Subgroups — C₄×C₂₃×Q₃₂ #15669793

Order 2944.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆×C₂₃	C₂	1	2	yes	maximal
3	C₂₃×#366	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#358	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₂₃	C₂²	1	2	yes	—
7	C₄×Q₈×C₂₃	—	2	2	no	—
8	C₂₃×Q₃₂	C₄	1	4	yes	direct product factor
9	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×#107	C₂²	1	2	yes	—
12	C₂₃×#103	—	2	2	no	—
13	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₂₃	—	2	2	no	—
15	Q₁₆×C₂₃	—	2	2	no	—
16	Q₁₆×C₂₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₂₃	—	2	2	no	—
20	C₄⋊C₄×C₂₃	—	4	2	no	—
21	C₄²×C₂₃	—	4	2	no	—
22	C₄²×C₂₃	D₄	1	1	yes	characteristic
23	C₁₆×C₂₃	—	2	1	no	—
24	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
25	Q₈×C₂₃	—	2	4	no	—
26	Q₈×C₂₃	—	4	2	no	—
27	C₂×C₄×C₂₃	—	4	2	no	—
28	C₂×C₄×C₂₃	—	4	2	no	—
29	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
31	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₈×C₂₃	—	2	1	no	—
33	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₂₃	#41	1	1	yes	characteristic
35	C₄×Q₃₂	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₃	—	2	1	no	—
38	C₄×C₂₃	—	4	4	no	—
39	C₄×C₂₃	—	8	2	no	—
40	C₄×C₂₃	Q₃₂	1	2	yes	direct product factor
41	C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₂₃	#135	1	1	yes	characteristic
43	C₂×Q₃₂	C₂×C₂₃	1	1	yes	characteristic
44	C₄×Q₁₆	C₂×C₂₃	1	2	yes	—
45	#366	C₂×C₂₃	1	1	yes	characteristic
46	#358	C₂×C₂₃	1	2	yes	—
47	C₄×C₁₆	C₂×C₂₃	1	1	yes	characteristic
48	C₂×C₂₃	C₄×D₈	1	1	yes	characteristic
49	C₂×C₂₃	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×C₂₃	#508	1	1	yes	characteristic
51	C₂×Q₁₆	C₂²×C₂₃	1	2	yes	—
52	C₄×Q₈	—	2	2	no	—
53	Q₃₂	C₄×C₂₃	1	4	yes	direct product factor
54	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
55	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
56	#107	C₂²×C₂₃	1	2	yes	—
57	#103	—	2	2	no	—
58	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
59	C₂₃	C₄×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×Q₈	—	2	2	no	—
61	Q₁₆	—	2	2	no	—
62	Q₁₆	C₂×C₄×C₂₃	1	4	yes	—
63	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
64	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	2	no	—
67	C₄²	—	4	2	no	—
68	C₄²	D₄×C₂₃	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	C₂×C₄×C₂₃	1	2	yes	—
71	Q₈	—	2	4	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
76	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
77	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
80	C₈	#41×C₂₃	1	1	yes	characteristic
81	C₂²	C₂×D₈×C₂₃	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	4	no	—
84	C₄	—	8	2	no	—
85	C₄	C₂₃×Q₃₂	1	2	yes	direct product factor
86	C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
87	C₄	C₂₃×#135	1	1	yes	characteristic
88	C₂	C₄×D₈×C₂₃	1	1	yes	characteristic
89	C₂	C₂×C₂₃×Q₃₂	1	1	yes	characteristic
90	C₂	C₂₃×#508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	D₈
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle, prime radical	C₂²×C₂₃	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂₃×Q₃₂	C₄	direct (N × H)
35. C₄×Q₃₂	C₂₃	direct (N × H)
40. C₄×C₂₃	Q₃₂	direct (N × H)
53. Q₃₂	C₄×C₂₃	direct (N × H)
59. C₂₃	C₄×Q₃₂	direct (N × H)
85. C₄	C₂₃×Q₃₂	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×Q₃₂	2
C₄×Q₁₆×C₂₃	2
C₂₃×#366	2
C₂₃×#358	2
C₄×C₁₆×C₂₃	2
C₄×Q₃₂	23

Subgroups — C4×C23×Q32 #15669793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×Q₃₂ #15669793