Subgroups — #44528901

Order 31168.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₈₇⋊C₄	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₄₈₇	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₄₈₇	C₂	1	1	yes	maximal, characteristic
4	C₄₈₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	#95×C₄₈₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₈₇	C₂²	1	2	yes	—
7	C₂²×Dic₄₈₇	C₂²	1	1	yes	characteristic
8	C₂²×Dic₄₈₇	C₂²	1	1	yes	characteristic
9	Dic₄₈₇⋊C₄	C₄	1	8	yes	complemented
10	C₄×Dic₄₈₇	—	2	4	no	—
11	C₄×Dic₄₈₇	C₄	1	4	yes	complemented
12	C₂²×C₄×C₄₈₇	C₂²	1	2	yes	—
13	C₂²×C₄×C₄₈₇	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₈₇	—	2	2	no	—
15	C₂×Dic₄₈₇	—	2	2	no	—
16	C₂×Dic₄₈₇	C₂×C₄	1	4	yes	—
17	C₂×Dic₄₈₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₄₈₇	C₂×C₄	1	4	yes	—
19	C₂×Dic₄₈₇	C₂×C₄	1	2	yes	—
20	C₂×Dic₄₈₇	D₄	1	2	yes	—
21	C₂×Dic₄₈₇	Q₈	1	2	yes	—
22	C₂³×C₄₈₇	C₂³	1	1	yes	characteristic
23	C₂×C₄×C₄₈₇	—	2	2	no	—
24	C₂×C₄×C₄₈₇	—	2	2	no	—
25	C₂×C₄×C₄₈₇	—	2	2	no	—
26	C₂×C₄×C₄₈₇	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₄₈₇	C₂×C₄	1	4	yes	—
28	C₂²×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄₈₇	C₂²×C₄	1	2	yes	—
30	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄₈₇	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₄₈₇	#41	1	2	yes	—
33	C₄×C₄₈₇	—	2	2	no	—
34	C₄×C₄₈₇	—	2	4	no	—
35	Dic₄₈₇	—	2	4	no	—
36	Dic₄₈₇	C₄²	1	4	yes	complemented
37	Dic₄₈₇	C₄⋊C₄	1	4	yes	complemented
38	C₂×C₄₈₇	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄₈₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄₈₇	#117	1	1	yes	characteristic
41	C₂×C₄₈₇	C₄×D₄	1	2	yes	—
42	C₂×C₄₈₇	C₄×Q₈	1	2	yes	—
43	C₄₈₇	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₄×C₄⋊C₄	—	487	1	no	maximal, Sylow
45	C₂×C₄⋊C₄	—	487	2	no	—
46	C₂×C₄²	—	487	2	no	—
47	C₂×C₄²	—	487	1	no	—
48	#95	—	487	1	no	—
49	#95	D₄₈₇	1	1	yes	characteristic
50	C₂²×C₄	—	487	2	no	—
51	C₂²×C₄	—	487	1	no	—
52	C₂²×C₄	—	487	1	no	—
53	C₂²×C₄	C₂×D₄₈₇	1	1	yes	characteristic
54	C₂²×C₄	C₂×D₄₈₇	1	2	yes	—
55	C₄⋊C₄	—	487	8	no	—
56	C₄²	—	974	4	no	—
57	C₄²	—	487	4	no	—
58	C₂³	C₂²×D₄₈₇	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	974	2	no	—
63	C₂×C₄	—	974	2	no	—
64	C₂×C₄	—	487	4	no	—
65	C₂×C₄	—	487	2	no	—
66	C₂×C₄	—	487	2	no	—
67	C₂×C₄	—	487	4	no	—
68	C₂×C₄	—	487	2	no	—
69	C₂×C₄	—	487	2	no	—
70	C₂×C₄	C₄×D₄₈₇	1	2	yes	—
71	C₂×C₄	C₄×D₄₈₇	1	4	yes	—
72	C₂²	C₂×C₄×D₄₈₇	1	1	yes	characteristic
73	C₂²	C₂×C₄×D₄₈₇	1	2	yes	—
74	C₂²	D₄×D₄₈₇	1	1	yes	characteristic
75	C₂²	Q₈×D₄₈₇	1	1	yes	characteristic
76	C₂²	#21441260	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	2	4	no	—
79	C₄	—	974	4	no	—
80	C₄	—	487	4	no	—
81	C₄	—	487	4	no	—
82	C₂	C₄²×D₄₈₇	1	1	yes	characteristic
83	C₂	C₄⋊C₄×D₄₈₇	1	1	yes	characteristic
84	C₂	#29510171	1	1	yes	characteristic
85	C₂	(C₂²⋊D₄₈₇)⋊C₄	1	2	yes	—
86	C₂	#29510180	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₈₇
commutator	C₂×C₄₈₇	C₂×C₄²
Fitting	#95×C₄₈₇	C₂
socle, prime radical, cosocle	C₂³×C₄₈₇	C₂³
hypercenter	#95	D₄₈₇
hypocenter	C₄₈₇	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
9. Dic₄₈₇⋊C₄	C₄	semidirect
11. C₄×Dic₄₈₇	C₄	semidirect
36. Dic₄₈₇	C₄²	semidirect
37. Dic₄₈₇	C₄⋊C₄	semidirect
43. C₄₈₇	C₄×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₄₈₇⋊C₄	2
C₂×C₄×Dic₄₈₇	2
C₄₈₇⋊#95	2
#95×C₄₈₇	2
C₄×C₄⋊C₄	487