Subgroups — #126×D₄₇ #15689646

Order 3008.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094019	C₂	1	3	yes	maximal, complemented
2	#13094018	C₂	1	1	yes	maximal, characteristic, complemented
3	#13094017	C₂	1	3	yes	maximal, complemented
4	C₄⋊C₄×D₄₇	C₂	1	3	yes	maximal, complemented
5	C₂²⋊C₄×D₄₇	C₂	1	3	yes	maximal
6	C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#126×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄₇	C₂²	1	3	yes	—
10	C₂×C₄×D₄₇	C₂²	1	3	yes	—
11	C₄⋊C₄×C₄₇	C₂²	1	3	yes	complemented
12	C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
13	C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
14	C₂²⋊Dic₄₇	C₂²	1	3	yes	—
15	(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
16	(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
17	C₄⋊Dic₄₇	C₂²	1	3	yes	complemented
18	Dic₄₇⋊C₄	C₂²	1	3	yes	complemented
19	Dic₄₇⋊C₄	C₂²	1	3	yes	complemented
20	C₄×Dic₄₇	C₂²	1	3	yes	complemented
21	C₂³×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×D₄₇	—	2	6	no	—
23	C₂²×D₄₇	C₂³	1	1	yes	characteristic
24	C₂²×D₄₇	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂³	1	3	yes	—
26	C₂×C₄×C₄₇	C₂³	1	3	yes	—
27	C₂×Dic₄₇	C₂³	1	3	yes	—
28	C₂×Dic₄₇	C₂³	1	3	yes	—
29	C₄×D₄₇	—	2	6	no	—
30	C₄×D₄₇	—	2	6	no	—
31	C₂²×C₄₇	—	2	3	no	—
32	C₂²×C₄₇	C₂⁴	1	1	yes	characteristic
33	C₂×D₄₇	—	2	3	no	—
34	C₂×D₄₇	—	4	4	no	—
35	C₂×D₄₇	#41	1	6	yes	—
36	C₄×C₄₇	—	2	3	no	—
37	C₄×C₄₇	—	2	3	no	—
38	Dic₄₇	—	2	3	no	—
39	Dic₄₇	—	2	3	no	—
40	C₂×C₄₇	—	4	1	no	—
41	C₂×C₄₇	C₂×#41	1	3	yes	—
42	D₄₇	—	4	1	no	—
43	D₄₇	#126	1	4	yes	direct product factor
44	C₂×#126	—	47	1	no	maximal, Sylow
45	C₄₇	C₂×#126	1	1	yes	characteristic, complemented, Sylow
46	#126	—	47	3	no	—
47	#126	—	47	3	no	—
48	#126	—	47	1	no	—
49	#126	D₄₇	1	1	yes	characteristic, direct product factor
50	C₂×C₄⋊C₄	—	47	3	no	—
51	C₂×C₂²⋊C₄	—	47	3	no	—
52	C₂×C₄²	—	47	1	no	—
53	C₂⁴	—	47	1	no	—
54	C₂²×C₄	—	47	3	no	—
55	C₂²×C₄	—	47	3	no	—
56	C₄⋊C₄	—	47	3	no	—
57	C₄⋊C₄	—	47	3	no	—
58	C₄⋊C₄	—	47	3	no	—
59	C₄⋊C₄	C₂×D₄₇	1	3	yes	complemented
60	C₂²⋊C₄	—	47	3	no	—
61	C₂²⋊C₄	—	47	3	no	—
62	C₂²⋊C₄	—	47	3	no	—
63	C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
64	C₄²	—	47	3	no	—
65	C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
66	C₂³	—	47	1	no	—
67	C₂³	—	47	1	no	—
68	C₂³	—	94	6	no	—
69	C₂³	C₂²×D₄₇	1	1	yes	characteristic
70	C₂×C₄	—	47	3	no	—
71	C₂×C₄	—	47	3	no	—
72	C₂×C₄	—	94	6	no	—
73	C₂×C₄	—	94	6	no	—
74	C₂×C₄	C₂²×D₄₇	1	3	yes	—
75	C₂×C₄	C₂²×D₄₇	1	3	yes	—
76	C₂²	—	2	3	no	—
77	C₂²	—	47	6	no	—
78	C₂²	—	94	3	no	—
79	C₂²	—	188	4	no	—
80	C₂²	C₂³×D₄₇	1	1	yes	characteristic
81	C₄	—	2	3	no	—
82	C₄	—	2	3	no	—
83	C₄	—	94	3	no	—
84	C₄	—	94	3	no	—
85	C₂	—	4	1	no	—
86	C₂	—	47	4	no	—
87	C₂	—	188	1	no	—
88	C₂	#41×D₄₇	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁴
Fitting	#126×C₄₇	C₂
prime radical	C₂³×D₄₇	C₂²
hypercenter	#126	D₄₇
hypocenter	C₄₇	C₂×#126
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. #13094019	C₂	semidirect
2. #13094018	C₂	semidirect
3. #13094017	C₂	semidirect
4. C₄⋊C₄×D₄₇	C₂	semidirect
6. C₄²×D₄₇	C₂	semidirect
7. #126×C₄₇	C₂	semidirect
11. C₄⋊C₄×C₄₇	C₂²	semidirect
13. C₄²×C₄₇	C₂²	semidirect
17. C₄⋊Dic₄₇	C₂²	semidirect
18. Dic₄₇⋊C₄	C₂²	semidirect
19. Dic₄₇⋊C₄	C₂²	semidirect
20. C₄×Dic₄₇	C₂²	semidirect
43. D₄₇	#126	direct (N × H)
45. C₄₇	C₂×#126	semidirect
49. #126	D₄₇	direct (N × H)
59. C₄⋊C₄	C₂×D₄₇	semidirect
65. C₄²	C₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094019	2
#13094018	2
#13094017	2
C₄⋊C₄×D₄₇	2
C₂²⋊C₄×D₄₇	2
C₄²×D₄₇	2
#126×C₄₇	2
C₂×#126	47

Subgroups — #126×D47 #15689646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #126×D₄₇ #15689646