Subgroups — #15688908

Order 3008.

56 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	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625350	C₄	1	1	yes	characteristic
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	#10625329	C₄	1	1	yes	characteristic
7	#10625324	—	2	1	no	—
8	C₈×D₄₇	—	2	1	no	—
9	C₁₆×C₄₇	—	2	1	no	—
10	C₄₇⋊C₁₆	—	2	1	no	—
11	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₄₇	—	2	1	no	—
13	D₁₈₈	C₈	1	1	yes	characteristic
14	C₄×D₄₇	—	2	1	no	—
15	Dic₉₄	C₈	1	1	yes	characteristic
16	C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄₇⋊C₈	—	2	1	no	—
19	C₂²×C₄₇	M₁₆	1	1	yes	characteristic
20	C₂×D₄₇	—	2	1	no	—
21	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
23	Dic₄₇	—	2	1	no	—
24	C₂×C₄₇	—	2	1	no	—
25	C₂×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
26	D₄₇	—	4	1	no	—
27	#350	—	47	1	no	maximal, Sylow
28	C₄₇	#350	1	1	yes	characteristic, complemented, Sylow
29	#131	—	47	1	no	—
30	M₃₂	D₄₇	1	1	yes	characteristic, complemented
31	C₂×C₁₆	—	47	1	no	—
32	#41	—	47	1	no	—
33	M₁₆	—	47	1	no	—
34	M₁₆	—	94	1	no	—
35	C₂×C₈	—	94	1	no	—
36	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	94	1	no	—
39	Q₈	—	47	1	no	—
40	D₄	—	47	1	no	—
41	D₄	—	94	1	no	—
42	C₂×C₄	—	94	1	no	—
43	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
44	C₈	—	94	1	no	—
45	C₈	D₁₈₈	1	1	yes	characteristic
46	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
47	C₂²	—	94	1	no	—
48	C₂²	#10625324	1	1	yes	characteristic
49	C₄	—	94	1	no	—
50	C₄	C₈×D₄₇	1	1	yes	characteristic
51	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	188	1	no	—
54	C₂	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₄₇
Fitting	M₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂²⋊C₈
prime radical	#10625350	C₄
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	M₃₂	D₄₇
hypocenter	C₄₇	#350
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇⋊C₁₆	C₂	semidirect
3. M₃₂×C₄₇	C₂	semidirect
28. C₄₇	#350	semidirect
30. M₃₂	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
C₂×C₄₇⋊C₁₆	2
M₃₂×C₄₇	2
#350	47