Subgroups — #15688879

Order 3008.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625329	C₂	1	1	yes	maximal, characteristic
2	#13093983	C₂	1	1	yes	maximal, characteristic
3	#117×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₄₇	—	2	1	no	—
6	C₂²⋊C₄×C₄₇	—	2	1	no	—
7	C₄²×C₄₇	C₄	1	2	yes	complemented
8	C₂²⋊Dic₄₇	—	2	1	no	—
9	C₄⋊Dic₄₇	—	2	1	no	—
10	C₄×Dic₄₇	C₄	1	2	yes	complemented
11	#10625329	—	2	1	no	—
12	#10625329	—	2	1	no	—
13	C₂×C₄₇⋊C₈	C₄	1	2	yes	complemented
14	C₂³×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	—	2	2	no	—
16	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	Q₈	1	1	yes	characteristic
22	C₂×Dic₄₇	—	2	2	no	—
23	C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇	—	4	1	no	—
25	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₄₇	—	4	2	no	—
29	C₄×C₄₇	C₄²	1	1	yes	characteristic
30	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
33	Dic₄₇	—	4	2	no	—
34	C₂×C₄₇	—	2	1	no	—
35	C₂×C₄₇	—	2	1	no	—
36	C₂×C₄₇	—	2	1	no	—
37	C₂×C₄₇	#95	1	1	yes	characteristic
38	H(3,ℤ/4)	—	47	1	no	maximal, Sylow
39	C₄₇	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₁₆	—	47	1	no	—
41	#117	—	47	1	no	—
42	#117	D₄₇	1	1	yes	characteristic
43	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
44	M₁₆	—	94	1	no	—
45	M₁₆	—	94	1	no	—
46	C₂×C₈	—	47	2	no	—
47	C₄⋊C₄	—	2	1	no	—
48	C₄⋊C₄	—	94	1	no	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	—	94	1	no	—
51	C₄²	—	47	2	no	—
52	C₄²	Dic₄₇	1	2	yes	complemented
53	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	94	2	no	—
56	C₂×C₄	Dic₉₄	1	1	yes	characteristic
57	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
58	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
59	C₂×C₄	D₁₈₈	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
62	C₈	—	94	2	no	—
63	C₂²	—	4	1	no	—
64	C₂²	Dic₄₇⋊C₄	1	1	yes	characteristic
65	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
66	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	188	2	no	—
69	C₄	C₄×Dic₄₇	1	1	yes	characteristic
70	C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
71	C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
72	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	2	1	no	—
75	C₂	—	2	1	no	—
76	C₂	C₄₇⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₄₇
commutator	C₄×C₄₇	C₄²
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	#117×C₄₇	C₂
socle	C₂×C₄₇	#95
prime radical	C₂³×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	#117	D₄₇
hypocenter	C₄₇	H(3,ℤ/4)
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
7. C₄²×C₄₇	C₄	semidirect
10. C₄×Dic₄₇	C₄	semidirect
13. C₂×C₄₇⋊C₈	C₄	semidirect
39. C₄₇	H(3,ℤ/4)	semidirect
52. C₄²	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625329	2
#13093983	2
#117×C₄₇	2
H(3,ℤ/4)	47