Subgroups — #20243004

Order 6016.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689526	C₂	1	4	yes	maximal
2	#15689503	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₈₈	—	2	2	no	—
6	#13094024	C₂²	1	2	yes	—
7	#13093957	—	2	8	no	—
8	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₄₇	—	2	2	no	—
10	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
11	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₄₇	—	2	2	no	—
13	C₂×Dic₉₄	—	2	2	no	—
14	Q₁₆×C₄₇	—	4	4	no	—
15	C₂×C₈×C₄₇	D₄	1	2	yes	—
16	C₄⋊C₄×C₄₇	—	2	4	no	—
17	C₄²×C₄₇	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₄₇	—	2	4	no	—
19	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
20	Dic₁₈₈	—	4	4	no	—
21	Q₈×C₄₇	—	4	4	no	—
22	C₂×C₄×C₄₇	—	4	2	no	—
23	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₄₇	—	4	2	no	—
26	Dic₉₄	—	4	4	no	—
27	C₈×C₄₇	D₈	1	4	yes	—
28	C₄₇⋊C₈	Q₁₆	1	8	yes	complemented
29	C₂²×C₄₇	#127	1	1	yes	characteristic
30	C₄×C₄₇	—	8	2	no	—
31	C₄×C₄₇	C₂×D₈	1	2	yes	—
32	C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
33	Dic₄₇	—	8	2	no	—
34	#1713	—	47	1	no	maximal, Sylow
35	C₂×C₄₇	#493	1	1	yes	characteristic
36	C₂×C₄₇	#494	1	2	yes	—
37	#500	—	47	4	no	—
38	#494	—	47	1	no	—
39	#494	D₄₇	1	1	yes	characteristic
40	C₈²	—	47	1	no	—
41	C₄₇	#1713	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	94	2	no	—
44	C₄⋊Q₈	—	47	2	no	—
45	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
46	#107	—	94	8	no	—
47	C₄×C₈	—	47	2	no	—
48	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	94	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	188	4	no	—
53	C₂×C₈	—	47	4	no	—
54	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	94	4	no	—
57	C₄²	C₂²×D₄₇	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	188	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	188	2	no	—
62	C₂×C₄	D₄×D₄₇	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
64	C₈	—	47	8	no	—
65	C₈	#10625334	1	4	yes	—
66	C₂²	#13094020	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	376	2	no	—
69	C₄	C₂×#10625334	1	2	yes	—
70	C₄	Q₁₆×D₄₇	1	4	yes	—
71	C₂	#15689499	1	1	yes	characteristic
72	C₂	#15689501	1	2	yes	—

	subgroup	G/H
center	C₂²	#13094020
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂²×C₄₇	#127
hypercenter	#494	D₄₇
hypocenter	C₄₇	#1713
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. C₄₇⋊C₈	Q₁₆	semidirect
41. C₄₇	#1713	semidirect