Subgroups — #20241420

Order 6016.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689488	C₂	1	1	yes	maximal, characteristic
2	#15688901	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#347	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094021	C₄	1	1	yes	characteristic
5	#13094016	C₄	1	1	yes	characteristic
6	#13093964	—	2	1	no	—
7	#13093946	—	2	1	no	—
8	#13093946	—	2	1	no	—
9	M₃₂×C₄₇	—	2	1	no	—
10	#97×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	—	2	1	no	—
12	C₂×D₁₈₈	—	4	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₄₇	—	2	1	no	—
17	Dic₄₇⋊C₄	—	4	1	no	—
18	C₁₆×C₄₇	—	2	2	no	—
19	C₄₇⋊C₁₆	—	2	2	no	—
20	C₂²×D₄₇	—	4	1	no	—
21	C₂×C₄×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₄₇	—	4	1	no	—
24	D₁₈₈	—	4	1	no	—
25	D₁₈₈	—	4	1	no	—
26	D₁₈₈	—	8	2	no	—
27	C₈×C₄₇	—	2	1	no	—
28	C₈×C₄₇	—	2	1	no	—
29	C₂²×C₄₇	#100	1	1	yes	characteristic
30	C₂×D₄₇	—	8	2	no	—
31	C₂×D₄₇	—	8	1	no	—
32	C₄×C₄₇	—	4	1	no	—
33	C₄×C₄₇	#104	1	1	yes	characteristic
34	C₄×C₄₇	#104	1	1	yes	characteristic
35	Dic₄₇	—	8	1	no	—
36	#1355	—	47	1	no	maximal, Sylow
37	C₂×C₄₇	—	2	1	no	—
38	C₂×C₄₇	#329	1	1	yes	characteristic
39	D₄₇	—	16	1	no	—
40	#490	—	47	1	no	—
41	#347	—	47	1	no	—
42	#347	D₄₇	1	1	yes	characteristic, complemented
43	C₄₇	#1355	1	1	yes	characteristic, complemented, Sylow
44	#127	—	47	1	no	—
45	#125	—	47	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	94	1	no	—
48	#102	—	94	1	no	—
49	#102	—	94	1	no	—
50	#97	C₂×D₄₇	1	1	yes	characteristic
51	C₂×D₄	—	94	1	no	—
52	C₂×D₄	—	188	1	no	—
53	C₂×C₈	D₁₈₈	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
55	C₄⋊C₄	—	94	1	no	—
56	C₄⋊C₄	—	188	1	no	—
57	C₄²	C₄×D₄₇	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	94	2	no	—
60	C₂³	—	188	1	no	—
61	D₄	—	376	2	no	—
62	D₄	—	188	1	no	—
63	D₄	—	188	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	188	1	no	—
66	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	376	2	no	—
70	C₂²	—	376	1	no	—
71	C₂²	#13093940	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	376	1	no	—
74	C₄	#13093950	1	1	yes	characteristic
75	C₄	#13093952	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	752	1	no	—
78	C₂	#15688862	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688862
commutator	C₄²×C₄₇	C₂×C₄
Frattini	#97	C₂×D₄₇
Fitting	C₄₇×#347	C₂
socle	C₂×C₄₇	#329
hypercenter	#347	D₄₇
hypocenter	C₄₇	#1355
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #15688901	C₂	semidirect
3. C₄₇×#347	C₂	semidirect
42. #347	D₄₇	semidirect
43. C₄₇	#1355	semidirect