Subgroups — #26103952

Order 12032.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20241586	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1422	C₂	1	1	yes	maximal, characteristic
4	#15688957	—	2	1	no	—
5	C₄×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₄₇×M₆₄	—	2	1	no	—
8	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊C₁₆	C₈	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₈	1	1	yes	characteristic
11	C₄×C₄₇⋊C₈	—	2	1	no	—
12	C₄₇⋊C₃₂	—	4	1	no	—
13	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₄₇	—	4	1	no	—
17	C₂×C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
19	C₄²×C₄₇	M₁₆	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	—	2	2	no	—
21	C₁₆×C₄₇	—	2	1	no	—
22	C₁₆×C₄₇	D₈	1	1	yes	characteristic
23	C₁₆×C₄₇	Q₁₆	1	1	yes	characteristic
24	C₄₇⋊C₁₆	—	2	1	no	—
25	C₄₇⋊C₁₆	C₁₆	1	2	yes	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₄₇	#107	1	1	yes	characteristic
29	C₈×C₄₇	#108	1	1	yes	characteristic
30	C₈×C₄₇	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₄₇	M₃₂	1	1	yes	characteristic
32	C₄₇⋊C₈	—	2	4	no	—
33	#7459	—	47	1	no	maximal, Sylow
34	C₂²×C₄₇	#364	1	1	yes	characteristic
35	C₄×C₄₇	—	2	2	no	—
36	C₄×C₄₇	#335	1	1	yes	characteristic
37	C₄×C₄₇	C₄⋊C₁₆	1	1	yes	characteristic
38	#1422	—	47	1	no	—
39	#1422	D₄₇	1	1	yes	characteristic
40	C₈×C₁₆	—	47	1	no	—
41	C₂×C₄₇	—	2	1	no	—
42	C₂×C₄₇	#1370	1	1	yes	characteristic
43	M₆₄	—	2	1	no	—
44	M₆₄	—	94	1	no	—
45	C₄×C₁₆	—	47	1	no	—
46	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic
47	C₈²	—	47	1	no	—
48	C₄₇	#7459	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₁₆	—	47	1	no	—
50	C₂×C₁₆	—	47	1	no	—
51	C₂×C₁₆	Dic₉₄	1	1	yes	characteristic
52	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
53	C₄×C₈	—	94	1	no	—
54	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
55	C₃₂	—	4	1	no	—
56	C₃₂	—	188	1	no	—
57	C₂×C₈	—	94	2	no	—
58	C₂×C₈	C₈×D₄₇	1	1	yes	characteristic
59	C₂×C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
60	C₄²	#10625324	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	—	47	2	no	—
63	C₁₆	—	94	1	no	—
64	C₁₆	#10625334	1	1	yes	characteristic
65	C₁₆	#10625337	1	1	yes	characteristic
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	Dic₄₇⋊C₈	1	1	yes	characteristic
68	C₈	—	94	4	no	—
69	C₈	#13093957	1	1	yes	characteristic
70	C₈	#13093959	1	1	yes	characteristic
71	C₈	C₁₆×D₄₇	1	1	yes	characteristic
72	C₈	#13093963	1	1	yes	characteristic
73	C₂²	#15688943	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	#15688875	1	1	yes	characteristic
76	C₄	Dic₄₇⋊C₁₆	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	#20241457	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	#10625334
commutator	C₈×C₄₇	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₄₇
Fitting	C₄₇×#1422	C₂
socle	C₂×C₄₇	#1370
prime radical	C₂²×C₄₇	#364
cosocle	C₄×C₁₆×C₄₇	C₂²
hypercenter	#1422	D₄₇
hypocenter	C₄₇	#7459
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
48. C₄₇	#7459	semidirect

Maximal subgroups

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

subgroup	index
#20241586	2
C₁₆×C₄₇⋊C₈	2
C₄₇×#1422	2
#7459	47