Subgroups — #20245617

Order 6016.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689503	C₂	1	1	yes	maximal, characteristic
2	#15688926	C₂	1	4	yes	maximal
3	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#500	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₈₈	—	2	1	no	—
6	C₂×Dic₁₈₈	C₂²	1	2	yes	—
7	#13094024	—	2	1	no	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₄₇	—	2	1	no	—
10	#107×C₄₇	—	2	1	no	—
11	#107×C₄₇	C₂²	1	2	yes	—
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₇	—	4	1	no	—
14	C₂×Dic₉₄	—	2	2	no	—
15	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₄₇	—	2	2	no	—
18	C₄⋊C₄×C₄₇	—	4	1	no	—
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₄₇	—	4	1	no	—
21	C₄⋊Dic₄₇	—	4	1	no	—
22	Dic₁₈₈	—	2	4	no	—
23	Dic₁₈₈	—	4	2	no	—
24	C₄₇⋊C₁₆	—	2	2	no	—
25	Q₈×C₄₇	—	8	2	no	—
26	C₂×C₄×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₄₇	—	4	2	no	—
31	Dic₉₄	—	4	2	no	—
32	Dic₉₄	—	4	2	no	—
33	C₈×C₄₇	SD₁₆	1	2	yes	—
34	C₈×C₄₇	#41	1	2	yes	—
35	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₄₇	—	8	2	no	—
37	C₄×C₄₇	SD₃₂	1	2	yes	—
38	C₄×C₄₇	Q₃₂	1	2	yes	—
39	C₄×C₄₇	#124	1	1	yes	characteristic
40	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₄₇	—	8	2	no	—
42	#2241	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	#486	1	1	yes	characteristic
44	C₂×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
45	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
46	#500	D₄₇	1	1	yes	characteristic
47	#494	—	47	1	no	—
48	#358	—	47	4	no	—
49	C₄×C₁₆	—	47	1	no	—
50	C₄₇	#2241	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₁₆	—	47	2	no	—
52	C₂×Q₁₆	—	94	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	94	1	no	—
55	C₂×C₁₆	—	47	2	no	—
56	#107	—	2	1	no	—
57	#107	C₂×D₄₇	1	2	yes	—
58	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	94	2	no	—
61	Q₁₆	—	94	4	no	—
62	Q₁₆	—	188	2	no	—
63	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	188	1	no	—
68	C₄⋊C₄	—	188	1	no	—
69	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
70	C₁₆	—	94	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	188	2	no	—
73	Q₈	—	188	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	188	2	no	—
76	C₂×C₄	#10625334	1	1	yes	characteristic
77	C₂×C₄	#10625334	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
79	C₈	#10625336	1	2	yes	—
80	C₈	#10625354	1	2	yes	—
81	C₂²	C₂×#10625334	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	376	2	no	—
84	C₄	#13093968	1	2	yes	—
85	C₄	#13093970	1	2	yes	—
86	C₄	#13094013	1	1	yes	characteristic
87	C₄	C₂×#10625336	1	1	yes	characteristic
88	C₂	#15689471	1	1	yes	characteristic
89	C₂	C₂×#13093968	1	1	yes	characteristic
90	C₂	C₂×#13093970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#500	D₄₇
hypocenter	C₄₇	#2241
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
50. C₄₇	#2241	semidirect