Subgroups — #44529446

Order 31168.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29510215	C₂	1	1	yes	maximal, characteristic
2	#29510146	C₂	1	4	yes	maximal
3	C₄×C₄₈₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₉₇₄	—	2	1	no	—
6	C₂×C₄₈₇⋊C₈	C₂²	1	2	yes	—
7	C₄⋊Dic₄₈₇	—	2	1	no	—
8	C₄⋊Dic₄₈₇	C₂²	1	2	yes	—
9	C₂×Q₈×C₄₈₇	—	2	1	no	—
10	C₄⋊C₄×C₄₈₇	—	2	1	no	—
11	C₄⋊C₄×C₄₈₇	C₂²	1	2	yes	—
12	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
13	Dic₉₇₄	—	4	2	no	—
14	C₂×Dic₄₈₇	—	2	2	no	—
15	C₄₈₇⋊C₈	Q₈	1	4	yes	complemented
16	Q₈×C₄₈₇	—	4	2	no	—
17	C₂×C₄×C₄₈₇	—	2	2	no	—
18	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
21	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₄₈₇	—	4	2	no	—
23	C₄×C₄₈₇	SD₁₆	1	2	yes	—
24	C₄×C₄₈₇	SD₁₆	1	2	yes	—
25	C₄×C₄₈₇	C₂×Q₈	1	2	yes	—
26	Dic₄₈₇	—	4	2	no	—
27	C₂×C₄₈₇	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₄₈₇	C₂×SD₁₆	1	1	yes	characteristic
29	C₂×C₄₈₇	C₂×SD₁₆	1	1	yes	characteristic
30	C₄₈₇	#498	1	1	yes	characteristic, complemented, Sylow
31	#498	—	487	1	no	maximal, Sylow
32	C₄⋊Q₈	—	487	1	no	—
33	C₄⋊Q₈	D₄₈₇	1	1	yes	characteristic
34	#106	—	487	4	no	—
35	C₄×C₈	—	487	1	no	—
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	974	1	no	—
38	C₂×C₈	—	487	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	974	1	no	—
41	C₄⋊C₄	—	487	2	no	—
42	C₄⋊C₄	C₂×D₄₈₇	1	2	yes	—
43	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	1948	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	974	2	no	—
48	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
51	C₈	—	487	4	no	—
52	C₂²	C₂×C₂²⋊D₄₈₇	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	1948	2	no	—
55	C₄	#21441248	1	2	yes	—
56	C₄	#21441249	1	2	yes	—
57	C₄	Q₈×D₄₈₇	1	2	yes	—
58	C₂	#29510213	1	1	yes	characteristic
59	C₂	C₂×#21441248	1	1	yes	characteristic
60	C₂	C₂×#21441249	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₈₇
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₄⋊Q₈×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₄₈₇
hypocenter	C₄₈₇	#498
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
15. C₄₈₇⋊C₈	Q₈	semidirect
30. C₄₈₇	#498	semidirect

Maximal subgroups

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

subgroup	index
#29510215	2
#29510146	2
C₄×C₄₈₇⋊C₈	2
C₄⋊Q₈×C₄₈₇	2
#498	487