	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	C₈×C₂₃	1	1	yes	characteristic
45	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	D₄×C₂₃	1	2	yes	—
48	C₂³	C₁₆×C₂₃	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₁₆×C₂₃	1	1	yes	characteristic
52	C₂×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
55	C₈	M₁₆×C₂₃	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×C₁₆×C₂₃	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
61	C₄	C₂₃×M₃₂	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂₃×C₂²⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₃	C₂²⋊C₄
commutator	C₂²	C₂×C₁₆×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
socle	C₂×C₂₃	C₂²⋊C₁₆
prime radical	C₂³×C₂₃	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×M₆₄	C₂	semidirect
23. #1400	C₂₃	direct (N × H)
31. M₆₄	C₂×C₂₃	semidirect
40. C₂₃	#1400	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×C₂₃×M₃₂	2
C₂₃×M₆₄	2
#1400	23

Subgroups — C23×#1400 #15669019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1400 #15669019