Subgroups — C₂×#16837819 #21437195

Order 7552.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837819	C₂	1	8	yes	maximal, direct product factor
2	C₂×#14273667	C₂	1	3	yes	maximal, complemented
3	C₂²×C₅₉⋊C₁₆	C₂	1	3	yes	maximal, complemented
4	C₂×#131×C₅₉	C₂	1	1	yes	maximal, characteristic
5	#14273667	C₂²	1	12	yes	complemented
6	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₅₉⋊C₁₆	C₂²	1	3	yes	—
8	C₂×C₅₉⋊C₁₆	C₂²	1	12	yes	complemented
9	C₂×#41×C₅₉	C₄	1	1	yes	characteristic
10	#131×C₅₉	C₄	1	4	yes	—
11	#131×C₅₉	C₂²	1	4	yes	—
12	C₂×M₁₆×C₅₉	C₄	1	3	yes	—
13	C₂²×C₈×C₅₉	C₂²	1	3	yes	—
14	#41×C₅₉	C₈	1	4	yes	—
15	#41×C₅₉	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₅₉	C₈	1	1	yes	characteristic
17	C₂×D₄×C₅₉	C₈	1	3	yes	—
18	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
19	M₁₆×C₅₉	C₂×C₄	1	12	yes	—
20	C₂×C₈×C₅₉	C₂×C₄	1	3	yes	—
21	C₂×C₈×C₅₉	C₂×C₄	1	6	yes	—
22	C₂×C₈×C₅₉	C₂³	1	6	yes	—
23	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
24	C₅₉⋊C₁₆	C₂³	1	2	yes	—
25	C₅₉⋊C₁₆	C₂³	1	6	yes	—
26	C₂³×C₅₉	C₂×C₈	1	3	yes	—
27	Q₈×C₅₉	C₂×C₈	1	4	yes	—
28	D₄×C₅₉	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₅₉	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₅₉	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂²×C₄	1	6	yes	—
33	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₅₉	C₂²×C₄	1	6	yes	—
35	C₈×C₅₉	C₂⁴	1	1	yes	characteristic
36	C₂²×C₅₉	—	2	6	no	—
37	C₂²×C₅₉	C₂²×C₈	1	6	yes	—
38	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₅₉	C₂²×C₈	1	6	yes	—
41	C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
42	C₂×#504	—	59	1	no	maximal, Sylow
43	C₂×C₅₉	—	2	6	no	—
44	C₂×C₅₉	#504	1	2	yes	complemented
45	C₂×C₅₉	C₂³×C₈	1	1	yes	characteristic
46	C₂×#131	D₅₉	1	1	yes	characteristic
47	#504	—	59	8	no	—
48	C₂×M₃₂	—	59	3	no	—
49	C₂²×C₁₆	—	59	3	no	—
50	C₅₉	C₂×#504	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	Dic₅₉	1	1	yes	characteristic
52	#131	Dic₅₉	1	4	yes	—
53	#131	C₂×D₅₉	1	4	yes	—
54	C₂×M₁₆	Dic₅₉	1	3	yes	—
55	C₂²×C₈	C₂×D₅₉	1	3	yes	—
56	M₃₂	—	59	12	no	—
57	C₂×C₁₆	—	59	12	no	—
58	C₂×C₁₆	—	59	1	no	—
59	C₂×C₁₆	—	59	3	no	—
60	#41	C₅₉⋊C₈	1	4	yes	—
61	#41	C₂×Dic₅₉	1	4	yes	—
62	C₂×Q₈	C₅₉⋊C₈	1	1	yes	characteristic
63	C₂×D₄	C₅₉⋊C₈	1	3	yes	—
64	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
65	M₁₆	C₂×Dic₅₉	1	12	yes	—
66	C₂×C₈	C₂×Dic₅₉	1	3	yes	—
67	C₂×C₈	C₂×Dic₅₉	1	6	yes	—
68	C₂×C₈	C₂²×D₅₉	1	6	yes	—
69	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
70	C₁₆	—	59	2	no	—
71	C₁₆	—	59	6	no	—
72	C₂³	C₂×C₅₉⋊C₈	1	3	yes	—
73	Q₈	C₂×C₅₉⋊C₈	1	4	yes	—
74	D₄	C₂×C₅₉⋊C₈	1	12	yes	—
75	C₂×C₄	C₂×C₅₉⋊C₈	1	3	yes	—
76	C₂×C₄	C₂×C₅₉⋊C₈	1	6	yes	—
77	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
78	C₂×C₄	C₂²×Dic₅₉	1	6	yes	—
79	C₈	C₂²×Dic₅₉	1	1	yes	characteristic
80	C₈	C₂²×Dic₅₉	1	6	yes	—
81	C₈	C₂³×D₅₉	1	1	yes	characteristic
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×C₅₉⋊C₈	1	6	yes	—
84	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
85	C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
86	C₄	C₂²×C₅₉⋊C₈	1	6	yes	—
87	C₄	C₂³×Dic₅₉	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#16837819	1	2	yes	direct product factor
90	C₂	C₂³×C₅₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₅₉
commutator	C₂×C₅₉	C₂³×C₈
Frattini	C₈	C₂³×D₅₉
Fitting	C₂×#131×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×C₈
hypercenter	C₂×#131	D₅₉
hypocenter	C₅₉	C₂×#504
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. #16837819	C₂	direct (N × H)
2. C₂×#14273667	C₂	semidirect
3. C₂²×C₅₉⋊C₁₆	C₂	semidirect
5. #14273667	C₂²	semidirect
8. C₂×C₅₉⋊C₁₆	C₂²	semidirect
44. C₂×C₅₉	#504	semidirect
50. C₅₉	C₂×#504	semidirect
89. C₂	#16837819	direct (N × H)

Subgroups — C2×#16837819 #21437195

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16837819 #21437195