Subgroups — #20241339

Order 6016.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688905	C₂	1	2	yes	maximal
2	C₄₇×#423	C₂	1	1	yes	maximal, characteristic
3	#13093964	—	2	2	no	—
4	C₂×M₁₆×C₄₇	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₄₇	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₄₇	—	2	2	no	—
8	C₂²×C₄×C₄₇	—	2	1	no	—
9	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
10	M₁₆×C₄₇	—	4	1	no	—
11	M₁₆×C₄₇	—	4	1	no	—
12	C₂×C₈×C₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	D₄	1	2	yes	—
14	C₄²×C₄₇	—	2	1	no	—
15	C₄²×C₄₇	C₈	1	1	yes	characteristic
16	C₄²×C₄₇	C₈	1	1	yes	characteristic
17	C₄₇⋊C₁₆	—	4	2	no	—
18	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₄₇	—	2	1	no	—
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	—	4	2	no	—
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₈×C₄₇	—	2	2	no	—
27	C₈×C₄₇	—	4	1	no	—
28	C₂²×C₄₇	—	2	1	no	—
29	C₂²×C₄₇	—	4	1	no	—
30	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₄₇	—	2	2	no	—
32	C₄×C₄₇	—	2	1	no	—
33	C₄×C₄₇	—	4	1	no	—
34	C₄×C₄₇	#99	1	1	yes	characteristic
35	C₄×C₄₇	#101	1	1	yes	characteristic
36	#1327	—	47	1	no	maximal, Sylow
37	C₂×C₄₇	—	2	1	no	—
38	C₂×C₄₇	—	4	1	no	—
39	C₂×C₄₇	#324	1	1	yes	characteristic
40	#423	D₄₇	1	1	yes	characteristic
41	#349	—	47	2	no	—
42	C₄₇	#1327	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	Dic₄₇	1	1	yes	characteristic
44	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
45	C₂×C₄²	Dic₄₇	1	1	yes	characteristic
46	M₃₂	—	94	2	no	—
47	C₄⋊C₈	—	2	2	no	—
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
54	C₄²	—	2	1	no	—
55	C₄²	C₄₇⋊C₈	1	1	yes	characteristic
56	C₄²	C₄₇⋊C₈	1	1	yes	characteristic
57	C₁₆	—	188	2	no	—
58	C₂³	#10625329	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	4	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#13093939	1	1	yes	characteristic
75	C₄	#13093943	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#15688849	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13093939
commutator	C₂×C₄×C₄₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#423	C₂
socle	C₂×C₄₇	#324
hypercenter	#423	D₄₇
hypocenter	C₄₇	#1327
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #423

Complements

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

N	H ≅ G/N	type
42. C₄₇	#1327	semidirect