Subgroups — #26137329

Order 12032.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245694	C₂	1	2	yes	maximal, complemented
2	Dic₁₅₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241603	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689552	—	2	2	no	—
7	Dic₇₅₂	C₂²	1	2	yes	—
8	#15688961	—	2	2	no	—
9	C₃₂×D₄₇	C₂²	1	1	yes	characteristic
10	C₄₇⋊C₆₄	C₂²	1	1	yes	characteristic
11	C₄₇×D₃₂	C₂²	1	2	yes	—
12	C₄₇×C₆₄	C₂²	1	1	yes	characteristic
13	#13094043	—	4	2	no	—
14	Dic₃₇₆	—	2	2	no	—
15	#13093968	—	4	2	no	—
16	C₁₆×D₄₇	D₄	1	1	yes	characteristic
17	C₄₇⋊C₃₂	D₄	1	1	yes	characteristic
18	D₁₆×C₄₇	—	2	2	no	—
19	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
20	#10625352	—	8	2	no	—
21	D₈×C₄₇	—	4	2	no	—
22	#10625335	—	8	2	no	—
23	Dic₁₈₈	—	4	2	no	—
24	C₈×D₄₇	D₈	1	1	yes	characteristic
25	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
26	C₄₇⋊C₁₆	D₈	1	1	yes	characteristic
27	D₄×C₄₇	—	8	2	no	—
28	C₂²⋊D₄₇	—	16	2	no	—
29	C₂×Dic₄₇	—	16	2	no	—
30	C₄×D₄₇	D₁₆	1	1	yes	characteristic
31	Dic₉₄	—	8	2	no	—
32	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
33	C₄₇⋊C₈	D₁₆	1	1	yes	characteristic
34	#13741	—	47	1	no	maximal, Sylow
35	C₂²×C₄₇	—	16	2	no	—
36	C₂×D₄₇	D₃₂	1	1	yes	characteristic
37	C₄×C₄₇	C₂×D₁₆	1	1	yes	characteristic
38	Dic₄₇	—	16	2	no	—
39	Dic₄₇	D₃₂	1	1	yes	characteristic
40	#2262	—	47	2	no	—
41	Q₁₂₈	—	47	1	no	—
42	SD₁₂₈	—	47	2	no	—
43	D₆₄	D₄₇	1	1	yes	characteristic, complemented
44	C₂×C₆₄	—	47	1	no	—
45	C₂×C₄₇	—	32	2	no	—
46	C₂×C₄₇	C₂×D₃₂	1	1	yes	characteristic
47	D₄₇	—	2	1	no	—
48	#508	—	94	2	no	—
49	Q₆₄	—	47	2	no	—
50	SD₆₄	—	94	2	no	—
51	D₃₂	C₂×D₄₇	1	2	yes	—
52	C₂×C₃₂	—	47	1	no	—
53	C₆₄	—	47	1	no	—
54	C₆₄	C₂×D₄₇	1	1	yes	characteristic
55	C₄₇	#13741	1	1	yes	characteristic, complemented, Sylow
56	#135	—	188	2	no	—
57	Q₃₂	—	94	2	no	—
58	SD₃₂	—	188	2	no	—
59	D₁₆	—	2	2	no	—
60	C₂×C₁₆	—	47	1	no	—
61	C₃₂	—	47	1	no	—
62	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
63	#41	—	376	2	no	—
64	Q₁₆	—	188	2	no	—
65	SD₁₆	—	376	2	no	—
66	D₈	—	4	2	no	—
67	C₂×C₈	—	47	1	no	—
68	C₁₆	—	47	1	no	—
69	C₁₆	D₄×D₄₇	1	1	yes	characteristic
70	Q₈	—	376	2	no	—
71	D₄	—	8	2	no	—
72	D₄	—	752	2	no	—
73	C₂×C₄	—	47	1	no	—
74	C₂×C₄	—	752	2	no	—
75	C₈	—	47	1	no	—
76	C₈	D₈×D₄₇	1	1	yes	characteristic
77	C₂²	—	16	2	no	—
78	C₂²	—	47	1	no	—
79	C₄	—	47	1	no	—
80	C₄	—	752	2	no	—
81	C₄	D₁₆×D₄₇	1	1	yes	characteristic
82	C₂	—	32	2	no	—
83	C₂	—	94	1	no	—
84	C₂	D₃₂×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₄₇
commutator, cosocle	C₃₂×C₄₇	C₂³
Frattini	C₃₂	C₂²×D₄₇
Fitting	C₄₇×D₆₄	C₂
socle	C₂×C₄₇	C₂×D₃₂
hypercenter	D₆₄	D₄₇
hypocenter	C₄₇	#13741
LCS	G ▷ C₃₂×C₄₇ ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. #20245694	C₂	semidirect
2. Dic₁₅₀₄	C₂	semidirect
3. #20241603	C₂	semidirect
4. C₆₄×D₄₇	C₂	semidirect
5. C₄₇×D₆₄	C₂	semidirect
43. D₆₄	D₄₇	semidirect
55. C₄₇	#13741	semidirect

Maximal subgroups

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

subgroup	index
#20245694	2
Dic₁₅₀₄	2
#20241603	2
C₆₄×D₄₇	2
C₄₇×D₆₄	2
#13741	47