Subgroups — (C₂×D₄₃)⋊C₆₄ #24984405

Order 11008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₄₃	C₄	1	1	yes	characteristic
5	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×D₄₃	—	2	1	no	—
7	C₃₂×D₄₃	—	2	1	no	—
8	C₄₃⋊C₆₄	—	2	1	no	—
9	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×C₆₄	—	2	1	no	—
11	C₂×C₈×D₄₃	C₈	1	1	yes	characteristic
12	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
13	C₁₆×D₄₃	—	2	1	no	—
14	C₁₆×D₄₃	—	2	1	no	—
15	C₄₃⋊C₃₂	—	2	1	no	—
16	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₄₃	D₄	1	1	yes	characteristic
18	C₃₂×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₄₃	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
21	C₂×C₄₃⋊C₈	C₁₆	1	1	yes	characteristic
22	C₈×D₄₃	—	2	1	no	—
23	C₈×D₄₃	—	2	1	no	—
24	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
26	C₄₃⋊C₁₆	—	2	1	no	—
27	C₂²×D₄₃	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×Dic₄₃	C₃₂	1	1	yes	characteristic
30	C₄×D₄₃	—	2	1	no	—
31	C₄×D₄₃	—	2	1	no	—
32	C₈×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₄₃	M₃₂	1	1	yes	characteristic
34	C₄₃⋊C₈	—	2	1	no	—
35	C₂²⋊C₆₄	—	43	1	no	maximal, Sylow
36	C₂²×C₄₃	C₂×C₃₂	1	1	yes	characteristic
37	C₂×D₄₃	—	2	1	no	—
38	C₂×D₄₃	—	2	1	no	—
39	C₂×D₄₃	C₆₄	1	2	yes	complemented
40	C₄×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
41	C₄×C₄₃	M₆₄	1	1	yes	characteristic
42	Dic₄₃	—	2	1	no	—
43	C₂²×C₃₂	—	43	1	no	—
44	C₂×C₆₄	—	43	1	no	—
45	C₂×C₆₄	D₄₃	1	1	yes	characteristic, complemented
46	C₂×C₄₃	C₂²⋊C₃₂	1	1	yes	characteristic
47	C₂×C₄₃	C₂×C₆₄	1	1	yes	characteristic
48	C₂×C₄₃	M₁₂₈	1	1	yes	characteristic
49	D₄₃	—	2	2	no	—
50	C₂²×C₁₆	—	43	1	no	—
51	C₂×C₃₂	—	43	1	no	—
52	C₂×C₃₂	—	86	1	no	—
53	C₂×C₃₂	—	86	1	no	—
54	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
55	C₆₄	—	2	1	no	—
56	C₆₄	—	86	1	no	—
57	C₄₃	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	—	43	1	no	—
59	C₂×C₁₆	—	43	1	no	—
60	C₂×C₁₆	—	86	1	no	—
61	C₂×C₁₆	—	86	1	no	—
62	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
63	C₃₂	—	86	1	no	—
64	C₃₂	D₁₇₂	1	1	yes	characteristic
65	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
66	C₂²×C₄	—	43	1	no	—
67	C₂×C₈	—	43	1	no	—
68	C₂×C₈	—	86	1	no	—
69	C₂×C₈	—	86	1	no	—
70	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
71	C₁₆	—	86	1	no	—
72	C₁₆	#10621872	1	1	yes	characteristic
73	C₁₆	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
74	C₂³	—	43	1	no	—
75	C₂×C₄	—	43	1	no	—
76	C₂×C₄	—	86	1	no	—
77	C₂×C₄	—	86	1	no	—
78	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
79	C₈	—	86	1	no	—
80	C₈	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
81	C₈	#13063264	1	1	yes	characteristic
82	C₂²	—	43	2	no	—
83	C₂²	—	86	1	no	—
84	C₂²	—	86	1	no	—
85	C₂²	C₃₂×D₄₃	1	1	yes	characteristic
86	C₄	—	86	1	no	—
87	C₄	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
88	C₄	#14582732	1	1	yes	characteristic
89	C₂	—	86	2	no	—
90	C₂	(C₂×D₄₃)⋊C₃₂	1	1	yes	characteristic
91	C₂	C₆₄×D₄₃	1	1	yes	characteristic
92	C₂	#19132805	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₆₄
Fitting	C₂×C₄₃×C₆₄	C₂
socle	C₂²×C₄₃	C₂×C₃₂
prime radical	C₂²×D₄₃	C₃₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	C₂²⋊C₆₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃⋊C₆₄	C₂	semidirect
3. C₂×C₄₃×C₆₄	C₂	semidirect
39. C₂×D₄₃	C₆₄	semidirect
45. C₂×C₆₄	D₄₃	semidirect
57. C₄₃	C₂²⋊C₆₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₂×D₄₃	2
C₂×C₄₃⋊C₆₄	2
C₂×C₄₃×C₆₄	2
C₂²⋊C₆₄	43

Subgroups — (C2×D43)⋊C64 #24984405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₄₃)⋊C₆₄ #24984405