Subgroups — #20241457

Order 6016.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₄⋊C₈
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#1370
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. C₄₇⋊C₈	C₁₆	semidirect
39. C₄₇	#1370	semidirect