Subgroups — #27186281

Order 12928.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#20266103	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#15692324	—	2	1	no	—
5	#15692305	—	2	1	no	—
6	D₈×D₁₀₁	—	2	1	no	—
7	D₁₆₁₆	C₄	1	1	yes	characteristic, complemented
8	#15692196	—	2	1	no	—
9	C₁₆×D₁₀₁	C₂²	1	1	yes	characteristic
10	D₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#87938	—	4	1	no	—
12	D₄×D₁₀₁	—	4	1	no	—
13	D₈₀₈	—	2	1	no	—
14	#13108059	—	4	1	no	—
15	C₈×D₁₀₁	D₄	1	1	yes	characteristic
16	#13108049	D₄	1	1	yes	characteristic
17	D₈×C₁₀₁	—	2	1	no	—
18	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₁₀₁	—	8	1	no	—
20	C₂×#87938	—	8	1	no	—
21	D₄×C₁₀₁	—	4	1	no	—
22	C₂²⋊D₁₀₁	—	8	1	no	—
23	D₄₀₄	—	4	1	no	—
24	C₄×D₁₀₁	D₈	1	1	yes	characteristic
25	C₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
26	#11717579	SD₁₆	1	1	yes	characteristic
27	C₂²×C₁₀₁	—	8	1	no	—
28	C₂×D₁₀₁	—	8	1	no	—
29	C₂×D₁₀₁	—	16	1	no	—
30	C₂×D₁₀₁	—	16	1	no	—
31	C₂×D₁₀₁	D₁₆	1	1	yes	characteristic
32	#87938	—	16	1	no	—
33	C₄×C₁₀₁	#102	1	1	yes	characteristic
34	Dic₁₀₁	SD₃₂	1	1	yes	characteristic
35	C₂×C₁₀₁	—	16	1	no	—
36	C₂×C₁₀₁	#357	1	1	yes	characteristic
37	D₁₀₁	—	16	1	no	—
38	D₁₀₁	D₃₂	1	1	yes	characteristic
39	D₁₀₁	SD₆₄	1	1	yes	characteristic
40	#1415	—	101	1	no	maximal, Sylow
41	C₁₀₁	#1415	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₁₆	—	101	1	no	—
43	C₂×C₃₂	—	101	1	no	—
44	#366	—	101	1	no	—
45	C₂×D₈	—	202	1	no	—
46	D₁₆	—	101	1	no	—
47	D₁₆	—	202	1	no	—
48	D₁₆	#87938	1	1	yes	characteristic, complemented
49	C₂×C₁₆	—	101	1	no	—
50	#107	—	202	1	no	—
51	C₃₂	—	202	1	no	—
52	C₂×D₄	—	404	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	404	1	no	—
55	D₈	—	202	1	no	—
56	C₂×C₈	—	101	1	no	—
57	C₄⋊C₄	—	404	1	no	—
58	C₁₆	—	101	1	no	—
59	C₁₆	C₂×#87938	1	1	yes	characteristic
60	C₂³	—	808	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	808	1	no	—
63	D₄	—	404	1	no	—
64	C₂×C₄	—	808	1	no	—
65	C₂×C₄	—	101	1	no	—
66	C₈	—	101	1	no	—
67	C₈	C₂²⋊#87938	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	808	1	no	—
70	C₂²	—	1616	1	no	—
71	C₂²	—	1616	1	no	—
72	C₂²	—	101	1	no	—
73	C₄	—	1616	1	no	—
74	C₄	—	101	1	no	—
75	C₄	#15692317	1	1	yes	characteristic
76	C₂	—	16	1	no	—
77	C₂	—	1616	1	no	—
78	C₂	—	101	1	no	—
79	C₂	—	101	1	no	—
80	C₂	#20266089	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20266089
commutator	C₁₆×C₁₀₁	C₂×C₄
Frattini	C₁₆	C₂×#87938
Fitting	D₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#357
prime radical	D₁₆×D₁₀₁	C₂
cosocle	C₁₆×D₁₀₁	C₂²
hypercenter	D₁₆	#87938
hypocenter	C₁₀₁	#1415
LCS	G ▷ C₁₆×C₁₀₁ ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₁₀₁⋊C₃₂	C₂	semidirect
2. #20266103	C₂	semidirect
7. D₁₆₁₆	C₄	semidirect
10. D₁₆×C₁₀₁	C₄	semidirect
41. C₁₀₁	#1415	semidirect
48. D₁₆	#87938	semidirect

Maximal subgroups

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

subgroup	index
D₁₀₁⋊C₃₂	2
#20266103	2
D₁₆×D₁₀₁	2
#1415	101