Subgroups — #44566202

Order 32192.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₀₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅₀₃	C₂	1	2	yes	maximal
3	C₂×Dic₅₀₃⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅₀₃⋊#95	C₂	1	2	yes	maximal
5	#95×C₅₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₀₀₆	—	2	4	no	—
7	C₂×Dic₁₀₀₆	—	2	2	no	—
8	C₂²×Dic₅₀₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₅₀₃	C₂²	1	2	yes	—
10	C₂²×Dic₅₀₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₅₀₃	—	2	4	no	—
12	Dic₅₀₃⋊C₄	—	2	2	no	—
13	C₂²×C₄×C₅₀₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅₀₃	C₂²	1	2	yes	—
15	Dic₁₀₀₆	—	2	8	no	—
16	C₂×Dic₅₀₃	—	2	1	no	—
17	C₂×Dic₅₀₃	—	2	2	no	—
18	C₂×Dic₅₀₃	—	2	2	no	—
19	C₂×Dic₅₀₃	—	2	1	no	—
20	C₂×Dic₅₀₃	—	2	1	no	—
21	C₂×Dic₅₀₃	—	2	2	no	—
22	C₂×Dic₅₀₃	D₄	1	4	yes	—
23	C₂×Dic₅₀₃	Q₈	1	2	yes	complemented
24	C₂³×C₅₀₃	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₅₀₃	—	2	2	no	—
26	C₂×C₄×C₅₀₃	—	2	2	no	—
27	C₂×C₄×C₅₀₃	—	2	2	no	—
28	C₂×C₄×C₅₀₃	D₄	1	2	yes	—
29	C₂×C₄×C₅₀₃	Q₈	1	4	yes	complemented
30	C₂²×C₅₀₃	C₂×D₄	1	2	yes	—
31	C₂²×C₅₀₃	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₅₀₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₅₀₃	C₂×Q₈	1	2	yes	—
34	C₂²×C₅₀₃	#41	1	1	yes	characteristic
35	C₄×C₅₀₃	—	2	2	no	—
36	C₄×C₅₀₃	—	2	4	no	—
37	Dic₅₀₃	—	2	4	no	—
38	Dic₅₀₃	—	2	2	no	—
39	Dic₅₀₃	—	4	1	no	—
40	C₂×C₅₀₃	#120	1	1	yes	characteristic
41	C₂×C₅₀₃	C₂²⋊Q₈	1	2	yes	—
42	C₂×C₅₀₃	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₅₀₃	C₄⋊Q₈	1	2	yes	—
44	C₂×C₅₀₃	C₄⋊Q₈	1	1	yes	characteristic
45	C₅₀₃	#395	1	1	yes	characteristic, complemented, Sylow
46	#395	—	503	1	no	maximal, Sylow
47	C₂²×Q₈	—	503	1	no	—
48	C₂×C₄⋊C₄	—	503	1	no	—
49	C₂×C₄⋊C₄	—	503	2	no	—
50	#95	—	503	2	no	—
51	#95	D₅₀₃	1	1	yes	characteristic
52	C₂×Q₈	—	1006	4	no	—
53	C₂×Q₈	—	1006	2	no	—
54	C₂²×C₄	—	503	1	no	—
55	C₂²×C₄	—	503	1	no	—
56	C₂²×C₄	—	503	2	no	—
57	C₂²×C₄	C₂×D₅₀₃	1	1	yes	characteristic
58	C₂²×C₄	C₂×D₅₀₃	1	2	yes	—
59	C₄⋊C₄	—	1006	4	no	—
60	C₄⋊C₄	—	1006	2	no	—
61	C₂³	C₂²×D₅₀₃	1	1	yes	characteristic
62	Q₈	—	1006	8	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	1006	2	no	—
67	C₂×C₄	—	1006	1	no	—
68	C₂×C₄	—	1006	2	no	—
69	C₂×C₄	—	1006	1	no	—
70	C₂×C₄	—	1006	2	no	—
71	C₂×C₄	—	1006	1	no	—
72	C₂×C₄	—	503	4	no	—
73	C₂×C₄	—	503	2	no	—
74	C₂×C₄	D₂₀₁₂	1	2	yes	—
75	C₂×C₄	Dic₁₀₀₆	1	4	yes	complemented
76	C₂²	D₄×D₅₀₃	1	2	yes	—
77	C₂²	C₂×D₂₀₁₂	1	1	yes	characteristic
78	C₂²	Q₈×D₅₀₃	1	1	yes	characteristic
79	C₂²	C₂×Dic₁₀₀₆	1	2	yes	—
80	C₂²	#22548882	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	4	no	—
83	C₄	—	2012	1	no	—
84	C₄	—	1006	4	no	—
85	C₄	—	1006	2	no	—
86	C₂	#30632834	1	1	yes	characteristic
87	C₂	#30632841	1	2	yes	—
88	C₂	#30632844	1	1	yes	characteristic
89	C₂	#30632863	1	2	yes	—
90	C₂	#30632864	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅₀₃
commutator, socle, prime radical, cosocle	C₂³×C₅₀₃	C₂³
Fitting	#95×C₅₀₃	C₂
hypercenter	#95	D₅₀₃
hypocenter	C₅₀₃	#395
LCS	G ▷ C₂³×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
23. C₂×Dic₅₀₃	Q₈	semidirect
29. C₂×C₄×C₅₀₃	Q₈	semidirect
45. C₅₀₃	#395	semidirect
75. C₂×C₄	Dic₁₀₀₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₀₀₆	2
C₂×C₄⋊Dic₅₀₃	2
C₂×Dic₅₀₃⋊C₄	2
C₅₀₃⋊#95	2
#95×C₅₀₃	2
#395	503