Subgroups — #15688927

Order 3008.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#13093958	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	complemented
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₇	—	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	C₂×Dic₄₇	—	4	1	no	—
15	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×C₄₇	D₈	1	1	yes	characteristic
18	C₄×C₄₇	—	4	2	no	—
19	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
21	Dic₄₇	—	8	1	no	—
22	C₂×C₄₇	#102	1	1	yes	characteristic
23	C₂×C₄₇	SD₃₂	1	1	yes	characteristic
24	C₂×C₄₇	Q₃₂	1	1	yes	characteristic
25	#358	—	47	1	no	maximal, Sylow
26	C₄₇	#358	1	1	yes	characteristic, complemented, Sylow
27	C₂×Q₁₆	D₄₇	1	1	yes	characteristic
28	C₂×C₁₆	—	47	1	no	—
29	#107	—	47	1	no	—
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	Dic₄₇	1	2	yes	complemented
33	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
34	C₄⋊C₄	—	94	1	no	—
35	C₁₆	—	94	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	188	1	no	—
40	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
41	C₈	C₂×Dic₄₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
43	C₂²	#10625334	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	376	1	no	—
46	C₄	#10625335	1	1	yes	characteristic
47	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
48	C₂	#13093945	1	1	yes	characteristic
49	C₂	#13093967	1	1	yes	characteristic
50	C₂	#13093970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625334
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	D₈
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	#358
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
6. Q₁₆×C₄₇	C₄	semidirect
26. C₄₇	#358	semidirect
32. Q₁₆	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₁₆	2
#13093958	2
C₂×Q₁₆×C₄₇	2
#358	47