Subgroups — (C₂×D₂₃)⋊C₆₄ #19212014

Order 5888.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₂₃	C₄	1	1	yes	characteristic
5	C₂×C₂₃⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×D₂₃	—	2	1	no	—
7	C₃₂×D₂₃	—	2	1	no	—
8	C₂₃⋊C₆₄	—	2	1	no	—
9	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
10	C₂₃×C₆₄	—	2	1	no	—
11	C₂×C₈×D₂₃	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₂₃⋊C₁₆	C₈	1	1	yes	characteristic
14	C₁₆×D₂₃	—	2	1	no	—
15	C₁₆×D₂₃	—	2	1	no	—
16	C₂₃×C₃₂	D₄	1	1	yes	characteristic
17	C₂₃×C₃₂	D₄	1	1	yes	characteristic
18	C₂₃⋊C₃₂	—	2	1	no	—
19	C₂×C₄×D₂₃	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
21	C₂×C₂₃⋊C₈	C₁₆	1	1	yes	characteristic
22	C₈×D₂₃	—	2	1	no	—
23	C₈×D₂₃	—	2	1	no	—
24	C₁₆×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₁₆×C₂₃	M₁₆	1	1	yes	characteristic
26	C₂₃⋊C₁₆	—	2	1	no	—
27	C₂²⋊C₆₄	—	23	1	no	maximal, Sylow
28	C₂²×D₂₃	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
30	C₂×Dic₂₃	C₃₂	1	1	yes	characteristic
31	C₄×D₂₃	—	2	1	no	—
32	C₄×D₂₃	—	2	1	no	—
33	C₈×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₈×C₂₃	M₃₂	1	1	yes	characteristic
35	C₂₃⋊C₈	—	2	1	no	—
36	C₂²×C₃₂	—	23	1	no	—
37	C₂×C₆₄	—	23	1	no	—
38	C₂×C₆₄	D₂₃	1	1	yes	characteristic, complemented
39	C₂²×C₂₃	C₂×C₃₂	1	1	yes	characteristic
40	C₂×D₂₃	—	2	1	no	—
41	C₂×D₂₃	—	2	1	no	—
42	C₂×D₂₃	C₆₄	1	2	yes	complemented
43	C₄×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₄×C₂₃	M₆₄	1	1	yes	characteristic
45	Dic₂₃	—	2	1	no	—
46	C₂²×C₁₆	—	23	1	no	—
47	C₂×C₃₂	—	23	1	no	—
48	C₂×C₃₂	—	46	1	no	—
49	C₂×C₃₂	—	46	1	no	—
50	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
51	C₆₄	—	2	1	no	—
52	C₆₄	—	46	1	no	—
53	C₂×C₂₃	C₂²⋊C₃₂	1	1	yes	characteristic
54	C₂×C₂₃	C₂×C₆₄	1	1	yes	characteristic
55	C₂×C₂₃	M₁₂₈	1	1	yes	characteristic
56	D₂₃	—	2	2	no	—
57	C₂²×C₈	—	23	1	no	—
58	C₂×C₁₆	—	23	1	no	—
59	C₂×C₁₆	—	46	1	no	—
60	C₂×C₁₆	—	46	1	no	—
61	C₂×C₁₆	C₄×D₂₃	1	1	yes	characteristic
62	C₃₂	—	46	1	no	—
63	C₃₂	D₉₂	1	1	yes	characteristic
64	C₃₂	C₂²⋊D₂₃	1	1	yes	characteristic
65	C₂₃	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	23	1	no	—
67	C₂×C₈	—	23	1	no	—
68	C₂×C₈	—	46	1	no	—
69	C₂×C₈	—	46	1	no	—
70	C₂×C₈	C₈×D₂₃	1	1	yes	characteristic
71	C₁₆	—	46	1	no	—
72	C₁₆	#67262	1	1	yes	characteristic
73	C₁₆	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
74	C₂³	—	23	1	no	—
75	C₂×C₄	—	23	1	no	—
76	C₂×C₄	—	46	1	no	—
77	C₂×C₄	—	46	1	no	—
78	C₂×C₄	C₁₆×D₂₃	1	1	yes	characteristic
79	C₈	—	46	1	no	—
80	C₈	#10624980	1	1	yes	characteristic
81	C₈	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
82	C₂²	—	23	2	no	—
83	C₂²	—	46	1	no	—
84	C₂²	—	46	1	no	—
85	C₂²	C₃₂×D₂₃	1	1	yes	characteristic
86	C₄	—	46	1	no	—
87	C₄	(C₂×D₂₃)⋊C₁₆	1	1	yes	characteristic
88	C₄	#13092250	1	1	yes	characteristic
89	C₂	—	46	2	no	—
90	C₂	(C₂×D₂₃)⋊C₃₂	1	1	yes	characteristic
91	C₂	D₂₃×C₆₄	1	1	yes	characteristic
92	C₂	#15671607	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₆₄
Fitting	C₂×C₂₃×C₆₄	C₂
socle	C₂²×C₂₃	C₂×C₃₂
hypercenter	C₂×C₆₄	D₂₃
hypocenter	C₂₃	C₂²⋊C₆₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃⋊C₆₄	C₂	semidirect
3. C₂×C₂₃×C₆₄	C₂	semidirect
38. C₂×C₆₄	D₂₃	semidirect
42. C₂×D₂₃	C₆₄	semidirect
65. C₂₃	C₂²⋊C₆₄	semidirect

Subgroups — (C2×D23)⋊C64 #19212014

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×D₂₃)⋊C₆₄ #19212014