Subgroups — C₂×#16840160 #21456318

Order 7808.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519777	C₂	1	2	yes	maximal
2	#16840160	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14519709	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₂₂	—	2	2	no	—
6	#14519777	—	2	4	no	—
7	#14519777	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₆₁	—	2	2	no	—
9	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
10	#14519709	C₂²	1	16	yes	—
11	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
12	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₆₁	C₂²	1	4	yes	—
14	C₂²×C₄×C₆₁	D₄	1	2	yes	—
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	—	2	4	no	—
17	C₂×Dic₁₂₂	—	2	8	no	—
18	C₂×Dic₁₂₂	—	4	8	no	—
19	C₂×C₈×C₆₁	Q₈	1	8	yes	complemented
20	C₂×C₈×C₆₁	C₂³	1	4	yes	—
21	C₄²×C₆₁	D₄	1	2	yes	—
22	C₄²×C₆₁	C₂³	1	2	yes	—
23	C₄⋊Dic₆₁	—	2	8	no	—
24	C₄⋊Dic₆₁	—	2	4	no	—
25	C₄⋊Dic₆₁	C₂³	1	8	yes	—
26	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	SD₁₆	1	8	yes	—
28	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₆₁	C₂×Q₈	1	4	yes	—
31	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	8	no	—
33	C₂×Dic₆₁	—	4	8	no	—
34	Dic₁₂₂	—	4	16	no	—
35	C₈×C₆₁	C₂×Q₈	1	8	yes	complemented
36	C₂²×C₆₁	C₄⋊Q₈	1	2	yes	—
37	C₂²×C₆₁	C₂×SD₁₆	1	4	yes	—
38	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
40	C₄×C₆₁	C₂×SD₁₆	1	8	yes	—
41	C₄×C₆₁	C₂²×Q₈	1	2	yes	—
42	Dic₆₁	—	4	8	no	—
43	C₂×#498	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	#498	1	4	yes	complemented
45	C₂×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₆₁	C₂²×SD₁₆	1	2	yes	—
47	C₂×C₄⋊Q₈	—	61	2	no	—
48	#498	—	61	8	no	—
49	C₂×#106	—	61	4	no	—
50	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
51	C₆₁	C₂×#498	1	1	yes	characteristic, complemented, Sylow
52	C₂²×Q₈	—	122	2	no	—
53	C₂²×C₈	C₂×D₆₁	1	2	yes	—
54	C₄⋊Q₈	—	61	8	no	—
55	C₄⋊Q₈	—	122	4	no	—
56	C₂×C₄⋊C₄	—	61	4	no	—
57	C₂×C₄⋊C₄	—	122	2	no	—
58	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
59	#106	—	61	16	no	—
60	C₄×C₈	C₂×D₆₁	1	4	yes	—
61	C₂×Q₈	—	122	8	no	—
62	C₂×Q₈	—	244	8	no	—
63	C₂²×C₄	—	122	4	no	—
64	C₂²×C₄	D₂₄₄	1	2	yes	—
65	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
66	C₂×C₈	Dic₁₂₂	1	8	yes	complemented
67	C₂×C₈	C₂²×D₆₁	1	4	yes	—
68	C₄⋊C₄	—	61	8	no	—
69	C₄⋊C₄	—	122	4	no	—
70	C₄⋊C₄	—	122	8	no	—
71	C₄²	D₂₄₄	1	2	yes	—
72	C₄²	C₂²×D₆₁	1	2	yes	—
73	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
74	Q₈	—	244	16	no	—
75	C₂×C₄	—	122	8	no	—
76	C₂×C₄	—	244	8	no	—
77	C₂×C₄	#11758190	1	8	yes	—
78	C₂×C₄	C₂×Dic₁₂₂	1	4	yes	—
79	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
80	C₂×C₄	C₂×D₂₄₄	1	4	yes	—
81	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
82	C₈	C₂×Dic₁₂₂	1	8	yes	complemented
83	C₂²	#14519777	1	2	yes	—
84	C₂²	C₂×#11758190	1	4	yes	—
85	C₂²	C₂²×D₂₄₄	1	1	yes	characteristic
86	C₄	—	244	8	no	—
87	C₄	#14519777	1	2	yes	—
88	C₄	C₂×#11758190	1	8	yes	—
89	C₄	C₂²×Dic₁₂₂	1	2	yes	—
90	C₂	#16840160	1	4	yes	direct product factor
91	C₂	C₂×#14519777	1	1	yes	characteristic
92	C₂	C₂²×#11758190	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	C₂×#498
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #16840160	C₂	direct (N × H)
19. C₂×C₈×C₆₁	Q₈	semidirect
35. C₈×C₆₁	C₂×Q₈	semidirect
44. C₂×C₆₁	#498	semidirect
51. C₆₁	C₂×#498	semidirect
66. C₂×C₈	Dic₁₂₂	semidirect
82. C₈	C₂×Dic₁₂₂	semidirect
90. C₂	#16840160	direct (N × H)

Subgroups — C2×#16840160 #21456318

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840160 #21456318