Subgroups — C₂×#16837241 #21426398

Order 7552.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₉₄₄	C₂	1	1	yes	maximal, characteristic
3	#16837241	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₂₃₆	—	2	1	no	—
6	C₂×D₄₇₂	—	2	1	no	—
7	Dic₄₇₂	—	2	1	no	—
8	Dic₄₇₂	C₂²	1	2	yes	complemented
9	D₉₄₄	—	2	1	no	—
10	D₉₄₄	C₂²	1	2	yes	—
11	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₃₂×C₅₉	C₂²	1	2	yes	complemented
13	C₂×D₂₃₆	—	4	1	no	—
14	C₂×Dic₁₁₈	—	4	1	no	—
15	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
16	Dic₂₃₆	—	2	2	no	—
17	Dic₂₃₆	—	4	1	no	—
18	D₄₇₂	—	2	2	no	—
19	D₄₇₂	—	4	1	no	—
20	C₁₆×C₅₉	D₄	1	1	yes	characteristic
21	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
22	C₂²×D₅₉	—	8	1	no	—
23	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
24	C₂×Dic₅₉	—	8	1	no	—
25	D₂₃₆	—	4	2	no	—
26	D₂₃₆	—	8	1	no	—
27	Dic₁₁₈	—	4	2	no	—
28	Dic₁₁₈	—	8	1	no	—
29	C₈×C₅₉	D₈	1	1	yes	characteristic
30	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₅₉	D₁₆	1	1	yes	characteristic
32	C₂×D₅₉	—	8	2	no	—
33	C₂×D₅₉	—	16	2	no	—
34	C₄×C₅₉	D₁₆	1	1	yes	characteristic
35	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
36	Dic₅₉	—	8	2	no	—
37	C₂×SD₆₄	—	59	1	no	maximal, Sylow
38	C₂×C₅₉	SD₆₄	1	2	yes	complemented
39	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
40	D₅₉	—	16	2	no	—
41	C₂×Q₃₂	—	59	1	no	—
42	C₂×D₁₆	—	59	1	no	—
43	SD₆₄	—	59	4	no	—
44	C₂×C₃₂	D₅₉	1	1	yes	characteristic, complemented
45	C₅₉	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	118	1	no	—
47	C₂×D₈	—	118	1	no	—
48	Q₃₂	—	59	2	no	—
49	Q₃₂	—	118	1	no	—
50	D₁₆	—	59	2	no	—
51	D₁₆	—	118	1	no	—
52	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
53	C₃₂	C₂×D₅₉	1	2	yes	complemented
54	C₂×Q₈	—	236	1	no	—
55	C₂×D₄	—	236	1	no	—
56	Q₁₆	—	118	2	no	—
57	Q₁₆	—	236	1	no	—
58	D₈	—	118	2	no	—
59	D₈	—	236	1	no	—
60	C₂×C₈	D₂₃₆	1	1	yes	characteristic
61	C₁₆	D₂₃₆	1	1	yes	characteristic
62	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
63	C₂³	—	472	1	no	—
64	Q₈	—	472	1	no	—
65	Q₈	—	236	2	no	—
66	D₄	—	472	1	no	—
67	D₄	—	236	2	no	—
68	C₂×C₄	—	472	1	no	—
69	C₂×C₄	D₄₇₂	1	1	yes	characteristic
70	C₈	D₄₇₂	1	1	yes	characteristic
71	C₈	C₂×D₂₃₆	1	1	yes	characteristic
72	C₂²	—	944	2	no	—
73	C₂²	—	472	2	no	—
74	C₂²	D₉₄₄	1	1	yes	characteristic
75	C₄	—	472	2	no	—
76	C₄	D₉₄₄	1	1	yes	characteristic
77	C₄	C₂×D₄₇₂	1	1	yes	characteristic
78	C₂	—	944	2	no	—
79	C₂	#16837241	1	2	yes	direct product factor
80	C₂	C₂×D₉₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₉₄₄
commutator	C₁₆×C₅₉	C₂³
Frattini	C₁₆	C₂²×D₅₉
Fitting	C₂×C₃₂×C₅₉	C₂
socle	C₂²×C₅₉	D₁₆
hypercenter	C₂×C₃₂	D₅₉
hypocenter	C₅₉	C₂×SD₆₄
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
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×Dic₄₇₂	C₂	semidirect
3. #16837241	C₂	direct (N × H)
4. C₂×C₃₂×C₅₉	C₂	semidirect
8. Dic₄₇₂	C₂²	semidirect
12. C₃₂×C₅₉	C₂²	semidirect
38. C₂×C₅₉	SD₆₄	semidirect
44. C₂×C₃₂	D₅₉	semidirect
45. C₅₉	C₂×SD₆₄	semidirect
53. C₃₂	C₂×D₅₉	semidirect
79. C₂	#16837241	direct (N × H)

Subgroups — C2×#16837241 #21426398

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16837241 #21426398