Subgroups — #20245259

Order 6016.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×Dic₄₇	C₂	1	2	yes	maximal
2	#15688951	C₂	1	1	yes	maximal, characteristic
3	#15688927	C₂	1	2	yes	maximal
4	#15688898	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₄₇	—	2	2	no	—
7	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
8	#13093958	C₂²	1	2	yes	—
9	#13093948	—	2	2	no	—
10	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₄₇	C₂²	1	2	yes	—
12	Q₃₂×C₄₇	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₄₇	—	2	2	no	—
15	Q₁₆×C₄₇	—	2	2	no	—
16	Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₄₇	—	2	2	no	—
19	C₄⋊Dic₄₇	—	4	2	no	—
20	C₄×Dic₄₇	—	4	2	no	—
21	C₄×Dic₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
23	C₁₆×C₄₇	C₂×C₄	1	2	yes	—
24	C₄₇⋊C₁₆	—	2	1	no	—
25	Q₈×C₄₇	—	2	4	no	—
26	Q₈×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	—	4	2	no	—
28	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₇	—	4	2	no	—
30	C₂×Dic₄₇	D₈	1	2	yes	—
31	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₄₇	#41	1	1	yes	characteristic
33	C₄₇⋊C₈	—	2	1	no	—
34	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
35	C₄×C₄₇	—	4	4	no	—
36	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
37	C₄×C₄₇	#135	1	1	yes	characteristic
38	Dic₄₇	—	2	2	no	—
39	Dic₄₇	—	8	2	no	—
40	#2176	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
42	C₂×C₄₇	#510	1	2	yes	—
43	C₂×Q₃₂	D₄₇	1	1	yes	characteristic
44	C₄×Q₁₆	—	47	2	no	—
45	#367	—	47	1	no	—
46	#358	—	47	2	no	—
47	#346	—	47	1	no	—
48	C₄₇	#2176	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	C₂×D₄₇	1	2	yes	—
50	C₄×Q₈	—	94	2	no	—
51	Q₃₂	Dic₄₇	1	4	yes	complemented
52	C₂×C₁₆	—	47	1	no	—
53	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
54	#107	—	47	2	no	—
55	#103	—	94	2	no	—
56	C₄×C₈	—	47	1	no	—
57	C₂×Q₈	—	2	2	no	—
58	Q₁₆	—	2	2	no	—
59	Q₁₆	C₂×Dic₄₇	1	4	yes	—
60	C₂×C₈	—	47	1	no	—
61	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
62	C₄⋊C₄	—	94	2	no	—
63	C₄⋊C₄	—	188	2	no	—
64	C₄²	—	47	1	no	—
65	C₄²	—	188	2	no	—
66	C₁₆	—	94	1	no	—
67	C₁₆	C₂×Dic₄₇	1	2	yes	—
68	Q₈	—	2	4	no	—
69	Q₈	—	4	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	47	2	no	—
72	C₂×C₄	—	188	2	no	—
73	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
74	C₈	—	94	1	no	—
75	C₈	#10625352	1	1	yes	characteristic
76	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
77	C₂²	D₈×D₄₇	1	1	yes	characteristic
78	C₄	—	4	4	no	—
79	C₄	—	94	2	no	—
80	C₄	—	376	2	no	—
81	C₄	D₄×Dic₄₇	1	1	yes	characteristic
82	C₄	#13094043	1	1	yes	characteristic
83	C₂	D₈×Dic₄₇	1	1	yes	characteristic
84	C₂	#15689565	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#2176
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
12. Q₃₂×C₄₇	C₄	semidirect
48. C₄₇	#2176	semidirect
51. Q₃₂	Dic₄₇	semidirect