Subgroups — C₂²×#14273727 #21437372

Order 7552.

1624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₁₈	C₂	1	2	yes	maximal
2	C₂×#14273727	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₄⋊Dic₅₉	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₁₈	—	2	16	no	—
6	C₂²×Dic₁₁₈	C₂²	1	24	yes	—
7	C₂³×Dic₅₉	C₂²	1	4	yes	—
8	#14273727	C₂²	1	64	yes	direct product factor
9	C₂×C₄⋊Dic₅₉	C₂²	1	48	yes	—
10	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₅₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₅₉	C₂²	1	12	yes	—
13	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₅₉	D₄	1	8	yes	—
15	C₂²×C₄×C₅₉	Q₈	1	16	yes	complemented
16	C₂²×C₄×C₅₉	C₂³	1	6	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	12	yes	—
18	C₂²×Dic₅₉	—	2	16	no	—
19	C₂²×Dic₅₉	C₂³	1	24	yes	—
20	C₂×Dic₁₁₈	—	2	96	no	—
21	C₂×Dic₁₁₈	C₂³	1	32	yes	—
22	C₄²×C₅₉	C₂³	1	16	yes	—
23	C₄⋊Dic₅₉	C₂³	1	64	yes	—
24	C₂³×C₅₉	C₂×D₄	1	4	yes	—
25	C₂³×C₅₉	C₂×Q₈	1	8	yes	—
26	C₂³×C₅₉	C₂⁴	1	3	yes	—
27	C₂×C₄×C₅₉	C₂×D₄	1	24	yes	—
28	C₂×C₄×C₅₉	C₂×Q₈	1	48	yes	complemented
29	C₂×C₄×C₅₉	C₂⁴	1	4	yes	—
30	C₂×C₄×C₅₉	C₂⁴	1	8	yes	—
31	C₂×Dic₅₉	—	2	48	no	—
32	C₂×Dic₅₉	C₂⁴	1	16	yes	—
33	Dic₁₁₈	—	2	64	no	—
34	C₂²×C₅₉	C₄⋊Q₈	1	16	yes	complemented
35	C₂²×C₅₉	C₂²×D₄	1	6	yes	—
36	C₂²×C₅₉	C₂²×Q₈	1	12	yes	—
37	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
38	C₄×C₅₉	C₂²×D₄	1	8	yes	—
39	C₄×C₅₉	C₂²×Q₈	1	16	yes	complemented
40	Dic₅₉	—	2	16	no	—
41	C₂²×C₄⋊Q₈	—	59	1	no	maximal, Sylow
42	C₂×C₅₉	C₂×C₄⋊Q₈	1	12	yes	complemented
43	C₂×C₅₉	C₂³×D₄	1	1	yes	characteristic
44	C₂×C₅₉	C₂³×Q₈	1	2	yes	—
45	C₂³×Q₈	—	59	2	no	—
46	C₂×C₄⋊Q₈	—	59	24	no	—
47	C₂²×C₄⋊C₄	—	59	4	no	—
48	C₂²×C₄²	D₅₉	1	1	yes	characteristic
49	C₅₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
50	C₂²×Q₈	—	59	24	no	—
51	C₂²×Q₈	—	118	16	no	—
52	C₂³×C₄	—	59	4	no	—
53	C₂³×C₄	C₂×D₅₉	1	2	yes	—
54	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
55	C₄⋊Q₈	—	59	64	no	—
56	C₂×C₄⋊C₄	—	59	48	no	—
57	C₂×C₄²	C₂×D₅₉	1	12	yes	—
58	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
59	C₂×Q₈	—	59	32	no	—
60	C₂×Q₈	—	118	96	no	—
61	C₂²×C₄	—	59	24	no	—
62	C₂²×C₄	—	118	16	no	—
63	C₂²×C₄	Dic₁₁₈	1	16	yes	complemented
64	C₂²×C₄	D₂₃₆	1	8	yes	—
65	C₂²×C₄	C₂²×D₅₉	1	12	yes	—
66	C₂²×C₄	C₂²×D₅₉	1	6	yes	—
67	C₄⋊C₄	—	59	64	no	—
68	C₄²	C₂²×D₅₉	1	16	yes	—
69	C₂³	C₂×Dic₁₁₈	1	8	yes	—
70	C₂³	C₂×D₂₃₆	1	4	yes	—
71	C₂³	C₂³×D₅₉	1	3	yes	—
72	Q₈	—	118	64	no	—
73	C₂×C₄	—	59	16	no	—
74	C₂×C₄	—	118	48	no	—
75	C₂×C₄	C₂×Dic₁₁₈	1	48	yes	complemented
76	C₂×C₄	C₂×D₂₃₆	1	24	yes	—
77	C₂×C₄	C₂³×D₅₉	1	4	yes	—
78	C₂×C₄	C₂³×D₅₉	1	8	yes	—
79	C₂²	#14273727	1	16	yes	direct product factor
80	C₂²	C₂²×D₂₃₆	1	6	yes	—
81	C₂²	C₂²×Dic₁₁₈	1	12	yes	—
82	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
83	C₄	—	118	16	no	—
84	C₄	C₂²×D₂₃₆	1	8	yes	—
85	C₄	C₂²×Dic₁₁₈	1	16	yes	complemented
86	C₂	C₂×#14273727	1	12	yes	direct product factor
87	C₂	C₂³×D₂₃₆	1	1	yes	characteristic
88	C₂	C₂³×Dic₁₁₈	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂⁵
Frattini	C₂²	C₂⁴×D₅₉
Fitting	C₂²×C₄²×C₅₉	C₂
socle	C₂⁴×C₅₉	C₂³
hypercenter	C₂²×C₄²	D₅₉
hypocenter	C₅₉	C₂²×C₄⋊Q₈
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#14273727	C₂	direct (N × H)
8. #14273727	C₂²	direct (N × H)
15. C₂²×C₄×C₅₉	Q₈	semidirect
28. C₂×C₄×C₅₉	C₂×Q₈	semidirect
34. C₂²×C₅₉	C₄⋊Q₈	semidirect
39. C₄×C₅₉	C₂²×Q₈	semidirect
42. C₂×C₅₉	C₂×C₄⋊Q₈	semidirect
49. C₅₉	C₂²×C₄⋊Q₈	semidirect
63. C₂²×C₄	Dic₁₁₈	semidirect
75. C₂×C₄	C₂×Dic₁₁₈	semidirect
79. C₂²	#14273727	direct (N × H)
85. C₄	C₂²×Dic₁₁₈	semidirect
86. C₂	C₂×#14273727	direct (N × H)

Subgroups — C22×#14273727 #21437372

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14273727 #21437372