Subgroups — #15689077

Order 3008.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625324	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093981	C₂	1	1	yes	maximal, characteristic
4	#13093935	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
13	Dic₄₇⋊C₄	C₄	1	2	yes	—
14	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	#10625324	C₄	1	4	yes	complemented
18	C₈×D₄₇	C₄	1	4	yes	complemented
19	C₂²×D₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₄₇	C₂×C₄	1	2	yes	—
25	C₄×D₄₇	C₂×C₄	1	2	yes	—
26	C₈×C₄₇	C₂×C₄	1	2	yes	—
27	C₈×C₄₇	C₂×C₄	1	2	yes	—
28	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₄₇	—	2	2	no	—
32	C₂×D₄₇	C₄²	1	2	yes	—
33	C₄×C₄₇	—	2	2	no	—
34	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	Dic₄₇	—	2	2	no	—
37	Dic₄₇	C₄²	1	2	yes	—
38	C₂×C₄₇	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄₇	#131	1	2	yes	—
40	D₄₇	—	2	2	no	—
41	#405	—	47	1	no	maximal, Sylow
42	C₄₇	#405	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	—	47	1	no	—
44	C₂²×C₈	—	47	1	no	—
45	#117	—	47	1	no	—
46	#97	—	47	1	no	—
47	#97	—	47	1	no	—
48	C₄×C₈	—	47	1	no	—
49	C₄×C₈	D₄₇	1	1	yes	characteristic, complemented
50	C₂²×C₄	—	47	1	no	—
51	M₁₆	—	47	4	no	—
52	C₂×C₈	—	47	1	no	—
53	C₂×C₈	—	47	1	no	—
54	C₂×C₈	—	47	4	no	—
55	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
57	C₄⋊C₄	—	47	2	no	—
58	C₂²⋊C₄	—	47	2	no	—
59	C₄²	—	47	1	no	—
60	C₄²	C₂×D₄₇	1	1	yes	characteristic
61	C₂³	—	47	1	no	—
62	C₂×C₄	—	47	1	no	—
63	C₂×C₄	—	47	2	no	—
64	C₂×C₄	—	47	2	no	—
65	C₂×C₄	—	47	2	no	—
66	C₂×C₄	C₄×D₄₇	1	2	yes	—
67	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
68	C₈	—	47	2	no	—
69	C₈	—	47	2	no	—
70	C₈	C₄×D₄₇	1	2	yes	—
71	C₈	C₄×D₄₇	1	2	yes	—
72	C₂²	—	47	2	no	—
73	C₂²	—	94	2	no	—
74	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	47	2	no	—
77	C₄	—	94	2	no	—
78	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
79	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
80	C₂	—	94	2	no	—
81	C₂	C₄²×D₄₇	1	1	yes	characteristic
82	C₂	#13094030	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₄×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₄
prime radical	C₂²×D₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	#405
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #13093935	C₂	semidirect
5. #13093934	C₂	semidirect
6. C₈×Dic₄₇	C₂	semidirect
7. C₄×C₈×C₄₇	C₂	semidirect
17. #10625324	C₄	semidirect
18. C₈×D₄₇	C₄	semidirect
42. C₄₇	#405	semidirect
49. C₄×C₈	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625324	2
C₂×C₈×D₄₇	2
#13093981	2
#13093935	2
#13093934	2
C₈×Dic₄₇	2
C₄×C₈×C₄₇	2
#405	47