Subgroups — C₂×#20265003 #27172909

Order 12928.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692189	C₂	1	2	yes	maximal
2	#20265003	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₁₀₁	—	2	2	no	—
5	#15692189	—	2	2	no	—
6	#15692189	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₀₁	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₁₀₁	C₂²	1	2	yes	—
10	C₂²×Dic₁₀₁	—	4	2	no	—
11	C₄⋊Dic₁₀₁	—	2	4	no	—
12	C₄⋊Dic₁₀₁	—	4	2	no	—
13	C₂²×C₄×C₁₀₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₀₁	Q₈	1	2	yes	—
17	C₂×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
18	C₁₆×C₁₀₁	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₀₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₀₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	Q₁₆	1	2	yes	—
23	C₂×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₀₁	—	4	4	no	—
25	C₂×Dic₁₀₁	—	8	4	no	—
26	C₈×C₁₀₁	C₄⋊C₄	1	2	yes	—
27	C₈×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₀₁	#107	1	2	yes	—
30	C₂²×C₁₀₁	D₁₆	1	2	yes	—
31	C₂²×C₁₀₁	Q₃₂	1	2	yes	—
32	C₂²×C₁₀₁	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₀₁	#107	1	2	yes	—
34	C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₁₀₁	—	8	4	no	—
37	C₂×C₁₀₁	#366	1	4	yes	complemented
38	C₂×C₁₀₁	C₂×#107	1	1	yes	characteristic
39	C₂×C₁₀₁	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₁₀₁	C₂×Q₃₂	1	1	yes	characteristic
41	C₂×#366	—	101	1	no	maximal, Sylow
42	C₁₀₁	C₂×#366	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₁₆	D₁₀₁	1	1	yes	characteristic
44	C₂×#107	—	101	2	no	—
45	#366	—	101	4	no	—
46	C₂²×C₈	C₂×D₁₀₁	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	202	2	no	—
48	C₂×C₁₆	Dic₁₀₁	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₁₀₁	1	2	yes	—
50	#107	—	101	4	no	—
51	#107	—	202	2	no	—
52	C₂²×C₄	—	404	2	no	—
53	C₂²×C₄	D₄₀₄	1	1	yes	characteristic
54	C₂×C₈	Dic₂₀₂	1	2	yes	—
55	C₂×C₈	D₄₀₄	1	1	yes	characteristic
56	C₂×C₈	C₂×Dic₁₀₁	1	2	yes	—
57	C₂×C₈	C₂²×D₁₀₁	1	1	yes	characteristic
58	C₄⋊C₄	—	404	2	no	—
59	C₄⋊C₄	—	202	4	no	—
60	C₁₆	C₂×Dic₁₀₁	1	4	yes	complemented
61	C₂³	D₈₀₈	1	1	yes	characteristic
62	C₂×C₄	—	808	4	no	—
63	C₂×C₄	—	404	4	no	—
64	C₂×C₄	C₄⋊Dic₁₀₁	1	2	yes	—
65	C₂×C₄	D₈₀₈	1	1	yes	characteristic
66	C₂×C₄	Dic₄₀₄	1	2	yes	—
67	C₂×C₄	C₂×D₄₀₄	1	1	yes	characteristic
68	C₈	C₄⋊Dic₁₀₁	1	2	yes	—
69	C₈	C₂²×Dic₁₀₁	1	1	yes	characteristic
70	C₈	C₂×Dic₂₀₂	1	1	yes	characteristic
71	C₂²	#15692189	1	2	yes	—
72	C₂²	D₁₆₁₆	1	2	yes	—
73	C₂²	Dic₈₀₈	1	2	yes	—
74	C₂²	C₂×D₈₀₈	1	1	yes	characteristic
75	C₄	—	808	4	no	—
76	C₄	#15692189	1	2	yes	—
77	C₄	C₂×C₄⋊Dic₁₀₁	1	1	yes	characteristic
78	C₄	C₂×Dic₄₀₄	1	1	yes	characteristic
79	C₂	#20265003	1	4	yes	direct product factor
80	C₂	C₂×#15692189	1	1	yes	characteristic
81	C₂	C₂×D₁₆₁₆	1	1	yes	characteristic
82	C₂	C₂×Dic₈₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈₀₈
commutator	C₈×C₁₀₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₀₁
Fitting	C₂²×C₁₆×C₁₀₁	C₂
socle, prime radical	C₂³×C₁₀₁	D₈
cosocle	C₂×C₈×C₁₀₁	C₂³
hypercenter	C₂²×C₁₆	D₁₀₁
hypocenter	C₁₀₁	C₂×#366
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #20265003	C₂	direct (N × H)
8. C₂×C₁₆×C₁₀₁	C₄	semidirect
18. C₁₆×C₁₀₁	C₂×C₄	semidirect
37. C₂×C₁₀₁	#366	semidirect
42. C₁₀₁	C₂×#366	semidirect
48. C₂×C₁₆	Dic₁₀₁	semidirect
60. C₁₆	C₂×Dic₁₀₁	semidirect
79. C₂	#20265003	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15692189	2
#20265003	2
C₂²×C₁₆×C₁₀₁	2
C₂×#366	101

Subgroups — C2×#20265003 #27172909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265003 #27172909