Subgroups — #20244554

Order 6016.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688984	C₂	1	3	yes	maximal
2	#15688890	C₂	1	3	yes	maximal
3	C₄₇×#543	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
6	C₄₇⋊#95	—	2	6	no	—
7	C₂²⋊Q₈×C₄₇	—	2	6	no	—
8	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
9	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
10	C₂×Q₈×C₄₇	—	2	2	no	—
11	C₂²×C₄×C₄₇	D₄	1	6	yes	—
12	C₂²×Dic₄₇	—	2	3	no	—
13	C₂²×Dic₄₇	—	2	3	no	—
14	C₂²×Dic₄₇	—	2	3	no	—
15	C₂²×Dic₄₇	Q₈	1	2	yes	complemented
16	C₄⋊C₄×C₄₇	—	2	6	no	—
17	C₂²⋊C₄×C₄₇	—	2	6	no	—
18	C₂²⋊Dic₄₇	—	2	6	no	—
19	C₂³×C₄₇	—	4	2	no	—
20	C₂³×C₄₇	C₂×D₄	1	3	yes	—
21	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
22	C₂³×C₄₇	#41	1	3	yes	—
23	Q₈×C₄₇	—	8	2	no	—
24	C₂×C₄×C₄₇	—	2	6	no	—
25	C₂×C₄×C₄₇	—	4	6	no	—
26	C₂×Dic₄₇	—	2	6	no	—
27	C₂×Dic₄₇	—	4	1	no	—
28	C₂×Dic₄₇	—	4	3	no	—
29	C₂×Dic₄₇	—	4	6	no	—
30	C₂×Dic₄₇	—	4	3	no	—
31	C₂²×C₄₇	—	2	6	no	—
32	C₂²×C₄₇	—	4	1	no	—
33	C₂²×C₄₇	—	4	3	no	—
34	C₂²×C₄₇	#120	1	1	yes	characteristic
35	C₂²×C₄₇	C₂²⋊Q₈	1	3	yes	—
36	C₂²×C₄₇	#124	1	3	yes	—
37	C₄×C₄₇	—	4	6	no	—
38	Dic₄₇	—	4	2	no	—
39	Dic₄₇	—	8	3	no	—
40	#2030	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	—	2	3	no	—
42	C₂×C₄₇	—	2	3	no	—
43	C₂×C₄₇	#393	1	1	yes	characteristic
44	C₂×C₄₇	#458	1	2	yes	—
45	#543	D₄₇	1	1	yes	characteristic
46	#381	—	47	3	no	—
47	#342	—	47	3	no	—
48	C₄₇	#2030	1	1	yes	characteristic, complemented, Sylow
49	C₂³×C₄	—	47	1	no	—
50	C₂²⋊Q₈	—	2	6	no	—
51	C₂×C₂²⋊C₄	—	47	3	no	—
52	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
53	#95	—	94	6	no	—
54	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
55	C₂×Q₈	—	2	2	no	—
56	C₂²×C₄	—	47	2	no	—
57	C₂²×C₄	—	94	3	no	—
58	C₂²×C₄	—	94	3	no	—
59	C₂²×C₄	—	94	3	no	—
60	C₂²×C₄	C₂²⋊D₄₇	1	6	yes	—
61	C₄⋊C₄	—	2	6	no	—
62	C₂²⋊C₄	—	2	6	no	—
63	C₂²⋊C₄	—	94	6	no	—
64	C₂³	—	4	2	no	—
65	C₂³	Q₈×D₄₇	1	1	yes	characteristic
66	C₂³	#10625354	1	3	yes	—
67	C₂³	C₂×C₂²⋊D₄₇	1	3	yes	—
68	Q₈	—	8	2	no	—
69	C₂×C₄	—	2	6	no	—
70	C₂×C₄	—	4	6	no	—
71	C₂×C₄	—	94	6	no	—
72	C₂×C₄	—	188	6	no	—
73	C₂×C₄	—	188	3	no	—
74	C₂×C₄	—	188	1	no	—
75	C₂×C₄	—	188	3	no	—
76	C₂²	—	2	6	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	3	no	—
79	C₂²	#13093993	1	1	yes	characteristic
80	C₂²	#13094000	1	3	yes	—
81	C₂²	#13094013	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	—	376	3	no	—
84	C₄	—	188	2	no	—
85	C₂	—	2	3	no	—
86	C₂	—	2	3	no	—
87	C₂	#15689034	1	1	yes	characteristic
88	C₂	#15689313	1	2	yes	—

	subgroup	G/H
center	C₂²	#13093993
commutator	C₂⁴×C₄₇	C₂³
Frattini	C₂⁴	C₂²×D₄₇
Fitting	C₄₇×#543	C₂
socle	C₂²×C₄₇	#120
hypercenter	#543	D₄₇
hypocenter	C₄₇	#2030
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

Complements

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

N	H ≅ G/N	type
15. C₂²×Dic₄₇	Q₈	semidirect
48. C₄₇	#2030	semidirect