Subgroups — C₂×#20241605 #26137327

Order 12032.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₅₂	C₂	1	1	yes	maximal, characteristic
2	#20241605	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×Q₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₇₆	—	2	1	no	—
6	Dic₇₅₂	—	2	1	no	—
7	Dic₇₅₂	C₂²	1	2	yes	—
8	C₄₇⋊C₆₄	C₂²	1	2	yes	—
9	C₂×Q₃₂×C₄₇	—	2	1	no	—
10	C₄₇×Q₆₄	—	2	1	no	—
11	C₄₇×Q₆₄	C₂²	1	2	yes	—
12	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₈₈	—	4	1	no	—
14	Dic₃₇₆	—	2	2	no	—
15	Dic₃₇₆	—	4	1	no	—
16	C₂×Q₁₆×C₄₇	—	4	1	no	—
17	Q₃₂×C₄₇	—	2	2	no	—
18	Q₃₂×C₄₇	—	4	1	no	—
19	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
20	C₃₂×C₄₇	D₄	1	1	yes	characteristic
21	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₄₇	—	8	1	no	—
23	C₂×Dic₉₄	—	8	1	no	—
24	Q₁₆×C₄₇	—	4	2	no	—
25	Q₁₆×C₄₇	—	8	1	no	—
26	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
27	Dic₁₈₈	—	4	2	no	—
28	Dic₁₈₈	—	8	1	no	—
29	C₁₆×C₄₇	D₈	1	1	yes	characteristic
30	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₄₇	—	8	2	no	—
32	Q₈×C₄₇	—	16	1	no	—
33	C₂×C₄×C₄₇	—	16	1	no	—
34	C₂×C₄×C₄₇	D₁₆	1	1	yes	characteristic
35	C₂×Dic₄₇	—	16	1	no	—
36	Dic₉₄	—	8	2	no	—
37	Dic₉₄	—	16	1	no	—
38	C₈×C₄₇	D₁₆	1	1	yes	characteristic
39	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
40	C₂×Q₁₂₈	—	47	1	no	maximal, Sylow
41	C₂²×C₄₇	D₃₂	1	1	yes	characteristic
42	C₄×C₄₇	—	16	2	no	—
43	C₄×C₄₇	D₃₂	1	1	yes	characteristic
44	C₄×C₄₇	C₂×D₁₆	1	1	yes	characteristic
45	Dic₄₇	—	16	2	no	—
46	C₂×Q₆₄	—	47	1	no	—
47	C₂×Q₆₄	D₄₇	1	1	yes	characteristic
48	Q₁₂₈	—	47	4	no	—
49	C₂×C₆₄	—	47	1	no	—
50	C₂×C₄₇	Q₁₂₈	1	2	yes	complemented
51	C₂×C₄₇	C₂×D₃₂	1	1	yes	characteristic
52	C₂×Q₃₂	—	2	1	no	—
53	C₂×Q₃₂	—	94	1	no	—
54	Q₆₄	—	2	1	no	—
55	Q₆₄	—	47	2	no	—
56	Q₆₄	—	94	1	no	—
57	Q₆₄	C₂×D₄₇	1	2	yes	—
58	C₂×C₃₂	C₂×D₄₇	1	1	yes	characteristic
59	C₆₄	—	47	2	no	—
60	C₄₇	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₁₆	—	4	1	no	—
62	C₂×Q₁₆	—	188	1	no	—
63	Q₃₂	—	2	2	no	—
64	Q₃₂	—	4	1	no	—
65	Q₃₂	—	94	2	no	—
66	Q₃₂	—	188	1	no	—
67	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
68	C₃₂	C₂²⋊D₄₇	1	1	yes	characteristic
69	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
70	C₂×Q₈	—	8	1	no	—
71	C₂×Q₈	—	376	1	no	—
72	Q₁₆	—	4	2	no	—
73	Q₁₆	—	8	1	no	—
74	Q₁₆	—	376	1	no	—
75	Q₁₆	—	188	2	no	—
76	C₂×C₈	#10625334	1	1	yes	characteristic
77	C₁₆	#10625334	1	1	yes	characteristic
78	C₁₆	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
79	Q₈	—	8	2	no	—
80	Q₈	—	16	1	no	—
81	Q₈	—	376	2	no	—
82	Q₈	—	752	1	no	—
83	C₂×C₄	—	16	1	no	—
84	C₂×C₄	—	752	1	no	—
85	C₂×C₄	#13093965	1	1	yes	characteristic
86	C₈	#13093965	1	1	yes	characteristic
87	C₈	C₂×#10625334	1	1	yes	characteristic
88	C₂²	#15688958	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	752	2	no	—
91	C₄	#15688958	1	1	yes	characteristic
92	C₄	C₂×#13093965	1	1	yes	characteristic
93	C₂	#20241605	1	2	yes	direct product factor
94	C₂	C₂×#15688958	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15688958
commutator, cosocle	C₃₂×C₄₇	C₂³
Frattini	C₃₂	C₂²×D₄₇
Fitting	C₂×C₄₇×Q₆₄	C₂
socle, prime radical	C₂²×C₄₇	D₃₂
hypercenter	C₂×Q₆₄	D₄₇
hypocenter	C₄₇	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₄₇ ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
2. #20241605	C₂	direct (N × H)
50. C₂×C₄₇	Q₁₂₈	semidirect
60. C₄₇	C₂×Q₁₂₈	semidirect
93. C₂	#20241605	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×Dic₇₅₂	2
#20241605	2
C₂×C₄₇⋊C₆₄	2
C₂×C₄₇×Q₆₄	2
C₂×Q₁₂₈	47

Subgroups — C2×#20241605 #26137327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241605 #26137327