Subgroups — #106×D₄₇ #15689152

Order 3008.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₄₇	C₂	1	2	yes	maximal
3	#13093956	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093955	C₂	1	2	yes	maximal, complemented
5	#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₇	—	2	2	no	—
7	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	Dic₄₇⋊C₄	—	2	2	no	—
12	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×D₄₇	C₄	1	4	yes	complemented
14	C₂²×D₄₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	—	2	2	no	—
16	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₇	—	2	2	no	—
18	C₂×Dic₄₇	D₄	1	1	yes	characteristic
19	C₄×D₄₇	—	4	4	no	—
20	C₄×D₄₇	C₂×C₄	1	2	yes	—
21	C₄×D₄₇	Q₈	1	2	yes	—
22	C₈×C₄₇	C₂×C₄	1	2	yes	complemented
23	C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
24	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
25	C₂×D₄₇	C₄⋊C₄	1	2	yes	—
26	C₂×D₄₇	SD₁₆	1	4	yes	—
27	C₄×C₄₇	—	4	2	no	—
28	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
30	Dic₄₇	—	4	2	no	—
31	Dic₄₇	C₄⋊C₄	1	2	yes	—
32	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄₇	C₂×SD₁₆	1	2	yes	—
34	D₄₇	#106	1	4	yes	direct product factor
35	C₂×#106	—	47	1	no	maximal, Sylow
36	C₄₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₈	—	47	1	no	—
38	C₂×C₄⋊C₄	—	47	2	no	—
39	#106	—	47	1	no	—
40	#106	—	47	2	no	—
41	#106	D₄₇	1	1	yes	characteristic, direct product factor
42	C₂²×C₄	—	47	1	no	—
43	C₂²×C₄	—	94	2	no	—
44	C₂×C₈	—	47	1	no	—
45	C₂×C₈	—	47	4	no	—
46	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
47	C₄⋊C₄	—	47	2	no	—
48	C₄⋊C₄	—	94	2	no	—
49	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
50	C₂³	—	47	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	47	1	no	—
53	C₂×C₄	—	47	2	no	—
54	C₂×C₄	—	47	2	no	—
55	C₂×C₄	—	94	2	no	—
56	C₂×C₄	—	188	4	no	—
57	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
58	C₈	—	47	2	no	—
59	C₈	C₄×D₄₇	1	2	yes	complemented
60	C₂²	—	47	2	no	—
61	C₂²	—	47	4	no	—
62	C₂²	D₄×D₄₇	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	—	47	2	no	—
65	C₄	—	188	2	no	—
66	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
67	C₄	Q₈×D₄₇	1	1	yes	characteristic
68	C₂	—	47	4	no	—
69	C₂	C₄⋊C₄×D₄₇	1	1	yes	characteristic
70	C₂	SD₁₆×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#106×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂²×D₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#106	D₄₇
hypocenter	C₄₇	C₂×#106
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #13093956	C₂	semidirect
4. #13093955	C₂	semidirect
5. #106×C₄₇	C₂	semidirect
13. C₈×D₄₇	C₄	semidirect
22. C₈×C₄₇	C₂×C₄	semidirect
23. C₄₇⋊C₈	C₂×C₄	semidirect
34. D₄₇	#106	direct (N × H)
36. C₄₇	C₂×#106	semidirect
41. #106	D₄₇	direct (N × H)
59. C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄₇	2
C₄⋊C₄×D₄₇	2
#13093956	2
#13093955	2
#106×C₄₇	2
C₂×#106	47

Subgroups — #106×D47 #15689152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #106×D₄₇ #15689152