Subgroups — #20245671

Order 6016.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689525	C₂	1	1	yes	maximal, characteristic
2	#15688950	C₂	1	2	yes	maximal
3	#15688948	C₂	1	2	yes	maximal
4	#15688899	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#500	C₂	1	1	yes	maximal, characteristic
6	#13094016	—	2	1	no	—
7	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	#13093958	C₂²	1	1	yes	characteristic
9	#13093958	C₂²	1	1	yes	characteristic
10	#13093956	—	2	1	no	—
11	C₄⋊Q₈×C₄₇	—	2	1	no	—
12	#107×C₄₇	—	2	1	no	—
13	#107×C₄₇	C₂²	1	2	yes	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	4	1	no	—
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₄⋊C₄×C₄₇	—	4	1	no	—
20	C₄²×C₄₇	D₄	1	1	yes	characteristic
21	C₄⋊Dic₄₇	—	2	1	no	—
22	C₄⋊Dic₄₇	—	2	1	no	—
23	Dic₄₇⋊C₄	—	4	1	no	—
24	Dic₄₇⋊C₄	—	4	1	no	—
25	C₄₇⋊C₁₆	Q₈	1	4	yes	complemented
26	Q₈×C₄₇	—	8	2	no	—
27	C₂×C₄×C₄₇	—	4	2	no	—
28	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₄₇	—	4	1	no	—
32	C₂×Dic₄₇	—	4	1	no	—
33	C₈×C₄₇	Q₁₆	1	2	yes	—
34	C₈×C₄₇	C₂×Q₈	1	2	yes	—
35	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₄₇	—	2	1	no	—
37	C₄×C₄₇	—	2	1	no	—
38	C₄×C₄₇	—	8	2	no	—
39	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
40	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
41	Dic₄₇	—	8	1	no	—
42	Dic₄₇	—	8	1	no	—
43	#2255	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	#500	1	1	yes	characteristic
45	C₂×C₄₇	#509	1	1	yes	characteristic
46	C₂×C₄₇	#510	1	1	yes	characteristic
47	#500	D₄₇	1	1	yes	characteristic
48	#499	—	47	1	no	—
49	#367	—	47	2	no	—
50	#366	—	47	2	no	—
51	#346	—	47	1	no	—
52	C₄₇	#2255	1	1	yes	characteristic, complemented, Sylow
53	C₄⋊Q₈	—	2	1	no	—
54	#125	—	94	1	no	—
55	C₂×C₁₆	—	47	2	no	—
56	#107	—	2	1	no	—
57	#107	—	47	1	no	—
58	#107	—	47	1	no	—
59	#107	C₂×D₄₇	1	2	yes	—
60	#106	—	94	1	no	—
61	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
62	C₂×Q₈	—	4	1	no	—
63	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	94	1	no	—
68	C₄⋊C₄	—	94	1	no	—
69	C₄⋊C₄	—	188	1	no	—
70	C₄⋊C₄	—	188	1	no	—
71	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
72	C₁₆	—	47	4	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	188	1	no	—
76	C₂×C₄	—	188	1	no	—
77	C₂×C₄	#10625334	1	1	yes	characteristic
78	C₂×C₄	#10625334	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
80	C₈	#10625337	1	2	yes	—
81	C₈	Q₈×D₄₇	1	2	yes	—
82	C₂²	C₂×#10625334	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	376	1	no	—
87	C₄	—	376	1	no	—
88	C₄	#13094022	1	1	yes	characteristic
89	C₄	C₂×#10625337	1	1	yes	characteristic
90	C₂	#15689526	1	1	yes	characteristic
91	C₂	#15689559	1	1	yes	characteristic
92	C₂	#15689564	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#500	D₄₇
hypocenter	C₄₇	#2255
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
25. C₄₇⋊C₁₆	Q₈	semidirect
52. C₄₇	#2255	semidirect