Subgroups — #15689165

Order 3008.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093983	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093958	C₂	1	2	yes	maximal, complemented
4	#13093956	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₇	—	2	1	no	—
8	M₁₆×C₄₇	C₄	1	4	yes	complemented
9	C₂×C₈×C₄₇	C₂²	1	2	yes	—
10	C₂²⋊Dic₄₇	—	2	1	no	—
11	C₄⋊Dic₄₇	—	2	1	no	—
12	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₄×Dic₄₇	—	2	1	no	—
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	Q₈	1	2	yes	—
20	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₇	—	2	1	no	—
22	C₂×Dic₄₇	—	2	1	no	—
23	C₂×Dic₄₇	—	2	2	no	—
24	C₂×Dic₄₇	—	4	2	no	—
25	C₈×C₄₇	C₂×C₄	1	4	yes	complemented
26	C₂²×C₄₇	—	2	1	no	—
27	C₂²×C₄₇	—	2	1	no	—
28	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
31	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
33	Dic₄₇	—	4	1	no	—
34	Dic₄₇	—	4	2	no	—
35	Dic₄₇	—	4	1	no	—
36	C₂×C₄₇	—	2	2	no	—
37	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₄₇	#137	1	1	yes	characteristic
40	#428	—	47	1	no	maximal, Sylow
41	C₄₇	#428	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	D₄₇	1	1	yes	characteristic
43	#117	—	47	1	no	—
44	C₂×C₄⋊C₄	—	47	1	no	—
45	#107	—	47	2	no	—
46	#106	—	47	2	no	—
47	C₂²×C₄	—	94	1	no	—
48	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
49	M₁₆	Dic₄₇	1	4	yes	complemented
50	C₂×C₈	C₂×D₄₇	1	2	yes	—
51	C₄⋊C₄	—	47	1	no	—
52	C₄⋊C₄	—	47	2	no	—
53	C₄⋊C₄	—	47	1	no	—
54	C₄⋊C₄	—	94	1	no	—
55	C₂²⋊C₄	—	94	1	no	—
56	C₄²	—	94	1	no	—
57	C₂³	D₁₈₈	1	1	yes	characteristic
58	C₂×C₄	—	94	1	no	—
59	C₂×C₄	—	94	1	no	—
60	C₂×C₄	—	94	2	no	—
61	C₂×C₄	—	188	2	no	—
62	C₂×C₄	Dic₉₄	1	2	yes	—
63	C₂×C₄	D₁₈₈	1	1	yes	characteristic
64	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₈	C₂×Dic₄₇	1	4	yes	complemented
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	C₄⋊Dic₄₇	1	2	yes	—
70	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
71	C₄	—	188	2	no	—
72	C₄	—	188	1	no	—
73	C₄	—	188	1	no	—
74	C₄	C₄⋊Dic₄₇	1	2	yes	—
75	C₄	C₂×Dic₉₄	1	1	yes	characteristic
76	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
79	C₂	#13094052	1	1	yes	characteristic
80	C₂	#13094057	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂³×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×M₁₆	D₄₇
hypocenter	C₄₇	#428
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13093958	C₂	semidirect
4. #13093956	C₂	semidirect
8. M₁₆×C₄₇	C₄	semidirect
25. C₈×C₄₇	C₂×C₄	semidirect
41. C₄₇	#428	semidirect
49. M₁₆	Dic₄₇	semidirect
66. C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093983	2
C₂×C₄⋊Dic₄₇	2
#13093958	2
#13093956	2
C₂×M₁₆×C₄₇	2
#428	47