Subgroups — C₂×#16839601 #21448121

Order 7808.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₉₇₆	C₂	1	1	yes	maximal, characteristic
3	#16839601	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₂₄₄	—	2	1	no	—
6	C₂×D₄₈₈	—	2	1	no	—
7	Dic₄₈₈	—	2	1	no	—
8	Dic₄₈₈	C₂²	1	2	yes	complemented
9	D₉₇₆	—	2	1	no	—
10	D₉₇₆	C₂²	1	2	yes	—
11	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₃₂×C₆₁	C₂²	1	2	yes	complemented
13	C₂×D₂₄₄	—	4	1	no	—
14	C₂×Dic₁₂₂	—	4	1	no	—
15	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
16	Dic₂₄₄	—	2	2	no	—
17	Dic₂₄₄	—	4	1	no	—
18	D₄₈₈	—	2	2	no	—
19	D₄₈₈	—	4	1	no	—
20	C₁₆×C₆₁	D₄	1	1	yes	characteristic
21	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
22	C₂²×D₆₁	—	8	1	no	—
23	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
24	C₂×Dic₆₁	—	8	1	no	—
25	D₂₄₄	—	4	2	no	—
26	D₂₄₄	—	8	1	no	—
27	Dic₁₂₂	—	4	2	no	—
28	Dic₁₂₂	—	8	1	no	—
29	C₈×C₆₁	D₈	1	1	yes	characteristic
30	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₆₁	D₁₆	1	1	yes	characteristic
32	C₂×D₆₁	—	8	2	no	—
33	C₂×D₆₁	—	16	2	no	—
34	C₄×C₆₁	D₁₆	1	1	yes	characteristic
35	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
36	Dic₆₁	—	8	2	no	—
37	C₂×SD₆₄	—	61	1	no	maximal, Sylow
38	C₂×C₆₁	SD₆₄	1	2	yes	complemented
39	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
40	D₆₁	—	16	2	no	—
41	C₂×Q₃₂	—	61	1	no	—
42	C₂×D₁₆	—	61	1	no	—
43	SD₆₄	—	61	4	no	—
44	C₂×C₃₂	D₆₁	1	1	yes	characteristic, complemented
45	C₆₁	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	122	1	no	—
47	C₂×D₈	—	122	1	no	—
48	Q₃₂	—	61	2	no	—
49	Q₃₂	—	122	1	no	—
50	D₁₆	—	61	2	no	—
51	D₁₆	—	122	1	no	—
52	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
53	C₃₂	C₂×D₆₁	1	2	yes	complemented
54	C₂×Q₈	—	244	1	no	—
55	C₂×D₄	—	244	1	no	—
56	Q₁₆	—	122	2	no	—
57	Q₁₆	—	244	1	no	—
58	D₈	—	122	2	no	—
59	D₈	—	244	1	no	—
60	C₂×C₈	D₂₄₄	1	1	yes	characteristic
61	C₁₆	D₂₄₄	1	1	yes	characteristic
62	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
63	C₂³	—	488	1	no	—
64	Q₈	—	488	1	no	—
65	Q₈	—	244	2	no	—
66	D₄	—	488	1	no	—
67	D₄	—	244	2	no	—
68	C₂×C₄	—	488	1	no	—
69	C₂×C₄	D₄₈₈	1	1	yes	characteristic
70	C₈	D₄₈₈	1	1	yes	characteristic
71	C₈	C₂×D₂₄₄	1	1	yes	characteristic
72	C₂²	—	976	2	no	—
73	C₂²	—	488	2	no	—
74	C₂²	D₉₇₆	1	1	yes	characteristic
75	C₄	—	488	2	no	—
76	C₄	D₉₇₆	1	1	yes	characteristic
77	C₄	C₂×D₄₈₈	1	1	yes	characteristic
78	C₂	—	976	2	no	—
79	C₂	#16839601	1	2	yes	direct product factor
80	C₂	C₂×D₉₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₉₇₆
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₂×C₃₂×C₆₁	C₂
socle	C₂²×C₆₁	D₁₆
hypercenter	C₂×C₃₂	D₆₁
hypocenter	C₆₁	C₂×SD₆₄
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₈₈	C₂	semidirect
3. #16839601	C₂	direct (N × H)
4. C₂×C₃₂×C₆₁	C₂	semidirect
8. Dic₄₈₈	C₂²	semidirect
12. C₃₂×C₆₁	C₂²	semidirect
38. C₂×C₆₁	SD₆₄	semidirect
44. C₂×C₃₂	D₆₁	semidirect
45. C₆₁	C₂×SD₆₄	semidirect
53. C₃₂	C₂×D₆₁	semidirect
79. C₂	#16839601	direct (N × H)

Subgroups — C2×#16839601 #21448121

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839601 #21448121