Subgroups — #44529663

Order 31168.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29510215	C₂	1	1	yes	maximal, characteristic, complemented
2	#29510210	C₂	1	4	yes	maximal
3	#29510206	C₂	1	4	yes	maximal, complemented
4	#29510195	C₂	1	2	yes	maximal
5	#29510180	C₂	1	2	yes	maximal, complemented
6	#29510172	C₂	1	1	yes	maximal, characteristic
7	#125×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₉₇₄	C₂²	1	2	yes	—
9	C₂×C₄×D₄₈₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₈₇	C₂²	1	4	yes	—
11	C₄⋊Dic₄₈₇	C₂²	1	4	yes	—
12	Dic₄₈₇⋊C₄	C₂²	1	2	yes	—
13	Dic₄₈₇⋊C₄	C₂²	1	4	yes	—
14	(C₂×D₄₈₇)⋊C₄	C₂²	1	2	yes	—
15	(C₂×D₄₈₇)⋊C₄	C₂²	1	4	yes	—
16	C₄×Dic₄₈₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₄₈₇	C₂²	1	4	yes	—
18	C₄⋊C₄×C₄₈₇	C₂²	1	2	yes	—
19	C₄⋊C₄×C₄₈₇	C₂²	1	4	yes	—
20	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
21	C₂²×D₄₈₇	C₂³	1	1	yes	characteristic
22	Dic₉₇₄	—	2	4	no	—
23	C₂×Dic₄₈₇	C₂³	1	2	yes	—
24	C₂×Dic₄₈₇	C₂³	1	4	yes	—
25	C₂×Dic₄₈₇	C₂³	1	1	yes	characteristic
26	C₄×D₄₈₇	—	2	2	no	—
27	C₂×C₄×C₄₈₇	C₂³	1	2	yes	—
28	C₂×C₄×C₄₈₇	C₂³	1	4	yes	—
29	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
30	C₂²×C₄₈₇	C₂⁴	1	1	yes	characteristic
31	C₂×D₄₈₇	—	2	1	no	—
32	C₂×D₄₈₇	—	2	2	no	—
33	C₄×C₄₈₇	—	2	2	no	—
34	C₄×C₄₈₇	—	2	4	no	—
35	C₄×C₄₈₇	#41	1	2	yes	—
36	Dic₄₈₇	—	2	1	no	—
37	Dic₄₈₇	—	2	4	no	—
38	Dic₄₈₇	—	2	2	no	—
39	C₂×C₄₈₇	C₂×#41	1	1	yes	characteristic
40	C₂×C₄₈₇	2₋¹⁺⁴	1	2	yes	—
41	D₄₈₇	—	4	1	no	—
42	C₄₈₇	#541	1	1	yes	characteristic, complemented, Sylow
43	#541	—	487	1	no	maximal, Sylow
44	C₄⋊Q₈	—	487	1	no	—
45	#126	—	487	4	no	—
46	#125	—	487	4	no	—
47	#125	D₄₈₇	1	1	yes	characteristic, complemented
48	C₂²⋊Q₈	—	487	2	no	—
49	C₄×Q₈	—	487	2	no	—
50	#117	—	487	1	no	—
51	C₂×Q₈	—	487	2	no	—
52	C₂²×C₄	—	487	1	no	—
53	C₄⋊C₄	—	487	2	no	—
54	C₄⋊C₄	—	487	4	no	—
55	C₄⋊C₄	—	487	4	no	—
56	C₄⋊C₄	—	487	4	no	—
57	C₄⋊C₄	C₂×D₄₈₇	1	2	yes	—
58	C₄⋊C₄	C₂×D₄₈₇	1	4	yes	—
59	C₂²⋊C₄	—	487	2	no	—
60	C₂²⋊C₄	—	487	4	no	—
61	C₄²	—	487	1	no	—
62	C₄²	—	487	4	no	—
63	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
64	C₂³	—	487	1	no	—
65	Q₈	—	974	4	no	—
66	C₂×C₄	—	974	2	no	—
67	C₂×C₄	—	487	2	no	—
68	C₂×C₄	—	487	4	no	—
69	C₂×C₄	—	487	1	no	—
70	C₂×C₄	C₂²×D₄₈₇	1	4	yes	—
71	C₂×C₄	C₂²×D₄₈₇	1	2	yes	—
72	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
73	C₂²	—	974	1	no	—
74	C₂²	—	974	2	no	—
75	C₂²	C₂³×D₄₈₇	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	2	2	no	—
78	C₄	—	974	1	no	—
79	C₄	—	974	4	no	—
80	C₄	—	974	2	no	—
81	C₄	#21441262	1	2	yes	—
82	C₂	—	1948	1	no	—
83	C₂	C₂×#21441262	1	1	yes	characteristic
84	C₂	#29510262	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₈₇
commutator, socle, cosocle	C₂²×C₄₈₇	C₂⁴
Fitting	#125×C₄₈₇	C₂
prime radical	C₂²×D₄₈₇	C₂³
hypercenter	#125	D₄₈₇
hypocenter	C₄₈₇	#541
LCS	G ▷ C₂²×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #29510215	C₂	semidirect
3. #29510206	C₂	semidirect
5. #29510180	C₂	semidirect
7. #125×C₄₈₇	C₂	semidirect
42. C₄₈₇	#541	semidirect
47. #125	D₄₈₇	semidirect

Maximal subgroups

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

subgroup	index
#29510215	2
#29510210	2
#29510206	2
#29510195	2
#29510180	2
#29510172	2
#125×C₄₈₇	2
#541	487