Subgroups — #15689170

Order 3008.

102 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	M₁₆×D₄₇	C₂	1	2	yes	maximal
3	#13093960	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093959	C₂	1	2	yes	maximal, complemented
5	#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
7	M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	#10625329	C₂²	1	2	yes	—
10	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	#10625324	—	2	2	no	—
12	#10625324	C₄	1	4	yes	—
13	C₈×D₄₇	—	2	2	no	—
14	C₂²×D₄₇	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₇	Q₈	1	1	yes	characteristic
17	C₄×D₄₇	C₂×C₄	1	2	yes	—
18	C₄×D₄₇	D₄	1	2	yes	—
19	C₈×C₄₇	—	2	2	no	—
20	C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₄₇⋊C₈	—	2	2	no	—
22	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
23	C₂²×C₄₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₄₇	—	4	1	no	—
25	C₂×D₄₇	C₄⋊C₄	1	2	yes	—
26	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
28	Dic₄₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄₇	—	2	1	no	—
30	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₄₇	—	2	2	no	—
32	#430	—	47	1	no	maximal, Sylow
33	C₄₇	#430	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₁₆	—	47	1	no	—
35	C₂×M₁₆	—	47	2	no	—
36	#108	—	47	2	no	—
37	#108	—	47	1	no	—
38	#108	D₄₇	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	47	1	no	—
40	M₁₆	—	47	4	no	—
41	M₁₆	—	47	2	no	—
42	M₁₆	—	94	2	no	—
43	M₁₆	C₂×D₄₇	1	2	yes	—
44	C₂×C₈	—	47	1	no	—
45	C₂×C₈	—	94	2	no	—
46	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
47	C₂³	—	47	1	no	—
48	C₂×C₄	—	47	1	no	—
49	C₂×C₄	—	47	2	no	—
50	C₂×C₄	—	47	2	no	—
51	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	47	2	no	—
54	C₈	—	94	2	no	—
55	C₈	C₄×D₄₇	1	2	yes	—
56	C₂²	—	47	2	no	—
57	C₂²	—	188	1	no	—
58	C₂²	Q₈×D₄₇	1	1	yes	characteristic
59	C₄	—	47	2	no	—
60	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
61	C₄	D₄×D₄₇	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	94	2	no	—
64	C₂	C₄⋊C₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#108×C₄₇	C₂
socle	C₂×C₄₇	C₂×C₄⋊C₄
prime radical	C₂²×D₄₇	Q₈
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#108	D₄₇
hypocenter	C₄₇	#430
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #13093960	C₂	semidirect
4. #13093959	C₂	semidirect
5. #108×C₄₇	C₂	semidirect
33. C₄₇	#430	semidirect
38. #108	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
M₁₆×D₄₇	2
#13093960	2
#13093959	2
#108×C₄₇	2
#430	47