Subgroups — C₂×Q₁₆×D₂₃ #13093192

Order 1472.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₃	C₂	1	2	yes	maximal
2	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#67275	C₂	1	2	yes	maximal, complemented
4	Q₁₆×D₂₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
8	Q₈×D₂₃	—	2	4	no	—
9	Q₈×D₂₃	C₂²	1	8	yes	—
10	C₂×C₄×D₂₃	—	2	2	no	—
11	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₆	—	2	2	no	—
13	C₂×Dic₄₆	C₂²	1	2	yes	—
14	Q₁₆×C₂₃	C₂²	1	4	yes	complemented
15	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	#67275	C₂²	1	8	yes	complemented
17	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
18	Dic₉₂	C₂²	1	4	yes	complemented
19	C₈×D₂₃	C₂²	1	4	yes	—
20	C₂²×D₂₃	D₄	1	1	yes	characteristic
21	Q₈×C₂₃	—	2	2	no	—
22	Q₈×C₂₃	C₂³	1	4	yes	—
23	C₂×C₄×C₂₃	—	2	2	no	—
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₃	—	2	2	no	—
26	C₂×Dic₂₃	D₄	1	1	yes	characteristic
27	C₄×D₂₃	—	2	8	no	—
28	C₄×D₂₃	D₄	1	2	yes	—
29	C₄×D₂₃	C₂³	1	2	yes	—
30	Dic₄₆	—	2	2	no	—
31	Dic₄₆	—	2	8	no	—
32	Dic₄₆	C₂³	1	4	yes	—
33	C₈×C₂₃	C₂³	1	2	yes	—
34	C₂₃⋊C₈	C₂³	1	2	yes	—
35	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
36	C₂×D₂₃	Q₁₆	1	4	yes	direct product factor
37	C₂×D₂₃	C₂×D₄	1	2	yes	—
38	C₄×C₂₃	—	2	4	no	—
39	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
40	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
41	Dic₂₃	—	2	4	no	—
42	Dic₂₃	C₂×D₄	1	2	yes	—
43	C₂²×Q₁₆	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	C₂×Q₁₆	1	2	yes	complemented
45	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
46	D₂₃	C₂×Q₁₆	1	4	yes	direct product factor
47	C₂²×Q₈	—	23	2	no	—
48	C₂×Q₁₆	—	23	2	no	—
49	C₂×Q₁₆	—	23	8	no	—
50	C₂×Q₁₆	—	23	1	no	—
51	C₂×Q₁₆	D₂₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₈	—	23	1	no	—
53	C₂₃	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	23	8	no	—
55	C₂×Q₈	—	23	2	no	—
56	C₂×Q₈	—	46	2	no	—
57	C₂×Q₈	—	46	4	no	—
58	C₂×Q₈	C₂×D₂₃	1	2	yes	—
59	C₂²×C₄	—	23	1	no	—
60	C₂²×C₄	—	46	2	no	—
61	Q₁₆	—	23	8	no	—
62	Q₁₆	—	23	4	no	—
63	Q₁₆	C₂×D₂₃	1	4	yes	direct product factor
64	C₂×C₈	—	23	1	no	—
65	C₂×C₈	—	23	4	no	—
66	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
67	C₂³	—	23	1	no	—
68	Q₈	—	2	2	no	—
69	Q₈	—	23	4	no	—
70	Q₈	—	46	8	no	—
71	Q₈	—	46	2	no	—
72	Q₈	C₂²×D₂₃	1	4	yes	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	23	1	no	—
75	C₂×C₄	—	23	2	no	—
76	C₂×C₄	—	23	2	no	—
77	C₂×C₄	—	46	8	no	—
78	C₂×C₄	—	46	2	no	—
79	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
80	C₈	—	23	2	no	—
81	C₈	C₂²×D₂₃	1	2	yes	—
82	C₂²	—	23	4	no	—
83	C₂²	—	23	2	no	—
84	C₂²	D₄×D₂₃	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	23	2	no	—
87	C₄	—	46	4	no	—
88	C₄	D₄×D₂₃	1	1	yes	characteristic
89	C₄	C₂³×D₂₃	1	1	yes	characteristic
90	C₂	—	23	4	no	—
91	C₂	Q₁₆×D₂₃	1	2	yes	direct product factor
92	C₂	C₂×D₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₄×C₂₃	C₂⁴
Frattini	C₄	C₂³×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂²×D₂₃	D₄
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	C₂²×Q₁₆
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×C₂₃	C₂	semidirect
3. C₂×#67275	C₂	semidirect
4. Q₁₆×D₂₃	C₂	direct (N × H)
5. C₂×Dic₉₂	C₂	semidirect
14. Q₁₆×C₂₃	C₂²	semidirect
16. #67275	C₂²	semidirect
18. Dic₉₂	C₂²	semidirect
36. C₂×D₂₃	Q₁₆	direct (N × H)
44. C₂×C₂₃	C₂×Q₁₆	semidirect
46. D₂₃	C₂×Q₁₆	direct (N × H)
51. C₂×Q₁₆	D₂₃	direct (N × H)
53. C₂₃	C₂²×Q₁₆	semidirect
63. Q₁₆	C₂×D₂₃	direct (N × H)
91. C₂	Q₁₆×D₂₃	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×Q₈×D₂₃	2
C₂×Q₁₆×C₂₃	2
C₂×#67275	2
Q₁₆×D₂₃	2
C₂×Dic₉₂	2
C₂×C₈×D₂₃	2
C₂²×Q₁₆	23

Subgroups — C2×Q16×D23 #13093192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×D₂₃ #13093192