Subgroups — C₂×#20241598 #26137314

Order 12032.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20241598	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×D₄₇	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₃₂	C₄	1	1	yes	characteristic
7	C₃₂×D₄₇	C₄	1	2	yes	—
8	C₃₂×D₄₇	C₂²	1	2	yes	—
9	C₄₇⋊C₆₄	C₂²	1	2	yes	complemented
10	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
11	C₄₇×C₆₄	C₂²	1	2	yes	complemented
12	C₂×C₈×D₄₇	C₈	1	1	yes	characteristic
13	C₂×C₄₇⋊C₁₆	C₈	1	1	yes	characteristic
14	C₁₆×D₄₇	C₈	1	2	yes	—
15	C₁₆×D₄₇	C₂×C₄	1	2	yes	—
16	C₄₇⋊C₃₂	C₂×C₄	1	2	yes	—
17	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×D₄₇	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄₇⋊C₈	C₁₆	1	1	yes	characteristic
23	C₈×D₄₇	C₁₆	1	2	yes	—
24	C₈×D₄₇	C₂×C₈	1	2	yes	—
25	C₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₄₇⋊C₁₆	C₂×C₈	1	2	yes	—
28	C₂²×D₄₇	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
30	C₂×Dic₄₇	C₃₂	1	1	yes	characteristic
31	C₄×D₄₇	C₃₂	1	2	yes	—
32	C₄×D₄₇	C₂×C₁₆	1	2	yes	—
33	C₈×C₄₇	C₂×C₁₆	1	1	yes	characteristic
34	C₈×C₄₇	C₂²×C₈	1	1	yes	characteristic
35	C₄₇⋊C₈	C₂×C₁₆	1	2	yes	—
36	C₂×M₁₂₈	—	47	1	no	maximal, Sylow
37	C₂²×C₄₇	C₂×C₃₂	1	1	yes	characteristic
38	C₂×D₄₇	—	2	2	no	—
39	C₂×D₄₇	C₂×C₃₂	1	2	yes	—
40	C₄×C₄₇	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
42	Dic₄₇	C₂×C₃₂	1	2	yes	—
43	C₂²×C₃₂	—	47	1	no	—
44	M₁₂₈	—	47	4	no	—
45	C₂×C₆₄	—	47	1	no	—
46	C₂×C₆₄	D₄₇	1	1	yes	characteristic, complemented
47	C₂×C₄₇	M₁₂₈	1	2	yes	complemented
48	C₂×C₄₇	C₂²×C₃₂	1	1	yes	characteristic
49	D₄₇	—	2	2	no	—
50	C₂²×C₁₆	—	47	1	no	—
51	C₂×C₃₂	—	47	1	no	—
52	C₂×C₃₂	—	47	2	no	—
53	C₂×C₃₂	—	47	2	no	—
54	C₂×C₃₂	C₂×D₄₇	1	1	yes	characteristic
55	C₆₄	—	47	2	no	—
56	C₆₄	C₂×D₄₇	1	2	yes	complemented
57	C₄₇	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	—	47	1	no	—
59	C₂×C₁₆	—	47	1	no	—
60	C₂×C₁₆	—	47	2	no	—
61	C₂×C₁₆	—	47	2	no	—
62	C₂×C₁₆	C₄×D₄₇	1	1	yes	characteristic
63	C₃₂	—	47	2	no	—
64	C₃₂	C₄×D₄₇	1	1	yes	characteristic
65	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
66	C₂²×C₄	—	47	1	no	—
67	C₂×C₈	—	47	1	no	—
68	C₂×C₈	—	47	2	no	—
69	C₂×C₈	—	47	2	no	—
70	C₂×C₈	C₈×D₄₇	1	1	yes	characteristic
71	C₁₆	—	47	2	no	—
72	C₁₆	C₈×D₄₇	1	1	yes	characteristic
73	C₁₆	C₂×C₄×D₄₇	1	1	yes	characteristic
74	C₂³	—	47	1	no	—
75	C₂×C₄	—	47	1	no	—
76	C₂×C₄	—	47	2	no	—
77	C₂×C₄	—	47	2	no	—
78	C₂×C₄	C₁₆×D₄₇	1	1	yes	characteristic
79	C₈	—	47	2	no	—
80	C₈	C₁₆×D₄₇	1	1	yes	characteristic
81	C₈	C₂×C₈×D₄₇	1	1	yes	characteristic
82	C₂²	—	47	2	no	—
83	C₂²	—	94	2	no	—
84	C₂²	C₃₂×D₄₇	1	1	yes	characteristic
85	C₄	—	47	2	no	—
86	C₄	C₃₂×D₄₇	1	1	yes	characteristic
87	C₄	C₂×C₁₆×D₄₇	1	1	yes	characteristic
88	C₂	—	94	2	no	—
89	C₂	#20241598	1	2	yes	direct product factor
90	C₂	C₂×C₃₂×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃₂	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₃₂
Frattini	C₃₂	C₂²×D₄₇
Fitting	C₂×C₄₇×C₆₄	C₂
socle	C₂²×C₄₇	C₂×C₃₂
prime radical	C₂²×D₄₇	C₃₂
cosocle	C₃₂×C₄₇	C₂³
hypercenter	C₂×C₆₄	D₄₇
hypocenter	C₄₇	C₂×M₁₂₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. #20241598	C₂	direct (N × H)
3. C₂×C₄₇⋊C₆₄	C₂	semidirect
4. C₂×C₄₇×C₆₄	C₂	semidirect
9. C₄₇⋊C₆₄	C₂²	semidirect
11. C₄₇×C₆₄	C₂²	semidirect
46. C₂×C₆₄	D₄₇	semidirect
47. C₂×C₄₇	M₁₂₈	semidirect
56. C₆₄	C₂×D₄₇	semidirect
57. C₄₇	C₂×M₁₂₈	semidirect
89. C₂	#20241598	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×C₃₂×D₄₇	2
#20241598	2
C₂×C₄₇⋊C₆₄	2
C₂×C₄₇×C₆₄	2
C₂×M₁₂₈	47

Subgroups — C2×#20241598 #26137314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241598 #26137314