Subgroups — #20241352

Order 6016.

98 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	#15688876	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
6	C₂×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₄₇	—	2	1	no	—
8	#107×C₄₇	C₄	1	1	yes	characteristic
9	#103×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₄₇	—	2	1	no	—
12	Q₁₆×C₄₇	—	2	1	no	—
13	Q₁₆×C₄₇	C₈	1	2	yes	complemented
14	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₄₇	—	2	1	no	—
17	C₄⋊C₄×C₄₇	—	4	1	no	—
18	C₄²×C₄₇	—	4	1	no	—
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	—	4	1	no	—
21	C₄₇⋊C₁₆	—	2	2	no	—
22	Q₈×C₄₇	—	2	2	no	—
23	Q₈×C₄₇	—	4	1	no	—
24	C₂×C₄×C₄₇	—	4	1	no	—
25	C₂×C₄×C₄₇	—	4	1	no	—
26	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
29	C₈×C₄₇	—	2	1	no	—
30	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₄₇	M₁₆	1	1	yes	characteristic
32	C₄₇⋊C₈	—	8	1	no	—
33	C₂²×C₄₇	#102	1	1	yes	characteristic
34	C₄×C₄₇	—	2	1	no	—
35	C₄×C₄₇	—	4	2	no	—
36	C₄×C₄₇	—	8	1	no	—
37	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₄₇	#104	1	1	yes	characteristic
39	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
40	C₄×C₄₇	Q₃₂	1	1	yes	characteristic
41	#1332	—	47	1	no	maximal, Sylow
42	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
43	C₂×C₄₇	#358	1	1	yes	characteristic
44	C₂×C₄₇	#359	1	1	yes	characteristic
45	C₄×Q₁₆	D₄₇	1	1	yes	characteristic
46	C₄×C₁₆	—	47	1	no	—
47	#335	—	47	1	no	—
48	C₄₇	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	Dic₄₇	1	1	yes	characteristic
50	C₄×Q₈	—	2	1	no	—
51	C₂×C₁₆	—	94	1	no	—
52	#107	Dic₄₇	1	1	yes	characteristic
53	C₄⋊C₈	—	94	1	no	—
54	#103	—	2	1	no	—
55	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×Q₈	—	2	1	no	—
57	Q₁₆	—	2	1	no	—
58	Q₁₆	C₄₇⋊C₈	1	2	yes	complemented
59	C₂×C₈	—	188	1	no	—
60	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₄⋊C₄	—	4	1	no	—
64	C₄²	—	4	1	no	—
65	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
66	C₁₆	—	94	2	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	#10625334	1	1	yes	characteristic
72	C₂×C₄	#10625335	1	1	yes	characteristic
73	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	376	1	no	—
76	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
77	C₈	#10625329	1	1	yes	characteristic
78	C₂²	#13093945	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
83	C₄	#13093951	1	1	yes	characteristic
84	C₄	#13093967	1	1	yes	characteristic
85	C₄	#13093970	1	1	yes	characteristic
86	C₂	D₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
87	C₂	#15688927	1	1	yes	characteristic
88	C₂	#15688930	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10625334
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	#102
hypercenter	C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#1332
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
13. Q₁₆×C₄₇	C₈	semidirect
48. C₄₇	#1332	semidirect
58. Q₁₆	C₄₇⋊C₈	semidirect