Subgroups — #20241263

Order 6016.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689147	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625329	—	2	2	no	—
4	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
5	C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	—
6	C₂²×C₈×C₄₇	C₄	1	2	yes	—
7	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₇	—	2	2	no	—
9	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₄₇	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₄₇	—	2	2	no	—
13	C₂×C₈×C₄₇	—	4	2	no	—
14	C₄²×C₄₇	C₂×C₄	1	2	yes	—
15	C₄²×C₄₇	D₄	1	2	yes	—
16	#10625329	—	4	2	no	—
17	#10625329	—	4	2	no	—
18	C₂×C₄₇⋊C₈	—	2	4	no	—
19	C₂³×C₄₇	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	—	4	1	no	—
23	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
29	C₂×C₄×C₄₇	Q₁₆	1	1	yes	characteristic
30	C₈×C₄₇	—	4	2	no	—
31	C₄₇⋊C₈	—	4	4	no	—
32	C₂²×C₄₇	—	2	1	no	—
33	C₂²×C₄₇	—	2	1	no	—
34	C₂²×C₄₇	#95	1	1	yes	characteristic
35	C₂²×C₄₇	#106	1	1	yes	characteristic
36	C₂²×C₄₇	#107	1	1	yes	characteristic
37	C₄×C₄₇	—	2	2	no	—
38	C₄×C₄₇	—	2	1	no	—
39	C₄×C₄₇	#100	1	1	yes	characteristic
40	C₄×C₄₇	#101	1	1	yes	characteristic
41	C₄×C₄₇	#102	1	2	yes	—
42	C₄×C₄₇	#103	1	2	yes	—
43	#1292	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	—	2	1	no	—
45	C₂×C₄₇	—	2	1	no	—
46	C₂×C₄₇	#338	1	1	yes	characteristic
47	C₂×C₄₇	#340	1	1	yes	characteristic
48	C₂×C₄₇	#343	1	1	yes	characteristic
49	#423	—	47	2	no	—
50	C₂×C₄⋊C₈	D₄₇	1	1	yes	characteristic
51	C₄₇	#1292	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	94	2	no	—
53	C₂²×C₈	Dic₄₇	1	2	yes	—
54	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	47	4	no	—
57	C₄⋊C₈	—	94	2	no	—
58	C₂²×C₄	Dic₉₄	1	1	yes	characteristic
59	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
61	M₁₆	—	188	2	no	—
62	M₁₆	—	188	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	94	4	no	—
66	C₄²	C₄×D₄₇	1	2	yes	—
67	C₄²	C₂²⋊D₄₇	1	2	yes	—
68	C₂³	C₄⋊Dic₄₇	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#10625325	1	2	yes	—
73	C₂×C₄	D₃₇₆	1	1	yes	characteristic
74	C₂×C₄	Dic₁₈₈	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
76	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
77	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	188	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₄₇⋊#95	1	1	yes	characteristic
84	C₂²	#13093956	1	1	yes	characteristic
85	C₂²	#13093958	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#13093941	1	1	yes	characteristic
89	C₄	#13093943	1	1	yes	characteristic
90	C₄	#13093946	1	2	yes	—
91	C₄	#13093949	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	C₄₇⋊#338	1	1	yes	characteristic
95	C₂	#15688886	1	1	yes	characteristic
96	C₂	#15688892	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄₇⋊#95
commutator	C₂×C₄×C₄₇	C₄²
Frattini	C₂×C₄²	C₂×D₄₇
Fitting	C₂×C₄⋊C₈×C₄₇	C₂
socle	C₂²×C₄₇	#95
hypercenter	C₂×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#1292
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
51. C₄₇	#1292	semidirect