Subgroups — #20265653

Order 6464.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₂₀₂	C₂	1	3	yes	maximal, complemented
4	#15692220	C₂	1	3	yes	maximal, complemented
5	#15692213	C₂	1	3	yes	maximal
6	#15692212	C₂	1	3	yes	maximal
7	C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₂	C₂²	1	3	yes	—
9	Q₈×D₁₀₁	C₄	1	8	yes	complemented
10	C₂×C₄×D₁₀₁	C₂²	1	3	yes	—
11	C₄⋊Dic₁₀₁	C₂²	1	3	yes	—
12	#13108053	C₂²	1	3	yes	—
13	#13108053	C₂²	1	3	yes	—
14	#13108051	C₂²	1	1	yes	characteristic
15	#13108051	C₂²	1	3	yes	—
16	C₄×Dic₁₀₁	C₂²	1	3	yes	—
17	C₄×Dic₁₀₁	C₂²	1	6	yes	—
18	C₂×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
20	C₄²×C₁₀₁	C₂²	1	3	yes	—
21	C₂²×D₁₀₁	C₂³	1	1	yes	characteristic
22	Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
23	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
25	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
26	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
27	C₂×Dic₁₀₁	C₂³	1	3	yes	—
28	C₂×Dic₁₀₁	C₂³	1	3	yes	—
29	C₄×D₁₀₁	C₂×C₄	1	12	yes	—
30	Dic₂₀₂	C₂×C₄	1	12	yes	—
31	C₂²×C₁₀₁	C₂⁴	1	1	yes	characteristic
32	C₂×D₁₀₁	—	2	1	no	—
33	C₂×D₁₀₁	—	2	1	no	—
34	C₂×D₁₀₁	C₂²×C₄	1	2	yes	—
35	C₄×C₁₀₁	—	2	3	no	—
36	C₄×C₁₀₁	—	2	1	no	—
37	C₄×C₁₀₁	C₂²×C₄	1	6	yes	—
38	Dic₁₀₁	—	2	1	no	—
39	Dic₁₀₁	—	2	3	no	—
40	Dic₁₀₁	C₂²×C₄	1	6	yes	—
41	C₂×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
43	C₂×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
44	D₁₀₁	—	2	2	no	—
45	C₁₀₁	#519	1	1	yes	characteristic, complemented, Sylow
46	#519	—	101	1	no	maximal, Sylow
47	C₂²×Q₈	—	101	1	no	—
48	C₄×Q₈	—	101	1	no	—
49	C₄×Q₈	—	101	3	no	—
50	C₄×Q₈	—	101	3	no	—
51	C₄×Q₈	D₁₀₁	1	1	yes	characteristic, complemented
52	#117	—	101	3	no	—
53	#117	—	101	3	no	—
54	C₂×Q₈	—	101	8	no	—
55	C₂×Q₈	—	101	3	no	—
56	C₂×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
57	C₂²×C₄	—	101	3	no	—
58	C₄⋊C₄	—	101	3	no	—
59	C₄⋊C₄	—	101	3	no	—
60	C₄⋊C₄	—	101	3	no	—
61	C₄⋊C₄	C₂×D₁₀₁	1	3	yes	—
62	C₂²⋊C₄	—	101	3	no	—
63	C₂²⋊C₄	—	101	1	no	—
64	C₄²	—	101	6	no	—
65	C₄²	—	101	3	no	—
66	C₄²	C₂×D₁₀₁	1	3	yes	—
67	C₂³	—	101	1	no	—
68	Q₈	—	101	12	no	—
69	Q₈	C₄×D₁₀₁	1	4	yes	—
70	C₂×C₄	—	101	3	no	—
71	C₂×C₄	—	101	12	no	—
72	C₂×C₄	—	101	1	no	—
73	C₂×C₄	—	101	3	no	—
74	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
75	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
77	C₂²	—	101	2	no	—
78	C₂²	—	202	1	no	—
79	C₂²	—	202	1	no	—
80	C₂²	C₂³×D₁₀₁	1	1	yes	characteristic
81	C₄	—	2	3	no	—
82	C₄	—	2	1	no	—
83	C₄	—	101	6	no	—
84	C₄	—	202	1	no	—
85	C₄	—	202	3	no	—
86	C₄	C₂×C₄×D₁₀₁	1	6	yes	—
87	C₂	—	202	2	no	—
88	C₂	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
89	C₂	#15692302	1	1	yes	characteristic
90	C₂	#15692303	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₁
commutator	C₂×C₁₀₁	C₂³×C₄
Fitting	C₄×Q₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂⁴
hypercenter	C₄×Q₈	D₁₀₁
hypocenter	C₁₀₁	#519
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₁₀₁	C₂	semidirect
3. C₄×Dic₂₀₂	C₂	semidirect
4. #15692220	C₂	semidirect
7. C₄×Q₈×C₁₀₁	C₂	semidirect
9. Q₈×D₁₀₁	C₄	semidirect
45. C₁₀₁	#519	semidirect
51. C₄×Q₈	D₁₀₁	semidirect