Subgroups — C₂×#20241599 #26137315

Order 12032.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20241599	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄₇⋊C₆₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇⋊C₆₄	C₂²	1	4	yes	complemented
5	C₂²×C₁₆×C₄₇	C₄	1	1	yes	characteristic
6	C₂×C₃₂×C₄₇	C₄	1	2	yes	—
7	C₂×C₃₂×C₄₇	C₄	1	1	yes	characteristic
8	C₂×C₃₂×C₄₇	C₂²	1	2	yes	—
9	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₇	C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₄₇	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₈	1	2	yes	—
13	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₄₇	C₂×C₄	1	2	yes	—
16	C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₁₆	1	2	yes	—
20	C₂×C₈×C₄₇	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₄₇	C₂×C₈	1	2	yes	—
24	C₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
26	C₂³×C₄₇	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₃₂	1	2	yes	—
28	C₂×C₄×C₄₇	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×C₁₆	1	2	yes	—
30	C₂×C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₄₇	C₂×C₁₆	1	2	yes	—
32	C₈×C₄₇	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₄₇	C₂²×C₈	1	1	yes	characteristic
34	C₂×M₁₂₈	—	47	1	no	maximal, Sylow
35	C₂²×C₄₇	—	2	2	no	—
36	C₂²×C₄₇	C₂×C₃₂	1	2	yes	—
37	C₂²×C₄₇	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₄₇	C₂×C₃₂	1	1	yes	characteristic
39	C₄×C₄₇	C₂×C₃₂	1	2	yes	—
40	C₄×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
41	C₂²×C₃₂	D₄₇	1	1	yes	characteristic
42	M₁₂₈	—	47	4	no	—
43	C₂×C₆₄	—	47	2	no	—
44	C₂×C₄₇	—	2	2	no	—
45	C₂×C₄₇	M₁₂₈	1	2	yes	complemented
46	C₂×C₄₇	C₂²×C₃₂	1	1	yes	characteristic
47	C₂²×C₁₆	Dic₄₇	1	1	yes	characteristic
48	C₂×C₃₂	Dic₄₇	1	1	yes	characteristic
49	C₂×C₃₂	Dic₄₇	1	2	yes	—
50	C₂×C₃₂	C₂×D₄₇	1	2	yes	—
51	C₂×C₃₂	C₂×D₄₇	1	1	yes	characteristic
52	C₆₄	—	47	4	no	—
53	C₄₇	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	C₄₇⋊C₈	1	1	yes	characteristic
55	C₂×C₁₆	C₄₇⋊C₈	1	1	yes	characteristic
56	C₂×C₁₆	C₄₇⋊C₈	1	2	yes	—
57	C₂×C₁₆	C₂×Dic₄₇	1	2	yes	—
58	C₂×C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
59	C₃₂	C₂×Dic₄₇	1	2	yes	—
60	C₃₂	C₂×Dic₄₇	1	1	yes	characteristic
61	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
62	C₂²×C₄	C₄₇⋊C₁₆	1	1	yes	characteristic
63	C₂×C₈	C₄₇⋊C₁₆	1	2	yes	—
64	C₂×C₈	C₄₇⋊C₁₆	1	1	yes	characteristic
65	C₂×C₈	C₂×C₄₇⋊C₈	1	2	yes	—
66	C₂×C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
67	C₁₆	C₂×C₄₇⋊C₈	1	2	yes	—
68	C₁₆	C₂×C₄₇⋊C₈	1	1	yes	characteristic
69	C₁₆	C₂²×Dic₄₇	1	1	yes	characteristic
70	C₂³	C₄₇⋊C₃₂	1	1	yes	characteristic
71	C₂×C₄	C₄₇⋊C₃₂	1	2	yes	—
72	C₂×C₄	C₄₇⋊C₃₂	1	1	yes	characteristic
73	C₂×C₄	C₂×C₄₇⋊C₁₆	1	2	yes	—
74	C₂×C₄	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
75	C₈	C₂×C₄₇⋊C₁₆	1	2	yes	—
76	C₈	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
77	C₈	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×C₄₇⋊C₃₂	1	2	yes	—
80	C₂²	C₂×C₄₇⋊C₃₂	1	1	yes	characteristic
81	C₄	C₂×C₄₇⋊C₃₂	1	1	yes	characteristic
82	C₄	C₂×C₄₇⋊C₃₂	1	2	yes	—
83	C₄	C₂²×C₄₇⋊C₁₆	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#20241599	1	2	yes	direct product factor
86	C₂	C₂²×C₄₇⋊C₃₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #20241599	C₂	direct (N × H)
2. C₂×C₄₇⋊C₆₄	C₂	semidirect
4. C₄₇⋊C₆₄	C₂²	semidirect
45. C₂×C₄₇	M₁₂₈	semidirect
53. C₄₇	C₂×M₁₂₈	semidirect
85. C₂	#20241599	direct (N × H)

Maximal subgroups

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

subgroup	index
#20241599	2
C₂×C₄₇⋊C₆₄	2
C₂²×C₃₂×C₄₇	2
C₂×M₁₂₈	47

Subgroups — C2×#20241599 #26137315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241599 #26137315