Subgroups — #20244790

Order 6016.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689171	C₂	1	3	yes	maximal
2	C₂×#13093942	C₂	1	3	yes	maximal
3	C₄₇×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
5	C₂×#10625329	C₂²	1	3	yes	—
6	#13093959	—	2	6	no	—
7	#13093942	—	2	6	no	—
8	C₂×M₁₆×C₄₇	C₂²	1	3	yes	—
9	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
10	C₂²×Dic₄₇	Q₈	1	2	yes	—
11	C₂×Dic₉₄	—	2	3	no	—
12	C₂×Dic₉₄	—	2	3	no	—
13	M₁₆×C₄₇	—	2	3	no	—
14	M₁₆×C₄₇	—	2	3	no	—
15	C₂×C₈×C₄₇	—	2	3	no	—
16	#10625329	—	2	3	no	—
17	#10625329	D₄	1	6	yes	—
18	C₂×C₄₇⋊C₈	—	2	3	no	—
19	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₄₇	#41	1	3	yes	—
22	C₂×Dic₄₇	—	2	6	no	—
23	Dic₉₄	—	4	3	no	—
24	Dic₉₄	—	4	1	no	—
25	C₈×C₄₇	—	4	3	no	—
26	C₄₇⋊C₈	—	2	6	no	—
27	C₂²×C₄₇	—	4	1	no	—
28	C₂²×C₄₇	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₄₇	#121	1	3	yes	—
30	C₄×C₄₇	#126	1	1	yes	characteristic
31	Dic₄₇	—	4	2	no	—
32	#2070	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	—	2	3	no	—
34	C₂×C₄₇	#396	1	1	yes	characteristic
35	#430	—	47	3	no	—
36	C₂×#101	—	47	3	no	—
37	#338	D₄₇	1	1	yes	characteristic
38	C₄₇	#2070	1	1	yes	characteristic, complemented, Sylow
39	C₂²×Q₈	—	47	1	no	—
40	C₂×M₁₆	—	47	3	no	—
41	C₂×M₁₆	C₂×D₄₇	1	3	yes	—
42	#108	—	94	6	no	—
43	#101	—	94	6	no	—
44	C₂×Q₈	—	94	3	no	—
45	C₂×Q₈	—	94	3	no	—
46	C₂²×C₄	—	47	2	no	—
47	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	47	6	no	—
51	M₁₆	—	94	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	94	3	no	—
54	C₂³	Q₈×D₄₇	1	1	yes	characteristic
55	Q₈	—	188	3	no	—
56	Q₈	—	188	1	no	—
57	C₂×C₄	—	94	6	no	—
58	C₂×C₄	#10625350	1	3	yes	—
59	C₂×C₄	D₄×D₄₇	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	94	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#13094002	1	3	yes	—
64	C₄	—	188	2	no	—
65	C₄	#13093997	1	3	yes	—
66	C₄	#13094018	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#15689047	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15689047
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#338	C₂
socle	C₂×C₄₇	#396
hypercenter	#338	D₄₇
hypocenter	C₄₇	#2070
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
38. C₄₇	#2070	semidirect