Subgroups — C₂³×C₂₃×Q₃₂ #19210253

Order 5888.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₂₃	C₂	1	2	yes	maximal
2	C₂²×C₂₃×Q₃₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₂₃	—	2	2	no	—
5	C₂²×Q₁₆×C₂₃	—	2	14	no	—
6	C₂²×Q₁₆×C₂₃	C₂²	1	28	yes	—
7	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₂₃×Q₃₂	C₂²	1	112	yes	direct product factor
9	C₂²×C₁₆×C₂₃	C₂²	1	14	yes	—
10	C₂²×Q₈×C₂₃	—	2	28	no	—
11	C₂²×Q₈×C₂₃	—	4	14	no	—
12	C₂³×C₄×C₂₃	—	4	2	no	—
13	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×Q₁₆×C₂₃	—	2	84	no	—
15	C₂×Q₁₆×C₂₃	C₂³	1	56	yes	—
16	C₂²×C₈×C₂₃	D₄	1	7	yes	—
17	C₂²×C₈×C₂₃	C₂³	1	7	yes	—
18	C₂₃×Q₃₂	C₂³	1	64	yes	direct product factor
19	C₂×C₁₆×C₂₃	C₂³	1	28	yes	—
20	C₂⁴×C₂₃	D₈	1	1	yes	characteristic
21	C₂×Q₈×C₂₃	—	2	56	no	—
22	C₂×Q₈×C₂₃	—	4	84	no	—
23	C₂²×C₄×C₂₃	—	4	28	no	—
24	C₂²×C₄×C₂₃	D₈	1	7	yes	—
25	C₂²×C₄×C₂₃	C₂×D₄	1	7	yes	—
26	Q₁₆×C₂₃	—	2	56	no	—
27	Q₁₆×C₂₃	C₂⁴	1	16	yes	—
28	C₂×C₈×C₂₃	C₂×D₄	1	21	yes	—
29	C₂×C₈×C₂₃	C₂⁴	1	7	yes	—
30	C₁₆×C₂₃	C₂⁴	1	8	yes	—
31	C₂³×Q₃₂	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₂₃	Q₃₂	1	8	yes	direct product factor
33	C₂³×C₂₃	C₂×D₈	1	7	yes	—
34	Q₈×C₂₃	—	2	16	no	—
35	Q₈×C₂₃	—	4	56	no	—
36	C₂×C₄×C₂₃	—	4	56	no	—
37	C₂×C₄×C₂₃	C₂×D₈	1	21	yes	—
38	C₂×C₄×C₂₃	C₂²×D₄	1	7	yes	—
39	C₈×C₂₃	C₂²×D₄	1	7	yes	—
40	C₈×C₂₃	C₂⁵	1	1	yes	characteristic
41	C₂³×Q₁₆	C₂×C₂₃	1	2	yes	—
42	C₂²×Q₃₂	C₂×C₂₃	1	28	yes	direct product factor
43	C₂³×C₁₆	C₂×C₂₃	1	1	yes	characteristic
44	C₂²×C₂₃	C₂×Q₃₂	1	28	yes	direct product factor
45	C₂²×C₂₃	C₂²×D₈	1	7	yes	—
46	C₄×C₂₃	—	4	16	no	—
47	C₄×C₂₃	C₂²×D₈	1	7	yes	—
48	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
49	C₂³×Q₈	—	2	2	no	—
50	C₂²×Q₁₆	—	2	14	no	—
51	C₂²×Q₁₆	C₂²×C₂₃	1	28	yes	—
52	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
53	C₂×Q₃₂	C₂²×C₂₃	1	112	yes	direct product factor
54	C₂²×C₁₆	C₂²×C₂₃	1	14	yes	—
55	C₂×C₂₃	C₂²×Q₃₂	1	14	yes	direct product factor
56	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
57	C₂²×Q₈	—	2	28	no	—
58	C₂²×Q₈	—	4	14	no	—
59	C₂³×C₄	—	4	2	no	—
60	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
61	C₂×Q₁₆	—	2	84	no	—
62	C₂×Q₁₆	C₂³×C₂₃	1	56	yes	—
63	C₂²×C₈	D₄×C₂₃	1	7	yes	—
64	C₂²×C₈	C₂³×C₂₃	1	7	yes	—
65	Q₃₂	C₂³×C₂₃	1	64	yes	direct product factor
66	C₂×C₁₆	C₂³×C₂₃	1	28	yes	—
67	C₂₃	C₂³×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
68	C₂⁴	D₈×C₂₃	1	1	yes	characteristic
69	C₂×Q₈	—	2	56	no	—
70	C₂×Q₈	—	4	84	no	—
71	C₂²×C₄	—	4	28	no	—
72	C₂²×C₄	D₈×C₂₃	1	7	yes	—
73	C₂²×C₄	C₂×D₄×C₂₃	1	7	yes	—
74	Q₁₆	—	2	56	no	—
75	Q₁₆	C₂⁴×C₂₃	1	16	yes	—
76	C₂×C₈	C₂×D₄×C₂₃	1	21	yes	—
77	C₂×C₈	C₂⁴×C₂₃	1	7	yes	—
78	C₁₆	C₂⁴×C₂₃	1	8	yes	—
79	C₂³	C₂₃×Q₃₂	1	8	yes	direct product factor
80	C₂³	C₂×D₈×C₂₃	1	7	yes	—
81	Q₈	—	2	16	no	—
82	Q₈	—	4	56	no	—
83	C₂×C₄	—	4	56	no	—
84	C₂×C₄	C₂×D₈×C₂₃	1	21	yes	—
85	C₂×C₄	C₂²×D₄×C₂₃	1	7	yes	—
86	C₈	C₂²×D₄×C₂₃	1	7	yes	—
87	C₈	C₂⁵×C₂₃	1	1	yes	characteristic
88	C₂²	C₂×C₂₃×Q₃₂	1	28	yes	direct product factor
89	C₂²	C₂²×D₈×C₂₃	1	7	yes	—
90	C₄	—	4	16	no	—
91	C₄	C₂²×D₈×C₂₃	1	7	yes	—
92	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
93	C₂	C₂²×C₂₃×Q₃₂	1	14	yes	direct product factor
94	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₃	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₂₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂₃×Q₃₂	C₂	direct (N × H)
8. C₂×C₂₃×Q₃₂	C₂²	direct (N × H)
18. C₂₃×Q₃₂	C₂³	direct (N × H)
31. C₂³×Q₃₂	C₂₃	direct (N × H)
32. C₂³×C₂₃	Q₃₂	direct (N × H)
42. C₂²×Q₃₂	C₂×C₂₃	direct (N × H)
44. C₂²×C₂₃	C₂×Q₃₂	direct (N × H)
53. C₂×Q₃₂	C₂²×C₂₃	direct (N × H)
55. C₂×C₂₃	C₂²×Q₃₂	direct (N × H)
65. Q₃₂	C₂³×C₂₃	direct (N × H)
67. C₂₃	C₂³×Q₃₂	direct (N × H)
79. C₂³	C₂₃×Q₃₂	direct (N × H)
88. C₂²	C₂×C₂₃×Q₃₂	direct (N × H)
93. C₂	C₂²×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
C₂³×Q₁₆×C₂₃	2
C₂²×C₂₃×Q₃₂	2
C₂³×C₁₆×C₂₃	2
C₂³×Q₃₂	23

Subgroups — C23×C23×Q32 #19210253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂₃×Q₃₂ #19210253