Subgroups — #26104181

Order 12032.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#20241592	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1425	C₂	1	1	yes	maximal, characteristic
4	#15688953	—	2	1	no	—
5	C₄₇⋊C₆₄	C₄	1	2	yes	—
6	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
7	C₄₇×#368	—	2	1	no	—
8	#13093960	—	4	1	no	—
9	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
10	#108×C₄₇	—	4	1	no	—
11	C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₄₇	Q₈	1	1	yes	characteristic
13	M₁₆×C₄₇	—	8	1	no	—
14	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
15	#10625329	—	8	1	no	—
16	C₁₆×C₄₇	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₄₇	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₄₇	D₁₆	1	1	yes	characteristic
19	C₈×C₄₇	—	16	1	no	—
20	C₈×C₄₇	#107	1	1	yes	characteristic
21	C₈×C₄₇	Q₃₂	1	1	yes	characteristic
22	C₄₇⋊C₈	—	16	1	no	—
23	#7547	—	47	1	no	maximal, Sylow
24	C₂²×C₄₇	Q₆₄	1	1	yes	characteristic
25	C₄×C₄₇	#366	1	1	yes	characteristic
26	C₄×C₄₇	D₃₂	1	1	yes	characteristic
27	C₂×C₆₄	—	47	1	no	—
28	#1425	—	47	1	no	—
29	#1425	D₄₇	1	1	yes	characteristic
30	C₂×C₄₇	—	2	1	no	—
31	C₂×C₄₇	#1423	1	1	yes	characteristic
32	C₂×C₃₂	C₂×D₄₇	1	1	yes	characteristic
33	#368	—	2	1	no	—
34	#368	—	94	1	no	—
35	C₆₄	—	47	2	no	—
36	C₄₇	#7547	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	188	1	no	—
40	C₃₂	Dic₉₄	1	1	yes	characteristic
41	C₃₂	C₄×D₄₇	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	376	1	no	—
44	C₂×C₈	#10625334	1	1	yes	characteristic
45	C₁₆	Dic₄₇⋊C₄	1	1	yes	characteristic
46	C₁₆	#10625337	1	1	yes	characteristic
47	C₂×C₄	#13093965	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	752	1	no	—
50	C₈	#13093957	1	1	yes	characteristic
51	C₈	#13093970	1	1	yes	characteristic
52	C₂²	#15688963	1	1	yes	characteristic
53	C₄	#15688948	1	1	yes	characteristic
54	C₄	#15688958	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#20241587	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688958
commutator	C₃₂×C₄₇	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₇
Fitting	C₄₇×#1425	C₂
socle	C₂×C₄₇	#1423
prime radical	C₂²×C₄₇	Q₆₄
cosocle	C₂×C₃₂×C₄₇	C₂²
hypercenter	#1425	D₄₇
hypocenter	C₄₇	#7547
LCS	G ▷ C₃₂×C₄₇ ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
36. C₄₇	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₆₄	2
#20241592	2
C₄₇×#1425	2
#7547	47