Subgroups — #20265379

Order 6464.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108061	C₂	1	2	yes	maximal
2	C₄×D₄₀₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11717579	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692179	C₂	1	2	yes	maximal, complemented
5	C₄⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₀₄	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₀₁	—	2	1	no	—
8	#13108061	—	2	4	no	—
9	C₂×#11717579	C₂²	1	2	yes	—
10	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
11	#13108051	—	2	1	no	—
12	C₂×Q₈×C₁₀₁	C₂²	1	2	yes	—
13	C₄⋊C₄×C₁₀₁	—	2	1	no	—
14	C₄⋊C₄×C₁₀₁	—	2	1	no	—
15	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×D₁₀₁	—	2	1	no	—
17	Q₈×C₁₀₁	—	2	2	no	—
18	Q₈×C₁₀₁	—	2	2	no	—
19	C₂×C₄×C₁₀₁	—	2	2	no	—
20	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₀₁	—	2	1	no	—
24	D₄₀₄	—	2	1	no	—
25	D₄₀₄	D₄	1	2	yes	—
26	C₄×D₁₀₁	—	4	2	no	—
27	#11717579	—	2	2	no	—
28	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
29	C₂×D₁₀₁	—	2	2	no	—
30	C₂×D₁₀₁	—	4	1	no	—
31	C₂×D₁₀₁	—	4	1	no	—
32	C₄×C₁₀₁	—	2	1	no	—
33	C₄×C₁₀₁	—	4	2	no	—
34	C₄×C₁₀₁	SD₁₆	1	2	yes	complemented
35	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₀₁	#41	1	1	yes	characteristic
37	Dic₁₀₁	—	4	1	no	—
38	C₂×C₁₀₁	#121	1	1	yes	characteristic
39	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
40	C₂×C₁₀₁	#137	1	1	yes	characteristic
41	D₁₀₁	—	4	2	no	—
42	C₁₀₁	#461	1	1	yes	characteristic, complemented, Sylow
43	#461	—	101	1	no	maximal, Sylow
44	C₂×SD₁₆	—	101	2	no	—
45	C₄⋊Q₈	D₁₀₁	1	1	yes	characteristic, complemented
46	C₄×D₄	—	101	1	no	—
47	C₄⋊C₈	—	101	1	no	—
48	#103	—	101	2	no	—
49	C₂×Q₈	C₂×D₁₀₁	1	2	yes	—
50	C₂×D₄	—	101	1	no	—
51	C₂²×C₄	—	202	1	no	—
52	SD₁₆	—	202	4	no	—
53	C₂×C₈	—	101	2	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	101	1	no	—
57	C₂²⋊C₄	—	202	1	no	—
58	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
59	C₂³	—	202	1	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	2	2	no	—
62	D₄	—	101	2	no	—
63	D₄	—	202	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	404	2	no	—
66	C₂×C₄	—	202	1	no	—
67	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
70	C₈	—	202	2	no	—
71	C₂²	—	404	1	no	—
72	C₂²	—	404	1	no	—
73	C₂²	—	202	2	no	—
74	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	404	1	no	—
78	C₄	#13108061	1	2	yes	complemented
79	C₄	D₄×D₁₀₁	1	1	yes	characteristic
80	C₄	#13108073	1	1	yes	characteristic
81	C₂	—	404	2	no	—
82	C₂	#15692226	1	1	yes	characteristic
83	C₂	C₂×#13108061	1	1	yes	characteristic
84	C₂	#15692286	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₄⋊Q₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₀₁
hypocenter	C₁₀₁	#461
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₄⋊#11717579	C₂	semidirect
4. #15692179	C₂	semidirect
5. C₄⋊Q₈×C₁₀₁	C₂	semidirect
34. C₄×C₁₀₁	SD₁₆	semidirect
42. C₁₀₁	#461	semidirect
45. C₄⋊Q₈	D₁₀₁	semidirect
78. C₄	#13108061	semidirect