Subgroups — #44528877

Order 31168.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₈₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#29510149	C₂	1	1	yes	maximal, characteristic
3	#107×C₄₈₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₄₈₇	—	2	1	no	—
5	C₄₈₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₄₈₇	—	2	1	no	—
8	C₂×Dic₄₈₇	—	4	1	no	—
9	C₂×C₄×C₄₈₇	—	4	1	no	—
10	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
11	C₈×C₄₈₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₈₇	Q₈	1	1	yes	characteristic
13	C₂²×C₄₈₇	D₈	1	1	yes	characteristic
14	C₄×C₄₈₇	—	8	1	no	—
15	C₄×C₄₈₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₄₈₇	Q₁₆	1	1	yes	characteristic
17	Dic₄₈₇	—	8	1	no	—
18	C₂×C₄₈₇	#107	1	1	yes	characteristic
19	C₂×C₄₈₇	SD₃₂	1	1	yes	characteristic
20	C₂×C₄₈₇	SD₃₂	1	1	yes	characteristic
21	C₄₈₇	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	487	1	no	maximal, Sylow
23	C₂×C₁₆	—	487	1	no	—
24	#107	—	487	1	no	—
25	#107	D₄₈₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	974	1	no	—
29	C₁₆	—	487	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	1948	1	no	—
32	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
33	C₈	C₄×D₄₈₇	1	1	yes	characteristic
34	C₈	Dic₉₇₄	1	1	yes	characteristic
35	C₂²	#21441246	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	3896	1	no	—
38	C₄	Dic₄₈₇⋊C₄	1	1	yes	characteristic
39	C₄	#21441251	1	1	yes	characteristic
40	C₂	#29510148	1	1	yes	characteristic
41	C₂	#29510158	1	1	yes	characteristic
42	C₂	#29510159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21441246
commutator	C₈×C₄₈₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₈₇
Fitting	#107×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	D₈
cosocle	C₂×C₈×C₄₈₇	C₂²
hypercenter	#107	D₄₈₇
hypocenter	C₄₈₇	#367
LCS	G ▷ C₈×C₄₈₇ ▷ C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₄₈₇⋊C₁₆	C₄	semidirect
21. C₄₈₇	#367	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₈₇⋊C₁₆	2
#29510149	2
#107×C₄₈₇	2
#367	487