Subgroups — 2₋¹⁺⁴×D₄₇ #15689955

Order 3008.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094072	C₂	1	5	yes	maximal, complemented
2	#13094071	C₂	1	10	yes	maximal, complemented
3	#41×D₄₇	C₂	1	10	yes	maximal, complemented
4	C₂×Q₈×D₄₇	C₂	1	5	yes	maximal, complemented
5	2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₄₇	C₂²	1	10	yes	complemented
7	C₂×Q₈×C₄₇	C₂²	1	5	yes	complemented
8	#10625354	C₂²	1	10	yes	complemented
9	Q₈×D₄₇	C₂²	1	10	yes	—
10	Q₈×D₄₇	C₂²	1	20	yes	complemented
11	#10625352	C₂²	1	30	yes	complemented
12	D₄×D₄₇	C₂²	1	10	yes	—
13	#10625350	C₂²	1	30	yes	complemented
14	C₂×C₄×D₄₇	C₂²	1	15	yes	—
15	C₂×Dic₉₄	C₂²	1	15	yes	complemented
16	C₂²×D₄₇	C₂³	1	5	yes	—
17	Q₈×C₄₇	C₂³	1	10	yes	—
18	D₄×C₄₇	C₂³	1	10	yes	—
19	C₂×C₄×C₄₇	C₂³	1	15	yes	—
20	C₂²⋊D₄₇	C₂³	1	20	yes	—
21	C₂×Dic₄₇	C₂³	1	15	yes	—
22	D₁₈₈	C₂³	1	10	yes	—
23	C₄×D₄₇	C₂³	1	10	yes	—
24	C₄×D₄₇	C₂³	1	30	yes	—
25	Dic₉₄	C₂³	1	30	yes	—
26	C₂²×C₄₇	C₂⁴	1	5	yes	—
27	C₂×D₄₇	—	2	10	no	—
28	C₂×D₄₇	C₂⁴	1	5	yes	—
29	C₂×D₄₇	C₂⁴	1	1	yes	characteristic
30	C₄×C₄₇	C₂⁴	1	10	yes	—
31	Dic₄₇	C₂⁴	1	10	yes	—
32	C₂×C₄₇	—	2	5	no	—
33	C₂×C₄₇	C₂⁵	1	1	yes	characteristic
34	D₄₇	—	2	5	no	—
35	D₄₇	2₋¹⁺⁴	1	2	yes	direct product factor
36	C₂×2₋¹⁺⁴	—	47	1	no	maximal, Sylow
37	C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
38	2₋¹⁺⁴	—	47	10	no	—
39	2₋¹⁺⁴	—	47	5	no	—
40	2₋¹⁺⁴	D₄₇	1	1	yes	characteristic, direct product factor
41	C₂×#41	—	47	10	no	—
42	C₂²×Q₈	—	47	5	no	—
43	#41	—	47	10	no	—
44	#41	—	47	30	no	—
45	#41	—	47	30	no	—
46	#41	C₂×D₄₇	1	10	yes	complemented
47	C₂×Q₈	—	47	10	no	—
48	C₂×Q₈	—	47	20	no	—
49	C₂×Q₈	—	47	15	no	—
50	C₂×Q₈	C₂×D₄₇	1	5	yes	complemented
51	C₂×D₄	—	47	10	no	—
52	C₂²×C₄	—	47	15	no	—
53	C₂³	—	47	5	no	—
54	Q₈	—	47	30	no	—
55	Q₈	C₂²×D₄₇	1	10	yes	—
56	D₄	—	47	20	no	—
57	D₄	—	47	10	no	—
58	D₄	C₂²×D₄₇	1	10	yes	—
59	C₂×C₄	—	47	15	no	—
60	C₂×C₄	—	47	10	no	—
61	C₂×C₄	—	47	30	no	—
62	C₂×C₄	C₂²×D₄₇	1	15	yes	—
63	C₂²	—	47	1	no	—
64	C₂²	—	47	5	no	—
65	C₂²	—	94	10	no	—
66	C₂²	C₂³×D₄₇	1	5	yes	—
67	C₄	—	47	10	no	—
68	C₄	C₂³×D₄₇	1	10	yes	—
69	C₂	—	2	5	no	—
70	C₂	—	47	2	no	—
71	C₂	—	94	5	no	—
72	C₂	C₂⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁴×D₄₇
commutator, socle, cosocle	C₂×C₄₇	C₂⁵
Fitting	2₋¹⁺⁴×C₄₇	C₂
hypercenter	2₋¹⁺⁴	D₄₇
hypocenter	C₄₇	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #13094072	C₂	semidirect
2. #13094071	C₂	semidirect
3. #41×D₄₇	C₂	semidirect
4. C₂×Q₈×D₄₇	C₂	semidirect
5. 2₋¹⁺⁴×C₄₇	C₂	semidirect
6. #41×C₄₇	C₂²	semidirect
7. C₂×Q₈×C₄₇	C₂²	semidirect
8. #10625354	C₂²	semidirect
10. Q₈×D₄₇	C₂²	semidirect
11. #10625352	C₂²	semidirect
13. #10625350	C₂²	semidirect
15. C₂×Dic₉₄	C₂²	semidirect
35. D₄₇	2₋¹⁺⁴	direct (N × H)
37. C₄₇	C₂×2₋¹⁺⁴	semidirect
40. 2₋¹⁺⁴	D₄₇	direct (N × H)
46. #41	C₂×D₄₇	semidirect
50. C₂×Q₈	C₂×D₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13094072	2
#13094071	2
#41×D₄₇	2
C₂×Q₈×D₄₇	2
2₋¹⁺⁴×C₄₇	2
C₂×2₋¹⁺⁴	47

Subgroups — 2−1+4×D47 #15689955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2₋¹⁺⁴×D₄₇ #15689955