Subgroups — #15689129

Order 3008.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#13093983	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093946	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₄₇	—	2	1	no	—
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×D₁₈₈	—	2	1	no	—
8	C₂×D₁₈₈	—	2	2	no	—
9	C₂×D₁₈₈	C₄	1	4	yes	complemented
10	C₂×D₁₈₈	C₂²	1	2	yes	—
11	M₁₆×C₄₇	—	2	2	no	—
12	C₂×C₈×C₄₇	C₂²	1	2	yes	complemented
13	C₂²⋊Dic₄₇	—	2	1	no	—
14	C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
15	C₄×Dic₄₇	—	2	1	no	—
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×D₄₇	—	2	4	no	—
18	C₂²×D₄₇	—	2	2	no	—
19	C₂²×D₄₇	—	4	4	no	—
20	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	D₄	1	2	yes	—
23	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₇	—	2	2	no	—
25	D₁₈₈	—	2	4	no	—
26	D₁₈₈	—	2	2	no	—
27	D₁₈₈	C₂×C₄	1	4	yes	—
28	C₈×C₄₇	—	2	2	no	—
29	C₂²×C₄₇	—	2	2	no	—
30	C₂²×C₄₇	C₂²⋊C₄	1	2	yes	—
31	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₄₇	—	2	4	no	—
33	C₂×D₄₇	—	4	8	no	—
34	C₂×D₄₇	—	4	4	no	—
35	C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
36	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	Dic₄₇	—	4	2	no	—
39	C₂×C₄₇	—	2	2	no	—
40	C₂×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
42	D₄₇	—	4	4	no	—
43	#418	—	47	1	no	maximal, Sylow
44	C₄₇	#418	1	1	yes	characteristic, complemented, Sylow
45	C₂²×D₄	—	47	1	no	—
46	C₂×M₁₆	D₄₇	1	1	yes	characteristic, complemented
47	#117	—	47	1	no	—
48	#102	—	47	4	no	—
49	C₂⁴	—	94	1	no	—
50	C₂×D₄	—	47	4	no	—
51	C₂×D₄	—	47	2	no	—
52	C₂×D₄	—	94	1	no	—
53	C₂×D₄	—	94	2	no	—
54	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
55	M₁₆	—	2	2	no	—
56	C₂×C₈	C₂×D₄₇	1	2	yes	complemented
57	C₄⋊C₄	—	47	2	no	—
58	C₂²⋊C₄	—	94	1	no	—
59	C₄²	—	94	1	no	—
60	C₂³	—	94	4	no	—
61	C₂³	—	94	2	no	—
62	C₂³	—	188	4	no	—
63	C₂³	D₁₈₈	1	1	yes	characteristic
64	D₄	—	47	4	no	—
65	D₄	—	94	4	no	—
66	D₄	—	94	2	no	—
67	C₂×C₄	—	94	2	no	—
68	C₂×C₄	C₄×D₄₇	1	2	yes	—
69	C₂×C₄	D₁₈₈	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
71	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	2	2	no	—
74	C₂²	—	94	4	no	—
75	C₂²	—	188	8	no	—
76	C₂²	—	188	4	no	—
77	C₂²	(C₂×D₄₇)⋊C₄	1	2	yes	—
78	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
79	C₄	—	188	2	no	—
80	C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
81	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
82	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	188	4	no	—
85	C₂	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
86	C₂	#13094052	1	2	yes	—

	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	C₂²×D₁₈₈	C₂
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×M₁₆	D₄₇
hypocenter	C₄₇	#418
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
2. #13093983	C₂	semidirect
3. #13093946	C₂	semidirect
4. C₂×M₁₆×C₄₇	C₂	semidirect
9. C₂×D₁₈₈	C₄	semidirect
12. C₂×C₈×C₄₇	C₂²	semidirect
14. C₄⋊Dic₄₇	C₂²	semidirect
44. C₄₇	#418	semidirect
46. C₂×M₁₆	D₄₇	semidirect
56. C₂×C₈	C₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₁₈₈	2
#13093983	2
#13093946	2
C₂×M₁₆×C₄₇	2
#418	47