Subgroups — #20249353

Order 6016.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇⋊#401	C₂	1	2	yes	maximal
2	#15689064	C₂	1	6	yes	maximal
3	#15689029	C₂	1	3	yes	maximal
4	#15689021	C₂	1	3	yes	maximal
5	C₄₇×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
9	C₄₇⋊#95	C₂²	1	6	yes	—
10	C₄₇⋊#95	C₂²	1	6	yes	—
11	C₄₇⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
13	#95×C₄₇	C₂²	1	3	yes	—
14	#95×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₂³	1	2	yes	—
19	C₂²×Dic₄₇	C₂³	1	6	yes	—
20	C₂×Dic₉₄	—	2	6	no	—
21	C₄²×C₄₇	—	2	6	no	—
22	C₄⋊Dic₄₇	—	2	6	no	—
23	Dic₄₇⋊C₄	—	4	6	no	—
24	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₄₇	—	2	3	no	—
26	C₂×C₄×C₄₇	—	2	3	no	—
27	C₂×C₄×C₄₇	—	2	3	no	—
28	C₂×C₄×C₄₇	—	2	6	no	—
29	C₂×C₄×C₄₇	—	2	3	no	—
30	C₂×C₄×C₄₇	#41	1	6	yes	—
31	C₂×Dic₄₇	—	2	6	no	—
32	C₂×Dic₄₇	—	2	6	no	—
33	C₂×Dic₄₇	—	2	6	no	—
34	C₂×Dic₄₇	—	2	6	no	—
35	Dic₉₄	—	4	4	no	—
36	C₂²×C₄₇	C₂×#41	1	3	yes	—
37	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
38	C₂²×C₄₇	2₋¹⁺⁴	1	3	yes	—
39	C₄×C₄₇	—	4	3	no	—
40	C₄×C₄₇	—	4	3	no	—
41	C₄×C₄₇	#126	1	4	yes	—
42	Dic₄₇	—	4	2	no	—
43	Dic₄₇	—	4	6	no	—
44	#2645	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
46	C₂×C₄₇	#541	1	3	yes	—
47	C₂×C₄₇	#542	1	3	yes	—
48	#401	—	47	2	no	—
49	#400	—	47	6	no	—
50	#391	—	47	3	no	—
51	#389	—	47	3	no	—
52	#376	D₄₇	1	1	yes	characteristic
53	C₄₇	#2645	1	1	yes	characteristic, complemented, Sylow
54	C₂²×Q₈	—	47	1	no	—
55	C₂×C₄⋊C₄	—	47	3	no	—
56	C₂×C₄⋊C₄	—	47	6	no	—
57	C₂×C₄²	C₂×D₄₇	1	3	yes	—
58	#95	—	47	6	no	—
59	#95	—	47	6	no	—
60	#95	—	47	6	no	—
61	#95	C₂×D₄₇	1	3	yes	—
62	#95	C₂×D₄₇	1	1	yes	characteristic
63	C₂×Q₈	—	94	6	no	—
64	C₂²×C₄	—	47	2	no	—
65	C₂²×C₄	—	47	6	no	—
66	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
67	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
68	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
69	C₄⋊C₄	—	94	6	no	—
70	C₄⋊C₄	—	188	6	no	—
71	C₄²	—	2	6	no	—
72	C₂³	C₂³×D₄₇	1	1	yes	characteristic
73	Q₈	—	188	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	94	6	no	—
80	C₂×C₄	—	94	6	no	—
81	C₂×C₄	—	94	6	no	—
82	C₂×C₄	—	94	6	no	—
83	C₂×C₄	#10625350	1	6	yes	—
84	C₂²	C₂×#10625350	1	3	yes	—
85	C₂²	#13094070	1	1	yes	characteristic
86	C₂²	#13094071	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	188	6	no	—
90	C₄	—	188	2	no	—
91	C₄	#13094018	1	4	yes	—
92	C₂	C₂×#13094018	1	1	yes	characteristic
93	C₂	#15689735	1	3	yes	—
94	C₂	#15689744	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#2645
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
53. C₄₇	#2645	semidirect