Subgroups — C₂×#16837240 #21426397

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	#16837240	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₃₆	—	2	1	no	—
6	Dic₄₇₂	—	2	1	no	—
7	Dic₄₇₂	C₂²	1	2	yes	complemented
8	C₅₉⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₅₉	—	2	1	no	—
10	D₁₆×C₅₉	—	2	1	no	—
11	D₁₆×C₅₉	C₂²	1	2	yes	—
12	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₅₉	—	4	1	no	—
14	C₂×Dic₁₁₈	—	4	1	no	—
15	D₈×C₅₉	—	2	2	no	—
16	D₈×C₅₉	—	4	1	no	—
17	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
18	Dic₂₃₆	—	2	2	no	—
19	Dic₂₃₆	—	4	1	no	—
20	C₁₆×C₅₉	D₄	1	1	yes	characteristic
21	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
22	C₂³×C₅₉	—	8	1	no	—
23	D₄×C₅₉	—	4	2	no	—
24	D₄×C₅₉	—	8	1	no	—
25	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
26	C₂×Dic₅₉	—	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	—	8	2	no	—
32	C₂²×C₅₉	—	16	2	no	—
33	C₂²×C₅₉	D₁₆	1	1	yes	characteristic
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	—	16	2	no	—
39	C₂×C₅₉	SD₆₄	1	2	yes	complemented
40	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
41	C₂×Q₃₂	—	59	1	no	—
42	C₂×D₁₆	D₅₉	1	1	yes	characteristic
43	SD₆₄	—	59	4	no	—
44	C₂×C₃₂	—	59	1	no	—
45	C₅₉	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	118	1	no	—
47	C₂×D₈	—	2	1	no	—
48	Q₃₂	—	59	2	no	—
49	Q₃₂	—	118	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	C₂×D₅₉	1	2	yes	—
52	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
53	C₃₂	—	59	2	no	—
54	C₂×Q₈	—	236	1	no	—
55	C₂×D₄	—	4	1	no	—
56	Q₁₆	—	118	2	no	—
57	Q₁₆	—	236	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
62	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
63	C₂³	—	8	1	no	—
64	Q₈	—	472	1	no	—
65	Q₈	—	236	2	no	—
66	D₄	—	4	2	no	—
67	D₄	—	8	1	no	—
68	C₂×C₄	—	472	1	no	—
69	C₂×C₄	#11745669	1	1	yes	characteristic
70	C₈	#11745669	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
72	C₂²	—	8	2	no	—
73	C₂²	—	16	2	no	—
74	C₂²	#14273668	1	1	yes	characteristic
75	C₄	—	472	2	no	—
76	C₄	#14273668	1	1	yes	characteristic
77	C₄	C₂×#11745669	1	1	yes	characteristic
78	C₂	—	16	2	no	—
79	C₂	#16837240	1	2	yes	direct product factor
80	C₂	C₂×#14273668	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14273668
commutator	C₁₆×C₅₉	C₂³
Frattini	C₁₆	C₂²×D₅₉
Fitting	C₂×D₁₆×C₅₉	C₂
socle	C₂²×C₅₉	D₁₆
hypercenter	C₂×D₁₆	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×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₇₂	C₂	semidirect
2. #16837240	C₂	direct (N × H)
3. C₂×C₅₉⋊C₃₂	C₂	semidirect
7. Dic₄₇₂	C₂²	semidirect
8. C₅₉⋊C₃₂	C₂²	semidirect
39. C₂×C₅₉	SD₆₄	semidirect
45. C₅₉	C₂×SD₆₄	semidirect
79. C₂	#16837240	direct (N × H)

Subgroups — C2×#16837240 #21426397

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16837240 #21426397