Subgroups — #20241370

Order 6016.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#15688899	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#446	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	—	2	1	no	—
5	C₂×C₄₇⋊C₁₆	—	2	1	no	—
6	C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₄₇	—	2	1	no	—
8	C₄⋊C₈×C₄₇	C₄	1	1	yes	characteristic
9	#97×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₄₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₄₇	—	2	1	no	—
16	C₄⋊C₄×C₄₇	C₈	1	1	yes	characteristic
17	C₄²×C₄₇	—	2	1	no	—
18	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₄₇⋊C₁₆	—	2	2	no	—
20	C₄₇⋊C₁₆	—	4	1	no	—
21	Q₈×C₄₇	—	4	1	no	—
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
27	C₈×C₄₇	—	2	1	no	—
28	C₈×C₄₇	—	4	1	no	—
29	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
31	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₄₇	—	2	1	no	—
33	C₄×C₄₇	—	2	1	no	—
34	C₄×C₄₇	—	4	1	no	—
35	C₄×C₄₇	—	4	1	no	—
36	C₄×C₄₇	#103	1	1	yes	characteristic
37	C₄×C₄₇	#104	1	1	yes	characteristic
38	#1338	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₄₇	#349	1	1	yes	characteristic
41	C₂×C₄₇	#350	1	1	yes	characteristic
42	#446	D₄₇	1	1	yes	characteristic
43	C₄⋊C₁₆	—	47	1	no	—
44	#346	—	47	1	no	—
45	C₄₇	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	Dic₄₇	1	1	yes	characteristic
47	C₂×C₁₆	—	94	1	no	—
48	C₂×C₁₆	—	94	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄⋊C₈	Dic₄₇	1	1	yes	characteristic
51	#97	—	2	1	no	—
52	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
53	C₂×Q₈	C₄₇⋊C₈	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₄₇⋊C₈	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
61	C₁₆	—	94	2	no	—
62	C₁₆	—	188	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
67	C₂×C₄	#10625329	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	4	1	no	—
71	C₈	#10625336	1	1	yes	characteristic
72	C₈	#10625337	1	1	yes	characteristic
73	C₂²	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#13093948	1	1	yes	characteristic
79	C₄	#13093951	1	1	yes	characteristic
80	C₂	Q₈⋊(C₄₇⋊C₈)	1	1	yes	characteristic
81	C₂	#15688905	1	1	yes	characteristic
82	C₂	#15688907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#446	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	#446	D₄₇
hypocenter	C₄₇	#1338
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #446

Complements

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

N	H ≅ G/N	type
45. C₄₇	#1338	semidirect