Subgroups — #20245297

Order 6016.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₁₆)	C₂	1	2	yes	maximal
2	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#15688899	C₂	1	2	yes	maximal
4	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
10	C₄⋊C₈×C₄₇	C₄	1	2	yes	—
11	C₄⋊C₈×C₄₇	C₄	1	1	yes	characteristic
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×Q₈×C₄₇	C₈	1	1	yes	characteristic
15	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₄₇	C₈	1	2	yes	—
19	C₄⋊C₄×C₄₇	C₈	1	1	yes	characteristic
20	C₄²×C₄₇	C₂×C₄	1	2	yes	—
21	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₄₇⋊C₁₆	—	2	1	no	—
23	C₄₇⋊C₁₆	—	2	2	no	—
24	C₄₇⋊C₁₆	Q₈	1	2	yes	complemented
25	Q₈×C₄₇	—	2	2	no	—
26	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₈×C₄₇	—	2	1	no	—
32	C₈×C₄₇	—	2	2	no	—
33	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
34	C₈×C₄₇	#41	1	1	yes	characteristic
35	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₄₇	—	2	2	no	—
37	C₄×C₄₇	—	2	2	no	—
38	C₄×C₄₇	—	2	1	no	—
39	C₄×C₄₇	M₃₂	1	2	yes	—
40	C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
41	C₄×C₄₇	#131	1	1	yes	characteristic
42	#2183	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	C₈×Q₈	1	1	yes	characteristic
44	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
45	C₂×C₄₇	#504	1	1	yes	characteristic
46	C₈×Q₈	D₄₇	1	1	yes	characteristic
47	C₄⋊C₁₆	—	47	1	no	—
48	C₄⋊C₁₆	—	47	2	no	—
49	#346	—	47	2	no	—
50	C₄×C₁₆	—	47	1	no	—
51	C₄₇	#2183	1	1	yes	characteristic, complemented, Sylow
52	C₄×Q₈	Dic₄₇	1	1	yes	characteristic
53	C₂×C₁₆	—	47	1	no	—
54	C₂×C₁₆	—	47	1	no	—
55	C₂×C₁₆	—	47	2	no	—
56	C₄⋊C₈	Dic₄₇	1	2	yes	—
57	C₄⋊C₈	Dic₄₇	1	1	yes	characteristic
58	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
59	C₄×C₈	C₂×D₄₇	1	2	yes	—
60	C₂×Q₈	C₄₇⋊C₈	1	1	yes	characteristic
61	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
62	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
63	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
64	C₄⋊C₄	C₄₇⋊C₈	1	2	yes	—
65	C₄⋊C₄	C₄₇⋊C₈	1	1	yes	characteristic
66	C₄²	C₂×Dic₄₇	1	2	yes	—
67	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
68	C₁₆	—	47	2	no	—
69	C₁₆	—	94	1	no	—
70	C₁₆	—	94	2	no	—
71	Q₈	—	2	2	no	—
72	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
73	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
75	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
76	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	2	no	—
79	C₈	Q₈×D₄₇	1	1	yes	characteristic
80	C₈	#10625354	1	1	yes	characteristic
81	C₂²	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	2	2	no	—
84	C₄	—	2	1	no	—
85	C₄	#13093964	1	2	yes	—
86	C₄	Q₈×Dic₄₇	1	1	yes	characteristic
87	C₄	#13094031	1	1	yes	characteristic
88	C₂	Q₈×C₄₇⋊C₈	1	1	yes	characteristic
89	C₂	C₂×#13093964	1	1	yes	characteristic
90	C₂	#15689540	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₈×Q₈×C₄₇	C₂
hypercenter	C₈×Q₈	D₄₇
hypocenter	C₄₇	#2183
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
24. C₄₇⋊C₁₆	Q₈	semidirect
51. C₄₇	#2183	semidirect