Subgroups — #44566556

Order 32192.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632894	C₂	1	2	yes	maximal
2	C₂×Dic₂₀₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632800	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632782	C₂	1	2	yes	maximal, complemented
5	#131×C₅₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₀₀₆	C₂²	1	2	yes	—
7	Dic₂₀₁₂	—	2	1	no	—
8	Dic₂₀₁₂	—	2	1	no	—
9	#22548873	—	2	2	no	—
10	#22548871	—	2	2	no	—
11	#22548867	C₂²	1	2	yes	—
12	#41×C₅₀₃	C₂²	1	1	yes	characteristic
13	M₁₆×C₅₀₃	—	2	1	no	—
14	M₁₆×C₅₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₅₀₃	—	2	1	no	—
16	C₂×C₈×C₅₀₃	C₂²	1	1	yes	characteristic
17	Dic₁₀₀₆	—	2	2	no	—
18	Dic₁₀₀₆	—	2	2	no	—
19	C₂×Dic₅₀₃	—	2	2	no	—
20	C₅₀₃⋊C₈	—	2	2	no	—
21	Q₈×C₅₀₃	D₄	1	1	yes	characteristic
22	D₄×C₅₀₃	—	2	1	no	—
23	D₄×C₅₀₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅₀₃	—	2	1	no	—
25	C₂×C₄×C₅₀₃	C₂³	1	1	yes	characteristic
26	C₈×C₅₀₃	—	2	1	no	—
27	C₈×C₅₀₃	D₄	1	1	yes	characteristic
28	C₈×C₅₀₃	D₄	1	1	yes	characteristic
29	C₂²×C₅₀₃	—	2	1	no	—
30	C₂²×C₅₀₃	#41	1	1	yes	characteristic
31	C₄×C₅₀₃	—	2	1	no	—
32	C₄×C₅₀₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅₀₃	C₂×D₄	1	1	yes	characteristic
34	Dic₅₀₃	—	4	2	no	—
35	C₂×C₅₀₃	—	2	1	no	—
36	C₂×C₅₀₃	—	4	1	no	—
37	C₂×C₅₀₃	#121	1	1	yes	characteristic
38	C₅₀₃	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	503	1	no	maximal, Sylow
40	#137	—	503	2	no	—
41	C₂×Q₁₆	—	503	1	no	—
42	#131	D₅₀₃	1	1	yes	characteristic
43	#108	—	503	1	no	—
44	#101	—	503	2	no	—
45	#41	C₂×D₅₀₃	1	1	yes	characteristic
46	C₂×Q₈	—	503	2	no	—
47	Q₁₆	—	1006	2	no	—
48	Q₁₆	—	1006	1	no	—
49	Q₁₆	—	1006	1	no	—
50	SD₁₆	—	1006	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	503	2	no	—
53	M₁₆	C₂×D₅₀₃	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₅₀₃	1	1	yes	characteristic
56	Q₈	—	1006	2	no	—
57	Q₈	—	1006	2	no	—
58	Q₈	D₂₀₁₂	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₂₀₁₂	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	1006	2	no	—
63	C₂×C₄	C₂²×D₅₀₃	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	1006	2	no	—
66	C₈	C₂²⋊D₅₀₃	1	1	yes	characteristic
67	C₈	C₂²⋊D₅₀₃	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#22548883	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2012	2	no	—
72	C₄	C₂×C₂²⋊D₅₀₃	1	1	yes	characteristic
73	C₄	C₂×D₂₀₁₂	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#30632838	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30632838
commutator, cosocle	C₂×C₄×C₅₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₅₀₃
Fitting	#131×C₅₀₃	C₂
socle	C₂×C₅₀₃	#121
prime radical	#41×C₅₀₃	C₂²
hypercenter	#131	D₅₀₃
hypocenter	C₅₀₃	#473
LCS	G ▷ C₂×C₄×C₅₀₃ ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₀₁₂	C₂	semidirect
3. #30632800	C₂	semidirect
4. #30632782	C₂	semidirect
38. C₅₀₃	#473	semidirect

Maximal subgroups

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

subgroup	index
#30632894	2
C₂×Dic₂₀₁₂	2
#30632800	2
#30632782	2
#131×C₅₀₃	2
#473	503