Subgroups — C₂²×#14273638 #21432500

Order 7552.

680 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×#14273638	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄²×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅₉⋊C₈	C₄	1	16	yes	complemented
5	C₂²×C₅₉⋊C₈	C₂²	1	12	yes	—
6	#14273638	C₂²	1	16	yes	direct product factor
7	C₂³×C₄×C₅₉	C₄	1	2	yes	—
8	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₅₉	C₄	1	6	yes	—
10	C₂×C₄²×C₅₉	C₂²	1	6	yes	—
11	C₂⁴×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅₉	—	2	8	no	—
13	C₂²×C₄×C₅₉	C₂×C₄	1	12	yes	—
14	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
15	C₂²×C₄×C₅₉	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
17	C₄²×C₅₉	C₂×C₄	1	12	yes	—
18	C₄²×C₅₉	C₂³	1	4	yes	—
19	C₂×C₅₉⋊C₈	C₂×C₄	1	48	yes	complemented
20	C₂×C₅₉⋊C₈	C₂³	1	8	yes	—
21	C₂³×C₅₉	C₄²	1	4	yes	—
22	C₂³×C₅₉	M₁₆	1	8	yes	—
23	C₂³×C₅₉	C₂²×C₄	1	3	yes	—
24	C₂×C₄×C₅₉	—	2	24	no	—
25	C₂×C₄×C₅₉	C₄²	1	12	yes	—
26	C₂×C₄×C₅₉	C₂²×C₄	1	12	yes	—
27	C₂×C₄×C₅₉	C₂²×C₄	1	8	yes	—
28	C₂×C₄×C₅₉	C₂²×C₄	1	3	yes	—
29	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
30	C₅₉⋊C₈	C₂²×C₄	1	16	yes	complemented
31	C₂²×C₅₉	#97	1	16	yes	complemented
32	C₂²×C₅₉	C₂×C₄²	1	6	yes	—
33	C₂²×C₅₉	C₂×M₁₆	1	12	yes	—
34	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
35	C₄×C₅₉	—	2	8	no	—
36	C₄×C₅₉	C₂×C₄²	1	6	yes	—
37	C₄×C₅₉	C₂³×C₄	1	2	yes	—
38	C₂²×#97	—	59	1	no	maximal, Sylow
39	C₂×C₅₉	C₂×#97	1	12	yes	complemented
40	C₂×C₅₉	C₂²×C₄²	1	1	yes	characteristic
41	C₂×C₅₉	C₂²×M₁₆	1	2	yes	—
42	C₂³×C₈	—	59	2	no	—
43	C₂²×C₄²	D₅₉	1	1	yes	characteristic
44	C₂×#97	—	59	12	no	—
45	C₅₉	C₂²×#97	1	1	yes	characteristic, complemented, Sylow
46	C₂³×C₄	Dic₅₉	1	2	yes	—
47	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
48	C₂²×C₈	—	59	16	no	—
49	C₂²×C₈	—	59	12	no	—
50	C₂×C₄²	Dic₅₉	1	6	yes	—
51	C₂×C₄²	C₂×D₅₉	1	6	yes	—
52	#97	—	59	16	no	—
53	C₂⁴	C₂×Dic₅₉	1	1	yes	characteristic
54	C₂²×C₄	—	2	8	no	—
55	C₂²×C₄	C₄×D₅₉	1	8	yes	—
56	C₂²×C₄	C₂×Dic₅₉	1	12	yes	—
57	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
58	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
59	C₂×C₈	—	59	48	no	—
60	C₂×C₈	—	59	8	no	—
61	C₄²	C₂×Dic₅₉	1	12	yes	—
62	C₄²	C₂²×D₅₉	1	4	yes	—
63	C₂³	#11745664	1	8	yes	—
64	C₂³	C₄×Dic₅₉	1	4	yes	—
65	C₂³	C₂²×Dic₅₉	1	3	yes	—
66	C₂×C₄	—	2	24	no	—
67	C₂×C₄	C₄×Dic₅₉	1	12	yes	—
68	C₂×C₄	C₂×C₄×D₅₉	1	12	yes	—
69	C₂×C₄	C₂²×Dic₅₉	1	8	yes	—
70	C₂×C₄	C₂²×Dic₅₉	1	3	yes	—
71	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
72	C₈	—	59	16	no	—
73	C₂²	#14273638	1	16	yes	direct product factor
74	C₂²	C₂×C₄×Dic₅₉	1	6	yes	—
75	C₂²	C₂×#11745664	1	12	yes	—
76	C₂²	C₂³×Dic₅₉	1	1	yes	characteristic
77	C₄	—	2	8	no	—
78	C₄	C₂×C₄×Dic₅₉	1	6	yes	—
79	C₄	C₂²×C₄×D₅₉	1	2	yes	—
80	C₂	C₂×#14273638	1	12	yes	direct product factor
81	C₂	C₂²×C₄×Dic₅₉	1	1	yes	characteristic
82	C₂	C₂²×#11745664	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₅₉
commutator	C₂×C₅₉	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₂²×C₄²×C₅₉	C₂
socle	C₂⁴×C₅₉	C₂×C₄
hypercenter	C₂²×C₄²	D₅₉
hypocenter	C₅₉	C₂²×#97
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#14273638	C₂	direct (N × H)
4. C₂²×C₅₉⋊C₈	C₄	semidirect
6. #14273638	C₂²	direct (N × H)
19. C₂×C₅₉⋊C₈	C₂×C₄	semidirect
30. C₅₉⋊C₈	C₂²×C₄	semidirect
31. C₂²×C₅₉	#97	semidirect
39. C₂×C₅₉	C₂×#97	semidirect
45. C₅₉	C₂²×#97	semidirect
73. C₂²	#14273638	direct (N × H)
80. C₂	C₂×#14273638	direct (N × H)

Subgroups — C22×#14273638 #21432500

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14273638 #21432500