Subgroups — #15689539

Order 3008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094030	C₂	1	1	yes	maximal, characteristic
2	#13093964	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093963	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625350	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	#10625329	C₄	1	1	yes	characteristic
9	#10625324	C₄	1	2	yes	—
10	C₈×D₄₇	C₂²	1	2	yes	—
11	C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇⋊C₁₆	C₂²	1	2	yes	—
14	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₄₇	C₈	1	2	yes	—
16	D₁₈₈	C₈	1	1	yes	characteristic
17	C₄×D₄₇	C₂×C₄	1	2	yes	—
18	Dic₉₄	C₈	1	1	yes	characteristic
19	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₄₇	C₂×C₈	1	1	yes	characteristic
23	C₂×D₄₇	C₂×C₈	1	2	yes	—
24	C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
25	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
26	Dic₄₇	C₂×C₈	1	2	yes	—
27	C₂×C₄₇	—	2	1	no	—
28	C₂×C₄₇	C₂²×C₈	1	1	yes	characteristic
29	D₄₇	—	2	2	no	—
30	#504	—	47	1	no	maximal, Sylow
31	C₄₇	#504	1	1	yes	characteristic, complemented, Sylow
32	#131	—	47	1	no	—
33	M₃₂	—	47	1	no	—
34	M₃₂	—	47	2	no	—
35	C₂×C₁₆	—	47	2	no	—
36	C₂×C₁₆	D₄₇	1	1	yes	characteristic, complemented
37	#41	—	47	1	no	—
38	M₁₆	—	47	1	no	—
39	M₁₆	—	47	2	no	—
40	C₂×C₈	—	47	2	no	—
41	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₁₆	—	47	2	no	—
43	C₁₆	C₂×D₄₇	1	1	yes	characteristic
44	C₁₆	C₂×D₄₇	1	1	yes	characteristic
45	Q₈	—	47	1	no	—
46	D₄	—	47	2	no	—
47	D₄	—	47	1	no	—
48	C₂×C₄	—	47	2	no	—
49	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
50	C₈	—	47	2	no	—
51	C₈	C₄×D₄₇	1	1	yes	characteristic
52	C₈	C₂²×D₄₇	1	1	yes	characteristic
53	C₂²	—	47	2	no	—
54	C₂²	C₈×D₄₇	1	1	yes	characteristic
55	C₄	—	47	2	no	—
56	C₄	C₈×D₄₇	1	1	yes	characteristic
57	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	94	2	no	—
60	C₂	C₂×C₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₄₇
commutator, socle	C₂×C₄₇	C₂²×C₈
Frattini	C₈	C₂²×D₄₇
Fitting	C₂×C₁₆×C₄₇	C₂
prime radical	#10625350	C₄
cosocle	C₈×C₄₇	C₂³
hypercenter	C₂×C₁₆	D₄₇
hypocenter	C₄₇	#504
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13093964	C₂	semidirect
3. #13093963	C₂	semidirect
4. C₁₆×D₄₇	C₂	semidirect
5. C₂×C₁₆×C₄₇	C₂	semidirect
31. C₄₇	#504	semidirect
36. C₂×C₁₆	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094030	2
#13093964	2
#13093963	2
C₁₆×D₄₇	2
C₂×C₁₆×C₄₇	2
#504	47