Subgroups — #20241347

Order 6016.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689202	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625324	—	2	1	no	—
5	C₄×D₁₈₈	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₁₆	—	2	1	no	—
7	C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
8	(C₂×D₄₇)⋊C₈	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	(C₂×D₄₇)⋊C₄	—	2	1	no	—
17	C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	—	2	1	no	—
19	#10625324	—	4	1	no	—
20	#10625324	—	4	1	no	—
21	C₁₆×C₄₇	—	2	2	no	—
22	C₄₇⋊C₁₆	—	4	1	no	—
23	C₂²×D₄₇	—	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	C₂×Dic₄₇	—	2	1	no	—
28	D₁₈₈	—	4	1	no	—
29	C₄×D₄₇	—	4	1	no	—
30	C₄×D₄₇	—	4	1	no	—
31	C₈×C₄₇	—	2	1	no	—
32	C₈×C₄₇	D₈	1	1	yes	characteristic
33	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
34	C₄₇⋊C₈	—	4	1	no	—
35	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₄₇	—	4	1	no	—
37	C₂×D₄₇	—	4	1	no	—
38	C₂×D₄₇	—	4	1	no	—
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	#102	1	1	yes	characteristic
42	C₄×C₄₇	#104	1	1	yes	characteristic
43	Dic₄₇	—	4	1	no	—
44	#1330	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₄₇	#349	1	1	yes	characteristic
47	C₂×C₄₇	#350	1	1	yes	characteristic
48	D₄₇	—	8	1	no	—
49	#436	—	47	1	no	—
50	C₄⋊C₁₆	—	47	1	no	—
51	#346	D₄₇	1	1	yes	characteristic, complemented
52	C₄₇	#1330	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	94	1	no	—
54	C₄×D₄	—	47	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	94	1	no	—
57	C₄⋊C₈	—	47	1	no	—
58	C₂²⋊C₈	—	94	1	no	—
59	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
60	C₂×D₄	—	47	1	no	—
61	C₂²×C₄	—	94	1	no	—
62	M₁₆	—	188	1	no	—
63	M₁₆	—	188	1	no	—
64	C₂×C₈	—	94	1	no	—
65	C₂×C₈	D₁₈₈	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
67	C₄⋊C₄	—	47	1	no	—
68	C₂²⋊C₄	—	94	1	no	—
69	C₄²	C₄×D₄₇	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	C₁₆	—	188	1	no	—
72	C₂³	—	94	1	no	—
73	D₄	—	188	1	no	—
74	C₂×C₄	—	94	1	no	—
75	C₂×C₄	—	188	1	no	—
76	C₂×C₄	—	188	1	no	—
77	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
78	C₂×C₄	#10625324	1	1	yes	characteristic
79	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	188	1	no	—
82	C₈	#10625325	1	1	yes	characteristic
83	C₈	D₃₇₆	1	1	yes	characteristic
84	C₂²	—	188	1	no	—
85	C₂²	—	188	1	no	—
86	C₂²	—	188	1	no	—
87	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	188	1	no	—
91	C₄	#13093946	1	1	yes	characteristic
92	C₄	#13093952	1	1	yes	characteristic
93	C₂	—	376	1	no	—
94	C₂	#15688852	1	1	yes	characteristic
95	C₂	#15688904	1	1	yes	characteristic
96	C₂	#15688908	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	#346	D₄₇
hypocenter	C₄₇	#1330
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. C₄₇×#346	C₂	semidirect
51. #346	D₄₇	semidirect
52. C₄₇	#1330	semidirect