Subgroups — #20245273

Order 6016.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689555	C₂	1	1	yes	maximal, characteristic
2	#15689239	C₂	1	2	yes	maximal, complemented
3	#15688929	C₂	1	2	yes	maximal, complemented
4	#15688898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094046	C₂²	1	2	yes	—
7	#13094032	—	2	2	no	—
8	Dic₃₇₆	C₄	1	1	yes	characteristic, complemented
9	#13093969	C₄	1	2	yes	complemented
10	D₇₅₂	C₄	1	1	yes	characteristic, complemented
11	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
12	#13093950	—	2	2	no	—
13	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	#108×C₄₇	C₂²	1	2	yes	—
16	#10625350	—	2	2	no	—
17	M₁₆×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄×Dic₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
21	Dic₁₈₈	C₂×C₄	1	2	yes	—
22	D₃₇₆	C₂×C₄	1	2	yes	—
23	#10625325	—	2	2	no	—
24	#10625324	—	4	2	no	—
25	C₈×D₄₇	—	4	2	no	—
26	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₄₇⋊C₁₆	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂²⋊D₄₇	—	4	2	no	—
31	C₂×Dic₄₇	—	2	1	no	—
32	D₁₈₈	—	2	2	no	—
33	C₄×D₄₇	—	4	2	no	—
34	Dic₉₄	—	2	2	no	—
35	C₈×C₄₇	—	4	2	no	—
36	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₄₇	#41	1	1	yes	characteristic
38	C₄₇⋊C₈	D₈	1	2	yes	—
39	C₂²×C₄₇	#135	1	1	yes	characteristic
40	C₂×D₄₇	—	4	2	no	—
41	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
43	Dic₄₇	—	4	1	no	—
44	Dic₄₇	—	4	2	no	—
45	#2179	—	47	1	no	maximal, Sylow
46	C₂×C₄₇	—	2	1	no	—
47	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
48	D₄₇	—	8	2	no	—
49	#508	—	47	1	no	—
50	#443	—	47	2	no	—
51	#368	D₄₇	1	1	yes	characteristic, complemented
52	#359	—	47	2	no	—
53	#346	—	47	1	no	—
54	C₄₇	#2179	1	1	yes	characteristic, complemented, Sylow
55	#135	—	47	2	no	—
56	#131	—	94	2	no	—
57	Q₃₂	—	47	1	no	—
58	SD₃₂	—	47	2	no	—
59	D₁₆	—	47	1	no	—
60	C₂×C₁₆	—	47	1	no	—
61	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
62	#108	C₂×D₄₇	1	2	yes	—
63	#104	—	94	2	no	—
64	C₄×C₈	—	47	1	no	—
65	#41	—	94	2	no	—
66	Q₁₆	—	47	2	no	—
67	SD₁₆	—	94	2	no	—
68	D₈	—	47	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	188	2	no	—
71	C₂×C₈	—	47	1	no	—
72	C₂×C₈	—	188	2	no	—
73	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
74	C₄²	—	47	1	no	—
75	C₁₆	—	94	1	no	—
76	C₁₆	C₄×D₄₇	1	1	yes	characteristic
77	C₁₆	C₄×D₄₇	1	1	yes	characteristic
78	Q₈	—	94	2	no	—
79	D₄	—	94	2	no	—
80	D₄	—	188	2	no	—
81	C₂×C₄	—	94	1	no	—
82	C₂×C₄	—	188	2	no	—
83	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	47	2	no	—
86	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
87	C₈	#10625354	1	1	yes	characteristic
88	C₂²	—	188	2	no	—
89	C₂²	#13094047	1	1	yes	characteristic
90	C₄	—	188	1	no	—
91	C₄	—	188	2	no	—
92	C₄	#13093986	1	1	yes	characteristic
93	C₄	D₈×D₄₇	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	376	2	no	—
96	C₂	#15689205	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#368	C₂
socle	C₂×C₄₇	C₄×D₈
hypercenter	#368	D₄₇
hypocenter	C₄₇	#2179
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #15689239	C₂	semidirect
3. #15688929	C₂	semidirect
4. #15688898	C₂	semidirect
5. C₄₇×#368	C₂	semidirect
8. Dic₃₇₆	C₄	semidirect
9. #13093969	C₄	semidirect
10. D₇₅₂	C₄	semidirect
51. #368	D₄₇	semidirect
54. C₄₇	#2179	semidirect