Subgroups — #20243548

Order 6016.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093958	C₂	1	4	yes	maximal
2	#15688993	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₄₇	—	2	4	no	—
5	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
6	#13093958	—	2	8	no	—
7	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₇	C₄	1	4	yes	complemented
10	C₂²×C₄×C₄₇	D₄	1	2	yes	—
11	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₂²×Dic₄₇	—	2	4	no	—
13	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₄₇	D₄	1	4	yes	—
15	C₂×C₈×C₄₇	Q₈	1	4	yes	—
16	C₄²×C₄₇	C₂×C₄	1	2	yes	—
17	C₄²×C₄₇	Q₈	1	2	yes	—
18	C₄⋊Dic₄₇	—	2	8	no	—
19	C₄⋊Dic₄₇	—	4	8	no	—
20	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₄₇	D₈	1	4	yes	—
23	C₂×C₄×C₄₇	Q₁₆	1	4	yes	—
24	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
26	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
27	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×Dic₄₇	—	4	4	no	—
29	C₂×Dic₄₇	—	4	8	no	—
30	C₈×C₄₇	C₄⋊C₄	1	8	yes	complemented
31	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₄₇	#127	1	1	yes	characteristic
33	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
34	C₂²×C₄₇	C₂×D₈	1	2	yes	—
35	C₂²×C₄₇	C₂×Q₁₆	1	2	yes	—
36	C₄×C₄₇	#107	1	8	yes	complemented
37	C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
38	C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
39	Dic₄₇	—	8	4	no	—
40	#1845	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	#384	1	1	yes	characteristic
42	C₂×C₄₇	C₂×#107	1	2	yes	—
43	C₂×C₄₇	#493	1	1	yes	characteristic
44	C₂×C₄₇	#494	1	1	yes	characteristic
45	C₂×C₄₇	#500	1	2	yes	—
46	C₂×#107	—	47	4	no	—
47	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
48	#384	—	47	2	no	—
49	C₄₇	#1845	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₈	C₂×D₄₇	1	2	yes	—
51	C₂×C₄⋊C₄	—	47	4	no	—
52	C₂×C₄⋊C₄	—	94	4	no	—
53	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
54	#107	—	94	8	no	—
55	C₄×C₈	Dic₄₇	1	4	yes	complemented
56	C₂²×C₄	—	94	4	no	—
57	C₂²×C₄	D₁₈₈	1	2	yes	—
58	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
59	C₂×C₈	Dic₉₄	1	4	yes	—
60	C₂×C₈	D₁₈₈	1	4	yes	—
61	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
62	C₄⋊C₄	—	94	8	no	—
63	C₄⋊C₄	—	188	8	no	—
64	C₄²	Dic₉₄	1	2	yes	—
65	C₄²	C₂×Dic₄₇	1	2	yes	—
66	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
67	C₂×C₄	—	188	4	no	—
68	C₂×C₄	—	188	8	no	—
69	C₂×C₄	D₃₇₆	1	4	yes	—
70	C₂×C₄	Dic₁₈₈	1	4	yes	—
71	C₂×C₄	C₄⋊Dic₄₇	1	4	yes	—
72	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
73	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
74	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
75	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
76	C₈	C₄⋊Dic₄₇	1	8	yes	complemented
77	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
78	C₂²	#13094021	1	1	yes	characteristic
79	C₂²	#13094024	1	1	yes	characteristic
80	C₂²	C₂×D₃₇₆	1	2	yes	—
81	C₂²	C₂×Dic₁₈₈	1	2	yes	—
82	C₄	—	376	4	no	—
83	C₄	#13093958	1	8	yes	complemented
84	C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
85	C₄	#13094024	1	2	yes	—
86	C₂	#15688993	1	1	yes	characteristic
87	C₂	C₂×#13093958	1	2	yes	—
88	C₂	#15689500	1	1	yes	characteristic
89	C₂	#15689503	1	1	yes	characteristic
90	C₂	#15689528	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1845
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₄×C₈×C₄₇	C₄	semidirect
30. C₈×C₄₇	C₄⋊C₄	semidirect
36. C₄×C₄₇	#107	semidirect
49. C₄₇	#1845	semidirect
55. C₄×C₈	Dic₄₇	semidirect
76. C₈	C₄⋊Dic₄₇	semidirect
83. C₄	#13093958	semidirect