Subgroups — #15688939

Order 3008.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093964	C₂	1	1	yes	maximal, characteristic
2	#13093960	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₇	—	2	1	no	—
5	Q₁₆×C₄₇	—	2	1	no	—
6	Q₁₆×C₄₇	C₄	1	2	yes	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	#10625329	—	2	1	no	—
9	C₄₇⋊C₁₆	—	2	1	no	—
10	Q₈×C₄₇	—	2	2	no	—
11	Q₈×C₄₇	—	4	1	no	—
12	C₂×C₄×C₄₇	—	4	1	no	—
13	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₄₇	D₄	1	1	yes	characteristic
16	C₄₇⋊C₈	—	4	1	no	—
17	C₂²×C₄₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₄₇	—	4	2	no	—
19	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₄₇	D₈	1	1	yes	characteristic
21	C₂×C₄₇	—	2	1	no	—
22	C₂×C₄₇	#102	1	1	yes	characteristic
23	#362	—	47	1	no	maximal, Sylow
24	C₄₇	#362	1	1	yes	characteristic, complemented, Sylow
25	C₂×Q₁₆	D₄₇	1	1	yes	characteristic
26	M₃₂	—	47	1	no	—
27	#108	—	47	1	no	—
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₄₇	1	2	yes	—
31	M₁₆	—	94	1	no	—
32	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
33	C₁₆	—	94	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
38	C₈	—	188	1	no	—
39	C₈	C₂×Dic₄₇	1	1	yes	characteristic
40	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
41	C₂²	#10625335	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	#10625334	1	1	yes	characteristic
44	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#13093945	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093945
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle	C₂×C₄₇	#102
prime radical	C₂²×C₄₇	SD₁₆
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	#362
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
24. C₄₇	#362	semidirect

Maximal subgroups

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

subgroup	index
#13093964	2
#13093960	2
C₂×Q₁₆×C₄₇	2
#362	47