Subgroups — #20241356

Order 6016.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₇₆	C₄	1	1	yes	characteristic
5	C₄×D₁₈₈	—	2	1	no	—
6	#13093958	C₄	1	1	yes	characteristic
7	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	#13093946	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	—	2	1	no	—
12	C₂×C₄×D₄₇	—	4	1	no	—
13	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	D₄	1	1	yes	characteristic
16	(C₂×D₄₇)⋊C₄	—	4	1	no	—
17	C₄⋊Dic₄₇	—	2	1	no	—
18	C₂×C₄₇⋊C₈	—	4	1	no	—
19	D₃₇₆	—	2	1	no	—
20	D₃₇₆	C₈	1	2	yes	complemented
21	C₁₆×C₄₇	—	2	2	no	—
22	C₂²×D₄₇	—	4	1	no	—
23	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
26	C₂×Dic₄₇	—	4	1	no	—
27	D₁₈₈	—	2	2	no	—
28	D₁₈₈	—	4	1	no	—
29	C₄×D₄₇	—	8	2	no	—
30	C₈×C₄₇	—	2	1	no	—
31	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₄₇	M₁₆	1	1	yes	characteristic
33	C₄₇⋊C₈	—	8	1	no	—
34	C₂²×C₄₇	#102	1	1	yes	characteristic
35	C₂×D₄₇	—	4	2	no	—
36	C₂×D₄₇	—	8	1	no	—
37	C₂×D₄₇	—	8	1	no	—
38	C₄×C₄₇	—	2	1	no	—
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₄₇	#104	1	1	yes	characteristic
42	Dic₄₇	—	8	1	no	—
43	#1333	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₄₇	#360	1	1	yes	characteristic
46	C₂×C₄₇	#361	1	1	yes	characteristic
47	D₄₇	—	8	2	no	—
48	C₄×D₈	—	47	1	no	—
49	#346	D₄₇	1	1	yes	characteristic, complemented
50	#334	—	47	1	no	—
51	C₄₇	#1333	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₈	—	47	1	no	—
53	C₄×D₄	—	94	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	#107	—	47	1	no	—
56	C₄⋊C₈	—	94	1	no	—
57	#102	—	94	1	no	—
58	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
59	C₂×D₄	—	94	1	no	—
60	C₂²×C₄	—	188	1	no	—
61	D₈	—	47	2	no	—
62	D₈	—	94	1	no	—
63	C₂×C₈	—	188	1	no	—
64	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
66	C₄⋊C₄	—	94	1	no	—
67	C₂²⋊C₄	—	188	1	no	—
68	C₄²	D₁₈₈	1	1	yes	characteristic
69	C₁₆	—	2	2	no	—
70	C₂³	—	188	1	no	—
71	D₄	—	94	2	no	—
72	D₄	—	188	1	no	—
73	C₂×C₄	—	376	2	no	—
74	C₂×C₄	—	188	1	no	—
75	C₂×C₄	#10625325	1	1	yes	characteristic
76	C₂×C₄	D₃₇₆	1	1	yes	characteristic
77	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	376	1	no	—
80	C₈	C₈×D₄₇	1	1	yes	characteristic
81	C₈	#10625324	1	1	yes	characteristic
82	C₂²	—	376	1	no	—
83	C₂²	—	376	1	no	—
84	C₂²	—	188	2	no	—
85	C₂²	#13093946	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	376	1	no	—
89	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
90	C₄	#13093952	1	1	yes	characteristic
91	C₂	—	376	2	no	—
92	C₂	#15688852	1	1	yes	characteristic
93	C₂	#15688934	1	1	yes	characteristic
94	C₂	#15688937	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093946
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂²×C₄₇	#102
hypercenter	#346	D₄₇
hypocenter	C₄₇	#1333
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #15688874	C₂	semidirect
3. C₄₇×#346	C₂	semidirect
20. D₃₇₆	C₈	semidirect
49. #346	D₄₇	semidirect
51. C₄₇	#1333	semidirect