Subgroups — #44529447

Order 31168.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29510214	C₂	1	2	yes	maximal
2	#29510147	C₂	1	1	yes	maximal, characteristic
3	#29510146	C₂	1	2	yes	maximal
4	C₈×Dic₄₈₇	C₂	1	1	yes	maximal, characteristic
5	#106×C₄₈₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₇₄	—	2	2	no	—
7	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₈₇	C₂²	1	2	yes	—
9	Dic₄₈₇⋊C₄	—	2	2	no	—
10	C₄×Dic₄₈₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₈₇	C₂²	1	2	yes	—
13	Dic₉₇₄	—	4	4	no	—
14	C₂×Dic₄₈₇	—	2	2	no	—
15	C₂×Dic₄₈₇	D₄	1	2	yes	—
16	C₄₈₇⋊C₈	Q₈	1	2	yes	complemented
17	C₂×C₄×C₄₈₇	—	2	2	no	—
18	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
19	C₈×C₄₈₇	Q₈	1	2	yes	complemented
20	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₄₈₇	—	4	2	no	—
22	C₄×C₄₈₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₄₈₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₄₈₇	—	4	2	no	—
25	Dic₄₈₇	SD₁₆	1	4	yes	—
26	C₂×C₄₈₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₄₈₇	C₂×SD₁₆	1	2	yes	—
28	C₄₈₇	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	487	1	no	maximal, Sylow
30	C₄⋊Q₈	—	487	2	no	—
31	#106	—	487	1	no	—
32	#106	—	487	2	no	—
33	#106	D₄₈₇	1	1	yes	characteristic
34	C₄×C₈	—	487	1	no	—
35	C₂×Q₈	—	974	2	no	—
36	C₂×C₈	—	487	1	no	—
37	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
38	C₄⋊C₄	—	974	2	no	—
39	C₄⋊C₄	—	487	2	no	—
40	C₄⋊C₄	C₂×D₄₈₇	1	2	yes	—
41	C₄²	—	487	1	no	—
42	Q₈	—	1948	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	974	2	no	—
45	C₂×C₄	—	487	2	no	—
46	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
47	C₈	—	487	2	no	—
48	C₈	Dic₉₇₄	1	2	yes	complemented
49	C₂²	D₄×D₄₈₇	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	1948	2	no	—
52	C₄	—	487	4	no	—
53	C₄	Q₈×D₄₈₇	1	1	yes	characteristic
54	C₄	C₂×Dic₉₇₄	1	1	yes	characteristic
55	C₂	#29510214	1	1	yes	characteristic
56	C₂	SD₁₆×D₄₈₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₈₇
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	#106×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	C₂×D₄
hypercenter	#106	D₄₈₇
hypocenter	C₄₈₇	#498
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
16. C₄₈₇⋊C₈	Q₈	semidirect
19. C₈×C₄₈₇	Q₈	semidirect
28. C₄₈₇	#498	semidirect
48. C₈	Dic₉₇₄	semidirect

Maximal subgroups

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

subgroup	index
#29510214	2
#29510147	2
#29510146	2
C₈×Dic₄₈₇	2
#106×C₄₈₇	2
#498	487