Subgroups — #20241558

Order 6016.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689487	C₂	1	1	yes	maximal, characteristic
2	#15688916	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#353	C₂	1	1	yes	maximal, characteristic
4	#13094016	C₄	1	1	yes	characteristic, complemented
5	#13093945	—	2	1	no	—
6	#13093945	—	2	1	no	—
7	#13093939	—	2	1	no	—
8	#13093935	C₄	1	1	yes	characteristic, complemented
9	#127×C₄₇	C₂²	1	1	yes	characteristic
10	#99×C₄₇	—	2	1	no	—
11	C₂×D₄×C₄₇	—	4	1	no	—
12	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂²⋊C₄×C₄₇	—	4	1	no	—
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊Dic₄₇	—	4	1	no	—
17	C₄⋊Dic₄₇	—	2	1	no	—
18	Dic₄₇⋊C₄	—	4	1	no	—
19	C₂×C₄₇⋊C₈	—	2	1	no	—
20	C₂³×C₄₇	—	2	1	no	—
21	C₂³×C₄₇	—	2	1	no	—
22	D₄×C₄₇	—	4	1	no	—
23	D₄×C₄₇	—	4	1	no	—
24	D₄×C₄₇	—	8	2	no	—
25	C₂×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×C₄₇	—	8	1	no	—
27	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₄₇	—	4	1	no	—
29	C₂×Dic₄₇	—	8	1	no	—
30	C₄₇⋊C₈	—	4	1	no	—
31	C₂²×C₄₇	—	4	1	no	—
32	C₂²×C₄₇	—	4	1	no	—
33	C₂²×C₄₇	—	8	1	no	—
34	C₂²×C₄₇	—	8	1	no	—
35	C₂²×C₄₇	#99	1	1	yes	characteristic
36	C₄×C₄₇	—	2	1	no	—
37	C₄×C₄₇	—	4	1	no	—
38	C₄×C₄₇	—	16	1	no	—
39	Dic₄₇	—	8	1	no	—
40	Dic₄₇	—	16	1	no	—
41	#1412	—	47	1	no	maximal, Sylow
42	C₂×C₄₇	—	2	1	no	—
43	C₂×C₄₇	—	8	1	no	—
44	C₂×C₄₇	—	8	1	no	—
45	C₂×C₄₇	#354	1	1	yes	characteristic
46	#490	—	47	1	no	—
47	#353	—	47	1	no	—
48	#353	D₄₇	1	1	yes	characteristic
49	C₄₇	#1412	1	1	yes	characteristic, complemented, Sylow
50	#127	C₂×D₄₇	1	1	yes	characteristic
51	#125	—	47	1	no	—
52	#102	—	94	1	no	—
53	#102	—	94	1	no	—
54	#99	—	2	1	no	—
55	#99	—	94	1	no	—
56	#97	—	47	1	no	—
57	C₂×D₄	—	4	1	no	—
58	C₂×D₄	D₁₈₈	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
60	C₂×C₈	—	94	1	no	—
61	C₄⋊C₄	—	94	1	no	—
62	C₄⋊C₄	—	188	1	no	—
63	C₂²⋊C₄	—	4	1	no	—
64	C₂²⋊C₄	—	188	1	no	—
65	C₄²	C₄×D₄₇	1	1	yes	characteristic
66	C₂³	—	2	1	no	—
67	C₂³	—	2	1	no	—
68	D₄	—	4	1	no	—
69	D₄	—	4	1	no	—
70	D₄	—	8	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	376	1	no	—
74	C₂×C₄	—	188	1	no	—
75	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
76	C₈	—	188	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	8	1	no	—
80	C₂²	—	8	1	no	—
81	C₂²	#13093938	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	16	1	no	—
85	C₄	—	376	1	no	—
86	C₄	—	752	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	8	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#15688917	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688917
commutator	C₄²×C₄₇	C₂×C₄
Frattini	#127	C₂×D₄₇
Fitting	C₄₇×#353	C₂
socle	C₂×C₄₇	#354
hypercenter	#353	D₄₇
hypocenter	C₄₇	#1412
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

Complements

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

N	H ≅ G/N	type
4. #13094016	C₄	semidirect
8. #13093935	C₄	semidirect
49. C₄₇	#1412	semidirect