Subgroups — #20265217

Order 6464.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108058	C₂	1	1	yes	maximal, characteristic
2	#15692214	C₂	1	1	yes	maximal, characteristic
3	#15692188	C₂	1	2	yes	maximal, complemented
4	#15692186	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	#13108058	C₄	1	4	yes	complemented
7	C₂×#11717579	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₁₀₁	—	2	1	no	—
11	C₄×Dic₁₀₁	—	2	1	no	—
12	C₂²×C₄×C₁₀₁	—	2	1	no	—
13	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₁	—	2	1	no	—
15	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	—	2	2	no	—
18	C₂×C₄×C₁₀₁	—	4	2	no	—
19	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	Q₈	1	2	yes	—
22	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₀₁	—	2	1	no	—
24	C₂×Dic₁₀₁	—	2	1	no	—
25	#11717579	C₂×C₄	1	4	yes	complemented
26	C₂²×C₁₀₁	—	2	1	no	—
27	C₂²×C₁₀₁	—	2	1	no	—
28	C₂²×C₁₀₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₀₁	—	4	2	no	—
31	C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
32	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₀₁	—	4	1	no	—
35	Dic₁₀₁	—	4	1	no	—
36	C₂×C₁₀₁	—	2	2	no	—
37	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₁₀₁	#137	1	1	yes	characteristic
40	C₁₀₁	#428	1	1	yes	characteristic, complemented, Sylow
41	#428	—	101	1	no	maximal, Sylow
42	C₂×M₁₆	—	101	1	no	—
43	#117	—	101	1	no	—
44	C₂×C₄⋊C₄	D₁₀₁	1	1	yes	characteristic
45	#107	—	101	2	no	—
46	#106	—	101	2	no	—
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
49	M₁₆	—	101	4	no	—
50	C₂×C₈	—	101	2	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	101	1	no	—
53	C₄⋊C₄	—	101	1	no	—
54	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
55	C₂²⋊C₄	—	202	1	no	—
56	C₄²	—	202	1	no	—
57	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	202	1	no	—
61	C₂×C₄	—	202	1	no	—
62	C₂×C₄	Dic₂₀₂	1	2	yes	—
63	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
64	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
66	C₈	—	101	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	#13108053	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	404	1	no	—
73	C₄	—	404	1	no	—
74	C₄	#13108053	1	2	yes	—
75	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
76	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×#13108053	1	1	yes	characteristic
79	C₂	#15692281	1	1	yes	characteristic
80	C₂	#15692286	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂×C₄⋊C₄×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	#428
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #15692188	C₂	semidirect
4. #15692186	C₂	semidirect
6. #13108058	C₄	semidirect
25. #11717579	C₂×C₄	semidirect
40. C₁₀₁	#428	semidirect